Project Blog

Tales of Real Electrical Engineering

Personal projects of the instructor

1) Spring 2012--audio power amplifier stereo class AB photos elsewhere in the web site can be powered with two rechargeable batteries of a portable screwdriver.

2) Fall 2012--designing a low-noise, DC to 10MHz, gain-300000 amplifier to listen to noise (thermal, shot, 1/f, whatever), amplify microphone, amplify WWV 5MHz, amplify photomultiplier, etc. Sensitivity like .3uV at 5kHz bandwidth. This project was stimulated by the IEEE Spectrum article, The Cool Sound of Tubes. I have two old 12AT7, Holland-made, twin-triode, vacuum tubes that may have lower noise than JFETs. The new TI OPA1662 may be the lowest noise for low source impedance, and I have some to compare. This project has several challenges. 1) Keep it from oscillating, the wide bandwidth and high gain is a problem. 2) Modular, cascaded gain sections to get just the gain you need. 3) Supply filtering to avoid coupling between sections. 4) Input tube stage changeable between single-ended AC coupled, simple, low-noise, minimum parts vs. balanced & DC coupled. 5) Provide tube, JFET, bipolar, and OPA1662 first stages to compare noise. 6) Feeding in a real input, such as a mic using XLR connectors and cable, is a challenge because you don't want radio stations piggybacking in.

This project aims to create a very quiet (electrically) compartment for amplifiers. I have made some audio amplifiers that had 60Hz hum and audio demodulation of broadcast radio. It was disappointing to build the amp and be stuck with the deficiencies. This project is a small-scale, amateur version in the manner of science labs that pursue leading-edge investigations, such as NIST studies and astrophysical investigations where they use rare materials and cryogenics.

This project of looking at noise can be extended to looking at 1/f noise. I found a neat web site for 1/f Noise: a Pedagogical Review by Edoardo Milotti that says that 1/f noise is seen in most measurements, even ocean currents and the length of objects! But measuring noise down to .001 Hz or .0000001 Hz means logging data to computer over hours to weeks because the 1/f noise keeps getting stronger as frequency goes down, as nanovolt/root hertz.

Audiophiles often use high-end amplifiers with 1940s-technology vacuum tubes. There are real audio reasons to use tubes to drive speakers for electric guitar, but other uses of tubes are fads. Some audiophiles get into a cult area by insisting on using carbon-composition resistors, paper capacitors, no electrolytics, and limited feedback, saying that the sound suffers from inferior parts. This is almost all junk science, and a microphoned recording studio is much more dependent on sound damping (less is not necessarily better) than electronic components, but it is true that low distortion and low noise are hard to measure and prove. It helps so much to think about distortion when you understand harmonics and Fourier analysis. Distortion of a 3kHz sine is almost inaudible because the distortion harmonics start at either 6kHz or 9kHz, so high that human hearing really doesn't sense those frequencies very much.

My low-noise amplifier includes a 12AT7 tube because a 1980s Spectrum article, The Cool Sound of Tubes, said that medium-mu triodes are the best for low noise combined with low distortion.

Progress Dec 3 2012: I needed to build up on a nylon breadboard, using leaded parts, one discrete, BJT diff-amp stage and follow it with an op-amp diff-to-single-ended amp, to see if the topology common to all four stages works, namely diff amp feeding into PNP cascodes that "reflect" signal back to grounded load resistors. Then through emitter followers. I recently decided to use a -50V supply with matched emitter resistors, instead of matched NPN current sources, to pull bias currents of 2mA from whatever diff amp is being used (BJT, JFET, or 12AT7 tube), since simple resistors should have less noise contribution. On the breadboard, I set up -35V to try this. Using my collection of old 1% resistors brought from Austin and 2N3904 & 2N3906 transistors, the circuit topology works as designed. Overall gain is 811 and the output op-amp diff amp is using TLC271 TI programmable-bias op amp in high-bias mode. CMRR does work, a DC bias of .53V raising up the common of the input shunt resistors (6.2k) changes the output as if the input had been unbalanced by 6.9mV, CMRR 38dB which is OK but not as great as if NPN current sources provided the 2mA diff-amp currents, I imagine. Sensitivity to -35V supply: changing it 2V changes output 2V. Doesn't sound too great. Don't know if this is all improved by matching the circuit's resistors closer than the 1%ers I am using, or matching transistors. Putting iron tip near one diff-amp NPN changes output a lot, so temp tracking of those transistors is proven to be critical and any first stage of the planned four stages that has discrete transistors (or tubes) is going to have a lot of drift. Other transistors and resistors are also sensitive but not as much as the diff-amp transistors. The CA3086 integrated transistor array may work pretty well but don't know if their noise is low. Chilling the whole breadboard about 15 deg F changes output 7V in 21 minutes. Hooked up Speaker Chair homemade amp to listen to whatever is coming out the TLC271 and hear hiss, which I figured I would hear. But it is quite a bit of hiss. But there is little hum and no audio demod of broadcast RF, good. Touching one input gives big hum. This breadboard trial is quite successful and is a green light to PCB design for some of the four-stage design with extensive supply filtering and shielding. Provide ways to match resistors and transistors closely. Found 3" ID galvanized pipe for stage 1-2 magnetic shielding but a foot is over $15, so the way to do that magnetic shielding would be to fabricate from flat stock and angle from Lowe's, maybe with some welding.

Summary of diff-amp feeding into PNP cascodes that "reflect" signal back to grounded load resistors--instead of the NPN diff amp having collector resistors up to +V, then emitter followers, there are indeed resistors up to +V but there are PNP cascodes with emitters on the NPN collectors, which is the standard cascode, but with PNP cascodes, the resistors to +V give both diff-amp bias and bias current down into the PNP emitters (and on down to grounded collector resistors). The advantage to PNP cascodes is that output is near ground, whereas NPN cascodes have output up near +V, which is not conducive to DC cascading of amplifiers. A disadvantage of PNP cascodes is that +V noise comes out as differential output noise if the +V resistors are unbalanced, like if purposeful unbalancing is being used as input-offset-voltage adjust, so you need extra regulation and/or filtering on +V if your +V resistors are unbalanced. The normal cascode feature of low impedance on the diff-amp collectors is retained when the cascodes are PNP.

Progress to Dec 20, 2012: 120VAC bulk supply of 13V with extra-low ripple, 2mV even before semiconductor regulation, is working. The trick is to use 3 filter caps and have a heavy, iron-core choke between two caps. This bulk supply will go to homemade DC-DC converter to get five supplies.

Submitted 160-word report to The Clubhou.se newsletter in case they wish to include it.

Dec 22: DC-DC converter board is populated & worked briefly at 63kHz with homemade, 5-output transformer to give several watts total at -22V, +33V, -73V, +155V, +255V. Then there were intermittent buzzing noises inside the transformer, which was the windings succumbing to corona. Need a transformer with more insulation. Got a bigger core, EE ferrite, with much bigger windows. The length of the windings is 1.25". Put the high voltage on inside and low voltage outside so that low voltage might continue to be useful even if high voltage needs even another iteration. In high-voltage windings, used some varnish like commercial transformers have. But I don't have the vacuum potting capability to get air bubbles out, which is the cause of corona. Each round of transformer is around five hours of work, with wire as thin as #36, which is pretty fragile. I built a simple, cranked coil winder so I can quickly get one layer done, then there is so much labor to insulate before the next layer. The brief success with first transformer proved the design of the five-output circuit, which is push-pull primary and the two lowest secondaries, then bridges for the three highest outputs. Each bridge is based on a lower DC voltage, not ground; it saves turns. (The -73V bridge is based off of the -22V supply, +155 is based on +33, and +255 is based on +155. I am seeing rectified voltages track the volts/turn (.72V/turn) quite well. Dec 31: transformer is working fine. On the five (six) series regulators, the MOSFETs used for high voltage need 7.5V zeners, back to back, G to S; may have lost a MOSFET when I first tried series pass at 200V without this gate protection.

The initial batch of PCBs is all etched: 120Hz bulk 13V supply with the low ripple, DC-DC converter, five series regulators (not built up until the transformer works), and "bridge board" for the 12AT7 tube, bridging from tube socket to the main first-stage amp board which will have another four first stages.

Dec 31: DC-DC converter board has had big problems. 1) was using common-emitter-connected TL494 transistors to feed gates when it should have been emitter-followers, so MOSFETs were way too hot and 11-16V bulk supply current was too much. 2) 580 ohm pulling down TL494 emitters is way too high, the MOSFET gates have a lot of current during switching. Experimented with +-11V gate drive through Class B, 2N3904/06 transistors and that got the MOSFETs fast and cool, but the Class B transistors are hot from too much current, so order some SOT-223, SMT transistors with heat-sinking tabs. 3) Need pot on Dead Time Control, pin 4, to play with that. 4) Need jumpered RT resistor selection to easily change freq, since I don't know specs of toroid cores. 5) Change soft start over to DTC from Feedback. 6) Purchase 60Hz transformers for +11-16V bulk supply and/or +-15V or +20/-10V for gate drive.

Jan 3 2013: Populated the "tube bridge board" with 12AT7 vacuum tube with support ckts on nylon breadboard. The tube amplifies with about 76% of expected gain, found an Rk-k that will give gain of 10 when Rcascode is 10k. The PNP cascoding "reflecting back toward ground" seems to work fine, got input offset working by trimming one 4k up on 110V. Did PCB layout for a plug-on module to interface TL494 to MOSFET gates, to switch them quickly, will get order to Mouser for the SOT-223 transistors. Ready to lay out verB of PWM PCB, see paragraph just above, items 3, 4, 5 and a place to plug the gate-drive module.

The gate-drive module and other features do indeed let the DC-DC converter work a lot better.

Jan 9 2013--Got a second DC-DC converter working to supply the main converter with +17V and -8V for the strong, fast gate drive, to reduce MOSFET switching loss. SOT-223, surface-mount, 800mA transistors will be ordered tomorrow to finish this out. A yellow toroid (with new windings) was reclaimed from a dismantled commercial power supply. The next step is packaging the supply assemblies in one metal container. (The bulk DC supply, 11-16V, will be separate.) The assemblies are: main DC-DC converter with gate-drive module, transformer, rectifiers-filter caps, six series regulators, current-limiting PNP with heat sink, DC-DC converter +17, -8. Much attention needs to be given to lowering EMI so as not to contaminate the 4-stage, gain-of-300,000 amplifier.

The next step is laying out the first stage amplifier with attention to many features, such as a) simple AC ampifiers to monitor any AC on the supplies serving the first stage and b) gain of 10 in each of the five first stages so their noise can be compared without scaling. A later job is putting a 9V alkaline battery in an 87 degree F oven to serve as a voltage reference for secondary and tertiary series passing of supplies.

Jan 15, 2013: All the supply assemblies are in a wooden structure which can have metal added, but 18-year-old TL494s that were stored in non-air-conditioned storage are having high failure rate. Had to buy some single-inline socket pins to put the main DC-DC converter's TL494 in socket, and I have some new TL494. Two new problems, loop compensation is not right and there is extreme oscillation in the loop, though with the big filter caps it would actually operate OK, but work on loop compensation some. And the +215V series pass is broken. January: loop compensation came out to be cap to ground, it is slow to respond to load change but the series regs following accommodate that. Supplies are usable.

Feb 16, 2013: 1st and 2nd stage amplifier PCB is etched and is being built up. Second stage works great, nearly balanced without R-to-20V fiddling since I screened five CA3086 for Vbe and Beta. Gain is 30 with em-em resistance 22.7ohms. Matched JFET for Vgs at 2mA, am building enough of 1st stage to try that out.

Mar 7, 2013: layout is finished for the "blue" supply regulator and 9V battery oven, and the 3rd-4th-stage amplifiers. These will be etched and gradually built up to test the many functions. After that, the "brown" supply regulators will be laid out to give very quiet supplies for the 1st-2nd-stage board. Just the 3rd-4th-stage amplification is 1000, and it will be interesting to see how input-offset-voltage adjustment works and how stable this amplifier is when room temperature varies.

Mar 17, 2013: 3rd-4th-stage amplifiers are built and work independently. Soon, I will cascade them and look at temp dependence. 3rd stage oscillated a lot at RF, that was cured by adding a lot of ground wires and adding more supply decoupling, all on the back of the board. 4th stage appears to have different balances for the low- and high-freq "halves," I need to trim cascode resistors to try to equalize those balances. The 50mW speaker amp works. Blue regulators work and the 87degree F oven is working. With tissue-paper insulation, the period of the oven heater is 2.5 minutes. This is with hysteresis resistor 10M, which gives 25mV hysteresis. The ability of the simple oven control (bridge with thermistor on PCB, op amp, and no thermistor on the battery) to maintain constant temp is probably pretty poor, I am guessing the "base" of the aluminum extrusion varies .5 degree F during the 2.5 minute period. Better control would be to keep on-off control of the heater resistors but add a thermistor on the battery to actually sense battery temp, plus microcontroller and a program to do PID control or state-variable control, with on-off cycle of the heaters at 2 sec (PWM) rather than 2.5 minutes. This could be enhanced by feed-forward control from a third thermistor sensing room temp. Since heater-resistor current flows in the grounding of the blue regulators, it would be best to do 1/f sampling of the four-stage amplifier only when the heater is off. In the 3rd and 4th stages, as I adjusted emitter-emitter resistors to set gain of 32, I noticed a 20-second time constant in delta-V_out as I applied delta-V_in. This is probably heating of the discrete transistors. It is bothersome to take a reading 5 seconds after applying a delta-V_in and see the DMM keep inching up for another minute.

Mar 18: Cascading 3rd to 4th stage was successful, no oscillation. 3rd stage's Vio adjust works to get 4th balanced, as planned. Adding speaker amp (on the end of that PCB) causes no oscillation, and I hear mainly a 120Hz buzz that is not from lights or soldering iron, but it is only moderately sensitive to touching one input (with other input grounded, and 383 ohms between inputs). (This is with overall gain 1000, pretty high.) (I am paying attention only to the single-ended output from op amp, 5000Hz BW or so, DC coupled.) Really can't hear hiss with the buzz in there, or rumble. D'Arsonval meter connected to the absolute-valuing op amp works as planned, and the meter does not have an inexorable drift toward amplifier saturation, the meter hovers around an average value. The big deal is that the meter fluctuates about .4V P-P. (Gain for the meter is 3000.) This could be 1/f noise, though I didn't expect it to show up at gain of only 3000. Manually took DPM data, about 40 points. Graphing it looks noisy, no pattern to it. Sorting shows what is probably a normal (bell-shaped) distribution, though I don't know enough statistics to test the normal-ness. Next step is to take the fragile PCB and box it up with resilient shielding and get pots and switches mounted so 3rd-4th stages are convenient and really useful. This may take care of buzz, and if it doesn't then I have some debug to do. Input transistors (2N3904 SMD) are definitely sensitive to unequal heating. The need for low-freq data logging to check noise statistics means that I need to break off from analog building and use ADC in Arduino Mega2560 to log data. This will be the entree to using Mega2560 as audio-freq oscilloscope, probably.

Mar 28, 2013: Found oscillation in 4th stage, which may have started when shielding went on and a ground was strung between 3rd and 4th stages. Added .1 uF caps decoupling -10 & +20, and big electrolytics, like for 3rd stage. Oscillation is cured now or is better. Am checking gains and other switch functions. 3rd & 4th stage oscillation was not expected because transistors are just garden variety 2N3904 & 06. This experience will affect future layouts.

With both 3rd-stage Vinput-offset pots, there seems to be a lot of resistance variation. Both pots are old and have been stored in summer heat. At Fry's, I bought $15 10 turn 10K Vishay/Spectrol wirewound which has resolution of 1 part in 5900 and a cheap 20k, end-adjust 15T trimmer. Looking at Bourns Potentiometer Handbook, Equiv. noise resistance applies to wirewound pots and can be 100 ohms out of 10k which is 1%. That sounds terrible for Vio adjust, but I wonder if ENR is while adjusting or static. And for cheap multi-turn trimmers, Murata says contact resistance variation can be 3% of total resistance. Again, sounds terrible. $15 Vishay pot works well for V_io trim, cheap 15T new trimmer is as bad as the old one. Just use Vishay pot. Drift of 3rd-4th stages is now low enough to proceed with packaging speaker & D'Arsonval meter, done on Ap 11. Proceed with "brown" supplies for 1st-2nd stages so I can hook those stages onto 3rd-4th stages and see 1/f noise.

