"ATU" design ideas and "SWR " measurement principles

The article posting goes to describe how both a manual and automatic ATU could be designed and built. Most automatic ATU designs will hunt around the load reactance components for the best match. From this posted article, it can be seen that an automatic ATU capable of the full calculation of an antenna match specification can be measured, calculated and then matched, all within a fraction of a second.

It is perhaps worth mentioning that if a transmission line matching section is used to bridge the impedance cap between the radio set and the antenna, the operating frequency of the radio is not required. Only the cut-off frequency of the matching transmission line must be within the requirements of the radio set operating frequency, an item that can be determined and the ATU design stage. Should however one was to use a lumped component to match the antenna by altering the antenna impedance, say with a series inductance or capacitance, then the radio set operation frequency is required in order to calculate the component reactance needed to determine the component value and type.

There are many ATU designs around, but the one shown here is an simpler design concept. The idea illustrated here is transmission line matching section based around a "T" section low-pass filter. The capacitor "C" in the below drawing is altered to adjust the impedance match quarter wave section between the transmitter "radio source" impedance and the aerial "antenna load" impedance. A "T - section" was chosen as depending upon whether the high or low impedance is planned, the inductor to capacitor arrangement would always be correct. That is whether the inductor is fed from the source or feeds the load impedance, from either a high or low impedance relative to the input or output terminals.

" ATU 1/4 wave transmission line matching impedance = SQR( R_source * R_load ) ".

date 6th Octber 2020 : foot note = using the hypotinuse ( right angle equation ), 1/4 match = SQR("R_source"^2 + "R_load"^2), reason why 5.6 = SQR(" 4^2" + "4^2" ), draw a right angle triangle on paper and use a ruler to verify.

The ATU 1/4 wave matching section design calculation equation achieved by a BBC Basic for windows program, to determine the component values. The over-riding design point need is the minimum frequency of use of the low-pass filter design. In this regard, the lowest cut-off frequency, the 3dB point, is the top end of the HF band plan, i.e. at 30MHz, while to include the 6m band, the top end cut-off frequency would need to be above 55MHz. The CAD program is shown below.

10 REM design concept for an HF ATU

20 R_source = 50

30 ind = 64E-9

40 PRINT

50 PRINT

60 PRINT

70 PRINT

80 PRINT

90 PRINT

100 PRINT

110 PRINT

120 PRINT

130 PRINT

140

150 PRINT TAB(3);"HF QRP ATU design details"

160 PRINT TAB(3);"R_source = 50 ohms, 1/4 wave line inductance = ";ind*1E9;"nH"

170 PRINT

180

190 FOR R_load = 15 TO 150 STEP 5

200 ATU = SQR(R_source * R_load)

210 cap = (ind/(ATU^2))

220 freq_cut_off = 1 /(2*PI*SQR(cap * ind))

230 PRINTTAB(2);"R_load = ";R_load;" ohms";TAB(22);"1/4 wave imped. = ";ATU;" ohms"

;TAB(59);"1/4 wave cap. = ";cap*1E12;"pF";TAB(89);" 3dB cut. = ";freq_cut_off/1E6;"MHz"

240 NEXT R_load

250 *CHDIR C:\Users\alastair\Pictures\HFaNTENNA

260 *SCREENSAVE HF_atu_64nH_corrections.bmp 1,1,2000,1100

The CAD design results are as listed below:

Most HF radio's with an internal ATU will only impedance match an SWR value of up to 3:1, from 15Ω to 150Ω. To use the "T" section low-pass filter design, each side of the inductance is half the 64nH, in other words 32nH each side or 10·6cm of straight wire, equating to 32nH. The capacitance value used to alter the 1/4 wave matching section, is the listed "1/4 wave cap" values, in this regard the 1/4 wave capacitance varies from 100pF to 5pF overall. The listed results of the design shown above would cover the Ham radio bands from "LF (135KHz) to 6m (50MHz)".

The inductive reactance of a tuned 1/4 wave wire is about 140Ω, irrespective of the band used that has the tuned quarter wave antenna section, be it an HF, VHF or even UHF or microwave band quarter wave antenna. The maximum "R_Load" is 150Ω, which would mean that the above circuit ATU design component values are able to impedance match a 1/4 wave section. To increase the impedance matching range of the ATU design, a 4:1 balam or even a 9:1 balam could be used. The 4:1 version would increase the top impedance to 600Ω and would impedance match a full wavelength wire, while a 9:1 design would go further up to a two and a quarter wavelengths, which equates to 1350Ω.