The objective of a low-cost, if complicated, device--the 10-turn precision pot for input offset adjust is most expensive:

$.01 per part $.1 $1 $10 $100

resistors electrolytic caps each DIY PCB 10-turn pot

transistors pwr transistors total $ for copper shielding

total $ for brass

Ap 29, 2013 Good progress on "brown" regulators, they are built up, some dividers adjusted to get 2.5V or 3.5V head room on certain cascaded series passes, two dividers adjusted on DC-DC converter regulators to get intended voltages. Hooked up the 2004 "Utility Amplifiers" middle C 1V RMS sine wave to 2.93M:629 ohm divider on input to 3rd stage & captured 4th-stage single-ended output using one of the brown regulator ground-loop-breaking diff amps, with GETTER MS Sound Recorder set for 16 bit mono & 44.2kS/s, passed the PCM file to Adobe Audition. Good results. 1) The sine wave reference has fundamental at least 47dB stronger than harmonics, so the Utility Amplifiers Wien bridge (or whatever) sine source followed by active filter is doing a good job. 2) DMM on ACV shows .342VRMS, not 1VRMS, though that meter has not reliably shown ACV in the past. Going with .342VRMS, the 2.93M:629 ohm divider into 3rd stage gives 73.4uVRMS, and designed gain of 3000 to single-ended output should give .22VRMS. Measured .336. But gain is definitely there, and no evidence of oscillation or even hum. Probably 7uV or less of noise in the Sound Recorder recording, which is .336V/7uV = 94dB, whereas 16 bit is 96dB, a nice match-up. Next step is ordering "wound inductors" in the 10mH range, which is merely 2W AC power packs with AC output, $3.25 from Jameco, use the secondary or even primary as a large inductor. This will give filtering for first-stage power, which will be built onto shielding (yet to be built) of 1st-2nd stages. Then it will be time to join 2nd-stage output to 3rd stage for the first time and see if the gain-300,000 amplifier is stable. (Gain 900,000 to the single-ended output.) If stable, then is thermal noise seen? And 1/f noise? And does DC coupling have usably-low drift for any of the five first stages? Need to make custom 11-16VDC raw supply with choke filtering for low ripple to power the DC-DC converter, confirm low hum contribution, then see how sensitive the built-in electret microphone is. If drift is low enough, set up Arduino Mega2650 to capture 10-bit data over weeks and look for the mysterious 1/f noise.

May 11 2013 Building up new 11-16VDC bulk supply. New features: charge 3x4700uF in bulk supply before letting supply out to DC-DC converter.; sense two temps in case of overheating, rapidly discharge six capacitors in bulk supply if there is an AC dropout, short across ripple-reducing series resistances during power-on surge, roughly regulate the voltage getting out onto reclaimed 16V 4700uF to keep them from over-voltaging and in case DC-DC converter needs a particular DC input, add a second 60Hz transformer in parallel in case that becomes necessary.

May 21 Yes, the second transformer was needed. PNP output switch using MJ2955 (TO-3) doesn't have enough beta to handle inrush current of DC-DC converter, and I am not going to revise the PCB of the bulk supply to correct that, so I put in a switch to short across the PNP during turn-on. It works well enough for now. DMM shows 3mV AC ripple! Having a working bulk supply, next is packaging "brown" regulators with additional LC filtering in mind, going into 1st and 2nd stages, then make those filters and shield the 1st and 2nd stages, then add input offset adjust on one side of XLR input connector, then work on interfacing 2nd stage to 3rd stage and see if it is stable, and start looking at noise.

June 5 There is one electrolytic cap in DC-DC converter that vents at power-on. Need to replace it, and it may be loading down turn-on and causing turn-on trouble. With a .3 sq inch solar-cell chip on 10" wires on input to 3rd stage, as a demo of the DC coupling of the amp, 3rd-4th stages have some oscillation. Need to RC filter the meter output, not just series R, and see if that helps. I have built up an aluminum structure for the two amp boards, two regulator boards, and wound inductors. It is not the steel baseplate I had planned, so I need to be careful to provide adequate shielding. The long-planned, highly shielded filter assemblies to feed power to 1st & 2nd stages are taking form as PCBs that are part of shielding. They also carry the various 1st-stage accessories (zener bias pot, XLR input offset, etc.).

March 29, 2014 The gain-300,000 amplifier has languished for months while other projects have gone ahead, seeing as how the 1st-2nd-stage shielding is tedious and the stinky, leaking electrolytic cap had to be found, turned out to be input cap for 12V on main DC-DC converter board. It leaked corrosive electrolyte onto one sq. inch of that board, I had to replace numerous SMD parts. With the DIY piecewise-linear sine oscillator a big success, I am back on the amplifier project. Half the second-stage shield is done, boards are etched for DC power entry to second and first stages and input offset adjust with the 10-turn pot, and two of those three boards are working. First and second stages (one PCB) are perched over the metal structure and second stage is powered and has measured AC gain of 24.2 at 350Hz. I am inclined to get the 3rd-4th stages working off 2nd-stage output, with a trial cable from 2nd to 3rd, to see what Xprotolab oscilloscope shows, then work on 1st-stage shielding.

April 5 Before hooking on the 3rd-4th stages, mount 1st-2nd stages and the power-entry boards. Am developing paper patterns for aluminum shields--this is a lot of work. In the meantime, soldered on the special, low noise, $1.70 TI op amp, OPA1662 and found it to work with no problem, with gain of 10 and 50. This will probably be the workhorse 1st-stage amplifier for low freq since it probably has the lowest input offset voltage and temp coefficient. JFET stage is the other 1st stage to work, has a lot of Vio, like .17V. Vio 10-turn pot is very useful. No problems detected with DC-DC converter switching noise tagging along on supply wires. No oscillation even though 1st stage is unshielded so far, and 2nd stage is only half shielded. Built-in electret mic works, though major 4.2kHz resonance. Also got the zener-diode built-in noise source zeroed out with trimpot on power-entry board (DC coupled) and found, as expected, quite a bit of noise. Doing Adobe Audition spectrum analysis, it is pretty flat from min. freq. shown (about 200Hz) to max. allowed by the sampling rate. No spikes of 60Hz (and harmonics) hum! What good news. Used one of the brown-regulator, ground-loop-breaking diff amps to get signal off the assembly. Listening with DIY audio system onto Speaker Chair, I touch the speaker cone and feel some low freq which might be 1/f noise. The pile of regulators, filters, and amplifiers looks outlandish. My decision a year ago to build the structure up from the 5-inductor filter box is working out well though the boards are quite exposed to getting knocks. The 1st-2nd stage PCB idea of including zener-mic-noisy carbon resistor-middle C voltage divider is working out well, having these sources at the first stage with no cabling and no noise from cabling is great.

Ap 25 2014 There is progress with the whole system. 3rd-4th stages are wired up to 2nd-stage output. Am using only the 4th-stage op-amp output (not the full-BW output) which reaches to 5kHz. There is a lot of body-proximity effect, you can see the moving-coil meter on 4th-stage output deflect when you approach to three feet away. The thing that is most sensitive is the shielded, tw. pair cable from 2nd-stage out to 3rd-stage input. I added quite a bit of thin aluminum (stiff) shielding, and what turned the corner on this proximity problem is adding temporary aluminum-foil shielding to that 2nd-to-3rd cable. Plus more foil elsewhere. As expected, the input-offset, 10-turn pot (hooked to XLR pin 2) is vital to getting the amplifier chain fully in the middle of operation (not clipping the 4th stage), and you can see the individual resistance wires of this $17 pot as the wiper goes across them (the output meter jumps to about six places as it goes from -clip to +clip). Very sensitive to setting this pot. The overload LEDs on 2nd and 3rd stages are very useful, and of course the output meter is the main thing to look at while adjusting Vio. My idea from a year ago, that to take 1/f data for hours to months requires substituting fixed resistors for this pot, is surely going to be needed. Noise is clearly heard and seen, both on moving-coil meter and on Xprotolab oscilloscope, so one of the aims of this extensive project is accomplished, DC-amplifying noise to where it can be seen and heard. The 4.2kHz resonance of the electret mic is no more, I hot-glued a paper support between PCB and capsule to keep it from vibrating on the .3" wires. Both JFET and OPA1662 operate OK, and the JFET diff amp has much less thermal drift than I would have expected. Go ahead to 12AT7 electron tube and it's "bridge board" which was the first assembly I did and tested, over a year ago, since this assembly occupies a lot of space above the 1st-2nd-stage amp PCB. I pulled the 1st-2nd-stage PCB out of the shielding to finish up surface-mount soldering of the support circuits. I have looked for interference coming from the DC-DC converter (SMPS) which so far has no shielding around it. Used SW radio within inches of the DC-DC converter but picked up only slight signal on AM band.

It is clear that the five, 1st-stage diff amps (JFET, two BJT, OPA1662, tube) on the PCB are not going to be the ones to give hours-to-months of 1/f data recording. That board is good for establishing that I can make a gain-of-300,000, DC-coupled amp that doesn't oscillate and which amplifies thermal and semiconductor noise, and it may be good for deciding which circuit has lowest noise, but the experience of having so much proximity sensitivity makes me want to make small 1st-2nd stages with excellent shielding, one for OPA1662 and probably one for JFET. The OPA1662 1st-2nd-stage amp will have only -10V and +20V supplies going in, and they will have better filtering. The JFET 1st-2nd-stage amp must have a way of dealing with input voltage offset, better than a large 10-turn pot. Beyond building these assemblies, there will be programming to accept and record to HDD the noise data, over hours to months. Low-pass filtering the amplified noise, to a BW of 100Hz or .01Hz or something, will be needed so that months of data is not a gigabyte. But it may be good to once in a while sample the amplified noise at 3kS/s to establish what the higher-freq noise is doing. Don't know if I will do Atmel CPLD to operate 16-bit ADC or use my big Arduino to do it. Don't know for sure if Arduino can send serial data to PC on USB or if RS-232 will be needed, though there has been success with the latter in the matter of Xprotolab screen captures working.

May 9: Input offset adjustment is going to be by a DAC, 13 bits. Two different uses: to find fixed Vio resistors to solder in before commencing a months-long 1/f session, and to bump Vio during 1/f logging if the fourth-stage output approaches saturation.

Technical note about DIY DAC for input offset adjustment of first-stage amplifier

The DIY, gain-300,000, DC-coupled amplifier is being built to investigate 1/f noise. It is known that 1/f noise, as measured by volts per root hertz, increases without limit at frequencies below about 100Hz, and at frequencies like .1 microhertz (period three months) the 1/f noise is still seen to have stronger volts per root hertz. Logging the amplifier output for months, with a digitization and time stamp every 10 seconds, requires special preparations, such as battery power and ambient temperature control.

This note lays out plans for a DAC to do input-offset-voltage adjustment.

A 13-bit DAC is planned for nulling input offset voltage of the first stage of the four-stage, DC-coupled, low-noise, gain-300,000 amplifier that will be used to record 1/f noise. Heretofore, a 10-turn wirewound pot has been used for Vio. But a DAC has two advantages: when the DAC is driven by buttons connected to Arduino, the Arduino can adjust out initial Vio, after the amplifier temperature is stable at the start of a months-long recording. Also, if an amplifier chain turns out, after some days of logging, to have too much drift on the output such that the output is nearing saturation, an Arduino-controlled DAC can put steps of input offset voltage onto the first-stage amplifier to get the ouput back away from saturation. (And the DAC bits have to be recorded on the logging device [Raspberry Pi] along with the digitized amplifier output.)

But these two uses of the DAC are in different circumstances. The initial Vio adjustment must cover a wider range, like 15mV (or even 100mV for discrete JFET first stage). This is a way to find a base-line Vio adjustment, and the intent is to solder onto the first stage fixed, thin-film resistors that provide most of the Vio adjustment for 1/f logging. After this, the DAC is used only for fine tuning, maybe over a 2mV range, over the months of automated data logging. This brings up a requirement for the DAC: it must have enough stability (accuracy) that drift in the DAC is not mistaken for 1/f noise.

I have two, $7, 16-bit DACs. They have serial input that can't be used without an Arduino. (Can't be used with just jumpers). They need about 30mA of -5V power. I thought about a DIY DAC and came up with a design that uses mainly positive power from batteries and little negative current. I have all the parts except thin-film 0803 .1% resistors for the R-2R ladder, and those resistors are $.08 each in 100 qty. It is an interesting design. This note describes this DIY DAC. Refer to the hand-drawn schematic.

The schematic shows four bits of the 13 bits. Toward the LSB end, simple 4011 gates (which can be powered by up to 15V) provide ground or 12V levels to the ladder. The approximately 250 ohms of output resistance of the 4011s (measured on one 4011 to be 95 ohms, below) can be partially compensated by reducing the 2R resistors. But toward the MSB end, this doesn't work because the inverse of 2^13 = 8192, in other words .01%, is the LSB step and the MSB must have that sort of precision to just be monotonic.

The answer is to use op-amp followers on the eight MSB bits, shown on the schematic at Q and R. Four of the eight can be an LM324, and the MSB four can be 741s with input-offset pots. I am prototyping four bits to confirm that a 4011 gate with sub-microamp load (the input bias current of the op amp) has sub-millivolt drop from supply rail to output.

The conventional design for a voltage-output DAC is to provide an inverting op-amp (P) with virtual ground at the minus input. The ladder current, N, causes a negative voltage at M, and the voltage output goes from zero to, for example, 2mA * 6k = -12V. But this means each follower op amp needs negative power, the thing I don't want. The answer is to change each ground connection, A B C E, to +2V so that the follower op amps can use ground for negative supply. M's range is then +2V to -8V, and the P op amp can be powered from -10V.

The only complexity, now, is that the 4011s need to have their inputs swing from +2 to +12V, whereas Arduino has ground and 3.3V outputs. The answer is to level translate with ICs that I have, ULN3002A. This is shown at the lower left of the schematic.

This DIY DAC is interesting and I will order the thin-film, .1% resistors for the R-2R ladder and see how the precision goes. Several ladder resistors must be trimmed below the .01% level and I have a simple plan to get that done. The PCB layout must cluster the most-significant half of the ladder resistors so they are the same temperature.

Vio is planned to be fed into the first stages (as many as I build, with JFET or OPA1662 etc. first stage) through a BNC connector. I will need just one Vio module. Provide a range of resistors to feed the Vio voltage onto XLR pin 2, since the ohms to ground for that pin 2 is different for various signal sources. Provide 10k and 66k on the Vio module, and within stage one provide 300k, 2M, and 20M.

I prototyped four of the 13 bits on May 9. The two MSB bits had op-amp buffers. I used 1%, 3.3k, leaded resistors. The RMS error was 16%. For the op-amp-buffered 4011s, measured supply-rail to 4011-output voltage drop was .4mV and .7mV, nice and low. For the unbuffered 4011s, one had 92.8mV rail-to-out drop while sourcing 1mA for Zout=96 ohms, and the other had 35.6mV drop while sinking .37mA for Zout=97 ohms.

June 26: the 13-bit DAC is about finished and is quite successful. See file 13 bit DIY DAC some results June 25.rtf on WinXP side of GRID. Precision is about 14 bit. Ended up with little trim on the R-2R resistors, just sorted them with high-precision bridge and put closest matches at the MSB end of DAC. The 10k trimpots for 741 Vio must not be narrowed down with divider resistors.

Equally significant is my first experience with Arduino programming in C++, though without even making functions. Arduino is pretty slow, 13us to write HIGH or LOW to a digital pin.

May 18: Orders are in for die-cast aluminum project boxes in which to build 1st-2nd stages, one for JFET discrete and one for OPA1662. Also three values of Susumu .1% 0805 thin-film, low-noise resistors and two values of wirewound 5W. And other parts to build with, like a very accurate 5V voltage ref from Maxim, MAX6350 to compare to ovenized 9V alkaline battery. Following the four-stage amplifier is a LC LPF, a ten-second integrator, a dual-gain signal conditioner, then into 16-bit ADS8505 which can take +-10V range. The integrator and signal conditioner are being designed.

June 9, 2014: PCBs for ADS8505 16-bit ADC and DIY 13-bit Vio adjuster are etched. Selection of 2k .1% resistors, by a bridge on an etched PCB, is so successful that the trimming plan is simplified: do not trim up to 2005 or 4010 ohms, just use short lengths (.5" and such) of nichrome wire (4.58ohms/ft) to trim any outliers on the most-significant bits. Most of the 2k .1% resistors are within .03%.

July 11, 2014: Big step forward, built up the little PCB with ADS8505 16-bit ADC. Put a little 4011 ckt on R/-C to get sampling going at 2kS/s. Put a slow sine, as low as 1Hz, on the ADC input. Without doing any Arduino programming, just putting audio amplifier onto the 8 digital output pins, one at a time, with BYTE high so I am listening to the MSB 8 bits, I hear signals that sound just right; as I dial up Vp-p from sine oscillator, more and more of the bits have digital highs and lows, and the less-significant bits have a lot more activity. There is more activity on the steepest slopes of the sine, more quiet as the sine peaks + and -. I am not inclined to rig the XProtolab to do 8-bit logic acquisition to check ADC. I think the next thing to do on the project is design the 512kB SRAM and 4020/CPLD logic to do the address & stuff the data into SRAM. I found out that Arduino shiftIn and shiftOut functions are specifically for shift registers, though I don't know that these functions get the job done any faster than digitalWrite and digitalRead, which are on a per-pin basis. It is looking like two CPLD may be needed (64 macrocells each), and the partition is pretty much worked out. And the same logic can take SRAM back into Arduino, and that would be really neat to see digitized sine or voice show up on Arduino's Serial Monitor.

This 16-bit ADC success does make me think about building a DIY 4.5-digit digital voltmeter of the bench style (not handheld), especially since I now have Maxim 5.000V voltage reference.

July 27, 2014: While working toward an Atmel CPLD to stuff higher-speed ADC into SRAM, then meter it out through (slow) Arduino to Raspberry Pi, I did an experiment CPLD to see if state-machine stability comes from feeding back the state bits through 3300ohm resistors, back into some input pins, and doing the AND-ORing for next state by using these fed-back bits, which are "held" about 14ns by the RC delay. (No physical cap, just the 8pF typical input cap of ATF1504AS.) I did a nine-stage ring oscillator using CPLD gates, two pins per gate, with 3300ohm resistors between gates. It needs initializing with 7kHz low pulses into the gates (using AND gates). The observed freq of 9 lows followed by 9 highs is 392kHz, when seen through a div-by-8 ripple counter. The observed sum of 3300ohm & gate propagation delays averages to 17.7ns. If actual gate tpd in the CPLD (-10 speed grade) is 6ns, calculated input cap is only 6.2pF and with 3300ohms, delay due to the RC is .693*3300*6.2E-12 = 14.2ns. This seems to be a good delay for holding, a short time, the D inputs of the state-machine flip flops after the global clock, and it is a good alternative to doing a master rank of state-machine flips flops followed by a slave rank, with two-phase clock. The CPLD design and experiment PCB has a second ring oscillator to try a different R value, and I think I will try 10k. Result: with 10k, delay due to the RC is 44.3ns, whereas 10k/3.3k*14.2ns would be 43.0ns, which sounds very accurate, but I am still assuming 6ns tpd in the gate & 6.4pF input cap. Ring oscillators are routinely done on larger logic chips to test propagation delay, and this is a neat thing to do with my Atmel CPLD. The same CPLD design has the 31-state state machine for the SRAM function, simplified down, and I will try that after a while before doing a full WinCUPL design for that state machine. Result of clocking the 31-state with a debounced switch: did not find any errors in next-state AND-ORing, and the state machine is stable (no races on D inputs). This is excellent results from this experiment board.

Aug 10, 2014 Atmel CPLD Tips & Tricks The CPLD for operating .5MB SRAM, for "calibration" or for 8-second 1/f data taking every hour, is mostly designed. It has a 31-state state machine that has already been tested on the above board. But when the full logic with all output pins is loaded up, there is a fan-in problem with the block that does the 31-state state machine. In Pro-Chip for Atmel CPLD, it helps to not click Fast Input and to click Always Logic Doubling. It seems to be sensitive to where extraneous signals come onto pins, and I think the 40-signal limit on a block is the bottleneck. Eliminating the synchronizing state machines for Cal & "8 second" did not help, in fact that took down the count of product terms. This is giving me practice interpreting the .fit report, which does not stop on first error. But this is seat-of-the-pants learning, I don't know of resources to guide the person who is trying to get the fitter to work. With WinCUPL & Pro-Chip (the free or low-cost EDA tools), the best success at placing state-machine flip flops inside a single logic block (thus minimizing clock skew), one of the four in an ATF1504AS, is to assign them into Block A, pins 4-22 on 84-pin PLCC. Pro-Chip's fitter always fills logic starting with A & ending with D, so play along with that. And it is best to do a trial placement, see how much cascading is needed for wide ORing, then assign pins in WinCUPL allowing for that cascading. Assign the first state bit at pin 21 or 22 & you can probably let the fitter assign the rest, they will be lain right into Block A, toward pin 4. There is little trouble with assigning global clocks, global OE, global clear at pins 83, 2 (these Gclk1, 2 inputs also are available to the global bus), 81 (Gclk3 is not available into global bus, it is a global clk only), 84, 1. However, I have experienced that the fitter looks for widely used flip-flop clocks & overrides a WinCUPL assignment, so far as taking my clock-phase-2 assignment at Gclk2 & putting it into Logic Blk C! It is typical for the fitter to try KEEPing pin assignments on first pass but give up on that with little provocation, yet the end result is that it uses most of your WinCUPL assignments.

I did try SR latches using .s and .r--that doesn't work. You have to do a D with Q to D connection, specify a clock (I did an input pin and will put ground on it), and use .ap and .ar as S & R. With enough experience with a current-source 5V limiter protecting against 5V to ground shorts during board bring-up, it really looks like the normal supply current is about 80mA even when little logic is programmed. You would think a CMOS chip would be low current at low clk freq, but that doesn't seem to be the case. Success at chip programming using JTAG is not 100% on first try, I have needed a 2nd try about once in 15 programmings. In WinCUPL, I think the only need for PINNODEs is buried flip flops, the ones that don't need an I/O pin. Intermediate logic variables do not need PINNODE. If you want "utility logic" such as inversions, NOR, NAND to help patch logic errors without doing an iteration of the design, you can assign them to Block D. Experience with designs that have few NC pins is that an iteration that changes a product term (the smallest change that WinCUPL can be asked for) usually swaps two to four pins but leaves the bulk unchanged. The swapped pins have nothing to do with the logic change. In WinCUPL, experience shows it can choke on a logic equation that is a NAND or NOR, but if you do, for example, !NANDout = inA & inB & inC; letting the inversion be shown on the left side of the =, it does better. Important in WinCUPL: don't end a signal name with a number (SRAM1) unless it is declared in list notation with [ ], such as pin [59,57..55] = [SRAM0..SRAM3]; or pin = [SRAM0..SRAM3]; if you are not assigning pins. And don't name a signal starting with a number, do eightsecond rather than 8second. When entering a major chunk of logic in WinCUPL, end with a find for + and *, they must not be used in equations (use # and &).

In Fitter, there is mention of latches, as if maybe macrocells can do a bistable within one macrocell, out of NAND or NOR connection--I wonder.

Aug 17: I have shifted the two 8-bit buses over to CPLD2, where there is room. CPLD1 now fits & is in good shape, but really needs a reset ability to escape from waits, and the "utility gates" that use up spare pins need some inverting outputs. CPLD2 has a new state machine, 14 states, that has been checked out in spreadsheet. CPLD2 is being entered in CUPL. I did an update on the .odg diagram of interchip wiring on the output end of the system. It is a dense diagram! The system goes way beyond just a data logger, and each addition is an increase on this diagram. The diagram points up some of the requirements for Arduino programming.

Sept 12: Received from Mouser small-outline ICs, 4020, 4021, & 595 that are key to the CPLD1 & 2 PCBs & SRAM-address-counter PCB. SRAM, CPLD1, & Arduino shields for pin breakout are designed & I hope to get transparencies today to start PCB fab. The SRAM & CPLD1 boards will have a long bring-up process; they both have intricate soldering & are static sensitive, so I am glad to have a low-static table & Hakko iron to do assembly. Received also from Mouser surface-mount, dual-row, .1"-spaced, .025" square-pin headers & IDC 14-contact ribbon-cable plugs that will reduce the number of holes I have to drill in boards.

The CPLD1 PCB, in particular, the one with the 31-state state machine to record 16-bit ADC to SRAM & read it back, will be a milestone in logging data. I proved out the state machine as noted above at July 27, so there may not be any big problem with that very complex state machine. All four boards, CPLD1, CPLD2, ADC, and SRAM, are needed to work together to get some data recorded. Arduino programming will be needed to lash it all together. The boards have a few high-frequency signals (clocks, -WE of SRAM, and R/-C of ADC) that can't stand long wiring. I am being guided on PCB layouts by a little paper mockup I did of the four boards. The new IDC-ribbon cable supplies are going to help a lot.

Arduino programming for a project that is needed to log megabytes of 1/f noise data over months, non-stop, is no simple job. I have read about the varying free SRAM between stack & heap, & I haven't come across any easy function that reports impending stack overflow (free memory underrun). MemoryFree library claims to have something, but I don't know if that requires a compilation step that I am not familiar with. One WWW site actually says that it is popular to try declaring a bunch of local variables in a function, if I have this right, assign values, then see if the values are stable, thus proving memory has not overflown, then get rid of the variables & put in the real ones you need. Fragmented heap or stack seems to be another problem. See Arduino stack overflow this isn't easy.txt on IRON for notes culled from WWW. Arduino use is going to be aided a lot by little breakout boards I am etching.

Sept 27 Programming Arduino is going ahead for event scheduling for 2.5s & 10s sampling of fourth-stage output. Looks like micros() function sails through 2³² overflow at 1hr 11min 24s with no hiccup. I am working on maintaining timing intact through multiple overflows, is tedious & hard to test because you have to wait 71 minutes to test it. Doing the I/O work of Arduino may be merely through function calls & may not be difficult at all. Switch case, based off the scheduling program, looks to be the way to call the functions, very organized.

Mar 30 2015: Purchased six LSK489 low-noise dual integrated JFET $5.60 at Round Rock TX Trendsetter Electronics. Intended application is 1/f noise measuring project, where the low-noise property of these JFETs is needed. Also, the integrated nature of these JFETs means they are closer in temp to each other & they have some matching of characteristics. This is really needed for this project, which needs to record fourth-stage output (total gain 300,000), with DC coupling, over months at a time. These JFETs have less capacitance than LSK389 & therefore amplify to wider bandwidth. They are made by Linear Integrated Systems, a specialty silicon-device design company.

May 28 2019: After diversions into audio power amplifier for 15" speaker and Arduino, I feel a pull back to this 1/f noise project. Two insights: 1) noise voltage per root hertz is semi-understandable when you are talking above 100Hz. But below a hertz, the square root of V is larger than V, and my mind rebels at the idea. Resolution: think about noise voltage per root microhertz. 2) A stable voltage reference of a 9V battery can surely be improved upon by using a physically larger battery; larger internal parts are bound to be more stable. Think about six alkaline D or C cells in series, or an AGM (absorbed glass mat) lead-acid battery. But beware of lead-acid self discharge. In any case, a battery must be temperature stabilized.

Arduino, maybe a Due with DAC, may be much better to use for control than Atmel CPLD. My last two Windows computers that handle WinCUPL and ProChip for CPLD programming quit or are on last legs, so CPLD may not be easy anymore.

Serial SRAM 8-pin IC may be best to record the bursts of noise up to 500Hz or 1kHz, every 10 minutes or hour. These serial SRAM have built-in address counter.

May 28 2019: After diversions into audio power amplifier for 15" speaker and Arduino, I feel a pull back to this 1/f noise project. Two insights: 1) noise voltage per root hertz is semi-understandable when you are talking above 100Hz. But below a hertz, the square root of V is larger than V, and my mind rebels at the idea. Resolution: think about noise voltage per root microhertz. 2) A stable voltage reference of a 9V battery can surely be improved upon by using a physically larger battery; larger internal parts are bound to be more stable. Think about six alkaline D or C cells in series, or an AGM (absorbed glass mat) lead-acid battery. But beware of lead-acid self discharge. In any case, a battery must be temperature stabilized.

Arduino, maybe a Due with DAC, may be much better to use for control than Atmel CPLD. My last two Windows computers that handle WinCUPL and ProChip for CPLD programming quit or are on last legs, so CPLD may not be easy anymore.

Serial SRAM 8-pin IC may be best to record the bursts of noise up to 500Hz or 1kHz, every 10 minutes or hour. These serial SRAM have built-in address counter.

July 2 2019 I have done a detailed design for monolithic JFET N-ch LSK489 first stage, discrete PNP 2nd stage which can both give maybe a MHz of bandwidth, but both DC coupled. Schematics done with Inkscape, on GETTER. Need about 1/2Mohm thin film, qty about 16, to do interleaved emitter resistors for PNP diff amp, that will spread out tempco of the resistors, where they go between +100V and the emitters, 2mA per Qe/Qf. I was going to order 0.1% thin films like I did about 5 years ago when they were $.11 in qty 100. But they are now $.44! But I found that by searching Mouser for 1%, thin film, a range of resistance values, but constraining tempco to 25PPM, Susumu brand is available at $.018 each in qty 500. I can use my DC bridge to select ones that are close.

3) Ongoing DIY DSO 8 bit 60MS/s--"CPLD2" PCB with SRAM, ABCD state machine, 60MHz LFSR address generator is starting to work. The initial clocking at low frequency (for testing) apparently had ringing clock, it needed a little test oscillator 2" from the CPLD board before it showed stable progress through the ABCD state machine and successful completion of the maximal-length, 12-bit LFSR. I am building up the 60MHz sine oscillator with intent to get delay lines working, for timing flexibility. Then it is on to the CPLD1 board with the Burr-Brown ADS830 ADC.

This project is shelved while I work on the low-noise amplifier. I bought some $.18, CMOS, 3.7ns, hysteresis-input, Fairchild Tiny-Logic, universal gates and some $.91 LVDS receivers that would simplify the delay-line design, and I am wondering if the complexity of the two PCBs as designed, with all-discrete delay lines, should be reduced by using these modern parts. Maybe should proceed with buildup of the two boards, there may be a time when CPLDs need redesign and will require new boards anyway if the fitter stirs pin assignments around.

4) CSRA Makers meeting Dec 28, I did a PCB etch demo that was well received. http://www.youtube.com/watch?v=IIQLqbT2jEM&noredirect=1 is Ed's video on YouTube, look for two parts. Thanks, Ed. At the Jan 25, 2013 meeting, I demonstrated the built-up board which has a crystal oscillator at 4,069,000 Hz with binary divide-down using CD4020, all the way down to 250 Hz, which is just 3Hz difference from B below middle C.

5) Nov 2013 Built a big electromagnet, U shape. Intended for students to see various effects: where flux lines go (like with little wire nails or iron filings or compass), how like poles repel (wire nails), a curious effect of a loose iron rod in the middle of a pole piece coming out easily, Lenz's Law (motion of aluminum bar upon change of flux), generation of voltage by moving coil, attraction/repulsion of a permanent magnet.

As seen in the photo, the poles are both in one plane and are large and open. The permeable core is of soft-steel nails with some paint or varnish coating each nail so that flux can change rapidly (a solid-iron core amounts to a shorted turn in the secondary of a transformer and prevents the flux from changing rapidly; the coated nails are like silicon-steel laminations in a transformer or AC motor)

The nail core is immobilized with paraffin. This is an economy project to show what a hobbyist can do: #16 magnet wire 3# $38 .75ohm per coil, 6# nails $7. 5V supply onto seriesed or paralleled coils gives 17W or 66W total, respectively. (In series, the power can be applied maybe 20 minutes before temp gets too high.)

The wire was purchased as the end of a 10# spool from D&L Industrial Services Inc. on Dixon Airline Road in Augusta.

This project follows on from a very successful electromagnet I did at TSTC Brownwood TX, which used 15# of #14 solid commercial wire (vinyl insulated, for conduit use), a 45# steel core that a student prepared from thick-wall pipe where he worked at an oil-well fab company, and a car battery. That magnet had so much pull on a 4# steel bar that no one could ever jerk the bar off the core. This Nov 2013 magnet is no where near that powerful but it is easily transported.

Here are some leading questions for students, when the magnet is hidden from view by a paper cover, but the poles are available just inside the paper. 1) Use some steel nails to prove there is a magnet inside the paper cover. 2) Is it permanent magnet or electromagnet? 3) Using nails or compass, find the north and south poles of the magnet. 4) Is it a straight, bar-shaped magnet or some other shape?