A question here is why would we think that a full wavelength wire is needed, or even a full wavelength vertical antenna. The reason is based around the concept of the electromagnetic coupling to the ether, the surrounding air and atmosphere. A 50Ω stub antenna has a physical length of only 8% of the band full wavelength, so in effect the electromagnetic coupling is just 8% of the full wavelength coupling of 100% of the signal given by a full wavelength vertical or wire antenna. In this regard, the signal electromagnetic coupling to the ether from a 50Ω stub antenna would irradiate just 8Watts of a 100Watt transmitter power output into the antenna, but the full wavelength would couple the full 100Watts into the surrounding ether. On the plus side, a quarter wave antenna is 25% of a full wave, so a quarter wave antenna would be 25% efficient.

Likewise the receiving antenna efficiencies are just as related to the antenna physical size and its band wavelength. A 25% efficient quarter wave would radiate 25% of the transmitter signal, and collect 25% of the received signal at the receiver end, thus equating to a transmission path minus any other losses to 1/16th of the transmitter signal or 6·25% efficient. A pure 50Ω stub at 8% is even more drastic, equating to an overall transmission path of 0·64% efficient, ignoring any other path losses. Even though, it does not bare well.

To construct a physically smaller full wavelength wire or vertical antenna, a lumped component of simulated wire section would be required. This simulated wire section would be an inductive coil inductor. A 1m section of wire equates to some 300nH, so a 80 metres wire would equate to an inductance of 24uH, or a top band wire or vertical of 160m, equates to 48uH. The current lobe radiated from the antenna would be more concentrated around the lumped component, namely the inductance coil. To this end, the effective radiated signal would be equivalent to the same long wire or full physical height normal antenna design. The "loading coil", which is effectively what we are describing here, would shorten the antenna design physical size to more manageable dimensions. A top band 160m vertical could be just 1metre in height, a 1metre whip with a 47·7uH coil either at the bottom or top loading mounting for the loading coil within the overall antenna.

Tuning the wire antenna with loading coil to lengthen or a load capacitor to shorten the effective wire, a BBC basic for windows program can be used to determine the loading reactance to lengthen or shorten the effect long wire. The below listed results show an example of such a calculations:

The above illustrate results show that with the use of a 20metre long wire, operating on the 10m band, the long wire inductive reactance is around 1100Ω. The load capacitance for a 50Ω match on the 10m band is around 5pF, but to use the 20metre long wire for MF band, requires a load inductance of 43uH to equate a 50Ω load match.

The BBC Basic code used for the above illustrated calculation results is listed below:

10 REM calculated load capacitance for long wire antenna though the HF bands

20 REM inductance to wire is 300nH / metre length

30 REM 15metres of wire is half wavelength at 10MHz, the wire has an inductance of 4.5uH equivalent coil

40 REM reason : 1 metre of wire is equal to 300nH

50

60 REM the Zo=SQR(RL^2 - XL^2) equation is the add on to the co-axial cable, the antenna end

70 REM Thus so, with XL = 50, then the above equation then equals zero, and hence does add to the

80 REM antenna with an antenna reactive loading.

90 REM

100

110 REM The value of reference in the Zo=SQR() equation is the cable impedance, as XL =50,

120 REM the added load of the antenna to the cable equates to zero offset.

130

140 REM By using the cable impedance, the wire is matched to the cable characteristic value.

150

160 REM However if a 1/4 wavelength wire inductive resonance reactance value is used as RL, RL = 141ohms,

170 REM then the wire is matched to the 1/4 wave length terminal impedance.

180

190 REM for the 1/4 wave length match to be used, the ATU would have an input PI section Low Pass Filter, Fc = 30MHz

200 REM the input of the LPF would be 50ohms to match the RF co-axial cable, but the LPF output would be 141ohms.

210

220

230 REM 15metres of wire

240

250 length_metres = 20

260 l = (length_metres*(300E-9))