(Judge this by using nails to find where the poles are.) 5) Can you guess the shape of the magnet's iron? 6) Can you tell the width of the "poles"? 7) Can you think of a reason that this magnets is not built in the shape of a bar magnet? 8) Why is this magnet so heavy?

Reference: In the 1930s, giant DC electromagnets were first used to make nuclear-particle accelerators (cyclotrons). By 1945, the large diameter of the vacuum ring required up to 300 tons of copper bar and 3700 tons of iron. See photo at http://www.scientificlib.com/en/Physics/Literature/LawrenceRadiationLaboratory/184InchSynchrocyclotron.html#Magnet. Before WWII, the U.S. government did not fund science like it now does. The financing was by rich philanthropists such as Alfred Loomis.

Reference: Motors have electromagnets in this shape:

Shown in blue is the stator iron. The rotor is also iron, rotating in the gap. It turns out that efficiency is related to keeping magnetic flux from getting out into the air. You shape the iron so "air gaps" are small and the flux is all in iron. But the consequence is that young people who want to learn about electromagnets don't have any household appliances that have large, exposed flux. The other problem for students is that household appliances mainly have alternating flux (60 cycles per second), and that doesn't give a compass a chance to show where the poles are.

Dec 2013 Built an add-on device for classroom use: air-core magnetic flux sense loops feeding into DC-coupled, cascaded diff amps with gain about 2500, feeding differential LEDs and a voltage to frequency converter so you can both see and hear the slow (below 10Hz) flux change of magnets and electromagnets that get near the sense loop. The emphasis is that generation of voltage is only when flux changes. There is enough sensitivity to detect the earth's magnetic field. When you get a sense loop near a 60Hz device or a breaker panel, you hear the 60Hz magnetic field FMing the VFC.

6) Nov 2013 For Mr. C's physics class at Lakeside HS, I had prepared a visible demo of an RC time constant. This was with a speaker in series with 22 ohms and a 22,000 uF electrolytic capacitor. The time constant is about .6 seconds, easily visible, but the cone movement is only .2", not so visible. So I rigged a lever to amplify the motion. In class, this was not very effective. Today, I made a movie of the time constant that makes it more visible. With the time/motion data into a spreadsheet, the data fit the expected exponential curve nicely. Following is the setup and spreadsheet.

Above is the setup. A 14V supply is briefly connected to the speaker-22ohm resistor and (in series) the shorted-out cap. This sets a DC current in the speaker voice coil and the speaker cone assumes a displaced, constant position. The 2W resistor can't take this too long, so within seconds the short across the cap is removed and the cap starts charging toward 14V. This gives less and less voltage available for the resistor and speaker, and the series current falls exponentially, e^-t/RC. The cone relaxes to the unpowered position in about 3 time constants, where the time constant, RC, is .616s. The mount plate of a camera tripod is in the lower right of the photo, from which the 19s movie was taken.

Above is the main part of the spreadsheet. The graph shows the raw data taken from a 19-second movie, in columns A and B. This looks pretty much like an exponential decay curve, as expected. With this encouragement, it is time to normalize the physical motion at column D and calculate the e^-t/RC curve to compare to the measured data. Parameters are assumed at cells e6 and f6 to try to get a good fit to the measured data. This good fit is below, red being measured and yellow being the exponential math. There are green and purple-gray curves that are + and - 10% on the time constant to indicate tolerances. This shows nice agreement between theory and measurement.

7) Dec 2013 Purchased a digital storage oscilloscope, Gabotronics Xprotolab, for $50 from SparkFun. It is only 1.6" long and the screen is only 128x64 pixels on the LED screen, but it has a lot of capability. 2MSps. Built-in sine wave with other functions, too. Sometime I will try the screen-capture upload function. This device is an Atmel XMEGA microcontroller plus a quad TL064 op amp. Someone did a lot of programming. It is very susceptible to body-static destruction. The Xprotolab may be a way to get the DIY 60MSps digital oscilloscope project back underway, since I now have some visibility of what is going on in the circuits if there is a need for debug.

Update Feb 6: The screen-capture upload to Windows XP Hyperterm is working, through serial port (RS-232).

This is an upload of the Xprotolab screen, looking at a transistor in the DC-DC converter that generates +28V and -22V for the Auxiliary Circuits. The top waveform is the collector of the one-amp power transistor that feeds one side of the step-up transistor, and the bottom is the base waveform. The ON base voltage is so large because the emitter is biased up at 2V, and the base voltage needs to clear that by .7V. 16 pixels is one division, both vert and hor. The cursors aren't significant here, I forgot to turn them off.

Using a fiberboard box from Hobby Lobby makes the system easy to carry. Battery at back, aux ckts just inside front edge, Xprotolab on wires up from aux ckts (near middle), SMPS at right back. Front has ESD discharge, +15.5V input for battery recharge, and serial port to upload screen .bmp.

A +-12V line transceiver, IC MC145406, is used to interface TX and RX on the Xprotolab with the serial port. The IC is on a big "auxiliary circuits" PCB I did. The board also boosts power of the AWG waveform, provides curve-tracer conveniences, provides x10 for one channel and AC coupling for both channels, provides a differential amplifier that lets sensitivity get better than 1mV/div, and series regulates 5V from 12V. Another board does DC-DC conversion to get +24V and -18V from 12V, and this board has a gel-cell charger to let the gel cell be charged from a variable DC supply.

8) Jan 2014 Purchased five Jameco $3 LiteOn LTLD505T red 650nm laser diodes. These are intended for bar-code scanning and laser pointers. Used at 5mW, they are not good for the retinas. On the first try, using an astable at 2kHz and 10% duty cycle to give minimal heating at 22mA, lasing happened with no trouble. The familiar speckle patterns characteristic of coherent light show up. Focusing with a short-focal-length lens is easy. These may be good for line-of-sight communication. But my real interest is making a DIY interferometer and checking diffraction, including the double-slit experiment.

Following is a gray-scaled, contrast-enhanced photo of the interference pattern from a double-slit experiment on Jan 5. The two slits are different widths and that may be why there is a bright band. The camera is my basic Canon camera set for 4-sec exposure and 4" focus. The major point is that you don't just get two bands of light like you would expect.

The slits aren't easy to make. It may be better to use a carbon-blacked glass plate and scratch slits. But this one is a piece of blue paper, cut in half, glued over a hole punched in a white card, with half a millimeter slit between the paper halves. Then glue a piece of #32 wire across the slit, making a double slit. The red laser light is 650nm, and the interference pattern is about 1,800 times coarser than that when viewed on a screen perpendicular to the beam. (18,000 times when screen is tipped as below.) This is related to the spacing between the slits. This experiment is commonly done in college physics lab by all the undergrad students.

Here is the camera setup. The top yellow arrow shows the screen that was photographed. Note the shallow angle of incidence--this spread the pattern out an added factor of ten or so. The bottom yellow arrow is the double slit. Note that there is no focusing lens, this experiment isn't dependent on focusing, just on the coherent light of the laser. When Young first did this in 1801, he made coherent light using a single slit before the double slit (not obvious why this would cause coherence!), and his sunlight source provided enough light so he could see the interference pattern with his eyes. When he didn't filter down to a single color, he saw rainbow colors. After taking down the tripod and screen, I tried different distances from slits to a handheld screen, viewing through the paper screen with a magnifier. Like 3" and 15". Handheld, without an optical bench, things are moving around too much to see how this affects the fringe spacing (if at all!).

If you look at double-slit experiment on Wikipedia, it goes quickly to the quantum aspects because single-electron-detection equipment has been available since about 1990 to show a gradual build-up of the interference pattern, which is not intuitive. (Each electron goes through one slit or the other but the path on the other side is influenced by both.) The Wikipedia article talks about the experiment done with uncharged molecules, even buckyballs, and they still see interference, directly contradicting common sense. That is how strange quantum effects are.

9) Jan 20 Last visit by J.M. for electronics merit badge. J.M. started with solderless breadboard and two-transistor mic amp, progressed to paper-cutout 7x PCB layout and etch-build, expanded to merit badge requirements.

10) Jan 25 2014 Visit by Boy Scouts Troop 10 dads and scouts to work on some of the electronics merit badge. Some of the things I pulled out, to remind me if more scouts want to go this route: DMM with 9 or 12V battery, clip leads, LED, resistors in parallel or series: predict LED light will be more or less, and measure resistance in parallel and series, and voltage of battery. Calculator. Write out Ohm's Law, do the algebra to show all three variations, look for V, I, R on DMM and say the units of measurement. Look at the taken-apart resistor and capacitor samples, and look at the old radio tuning variable cap. (Future: capacitance measured between cookie sheets, also roll up a paper-foil cap.) Look at breaker panel, calculate power available at an AC outlet. Carefully measure volts AC coming from an outlet. Magnifier looking at silicon chips of metal-cased transistors. Three leads of transistor can be thought of, most basically, as common, input, output. But diode, LED, battery, solar cell, resistor, cap, fuse have two leads. But transformer has four leads and fully independent input and output. Future: hear AC coming through a cap into earphone. Also effect of various resistors in series with earphone. Future: string of resistors in series, to measure and to see reduction in LED light. Statement with examples: three uses of caps are passing AC, smoothing power supply (energy storage for camera flash), radio tuning. Stepup transformer with neon lamp. Simple soldering eqpt and desoldering wick. Homemade PCB in various stages of etch and build. Plasma TV PCB with heat sinks. Wall switch with continuity tester. Relay operating with a 120VAC load. Speaker & resistor to hear 120VAC, compare to DC. CdS cell, thermistor. Joshua's mic amp and computer speakers. Charge an electrolytic cap and see it discharge, with DMM and LED. Display of leaded and SMD parts and prices.

11) Transistor beta tester built up for 20uA and 2mA emitter currents, NPN and PNP, also N-channel JFET/MOSFET to find Vgs. Instead of setting a fixed base current and find the resulting collector current, this tester sets emitter current and you measure the drop on a choice of base resistors to find Ib. The base resistors are 10k, 100k, 1M, 30M. For 1M and 30M, a DMM on volts loads the base resistor too much, so there is a built-in JFET to aid measuring the drop from ground to base. The 30M base resistor is useful for Darlingtons.

12) Laser Diode PCB follows on from the earlier January 2014 work to give a permanent PCB to work with. The board has an astable to do low duty cycle at 1kHz or 13kHz (the former is easily heard by a light receiver). Three green LEDs give an alternative to laser diode. Current to the diodes is set by an adjustable current source, to check out the threshold of coherent lasing. A switch selects low duty cycle or 100% duty cycle. The light may be modulated in the baseband by a cap-coupled audio amplifier or a 100-ohm-coupled TinyLogic gate, which can reach +-32mA. The gate can be powered by 3.3V or 5V.

13) To go with the laser-diode board, a light receiver with a phototransistor can be used to receive audio modulation. There are three choices of load resistor for the PTX, and also a JFET to try for automatic AGC. One thing to listen to is an infrared TV remote control.

14) Audio sine oscillator--Feb 9, 2014--making plans for a neat, low distortion, all-analog, sine oscillator, also triangle and square, voltage controlled. Reason: the Nov 2, 2009 oscillator is triangle output, with switch to put in a low-pass filter and get a reasonable sine, but over the freq span of each range there is a big drop of Vout due to the LPF. It is a relaxation oscillator using hysteresis and Darlingtons, so freq range is good but Darlingtons limit upper freq.

I have thought much about getting low distortion sine, including Raspberry Pi or Arduino doing sine calculation and a DAC to get output, or use the 16-bit DAC I have. I don't want Wien bridge because of the special, air-variable cap it needs.

Today's design is a precision triangle generator, voltage controlled, large swing to minimize diode-drop variation with temp, going into diode clamps to do ramp-to-sine conversion. Each clamped section (3 in all, plus one that isn't clamped, per half sine wave) feeds current into a common-base current summer, and zener level shift gets sine back to ground. 10uF as the relaxation-oscillator timing cap can give down to 1Hz or lower, nice. The piecewise-linear clamp design is complex, I used a paper sine wave to select clamp voltages and Open Office spreadsheet on IRON computer to model the situation and choose current-summing resistors. The resistors interact, it takes a long time to narrow down to a set of resistors. (There are 7 variables bouncing off each other.) Then I did an RMS analysis of errors and it shows errors at -41dB, sounds OK.

The 2009 oscillator also has a balanced amplifier, diff in and out. But the input x11 dividers weren't matched and the amplifier in all was not usable. The diff amp on the new Aux Ckts for Gabotronics Xprotolab works well, 74dB CMRR at DC, try that on the sine osc PCB and keep all the pots and switches of the 2009 oscillator.

2-25-2014 Good progress. I partitioned the design into three boards, and there are very few inter-board connections required. All three boards are complete and interconnected, I have seen some sine waves and a good freq range but there are problems on the current-steering board, which may need a re-do. Even if harmonics are 41dB down, harmonics are what you hear when you dial up through 1Hz. The 4011 quad NAND has a lot of supply current transient when inputs are near threshold (which I knew about). Various bias voltages, from dividers, are better done with one divider per function, not shared. With little trimming, the voltage-to-freq conversion is working over a 100:1 to 200:1 ratio. With 330pF, freq range is 2300 Hz to 450 kHz, reaching a higher freq than I expected, but I have no way of measuring harmonics that high. With 1uF cap, I get .5% error, measured to calculated, where calculated period is 2*CV/I = 2*1E-6*26/10mA. The middle-C filter works well but I haven't tried to tune it to 261.6Hz from 267Hz. The main problems on the current-steering board, which has the timing cap, are transient currents in 4011 and bias dividers. There have been a lot of touch and even proximity effects. I put in a 1"-wide ground strap between boards and I think that helped. What has worked at 2kHz has sometimes not worked at 2Hz.

March 21 The DIY sine oscillator is working pretty well and is all packaged up except for transparent sides and back, and the 38V DC-DC converter needs boxing up. A replacement current-steering board (ver2) is so much better than the first; I substituted it in and it just worked, no tinkering needed. The large number of bias voltages is handled by a plug-on daughterboard and that was a good idea, keeping the high-freq ckts in a tighter bundle on the main current-steering board. The board has a beta mirror for the Qt transistor, and in combination with the trim on the VFC op amp that allows a large VFC tuning range, like 3000:1 ratio of frequency (or maybe even 8000:1), so that even when you are on the 130kHz range (Cs=1200pF+100pF+28pF stray), at minimum of the tuning pot you see the LEDs flickering at 15Hz or so. The lowest marked calibration is .5Hz but, using the max Cs of 22uF, it reaches down to a period of about five minutes.

The diff amp is probably CMRR at DC of 90 or 100dB, not just 74dB. Even the three-op-amp instrumentation amp, without resistor-ratio trimming, seems to be over 85dB CMRR at DC, but when oscillator goes over 5kHz there is interference that comes over from the other op amps in the quad package.

Freq-cal marks on the front panel are quite accurate where we checked against the Yamaha keyboard, mostly less than 4Hz off over an octave from G to middle C and on to G. This was accomplished with a trial printout of the front panel, marking dots in pencil using DMM on Hz, then used protractor and CorelDRAW to transfer those angles onto the final printout.

I used Gabotronics Xprotolab to make screen prints of some key waveforms, then put those in a document that is in the project binder.

15) Audio amplifiers for Mr. Cosper's STEM Academy during week of June 16, 2014--I am invited to send students through an algebra exercise, calculating the attenuation of an audio signal due to the Rtop, Rbottom bias resistors for a Class A power output stage. The algebra is compound fractions resulting from paralleled resistors. To provide audio signal to the gain-of-1 output emitter followers, I have a distribution amplifier powered from +24V that can swing 6V peak onto four 1k resistors, then from each 1k you go to the Class A Darlingtons, quantity four. Each Class A output stage is powered from a current-limiting +12V supply. I intend that students select different impedances for the Class-A voltage divider for the Q point, solder on resistors, and look for clipping.

16) Through Boy Scouts Troop 10, Fred Ricketson sold me a Tasco 60mm refractor telescope with a motorized alt-azimuth mount and microprocessor controller. The software is a bit buggy (during alignment, the controller is happy to run the eyepiece end of the tube into the mount) but this is the nicest telescope I have had in decades. We saw the rings of Saturn on June 14, so clearly.

Moved from Grovetown, GA to south Austin, TX May 2016

17) Built a simple pan balance using balsa wood, straight pins, and paper. It is not well balanced between right and left distance-to-fulcrum but it is sensitive, .01 gram. The fulcrum is very simple, a straight pin rolls across steel supports.

18) Aug 3 2016 Concluded a long investigation of math: when you use an algebra trick (that I learned when I was in middle school) to find the ratio of integers that produces a repeating decimal, like 3.013467013467013467... = 3013464 / 999999, very often the denominator of the ratio is all nines, or all threes or ones. For a long time, that has sort of bothered me that nines, threes, and ones should show up so much, to the virtual exclusion of other numbers. It didn't seem fair to other numbers. But what I found was that all-ones denominators have a lot of prime factors, they are rarely primes themselves, and various 0-and-1 numbers are building blocks that multiply out to all-ones numbers. The most common prime factors of all-ones numbers, up to 42-digit all-ones numbers, are 11, 101, 3, 37, 41, 271, 9091, 7, 13, 239, 4649, 73, 137, 53, 79, 31, 2906161. These pairs, or even the one triple, show up together in a reliable, periodic structure as factors of the all-one numbers. I made use of the periodicity to factor all all-ones numbers through 28 digits, and also 30, 36, and 42 digits. So, not only are the denominators of these ratios partial to all-9s, all-3s, and all-1s, but also a very limited set of primes are factors of these denominators. Of the integers up to 271, 57 are primes, and only 15* are needed to be factors for the denominators I have studied. (See chart with blue squares, the second chart below.)

www.javascripter.net/math/calculators/primefactorscalculator.htm is a great, 20-digit factoring program, and Ruby's arbitrary precision is key to doing factoring above 20 digits. With wolframalpha.com, you can type in any positive, base-10 integer up to about 45 digits and it will spit out the factors.

file on newGETTER, the new Ubuntu 16.04 powerful computer: repeating decimal fraction resolved to division of integers puzzle of 9s verF.ods or .xls.

By Dec 2017, the spreadsheet of my work is up to verJ. I found a name for the all-ones denominator, repunit, for repeating ones. This name was given in 1966. Knowing the name, I can find lots of information on Internet, and I find that none of my work is original. Whether or not others find the dominance of repunits in finding the ratios that give repeating decimals to be suspicious or bothersome, I don't know. But I suspect that repunits are the denominators in other bases.

I don't know if the "building block" nature of the factors of large repunits is special, but I suspect it is. (One building block is 100001000010000100001 = 21401*25601*182521213001 . This block is used to multiply 11111 to get the repunit with 24 ones. Obviously, you can get very long repunits by multiplying 11111 by 100001000010000100001 or 1000010000100001000010000100001000010000100001, etc. This is why the factors of repunits keep showing up every so often.) A different kind of building block may be 91, 9901, 99990001, 90090991, 900099009991, and 999999000001.

There is a fairly limited* set of primes that is well suited to generating repunits by multiplying by each other. The most common are 3 7 11 13 37 41 101 271. These are the leftmost blue dots in the chart below. One of these, 11, is itself the repunit with length 2. By just taking certain pairs of these eight primes and multiplying, we get repunits with length 3, 4, and 5. (3*37, 11*101, 41*271) Six repunit still uses this set of eight, 1001*111 = 7*11*13*3*37. Once we ask for seven repunit, we need bigger primes that are outside the set of eight, 239×4649. When I chart these common prime factors, I see this.

To repeat the key thing I found in the spreadsheet, these factors are needed at very predictable times as we consider longer repunits. 239 and 4649 in the chart are needed for the 7 repunit, 14 repunit, 21 repunit, etc. (1111111, 11111111111111, 111111111111111111111)

The chart has a weak pattern. There is the definite trend with positive slope, suggesting that ever-bigger primes are needed for longer repunits. Then there is the lower-right fork of small primes that are used infrequently. I have recently seen a repunit web page where a man claims that every longer-by-one-digit repunit requires a new factor. My observation that every repunit factor gets used, periodically, means that the width of the above chart is unlimited. Probably the new factors have very long periods.

Ap 13, 2019 The chart above follows a lead I found at http://www.elektrosoft.it/matematica/repunit/theory.htm where they say that the factors of repunits

are 2kp+1 where p is primes and k is integers 1 and above, I suppose. A spreadsheet on my GETTER Ubuntu computer,

repunit 2kp plus 1 factors.ods, finds that they are in there, but to find the factors from my chart above, above 4649, requires that k be pretty large.

My chart above, Is There a Pattern in How Often the Prime Factors of Repunits Get Used?, is, I think, a significant chart.

The section of spreadsheet above is one example of hundreds possible of multiplying factors of a repunit, while seeing "building blocks" or interesting numbers during the multiplication process. The example above is for the eighteenth repunit, 111111111111111111.

As I consider the suspiciousness of repunits dominating the resolution of repeating decimals, it seems to me even more exotic that there would be repeating decimals at all. And this finally seems to be somewhat of a satisfaction to me. Wikipedia has a whole article about repeating decimals! It has some customary math terms for what I have been seeing. Repetend is a standard term, but repunit isn't showing up so much. Wikipedia about repeating decimals has this:

x = 0.(A₁A₂…A_n)

10ⁿx = A₁A₂…A_n.(A₁A₂…A_n)

(10ⁿ − 1)x = 99…99x = A₁A₂ … A_n

x = A₁A₂…A_n/(10ⁿ − 1)

= A₁A₂…A_n/99…99

which is some sort of notation close to repunits. "Repeating decimal with period n." The Wikipedia article gets pretty interesting but I don't quite follow it.

Wolfram’s http://mathworld.wolfram.com/DecimalExpansion.html I found this Wolfram site by searching Internet for 2906161, the prominent repunit factor that is needed every 15th repunit.

Clicking on one of the Wolfram page’s links is http://stdkmd.com/nrr/repunit/ which shows all repunit factorizations to 100 ones, far higher than I had reached.

http://stdkmd.com/nrr/repunit/repunitnote.htm is interesting in that it references several repunit web pages at 1.4

https://gmplib.org/~tege/repunit.html has some narrative.

The currently known prime repunits have 2, 19, 23, 317, 1031, 49081, 86453, 109297, and 270343 digits. I had confirmed that the 19 repunit is prime, and I suspected that the 23 repunit is prime. Then it is a big jump to 317. Up through 317, these are themselves all prime numbers. Are they all prime numbers?

Consider how the prime repunits compare to the third chart above. A prime repunit has no factors, and in particular has no factors like 3, 11, 37, and 101 that are so abundant in the third chart above. One can readily see that the repunits which are prime numbers, with 317 and 1031 ones (and 49081, 86453, 109297, and 270343, sequence A004023 in OEIS.org) are repunits that could be shown in a chart like three charts above, and they would be the rare repunits that fall in the rare gaps where the periodic factors all skip. That is why the prime repunits are so rare.

Aug 31, 2018: Another search of Internet, for 31 * 2906161, from the second chart above, which equals 90090991, turns up https://oeis.org/A019328, where oeis is online encylopedia of integer sequences. Cyclotomic polynomials at x=10 is a list that includes my "building blocks." I can't follow the web sites about cyclotomic. https://en.wikipedia.org/wiki/Unique_prime, at the heading Decimal unique primes, also has my building blocks.

June 2019 I have added to the spreadsheet on GETTER (Ubuntu) computer, file name

repeating decimal fraction resolved to division of integers puzzle of 9s repunits verK.ods

at AO222

to see factors of repunits around the size of the R317 repunit (317 ones). Now, R317 is a prime repunit, the first after R23 and the prime repunit that is below R1031.

I wanted to see whether composite repunits in the area of R317 have abundant factors or whether there are many repunits in that area that are "almost primes." To my surprise, there are several (R311, R323, see below) that have only very large factors, like 20- or 40-digit prime factors. And there are four times as many that I would call "almost primes."

In looking at repunits around R317, I used the color coding of the 24 most common factors, the ones that repeat up to "every 22nd" and I found, indeed, that R317, and several others, are where the repetitions all skip, all at once.

What I don't know, as of July 7, is whether anybody else pays attention to the various periods of the common repunit factors. That, to me, is the most remarkable thing about repunits.

I made use of the web site

http://kurtbeschorner.de/fact-2500.htm

to see factors of this range of repunits. But a little below on this web page is Studio Kamada which does a better job.

• • n = 311: 4344673058714954477761314793437392900672885445361103905548950933 (Kazumaro Aoki/T. Shimoyama) * 2557410180......P247

  • n = 312: 313 * 1101673 * 1358074433371719716641 * 291593563046646669491593 * 7323941687......P43

  • n = 313: 1879 * 2099818661161079 * 2816105491......P294

  • n = 314: 4397 * 3641773 * 5677249457......P146

  • n = 315: 631 * 142809770881 * 1110829052......P131

  • n = 316: 5689 * 507998564486483655774880939989709 (Bruce Dodson) * 646301962916453492325383567253991760083617720844121 (NFS@Home) * 5300840448......P69

  • n = 317: 1111111111......P317

  • n = 318: 3499 * 2784091 * 54137839415767 * 917813298871770308465539 (A. K. Lenstra/M. Manasse) * 26526333976234009593263527 (A. K. Lenstra/M. Manasse) * 8558521377......P31

  • n = 319: 723493 * 798763879 * 25815444138362212501215782602427193330961 (Nicolas Daminelli) * 6032678170......P225

  • n = 320: 9999999999......P128

  • n = 321: 167805961 * 5368706186......P204

  • n = 322: 967 * 1569936761 * 1203881882727712699967 (Silverman) * 23391028206417273637358380573 (Silverman) * 7775058388319250595762800404689 (Silverman) * 3309383964......P40

  • n = 323: 851908127328669427 * 1056451947......c271

There is shorthand in this web site. I suspect P40 means the 40th repunit, a composite number, and C271 is some sort of composite number or collection--not sure.

In my GETTER spreadsheet

various repunit prime factors multiplied in pairs b.ods

there is an example of a palindrome, 12345554321 multiplying by a 9-and-0 factor,

900009090090909909099991 (both of these factors are themselves composites)

to get R35. The full long multiply is worked out in the spreadsheet. It is quite interesting to see the long columns and carries add up to 11, 21, 31, 41, 51, 61, 71, and 81.

The definite trend is that many examples of multiplying factors of repunits give palindromes, and when you can form up a palindrome, there is a 9-and-0 product of other factors of a repunit that is needed to get to the full repunit.

Another GETTER spreadsheet is

products of permutations of repunit factors for 18th.ods

Here are some web sites that help.

wolframalpha.com type in permutations 1 2 3 4 5 to see all permutations of these five symbols, but for non-subscribers it is an image, not text. See mathisfun.com below for copyable.

wolframalpha.com type in factors 6469693230 or any integer to see prime factors.

Studio Kamada at stdkmd.net/nrr/repunit for factors of repunits, done better than http://kurtbeschorner.de/fact-2500.htm

factordb.com which is an amazing database of numbers that people have asked to have factored. There are millions of fulfilled requests.

gmplib.org/~tege/repunit.html

book: The Joy of Factoring $42 Wagstaff

mathisfun.com/combinatorics/combinations-permutations-calculator.html "without repetitions" gives a text version that is copy-pastable, up at least to the 720 combinations for six symbols.

Factoring algorithms for integers include ECM (elliptic curve method), multiple polynomial quadratic sieve, general number field sieve (NFS). Wikipedia The wonderful web site factordb.com uses some of these algorithms.

Various repunit sites show factors of numbers, and include p and c numbers.

p90 means a 90-digit prime, c201 means a 201-digit composite number. From https://homes.cerias.purdue.edu/~ssw/cun/notat

Where the repunit sites intend that you discover the p and c numbers, I don't know.

project blog: Unique Primes (see Wikipedia) are some of the "building blocks" I have stumbled upon in my repunit work, see the spreadsheets on GETTER computer. (...repeating...ods)

3, 11, 37 (3*37=111), 101, 9091, 9901, 333667, 909091, 99990001, 999999000001, 9999999900000001, 909090909090909091, 1111111111111111111, 11111111111111111111111, 900900900900990990990991, 909090909090909090909090909091

which is OEIS A040017. Abundance of the digits 0, 1, and multiples of 3. I especially like 333667. The definition of Unique Prime takes quite a bit of thought to understand it.

July 5 2019 Something suggested looking at repunits as Lucas Sequence. Wikipedia says the Lucas Sequence U_n(11,10) is the repunits sequence for base 10, whiich is 11, 111, 1111, 11111, etc. ( n is 2, 3, 4, 5 for these repunits, P=11, Q=10 ) It is interesting that repunit for any base x can be had by using the appropriate P and Q. I could understand enough of the Wikipedia article to start with U₀(11,10)=0, U₁(11,10)=1, U_n(11,10)=11*U_n-1(11,10)-10*U_n-2(11,10) and generate the repunits.

For n=2, U₂=11*U₁-10*U₀ = 11*1-10*0 = 11-0 = 11.

For n=3, U₃=11*U₂-10*U₁ = 11*11-10*1 = 121-10 = 111.

For n=4, U₄=11*U₃-10*U₂ = 11*111-10*11 = 1221-110 = 1111.

It goes on from there, in the form 122222221 - 011111110. It never gets more elaborate.

What I don't know is whether the numerous properties of Lucas Sequences yield information about repunits and their factors.

April 11 2020 I got the old GRID computer unwrapped from when we shipped it to San Antonio from S. Austin. This is the capable computer that was beside the 32" TV. It has Ruby in Aptana on the Ubuntu side, and Ruby can do arbitrary-precision math. I had spotted Repunit 313 close to the prime R317 while looking at stdkmd.net/nrr/repunit , and Mr. Kamada leaves a factor of R313 abbreviated! Now, it is a 294-digit factor, a prime, but I was curious if Ruby could find this mystery number. Indeed it did! I made a little program, bigdivision.rb that includes the following code. f is R313.

# 1 2 the 313th repunit 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 313

f = 1111111111_1111111111_1111111111_1111111111_1111111111_1111111111_1111111111_1111111111_1111111111_1111111111_1111111111_1111111111_1111111111_1111111111_1111111111_1111111111_1111111111_1111111111_1111111111_1111111111_1111111111_1111111111_1111111111_1111111111_1111111111_1111111111_1111111111_1111111111_1111111111_1111111111_1111111111_111

puts f

puts f/1879

puts f/2099818661161079

puts f / 2099818661161079 / 1879 #factors from studio kamada stdkmd.nte/nrr/repunit this is a 294-digit prime number, the longest factor of repunits in the area of R317

puts 1879 * 2099818661161079 * 281610549145340670875530572295911650613447664512433824813528389571669384474043762357056898880154418118236146141986844719186603026177734005061357862428585505468782629421752945521024248741622964333059827025642538885425301838044666631121900885526792151665947943735117027305821260400695494881970871

The code line, puts f / 2099818661161079 / 1879, causes the 294-digit prime number to print on the console of Ruby. To check, the last puts of code multiplies the 294-digit factor by the other two (much shorter) factors and it does come up with the 313th repunit. Hooray for Ruby. And hooray for gedit and Google Sites which can copy and paste such a long number.

19) Purchased a TI-84 Plus C Silver Edition graphing calculator so I can do the math that school students are doing. To April 2020, this fancy calculator has had no use.

20) Having purchased some physics, bio, and chemistry gear from Home Training Tools, I am going ahead to outfitting quite a chem lab for benefit of students at church and our grandchildren.

More about why I am doing this: a) the neat but dry book, Exploring Chemical Elements and Their Compounds by Heiserman highlights which elements are rare. There are surprises: the military-aircraft metal titanium is not rare, it is the ninth most abundant element in the earth's crust. Argon, the noble gas heavier than neon, is a whole 1% of the atmosphere, beating out the lighter neon which is only 18 ppm. Neodymium, in a ratio of 2 to 14 of iron and 1 of boron, is in the strong magnets that are popular around the house and are critical in hard drives, electric-vehicle motors (4 kilogram per car), and wind turbines. But it is only 24 ppm in the earth's crust. The world supply of neodymium is centered in China and there is concern that demand will outstrip supply, or that the communist government can play blackmail with this element. These are neat chemistry factoids. b) common food ingredients are thiamin mononitrate, folic acid, calcium phosphate, calcium lactate, dextrose, diglycerides, calcium iodate, potassium bromate, and disodium inosinate. (Just read the ingredient lists on the packages in your pantry.) What are these chemicals that we are eating? c) I sometimes read about organic molecules, and I can build them with my Molymod teacher set.