270 length_feet = ((100/2.54)*length_metres)/12

280

290 REM in this example the cable impedance is used as the reference for RL

300 reactance_resonant_impedance = 50

310 PRINT

320 PRINT

330 PRINT

340 PRINT

350 PRINT

360 PRINT

370 PRINT

380 PRINT

390 PRINT

400 PRINT

410 PRINT

420

430

440

450

460 PRINT " reactance resonant impedance = ";reactance_resonant_impedance;"ohms"

470 PRINT " inductance of wire / coil = ";l*1E6;"uH"

480 PRINT " length of equivalent wire = ";INT(length_feet);"feet or ";length_metres;"metres"

490

500 PRINT

510

520 FOR f = 0.1 TO 0.4 STEP 0.3

530

540 REM inductive reactance

550 XL= (2*PI*(f*1E6)*l)

560

570 REM RL is low to 50ohms, thus the wire is capacitive and needs inductive loading

580 IF XL <= reactance_resonant_impedance THEN PROC_low

590

600 REM RL is high to 50ohms, thus thwe wire is inductive and needs capacitive loading

610 IF XL > reactance_resonant_impedance THEN PROC_high

620

630 NEXT f

640

650

660 FOR f = 1 TO 30 STEP 2

670

680 REM inductive reactance

690 XL= (2*PI*(f*1E6)*l)

700

710 REM RL is low to 50ohms, thus the wire is capacitive and needs inductive loading

720 IF XL <= reactance_resonant_impedance THEN PROC_low

730

740 REM RL is high to 50ohms, thus thwe wire is inductive and needs capacitive loading

750 IF XL > reactance_resonant_impedance THEN PROC_high

760

770 NEXT f

780

790

800

810

820 *CHDIR C:\Users\alastair\Pictures\HFaNTENNA

830 *SCREENSAVE load_reactance_50ohms.bmp 1,1,2000,1100

840

850 END

860

870

880

890

900 REM RL is low to 50ohms, thus the wire is short and capacitive thus needs inductive loading

910 DEF PROC_low

920 Xc_low = (reactance_resonant_impedance - XL)

930 REM Xc_low used as XL, as opposite reactance required

940 XLoad = Xc_low/((2*(f*1E6)))

950 PRINT TAB(1);" freq= ";f;"MHz";TAB(19);" XL=";XL;TAB(35);" Xload for ";reactance_resonant_impedance;"ohms = ";XLoad*1E6;"uH"

960 ENDPROC

970

980

990 REM RL is high to 50ohms, thus the wire is long and inductive thus needs capacitive loading

1000 DEF PROC_high

1010 XL_high = (XL - reactance_resonant_impedance)

1020 REM XL used as Xc, as opposite reactance required

1030 Xcload = 1/((2*PI*(f*1E6)*XL_high))

1040 PRINT TAB(1);" freq= ";f;"MHz";TAB(19);" XL=";XL;TAB(35);" Cload for ";reactance_resonant_impedance;"ohms = ";;Xcload*1E12;"pF"

1050 ENDPROC

1060

To alter the design values, program lines 250 for the wire length, and program line 300 for the designed impedance match requirement, together would enable a custom made wire antenna with its appropriate load reactance match to be determined.

Although the load impedance can be matched by various means, measuring the antenna load impedance to determine any of the antenna match components needs to be achieved first. The below math process is also illustrated below can also the found within the antenna article on the companion website www.radiohamtech.com which is related to this blog "Radio Ham Technology".

Below is a illustrated section of the antenna article, found on the "antenna lumped component" page and demonstrates how the antenna load impedance can be found.

"From a standard “forward and reflected voltage” ratio, the “swr” can be found. By re-arranging the following equation and assuming the signal current is constant using Kirchhoff's circuit laws, from this only the signal voltages and the companion resistances would alter:

matching ratio “r” = (forward voltage) / (reflected voltage)

note : reverse the equation to "r" = reflect / forward, thus calculates the transmitters output matching ratio, reference to the 50ohm dummy load for the antenna loading.

The equation of :

WR ratio = matching ratio “r”

Then RL the unknown equates to the following equation:

RL = SWR ratio * Zo

where “Zo” is the 50Ω, the designed termination impedance of the signal source ( the radio )"

Once this is completed, the antenna load reactance is found by following method.

The characteristic impedance formulae for transmission lines, Zo = SQR( L/C ) is used to find the load reactance values. Both the characteristic impedance and the capacitance per metre are published and from these figures the co-axial line inductance per metre can be calculated. From my own used references at a similar moment, I found that in round figures, the inductance of a metre length of wire irrespective the capacitance or cable impedance, was found to be 300nH/m for every metre length of wire.