Instead of ordering what I guess at, have on order Illustrated Guide to Home Chemistry Experiments: All Lab, No Lecture. This book acknowledges that the neat chemistry sets of the 1950s through 1970s are no more, there is too much liability. At Lowes' and Walmart, I have purchased larger quantities of concentrated sulfuric acid, Plaster of Paris (calcium sulfate), crystalline Drano (sodium hydroxide), magnesium sulfate (Epsom salt), calcium chloride anhydride, TSP. Sciencecompany.com has bigger quantities of chemicals than Home Training Tools. I may purchase a hot plate with magnetic stirrer for organic chemistry recrystallization separations. We have done liter-size hydrogen-oxygen electrolysis and sugar-sulfuric acid carbon snake.

The chemicals are coming in Aug 23:

File chemical list at home Aug 2016.odt on GETTER

Hydrogen peroxide 30%, 30 ml x 2

Hydrochloric acid conc., 30 ml

Acetic acid glacial, 30 ml

Potassium permanganate, 30 g

Calcium metal, turnings, 10 g

Magnesium ribbon, 60 cm

Potassium Nitrate, Saltpeter, 100g, Food Grade

Zinc, metal electrode, 4"

Tungsten lamp filament

Nichrome resistance wire 30 gauge 4.68ohms per foot or thicker from blow dryer

Mercury in a large, glass, tilt switch

Lead sinkers

Artist graphite

Potassium iodide, 30 g

Sodium bisulfite, 30 g

Ammonium nitrate, 30 g

Ammonium hydroxide, 30 ml

Oxalic Acid, 500g

Potassium Hydrogen Tartrate 42g

Barium Hydroxide, 100g

Ammonium Thiocyanate, 100g

Phenolphthalein powder 5g

Methylcellulose 1.5% solution for protozoa

Sulfur 90% inert 10% 1#

Calcium Chloride Damp Rid 1#

Copper Sulfate pentahydrate Zep Root Kill 2#

Sodium Carbonate washing soda 3#

Borax B4Na2O7 10H2O alternating 4B & 4O with one bridging O, also two outrigger O with Na, decahydrate 20 Mule Team 4#

Potassium Chloride lite salt 80g

Sodium Chloride non-iodized 1#

Magnesium Sulfate 4# Epsom

Trisodium Phosphate 1#

Mineral Oil

Sulfuric Acid conc. with pink dye drain cleaner 32oz

Sodium Hydroxide granules Drano 1#

Calcium Sulfate with some MgSO4 and silica plaster of Paris

Calcium Ammonium Nitrate cold pack 1#

These chemicals are sufficient for almost all the early experiments in the Illustrated Guide.

I took a tip from the Illustrated Guide book about Tx state registration of flasks etc. (because the Legislature acted against illegal drug labs, instead of doing nothing) and found on-line where DPS does require registration before purchase (Texas Administrative Code 13.104, 13.186)

Distilling apparatus.

Vacuum drier.

Three-neck flask.

Distilling flask.

Tableting machine.

Encapsulating machine.

Buchner, filter and separatory funnels.

Erlenmeyer, single-neck, two-neck, round bottom, Florence,thermometer, and filtering flask.

Soxhlet extractor.

Transformer.

Flask heater.

Heating mantle.

Adapter tube.

I put the paper request in and got e-mail back in two weeks. For free, an inspector is going to call and schedule a visit. I had to put a locking knob on the closet and have fire extinguisher nearby, for the glassware. I can't order the regulated glassware until approved. None of the chemicals I am using is on the regulated list.

With oxalic acid and ammonium thiocyanate received, it is more interesting to read on-line about these chemicals. The labels on the bottles are very useful. Ammonium thiocyanate indeed has a lot of cyanide in it, but being solid it isn't too dangerous, it is storage code green. But you dare not mix acid with it, otherwise you generate gaseous hydrogen cyanide. Ammonium thiocyanate is used in a lot of chemical reactions. It detects small amounts of ferric ions in carbonated beverages and in drinking water where the soil is red from iron.

2016 Aug 30 Geoff, Field Compliance Auditor, Compliance Enforcement Services, Tx DPS, visited, checked that the closet door locks, and went through a checklist. He doesn't often have to audit small operations like mine. The quantity of glassware is not so important as the types, a document he has doesn't give the quantities. He seemed to say that online vendors will reject orders for regulated chemicals and glassware, it isn't so much that a Texas resident will be a third-degree felony offender by unknowingly ordering regulated things. He probably glanced around to see the general nature of the right bedroom (lab things, astronomy, books, computers). His report goes through management, now.

Progress on the roll-around chemistry stand: two sides of pegboard are built up, a work surface is at 47" above the floor, to limit what grandchildren can grab. A foam-core safety cover can cover the other two sides to further limit grandchildren. The work surface is covered in plastic for liquid resistance and has pebbles all over the plastic to make it non-combustible, also aluminum foil lines the pegboard above the work surface. A little drain is provided with a big funnel through the work surface, it drains to a gallon bottle. 3/8" steel rods are provided to mount 3" and 4" rings and clamps. Polycarbonate panes are provided at the front to catch splashes.

Two old vacuum cleaners are connected in series to provide some degree of vacuum for filter flasks that are yet to be ordered. Vacuum cleaners are low-psi and high volume whereas I need high psi and low volume. The solution might be to make an airtight wooden bottle of one or two cubic feet and draw down the pressure in that as needed, to limit the heating in the vacuum cleaners when there is almost no air flow; they would be operated by 12V-coil relay Jameco 137358 or 2167453 with a pulse width modulating circuit.

Sept 10 2016 The permit from DPS came. The big thing is making sure what I order comes to me, that it doesn't get stolen en-route. And also that it isn't stolen from the closet in our apt. There is a carbon form Nar-22, specifying vendor, the controlled products ordered, and me. It has to be mailed back to DPS by the vendor. The 8.5"x11" permit--I couldn't quite tell if it stays with me, stays with the vendor, of goes back to DPS with Nar-22. I contacted my chosen vendor and they said they will ship me anything I want, and any paperwork for Texas they can fill out. This isn't nearly as locked down as the Texas auditor made it sound. I decided to do two orders, some additional non-regulated items by web order and the regulated items by a paper order through USPS, with the Nar-22 and permit in same envelope, with an addressed, stamped envelope to DPS enclosed to make it easy for the vendor. I even put four orange stick-on arrows on the Nar-22 to be sure they see where to put invoice # and sign off. They filled the order Sept 21 and it is due in on Sept 27. That makes for only about a month for the Texas permitting cycle.

The vacuum-cleaner "bottle" is built. The ping-pong-ball valve, pressing down on a rubber balloon stretched across a hole in 3/4" MDF, is probably not sealing very well, or air is getting in alongside all the screws (this can be sealed with silicone, will try it). I put an additional 1" hole in the MDF for a #6.5 stopper, with a glass 5mm tube out, to suck up water from a reservoir and found that the Dirt Devil hand vac is about 1/3 the suction of the big upright vac. Operating together, they can do .72 psi = 20" of water, not very much. When the Buchner funnel and filter flask come, it will be interesting to see if this hastens filtering very much. The relay-timer control for the vacs might be done as turn-on-one-vac-at-a-time-as-the-other-cools-off. An alternative to vacuums might be a water-draining approach; have a sealed water reservoir up near the ceiling, drain it out with a little siphon tube down to a pan on the floor, restrict the drain tube at the bottom so air can't sneak in backwards. This pulls a partial vacuum in the reservoir, attach a vinyl tube from the top side of reservoir to filter flask, which can be down at table level. This works if the amount of air coming through the Buchner funnel is low, and it can be 4x the psi of the vacs. The state-controlled glassware came in. The filter flasks need 3/8" IC vinyl tubing, bought 20'. The vacuums do increase filtering rate, maybe 3x, so go ahead with plans for electronic controller for vacuums, by relays. By Nov 1, the circuit boards are designed and almost ready to be etched.

Oct 2016 To design the chemistry-stand PCBs, I needed vector graphics program, but the old Windows XP GETTER computer with CorelDRAW quit. But I had backed up lots of files, especially the parts library parts library without grey.cdr. And I had already apt-get installed Inkscape on newGETTER, the very capable Ubuntu 16.04 computer. I was surprised that Inkscape opens .cdr files with few difficulties, plus it cooperates with the Bamboo stylus and tablet from Wacom. So with no trouble, I move on to PCB design with Inkscape! But there is the learning curve for Inkscape, much as there was a learning curve for CorelDRAW in 1994.

By Nov 28, the PCBs are all built up and function. Relays are on order. It seems I static-shocked the programmable CPLD on the logic output pin emerg_shutdown which goes to pushbutton PB3 on the control panel. For a while, it was stuck high, then it went stuck low. The three inputs to the emerg_shutdown gate, an OR gate, are available outside the chip, and I was able to wire 3 emitter followers to do a substitute OR function.

The sensor PCB, above the work surface and looking down at the work surface, has a "flash" sensor with a visible-light phototransistor that is intended to look for flashes of light, like from an explosion. There is a parallel combo of visible-light phototransistor and IR phototransistor that is sensitive to a small flame of a match from two feet. That is better sensitivity than I expected. The thermistor senses temperature from any possible fire on the work surface.

The 120VAC sensor for the output of the household timer works, to shut down AC outputs when the timer is programmed to do that.

The control panel only needs to be labeled.

The selectable sequences for the two vacuums both work. Yet to be determined is whether the high (tens of amps) current transients upon starting the vacuums cause EM disturbance to the board.

Four strips of white LEDs are set up to provide illumination for the chemistry stand.

Dec 9 2016 The PCBs and control box for the chemistry stand are just about finished. Functions all work, that was a lot of planning to get so many functions to work, when some functions interrelate to others.

The thing that isn't working now is interference from 120VAC switching transients into sensors. The flash latch often comes on due to transient. I need to experiment with a bigger filter cap on the main PCB, for flash sensor. With winter home heating, the above-the-work-surface temp sensor (thermistor) often senses heat blowing out the room's ceiling vent a minute before the the compensating (bottom) sensor (under the work surface) is able to track the room temp. Also, the fluorescent work lamp is below the temp sensor, and that sometimes raises the temp sensor's temp artificially. I have 390k resistor paralleling the bottom sensor (47kohm thermistors) to help with this, but it may need an added, parallel resistor with a switch to make it better.

The vacuum sequencing experiences no upset from AC switching by the relays. The idea of using 555 timer ICs in monostable mode to get a ring oscillator is working well, but only because I took the trouble of creating a kickoff pulse after POR (power-on reset), sent it to 555 B, and reset all 555s during POR.

The flash-sensor sensitivity to interference was because the intended .1uF filter cap didn't get soldered on, I thought it was going to be .01 or something and I initially went with no cap at all. With a .1uF in there, interference doesn't seem to be a problem. Main usage problem is now just the room-heating transient affecting the over-temp sensor, as mentioned above.

21) Feb 20 2017 Distillation of water, like food-coloring-colored water, is something to do with Tx Oaks Baptist Church Wednesday Tech and Truth for children. We don't want a flame at church, so I am using #30 nichrome wire, of which I have plenty. Glass beads from Hobby Lobby insulate the wire without melting. A 60W transformer, 28Vrms heats the nichrome. I wish I had a glass receptacle with a neck in the middle, but what I am using is a plastic peanut jar. There is a neck 3/4 up the jar. When I put 3/4 cup of starting solution in the bottom and tilt the jar to 75 degrees from vertical, the starting solution comes up just below the neck, and any condensate trickles down to the little area above the neck. I can drill a hole and let the condensate drain out. I lined up the bead-insulated wire, back and forth under the area of the jar that has the starting solution. I have tried masking tape to hold it in place but it scorches a little. Plumbers' Teflon tape will be better. The heated solution got to 70 deg. C today. You have to chill the condensate area. Once it is up to temp, it gives maybe a milliliter per 10 minutes. The food coloring does not go with the vapor.

22) Feb 2017 The home-school group I work with, four children, took up a challenge after I told the moms what it would be like and how soldering and chemistry would work in. We built a surface-mount version of the 1997 TSTC audio amplifiers that I built using perfboard, to demonstrate how a mic needs a lot of gain to get up to speaker strength. The 1997 amplifiers were gain-of-10 each and we did four, plus a volume control. The 2017 design is better, it has little sensitivity to power-supply hum. Each amplifier has 6 transistors, with a TIP31 NPN power transistor as output for each module. Gain is 11 to 15 per module. Three cascaded are enough. The surface-mount layout was done as I led Joshua in Augusta to do a mic amplifier, we have lots of pad patterns at about 5.5x so they are easy to handle. Starting with a schematic I did, the students taped down pads and drew connecting traces. I scanned the result and shrank it to final size (2" x 3"), and added traces, thicker grounds, and spare pads. We all did the exposing and etching. Just as I am always impressed by the blue pattern coming visible during development, the students were surprised. The etch was done using a little agitation from a LEGO motor stepped down with pulleys and worm gear. Students really wanted to build with LEGO gears more than solder. But they got two boards done, and I did another two. Solder bridges were the main defect during assembly. The parts value per board, including the board, is $3.41. The result is good. Even with 4 amplifiers cascaded, there is no oscillation due to supply feedback or coupling through ground. With computer speakers as output, distortion is low if you don't overdrive the signal. There is a lot of hiss, more than I would have expected.

The home-school students wrote reports and in return received certificates for the considerable work they did on this project. Lamar: The LEGO ferric-chloride stirrer was cool. He like soldering, the iron was super hot. It was a lot of work. Casey, Lamar's older sister: liked soldering. Care was needed to position the tiny parts. Solder bridges caused shorts which had to get fixed. A brand new experience.

On Wednesday Feb 22 at TOBC, I intend to work the students through the interconnection of the modules, starting with no amplifiers, just headphones to mic, then add one module at a time to see how the volume builds. Then we can see how many want to compete to see who can do the connections fastest. The Bible story is the chain of patriarchs, Abraham to Joseph, which is a play on the chain of amplifiers.

23) 2017 Feb Home schoolers used Lego Technic teacher set that my mother-in-law purchased for my children about 30 years ago. The students want to make vehicles that go, and their need is not served by the AC-to-DC supply I am using. But I am not willing to buy batteries. So I made a long wire to use an old, rechargable, 6V, lead-acid sealed battery. This is for the new gearmotors that are sold at the Lego store in Barton Creek Square Mall. They are 9V motors. A clutch comes with the motor set. I also purchased some white, 5-high, 6-wide walls and some black, right-angle, L shapes, which the teacher set was short on. I see that Lego's intention is to always build upward, never sideways. But with Technics gears, sometimes you need to build sideways, and the L shapes may allow that.

24) 2017 March "Fun Sounds" project is audio-oriented PCBs with voltage-controlled oscillator (VCO) that is easy to get frequency modulation (FM) with. This is what I did with the big 2014 VCO that has conversion from triangle to sine wave using piecewise linear converter using diodes. (See this web page for the 2014 project.) This project doesn't have sine wave, just the triangle. There are plenty of user controls to make sound effects easy. The FMing has two inputs plus the base frequency set. FMing sounds very neat, flying saucer landing sounds. The big step ahead with the PCB is adding audio double-balanced mixer to see what that sounds like--it turns out to be just what you hear with a shortwave radio when you listen to single-sideband without adding beat frequency. I am surprised that voice is not intelligible, and music is changed very much so that you sometimes can't identify what the tune is. Double-balanced mixer is merely inverting the signal when the second input goes negative. The circuit I use is op amps; using two JFETs as analog gates, the circuit lets through either the unchanged signal or the inverse. Double balancing is supposed to suppress both of the input signals, letting through mainly the sum and difference frequencies. An added potential is FMing the second mixer input. The prototype PCB works pretty well but I identify several enhancements for a second one, and both circuits can be used with home school and TOBC Tech and Truth. One enhancement is low-pass filtering the sum/diff freq output to give bass boost. There is a control panel with many controls. Mounting so many switches and potentiometers has been a problem in past projects; this time, I am putting controls on aluminum flashing, doubled over to get a little more strength. With a second circuit, regular audio mixing of a voice or music with the sum/diff signal should be an interesting experiment. I had thought earlier that adding commercial flanger effect would be good, but now I don't think so, there is already so much going on. But a delay effect (echo) might be good. Another experiment is to add feedback between boards so there is a closed loop, like sum/diff output going back in as FMing. Output using computer speakers is likely. I am using 2-56 and 4-40 screws, half-inch, with alligator clips, as I/O rather than having patching with phono jacks. This emphasizes to young people the importance of clip leads. An interesting build problem was that one of the two power-transistor speaker outputs using TIP-31 NPN was accidentally built up with a PNP TIP-42. That took a while to find, and it was disturbing the VCO by doing large transients. With a download of Audacity to GETTER computer (Ubuntu 16.04), I was able to record audio of the sum-and-difference circuit (doubly balanced mixer). Using OpenShot video editor in Ubuntu 16.04 on my GETTER computer (with none of the problems that I see in comments on the offering screen, visible through the Ubuntu button "Ubuntu Software"), I was able to make a 25-second YouTube video (my first on YouTube) with two audio clips. https://youtu.be/3q7HTLb72cQ

On Apr 26, used Audacity program on Ubuntu GETTER computer to record the blue waveform above, which is the output of the doubly balanced mixer of the Fun Sounds board. This is a nice rendition, I used a 9k-330 ohm divider on the utility mixer output to avoid overloading the sound-card line input. I did this for four sine-wave frequencies, just one is shown here. Input 1 is sine wave from my homemade piecewise linear generator, input 2 is the Fun Sounds VCO 1/2V square wave.

The waveform isn't exactly what I expected, but when you Analyze in Audacity it gives nice purple spectra, shown above, that show essentially no trace of the two inputs, just like a doubly balanced mixer is supposed to do. The mixer is supposed to give out sum and difference frequencies, and the peaks of these are marked by S and D labels on the spectra. Like it says in little bitty text, "dialing down the sine-wave frequency and observing the consequent raising of the difference and lowering of the sum." The black dots show the sine freq input (the left dot) and the constant VCO freq (the right dot) in each of the four recordings. As I expected, there are lots of harmonics accompanying the sum and difference due to the abrupt switching of the mixer upon the rises and falls of the Input 2 square wave.

What you hear on a speaker is the sum and difference; using a little computer speaker, you only hear the difference frequency when it gets above 100 or 150 Hz. This would be more interesting if you passed the mixer output into a low-pass filter of 750 Hz, or a graphic equalizer, and had a large speaker with good low-freq performance.

25) 2017 Ap 19 Estes-brand model rocket launched for Texas Oaks Baptist Church Tech and Truth youth class on this Wednesday evening. Purchased $10 kit "Firestreak," selected because it only goes up 330 feet. Also $11 pack of four 1/2 A3-2T motors. Fireproof wadding wasn't in the kit so I made some using toilet tissue wetted with a saturated solution of Epsom salt, then air dried. The Tech and Truth class talked over angry Pharisees, which the students saw in the TOBC Trail of Life the day before Easter. Then we proceeded to put wadding, streamer, nosecone, motor, and ignition wire in the little rocket. Cameron helped, he has done these before. We took it outside on the church property and used my homemade launch controller to do four launches. Someone told me Estes rockets had been done before from the big lot north of the church, but there was too much wind and the rocket came down on the other side of Slaughter Lane. Everyone present took a turn with sliding the rocket onto the guide rod and using the two buttons on the homemade launch controller. We delayed launch until traffic on Bilbrook was clear. We angled the guide rod toward the light breeze. The rockets went up maybe 300', topped out, then the ejection charge in the motor popped out the streamer. All 4 launches had the rocket coming down within 50' of the launcher! Students who weren't pushing the buttons were inside the playground fence, nice and safe. This was a fun activity. Marty, working security, said it was fun.

The homemade controller was to give more realism to the launches. I had purchased a $35 Riptide kit to get the launch stand and controller, so I knew what the controller function was. It sends a continuity current, less than .5A, through the starter wire and lights an LED, then to launch it bypasses the LED and sends over 2A through the starter. My controller has a safety key just like the Estes controller, but it is a big pushbutton with a plastic safety cover that flips open, just like you see on movies. Whereas the Estes controller uses four AA cells, my controller plugs into the lighter outlet of a car and uses 12V. This means a lot more power dissipation in resistors that set the continuity and launch currents. My controller also copies the launch button, but I put my launch pushbutton in an old cocoa box with a safety cover and a ten foot cable so the launch director is out of the car and able to look for vehicles on the street. There is an LED beside the launch button to let the launch director know when the safety key is on. When the safety key is on, there is a loud tone from a 555 timer IC, through a TIP31 transistor and an old speaker. This gives a nice audible warning that launch is possible.

On our second launch, the plastic motor nut that bayonets over the motor fell off when the rocket landed on asphalt. There was a spare in the package.

My controller puts about 3A through the starter wire. It takes a long time, two seconds, to get the starter hot enough to ignite the fuel.

26) For the teacher at One Day Academy, currently meeting across the fence from Prescott Woods apartments, at Westoak Woods Baptist Church, who may have Engineering 3 course in the Fall with Arduino, I have been developing stepper-motor drivers. The high-speed driver, up to 1A or 1.5A, is a complex board that has an H bridge for bipolar motors, and also a .9A Arduino 7.5V supply and a circuit to automatically make motor current fall back to 1/3 when the motor is idling, to save power and keep the motor cool. The supply may be 12V or 24V, depending on what the motor needs. The H bridge is not sophisticated, it limits current to the motor by putting power resistors in series with each phase. The board has EMI filtering on the motor leads. I found a 10W-class bipolar stepper for $6 (instead of the normal $22) at Jameco, 2158531. Purchased two, they come with a 14-tooth, 32-pitch gear on the 5mm shaft. Hobbytown has a limited stock of steel, 32-pitch gears (like RRP1723, and solid brass shaft K&S 8167 .114" diam.) to mesh with the motor's gear, but the Hobbytown gears are $6, as much as the motor! I have purchased a lot of power resistors to put in series with motor coils. I also purchased three 12V 3A $12 supplies and one 24V 6A $22 metal-enclosed supply.

A simpler, lower-cost motor driver would merely be relays interfacing Arduino logic signals to a motor, doing the polarity changing with DPDT contacts. Jameco has a DPDT relay 2158338 at $2 that can do this. Contacts are 2A, not 10A, so LC filtering should be used with motor to lessen contact arcing. Typical steppers can go at 700 steps per second or 1000 sps, but the relay approach would have a top rate around 80 sps. If I make a PCB for the relay approach, add a relay to cut back current when idling, with Arduino logic input. That makes three relays per motor, because each of the two phases needs a relay.

Marlin P. Jones Associates has surplus steppers at NEMA size 23 for $10 and less, 1.1 pound to 2.2 pound. Get at least two to have a range of stepper sizes. Get a 100W 12V supply. Build a relay driver.

For Jameco 10W-class bipolar stepper, NEMA size 17, 2158531, 41mm on a side, $6, at motor phase current of 10V/(1.55 + 6)ohms = 1.32A, 13 steps/sec, at high-current duty cycle 97%, motor sitting on bench (no heat sinking from mounting), motor surface temp = 45 deg C. The cluster of power resistors that set the current are 6 ohm R_lower, 10 ohm R_higher, and they are about 93 deg C. The 3A diode from Vcc_selected to the .1 ohm resistor gets very hot even with some copper-foil sinking on its leads, so I put a 40mm fan on the driver board and that cools the diode a lot and cools the TIP31 transistors that are operating without sinks.

The logic inputs are coming from a square-wave source to phase A, and also to a 6200ohm/1uF low-pass filter which gives some time delay, then to phase B input. This lets the motor step without Arduino, up to 60 Hz square wave, which is 120 steps/second. I have the series-regulation hot parts mounted from PCB to 8-terminal solder-lug strip, and also a barrier strip to go to multiple Arduino plugs and supplies. The plywood base is 11" x 5.5".

Low-friction bearings for heavy loads have been a problem for me, but only because I didn't ask around and check web site of Advance Auto Parts. The bearing that is easy to use is a taper bearing, or (Wikipedia) tapered roller bearing. At Advance Auto, they start at $5 and each store has some. The low price is because they are made in China. The price is 1/10 what I would have expected. I purchased a $6 taper bearing set and an $8 wheel bearing so I can see them. The wheel bearing, Driveworks S-6408, seen in the picture, lacks an inner race, so it is useless to me. http://i.ebayimg.com/images/i/121647399030-0-1/s-l1000.jpg makes it look like a hub fits inside an inner race, for cars, and think it is a press fit. In the ebayimg image, it is obvious that the axle splines into the hub through the inner race's ID.

But the taper bearing can take axial and radial loads, and the cone assembly self-centers in the cup.

To use this taper bearing to demonstrate stepper-motor power, you make a custom stool that supports the bottom edge of the cup but has a cutout to give clearance for the bottom edge of the cone assembly. The top edge of the inner ring (out of sight above) has a flange that is 49mm diameter, and that is what you put a rotating seat on. A person can sit on the seat and experience the torque of a stepper, like a NEMA size 23 stepper from Marlin P. Jones Associates, about $12. To complete this stool device, you have to attach a 12"-long cylindrical post or shaft below the seat with the post extending down through the hole in the inner ring. Couple this post to the stepper. Add a loose journal bearing at the lower extremity of the post to give it stability if a person sits on the edge of the seat, but once seated, the person needs to get balanced so the journal bearing is non-contacting and the steel taper bearing supports all the weight and gives stability. Then the friction should be very low (add some grease) and the stepper will have no problem in gradually turning up the RPM. Or instead of having a rough journal bearing for initial stability, add another taper bearing at the bottom of the post.

This stool idea makes me wonder if you can make a big gyroscope with taper bearings and a larger DC motor that can get a mass up to 1800 RPM. It could be dangerous.

By July 28, I have two homemade dual H bridge stepper driver boards built. One can take either 12V or 24V for motor power. They both have Arduino 7.5V supplies. The custom board, Triple Interrupt Oscillator, is working with one stepper, with 4-bit DAC control of step rate. I am close to running two steppers at once with interrupts. Need to lay out a unipolar drive board. A Marlin P. Jones and Associates order is out for some NEMA size 23 steppers and 2mm drive belt. Walmart $53 Uno with many LEDs and sensors came in, also China-built $11 Mega 2560 qty. 3. Amazon order for two Due $21 and another Mega 2560 $12 is out.

Using the second H-bridge driver, I have a larger bipolar stepper running. It doesn't seem to want to step fast, I have it going up to about 400 sps. The coils are 10ohm, am using .71A. Needs fan to keep it cool. Planning a 7-shelf stepper "tower" to hold supplies, the various driver boards and interrupt oscillator, various Arduinos and solderless breadboards, and a stepper pulling a mass up with a string. This is necessary to keep from littering a table top with equipment, then have to tear it down at end of class.

By August 18, the stepper test-bed tower is working. A Marlin P. Jones 17153 2.2 pound bipolar stepper is being driven from Arduino through a relay driver using 5V computer supply for power. Due has not worked yet with interrupts, I am using the interrupt oscillator C channel with one of the Mega 2560s and a transistor driver. But the two lowest DAC settings are not working with interrupts.

Purchased two Barnes and Noble books, Programming Arduino Next Steps and C++ for Dummies. The Next Steps book has some neat Arduino programming.

27) For Tx Oaks Baptist Wednesday Tech and Truth on June 21, "Beach Blast Sound" using IASCA sound reference CD, we took the Phillips stereo system (with 5-CD changer) to TOBC to play through 8-ohm speakers (monitor speakers with 12" woofer, tweeter) in worship center. Sounds pretty good. At the low-freq sine test, I hear whistling at the bass-reflex ports, and the air velocity is quite high, no wonder it whistles. The ports are merely holes in the plywood mounting surface, there are no cylindrical tubes with rounded ends that would lessen whistling. The whistling stops above freq about 50Hz.

28) Programmable logic with DIP pinout for use by students

DIP package is easy to use with solderless breadboard, so this is the natural choice when students are involved. As I see One Day Academy students use Arduino with solderless breadboards, giving middle and high schoolers access to programmable logic makes sense.

Rick Frankenburger, IEEE life member in San Antonio, imported (purchased) a China-made Mini Pro TL866A $38 universal programmer and gave it to me. With a lot of effort, I got it working on my Windows 8.1 computer. It is able to program the EEPROMs I have, X28C256P 250ns, but I could not find any combination of Vpp and plain, A, B, C, or D version that would program GAL20V8. I was able to use WinCUPL to get a .JED file, though.

The next step up on universal programmers, which would surely work with GALs, is CHIPMAX 2 at Fry's for $550 or $483 plus shipping at Mouser, and B&K Precision programmers in that price range. But as I look through Internet, I notice that GALs are less available as more modern logic does more for about the same price. If I paid so much for CHIPMAX 2, is it possible the GAL supply would dry up? (The most modern GAL is 22V10.)

Would the following be workable? Use Atmel ATF1504AS in TQFP 44-pin package (ATF1504AS-10AU44 Mouser $4) which I have used before, use WinCUPL for design like I have done for six years, use the newer Atmel ATF15xx-DK3-U kit with USB (Mouser $163) for JTAG programming, and make the TQFP have DIP pins by using a little PCB with right-angle .1" pins. Maybe I would get into the DIY CAD/commercial PCB line of work and get commercial-grade little boards, double-sided, that would solder easily. I think they are less than $10. If I do a DIY commercial PCB for TQFP, include the JTAG 2x5 header and pullup resistors, also two TinyLogic gates to get hysteresis for the two clock pins.

Maybe level conversions between 5V and 3.3V.

Is the low-power ATF1504 chip the same pinout as the AS version that I have used, which is about 130mA?

EEPROMs can store data, preferably in Intel HEX format for use with TL866A. See Wikipedia for this, it takes a little programming to make up such a data file. A project I have had in mind for eight years is a low-distortion, unlimited-low-freq sine generator using DAC for output. The sine data would be in EEPROM. Vary the frequency by varying the EEPROM clock.

29) 2017 Sept. 20 Recent stepper-motor work with Arduino: the seven-level Stepper Motor Test Bed has three bipolar motor drivers. The latest is a 4.1Amp per phase driver for the $8 (on sale) MPJA.com 17153, a 2.2 pound NEMA 23 stepper which has only .41 ohm per phase, so a 5V computer supply is good and cheap. Using 5V, this driver (with generous sinks and a built-in fan) could go to 8Amp since the transistors, RFP12N10L $.59 from Jameco, have 12A rating. The Arduino program does half stepping, with the num variable being 1 to 8. I am starting to use delayMicroseconds() since this motor seems to be able to go above 1000 half steps per second. The low, 13" diameter platform with automotive taper bearing, $6 Driveworks S-A-5 from Advance Auto, is working pretty well with the 17153 motor. It will probably bear a 150 pound load from a standing person and will rotate the person through 300 degrees. The drive uses GT2 cog belt from MPJA.com.

I am using delay() in most Arduino programs so that I can rapidly try out motors and half stepping, and so that the programs are less cryptic for One Day Academy Engineering 3. The thing that is better than delay() is polling or interrupts, and I may get back into those.

30) Nov. 2017 For a home-school co-op that meets in San Marcos, I made a version of James Joule's famous paddlewheel experiment that gave a number for the mechanical equivalent of heat, 4186 Joules / ºC kg for water. Since I don't have a way to make his neat paddlewheel assembly (which had a rotor and stator, see the You Tube re-creation), I chose a simple apparatus,two grape-juice bottles joined by PVC pipe, with almost a full bottle of water. Sealed with silicone. Insulated with bubble wrap, coated with aluminum foil to block infrared and visible light which warms the LM35 temperature sensors. Inverting this assembly 60 times lets the water descend 0.76m * 60 which raises the water temperature 0.155ºC. This tiny temperature rise is measured by LM35, two of them, amplified by 100 times to get 1V/1ºC. Data acquisition by Arduino, averaging 500 readings to reduce noise. Got 31% error, a disappointment, but then I only paid $17 for the apparatus. Joule used an amazing mercury thermometer which had about a centimeter per ºC. This is a neat experiment.

31) Nov. 2017 Continuing stepper-motor work for One Day Academy (C. Lewis, see 2017 Sept. 20), the golf ball-dispensing mechanism (an arm) with a stepper and a servo is now mounted on a vertical post. The perch for the balls on the arm requires that each ball be delivered with low kinetic energy. A separate mechanism is being built to meter balls onto the arm; the mechanism is a two-phase comb on a shallow incline that queues balls. The two combs are to be driven by cams, which are operated by a DC motor and cog belt with step-down by a large cardboard drum. An advantage of this mechanism is that vacant places in the queue can be rapidly passed through. This will increase the ball-dispensing rate of the arm. I hope that a ball elevator and funnel will be able to feed balls onto the queue, at higher kinetic energy.

Then I found $8, higher-power servomotors at Amazon.com. Just one of these could move both combs. But I have the cam and drum ready to go and am inclined to finish out the DC-motor cam approach, it will be a curiosity and will have more mechanical force, if more force is needed. But this was abandoned when the torque needed from DC motor to turn cam out of the most-in position was excessive.

The five meetings that I helped with for Mrs. Lewis' Engineering 3 course, for One Day Academy at Point Community Church, on Fridays from 12:45 to 2:15, were from September 8 to October 6. The ten students used Mrs. Lewis' personally purchased $25 Arduino (Uno) kits with solderless breadboards, buzzer, servo, and numerous small parts. Mrs. Lewis does not have much coding background and that is the topic I helped with most. My long experience with electrical parts and solderless breadboards was also valuable. I was able to look over the shoulders of students who had compile errors and find problems, and help with wiring problems. Distinguishing between coding and hookup problems was a definite plus. As students progressed into putting pieces of textbook sketches together for their final EE project, I advised about problems they had. One student had a wheeled kit with three servos, and reported interactions that puzzled him. I asked if he was using delay(). "Yes." I advised that he look at polling (computer science) on Wikipedia, and non-blocking I/O.

I led the way to showing that stepper motors work and helped students understand the phases. I provided the high-current drivers they needed to see larger motors work. I suggested to Mrs. Lewis a servo/stepper mechanism that would be instrumental for a modular Rube Goldberg machine, one that can be built as modules and which can be instantly assembled during class from modules that come from students' homes. This may come about after Christmas.

On October 6, I provided a brief presentation about analog data acquistion with Arduino. My case study was the three-phototransistor rotation sensor I have equipped my 13" rotating platform with. The brief talk used ten photos and screen captures. My concluding remark was that industry and academe use a lot of automated data collection, and it is neat to see a $9 Arduino doing a good job of data collection, in a format (through Serial Monitor) that is easily imported to spreadsheet and charted.

As I was suggesting topics for brief presentations that I could offer to round out the students' knowledge, I kept in mind Mrs. Lewis' needs for class time. I know from teaching at Texas State Technical College for 12 years that almost all class time is needed to cover the syllabus and check for student understanding. Little class time is surplus.

32) January 2018 Purchased Tektronix DPO 2002B with serial-bus decoding. $2000 from Newark. It is a big step up from the entry-level, $800 instruments that are roundly criticized in on-line reviews. It is said to be digital phosphor, it indeed shows on-screen older traces as dimmer. 70MHz. I have been without an oscilloscope for 28 years, since the Telequipment ($800 in 1976, switch problems by 1990) and this one gives new abilities. I see that 8-bit data is not a drawback, the spot size of analog oscilloscopes is probably coarser than 8 bits. I am very concerned that ESD will ruin this instrument, especially as I let home-school students use it. I have a simple protector with two channels in use, it merely has spark gaps etched on DIY PCB, paralleled with neon lamps, with about 10k following the gap, on the way into 6" RG-58. This dumps the static surge onto the outside of the coax braid, from which it dumps onto the outside of the metal case of the oscilloscope and then goes to ground by the power cord. A much better protector is under development, a JFET-input active probe that shows signs of 45MHz bandwidth. Reduction to practice was on Jan 30 2018, I have photos. The prototype probe is 5.5" long and has 15 feet of RG-59 soldered to it. This device has been used with DPO 2002B to look at mild static sparking during winter dryness. The probe seems to clamp the voltage transient nicely. I have seen the neon lamp flicker upon static discharge (night darkness), and once I saw a white flash at the etched spark gap, which turned out to be .008". The probe has three, seriesed, 1206, 360ohm resistors between the spark gap (series resistors share thousands of volts of input spark and make it more likely that they won't be damaged) and clamping diodes (size 1206, too), then another 360ohm before the JFET gate. The grounding of the spark gap and neon lamp is by a #26 insulated wire, around the outside of the probe's shielding, to a section of bare coax braid. This path for surge current keeps the surge away from the semiconductors inside the probe's shield. My knowledge of where ESD current flows comes from experience in the 1980s at IBM Austin. As limiting as IBM's culture was to personal development (engineering knowledge of the EEs), I did get a lot of experience with ESD and EMI (and TEMPEST) and I had use of the excellent EMC facility and metal-fabrication shop in Building 045, plus exposure to EMC facilities at SwRI San Antonio, Atlantic Research Corporation at Alexandria http://surflibrary.org/ses/TEMPIND.html and http://www.dtic.mil/dtic/tr/fulltext/u2/a081830.pdf, IBM Federal Systems Division (sold to Loral in 1994, then maybe to Lockheed Martin in 1996), and Honeywell TEMPEST at San Antonio (offshoot from Annapolis). http://surflibrary.org/ses/TEMPIND.html

The JFET is used as source follower and has drain bootstrapping to improve bandwidth. This is followed by paralleled 2N3904 TO-92 transistors as emitter followers. To get -9V to +12V input range, I use supplies into the probe of +24V and -30V. The 2N3904 followers go into a 10:1 resistive divider that has 75ohm Thevenin resistance, then to RG-59 coax, to a little brass termination box with 80ohms to ground, then 100 ohms onto a commercial male BNC panel-mount connector for attachment to the vertical channel. The oscilloscope's 11.5pF surely causes reflection back into the coax, but the 75ohm termination at the probe output is so good that I see no reflection at the oscilloscope.

The probe runs too hot, since I have to draw a lot of current toward negative supply to keep the 2N3904s supplied with current even when the input goes to -9V. Instead of compromising on input range to reduce power, I am pursuing a big circuit that varies the negative supply, making it more negative (to -36.2V) when the input goes negative, and letting the negative supply rise toward ground, to -12.5V, when the input is over -1.3V. (See below at May 9.) The circuit is quite large. The raw supply is -48V, a commercial .9A supply. I intend to do a DIY DC-DC converter to get +24V. Arduino is to be included to model probe power and cut back the negative supply when the modeled temperature in the probe is too high. It is a small step further to use the Arduino to log data (like to a SD card, at 10 bits resolution), and an op amp to level-translate the RG-59 signal is in the plan. It is obvious that I can put in a two-character, 14-segment LED display to show faults and voltages, and the temperature-modeling circuits include current monitoring of the negative supply, so this has blown up into quite a project, and it is very neat.

The input impedance of the JFET is very high. I soldered in 10Mohm to ground (from the JFET gate to ground) and the consequent open-circuit voltage is negligible. The bandwidth of the probe is surprising, I would have expected 4 x 360ohms before the gate to limit the bandwidth. I intend to order SMD resistors in about 10 values to replace series and parallel combinations that the prototype uses, to reduce the probe size.

By April 3, version K of the active probe is built using the 10 values of resistors that I specially ordered. The probe, at 4.7" long, hasn't shrunk much but it looks a lot smaller. The heat sinking on 2N3904s is much improved; it is now with brass tubing. Though the heat sinking gets hot, calculation shows that the junction temperatures are no where near 150ºC even with fixed -30V supply.

Measuring at Q5 emitter, before the 10:1 divider, rise time is 10.8ns, very good, but fall time is longer (as it was in the original prototype) at 21.8ns. When I get the oscilloscope-end terminator box finished for version K, these numbers might get a little better. (No, they didn't.) I think the problem with falling edges is that pull-down currents are smaller than pull-up currents, the latter coming from NPN or N-channel transistors. Using 660k between a Tiny Logic fast edge and the active-probe input, it shows the probe's input capacitance to be 11pF, more than I hoped for, but remember that this probe has a lot of ESD tolerance, a big attribute. If I do a version L, take away the ground plane below the four 360ohm resistors at the input and see if input capacitance goes down. I have boards etched or soon to be etched for 4-digit display, +24V DC-DC converter, varying negative supplies, and a 555-driven Tiny Logic signal source with fast edges.

On April 26, the DC-DC converter for getting +24V from the raw -48V is working with an enable signal coming from Arduino. Arduino is sensing both of these supplies through the "support" board. There is a new, complicated state machine (10 states) working in Arduino to monitor both supplies. This is the first state machine I have made in Arduino; it came together quickly and easily, and uses switch case. This is favorable for the practicality of two more state machines, one for the 4-character display and one to control negative power for each of three probes.

The screen capture from LibreOffice spreadsheet, charting data from Arduino's Serial Monitor, shows the state numbers in real time on the blue trace, and the two supplies. This is such a neat capability of Arduino, and LibreOffice does such a quick and showy display of data. Arduino Mega 2560's coarse 10 bits of analogRead, going through averaging of three samples at a time to reduce noise, gives a nice waveform. Arduino is providing three time delays in the state machine, using polling, not delay().

See related info at the bottom of this web page: https://sites.google.com/site/solderandcircuits/home/more-circuit-design/arduino-and-stepper-motors-1

May 9, 2018

While bringing up the first varying negative supply for JFET anti-ESD probe (planning is mentioned above), needed a pulse generator to simulate a probe output (the Q9 output, the unattenuated Q4 output that lets the neg. supply know how far negative to be set) to see if the design for the negative supply is adequate. I stopped and built a special pulse generator that can position a 72us negative pulse, at low duty cycle, up to 21V amplitude, anywhere in voltage, with the top level being +12V to -9V, just like the JFET probe. To simulate the probe, I don't need excursions below -9V, but this generator can do 21V down from -9V, even, reaching -30V. This capability was possible because I use -48V, and +24V, as supplies for the generator, providing lots of headroom.

The oscilloscope screen capture shows off the Tek 2002B measurement capability, showing four measurements. Very neat. The rise and fall times at this amplitude are about 300ns.

I will now return to the varying negative supply bringup and use this generator to test the circuit.

May 13, 2018

I got the mess of boards set up in a cardboard comb to get some organization. Updated sketch to F to get in control of the Q18 negative power switch. Connected probe to the RJ-11 jack/alphanumeric PCB with much checking that +24V and varying negative supply are not reversed. Connected pulse generator to probe. Careful measurements with oscilloscope show the negative supply doing as planned! Wrote up a report summarizing the project so far, varying neg supply on verK anti-ESD probe report.odt on ANODE. The thermistor on back side of probe runs up to 17ºC cooler than using a fixed supply of -32V, or maybe 23ºC cooler than -36V.

Sooner or later, I will add brass shields to the probe. I have a rubber belt for a Van de Graaf generator and I might build one up to do controlled static discharges. But I need a 3.5kV (transfer high voltage) surplus power supply to put charge on the belt.

May 30, 2018

The effort toward controlled static discharges to test the JFET oscilloscope probe is on the move. I took a microwave-oven transformer, which is a deadly item, put a fuse holder on the primary, took Amazon capacitors and Mouser 4kV rectifiers, and made a 6-stage multiplier. It worked about 5 minutes and then blew the 8A fuse. While it was working, it lit a neon lamp in series with a leaded 10M that was positioned up to .35" away from the high-voltage, negative output. Surely the 10M was arcing over inside the resistor. I was seeing a faint, purple glow (corona?) on the groundward side of the gap, which was the pointy lead of the 10M resistor. 0.35" suggests 28kV but maybe it was 20kV, which is nice. It turns out that the Amazon caps, supplied through an individual, were not 4kV at all, they are safety caps X1 Y2 rated at 400VAC (for X1), 2200pF. I seriesed 4 of these for each cap in the ladder but that is asking for 1000V each, with quite a bit of AC in that, and AC high voltage creates "partial discharges" and corona at the surface of the ceramic dielectric. Call this a learning experience, and it sets me up for a next try.

The next try is Mouser 3kVDC ceramics at $.11 each or 6kVDC polypropylene at $.46 each. I can series some of each and slap them on the microwave transformer secondary (not as part of a multiplier, just caps on secondary) and see if they last.

Another approach for capacitors is using window glass and aluminum screening to make DIY caps. There is a neat geometry of capacitor plates that can make multiplier ladders. I will get some glass and see if it withstands the transformer. But consider what sort of capacitors can be purchased for equivalent dollars.

Internet says microwave-oven transformers put out 1800 to 2800 Vrms. Vpeak is 1930V to 3948V!

A handicap I am working with is the inability to measure high voltages, like with resistor divider. (I could order a DMM with a high-voltage probe, but what are the alternatives?) If I series 10M 1/2W, they can take only about 500V each, but even 30 of them gets 300Mohm which produces 1.33W at 20kV which is very much conflicted with the micropower available at 60Hz from 1000pF-range capacitors in a ladder. Mouser high-voltage resistor is $8 for 500M but it is only worth 3kV. What about graphite track on paper? With artist graphite on regular copier paper, a rough track about .1" wide and 20" long is about 30M. As I move the DMM probe along, I get less and less resistance. I need an experiment that would produce 300M or 1Gohm, with a bottom-of-the-divider of maybe 1M, or just a regular resistor of that value. The safety aspect of such a large piece of paper with 20kV on it sounds risky, so easy to touch accidentally. It could be rolled with small-bubble bubble wrap into a cylinder, if bubble wrap is non-conductive (beware of pink). If I can make a track .05" wide, 20" gives 60M. On 8.5" x 11" paper, I can do 8 of those. That is 480Mohm. But that would be 1/2W at 20kV, 42uA! Compare to the capacitive reactance of four 2000pF caps in series, at 60Hz. It is 5Mohm. If I go with soft pencil at maybe .015" wide, that could get 16 hairpins on 8.5" x 11", maybe 4x more than pure graphite, for 480M x 4 x 16/8 x .05/.015 = 12.8Gohm. I imagine that humidity in the paper might parallel such a resistance. What if you spray the paper with varnish after making the track? If there is a concentration of voltage across small voids in the thin pencil track, there would be a glow or corona or something bridging the void. Would need to protect against sudden fire consuming the whole page of resistance track. These are thoughts about how to make a voltage divider, even with +-50% error. You can come up with some interesting ideas.

More Internet reading tells me why the microwave-oven transformer is having fuse problems. I keep blowing 8A fuses and blaming it on capacitor breakdown. That isn't the case. Internet comments say that manufacturers of cheap microwave ovens don't put as much iron in the core, and it operates a little into saturation. Also, the copper is a little undersized. Both of these are reasons my transformer is warming more than other transformers. I had suspected there might be a shorted turn, but I think that is not the case. For my purpose of low current and occasional sparks, it is good to add about 1 or 1.5ohms in series with the primary to reduce the primary voltage by about 10VACrms. Got this done June 2. The glass-dielectric, 270pF cap buzzes along just fine. About ready to reconnect the Amazon 400VAC 2200pF multiplier with the graphite-track divider and see if I can measure the high voltage DC. Yes, when high voltage is on the 16-hairpin pencil track, any tiny gaps in the track are being arced across and the resistance is 323Mohm, not in the gigohms. That is OK, with 470k as the lower (grounded) resistor in a voltage divider it gives around 5V into a 1M-input-resistance DMM voltmeter. But I still can't measure the open-circuit voltage.

Went ahead to build a #2 multiplier using the better $.46 and $.11 caps from Mouser. It works better, gives a nice little snappy spark several times per second over .35" gap. At greater gap, there is the dim purple corona I saw with multiplier #1. The plan for a Marx generator to supply 30kV from 50pF for JFET probe testing is to make three 150pF caps that get connected in series by the Marx discharge, giving 50pF equivalent. I purchased six cheap aluminum baking pans at Dollar Tree for $3 to make air-dielectric caps. These thin pans have to be stiffened by corrugated cardboard, adhered by candle wax, and that may give enough plate stiffness to get 0.15" spacing of the dielectric, and 120pF on each cap. But I realized that just one cap, 120pF, charged to 10kV, can have one of the plates drop away from the other plate (like by gravity), hit a discharge electrode connected to a JFET probe, and get the 30kV from 40pF without a Marx generator. I am building up the one specialized cap now, June 7. This is a neat application of C = Q/V, or V = Q/C, where the charge from 10kV at the 0.15" spacing is on a 120pF cap and the voltage is boosted to 30kV when the spacing increases to 0.45". Using E = 1/2 C V², there is an increase in energy at the wider spacing. This is from energy fed into the cap by pulling the plates apart against the attractive force from the electric field, the plates being attracted by difference in voltage.

This story is continued with photos on the Project Blog 2 web page, this first project blog is getting too long.