The reference used at the time put the cable impedance at 50ohms and the capacitance as 120pF/m, equating to a base line inductance of 300nH/m.

By swapping the cable impedance "Zo" for "RL" in the equation Zo = SQR( L/C ), using the new Zo = RL, the RL found from the forward and reflected voltages of the SWR metre, the antenna load can be calculated as an equivalent transmission line impedance, just like a co-axial line, but in this case the calculation of the transmission line equation would be the resulting load antenna. Any overall found reactance of inductance or capacitance exhibited by the antenna load can then be determined.

As a 50Ω long wire is a physical length of 8% of a full wave length, then any additional wire would equate the wire to having too much inductance at 300nH/m, then would be inductive relative to the 50Ω antenna load requirement. The reverse is also true, any shorter than the 8% of full wavelength would equate to a reduction on inductance at 300nH/m relative to the 50Ω antenna load requirement, thus the shorter length and would be then capacitive relative to the required 50Ω antenna matching load.

Hence if RL is above 50Ω, the long wire would be inductive, the SWR example would indicate an example of SWR = 1:1·50, the referenced then used is the co-ax capacitance at 120pF/m in order to find the overall antenna inductance as a transmission line equation representation of the antenna load.

If however the RL is below 50Ω, the long wire too short then capacitive, the SWR would indicate an example of SWR = 1:0·50, the referenced then used is the co-ax inductance of 300nH/m to find the overall capacitance, as a transmission line equation representation of the antenna load.

In any regard, a transmission line impedance equation for the load antenna can be determined.

A "inserted video" illustrates how an Arduino program can calculate the antenna load between the radio changing from transmit to receive mode. On transmit mode, the SWR measurement made and the SWR calculation is shown, while on receive mode the load antenna transmission line impedance is calculated from the originally shown SWR value and then displayed as a transmission line impedance. Four arduino analogue ports are presented with test voltages, one each for the "Rx signal meter" and the "Tx power meter", while one more each for the "SWR forward" and "SWR reflected" voltages.

The "you tube video" was achieved with the web camera, but unfortunately the web camera auto focus made recording the video a bit tricky.

By the way, the variable "R ohms" in the pictures and video, is actually supposed to be "Z ohms", a little typo in the arduino code.

Below are two photographs of the arduino code determining the transmission line antenna load impedance to forward and reflected test fault voltages on two of the analogue ports of the arduino microprocessor.

The first photograph illustrates a inductive loaded antenna with the calculation referenced to the model line capacitance of 120pF/m, the SWR = 1:1·918 relates to the calculation of the antenna load as R = 95·9Ω, the inductance as 1·1uH and the capacitance 120pF.

The second photograph illustrates a capacitive load antenna with the calculation referenced to the model line inductance of 300nH/m, the SWR = 1:0·198 relates to the calculation of the antenna load as R = 9·9Ω, the inductance as 300nH and the capacitance 3·1nF.

With the directly calculate the antenna load match for the ATU, by using the "quarter wave line matching section" as well as any additional load reactance to bring down the antenna loading to within the ATU design matching limits, the mathematical model of which can now be accomplished.

Most auto ATU's will hunt switch the relay circuits for a correct value match for an unknown antenna loading, but with the above mathematical process illustrated within the you tube video, it can be seen and shown that the load antenna can be measured then calculated and matched with practically one sounding click of a relay circuit, all done within a fraction of the time usually taken for an unknown antenna load at any moment in time.

Now just a last part to mention.

All us radio ham or professional RF engineers, are lead to the believe that if the transmitter design output impedance is said to be 50Ω, the question is "is it 50Ω". There is a trick to measuring the output terminal impedance of a radio transmitter, and that is as one would of thought, use a 50Ω dummy load, but the mathematical trick is this:

If the transmitter terminal impedance is higher than the 50Ω dummy load, then from a standard SWR bridge, the dummy load would look as a low impedance load, because the SWR bridge would reference the forward and reflected voltages to the transmitter terminal impedance, even though it is the dummy load that is being measured.

Should the dummy load measurement indicate say "SWR = 1:0·50", then the dummy load would be a capacitive load, i.e. below 50ohms. However the trick to determining the transmitter, is to reciprocate the SWR measurement :

SWR transmitter = 1/ ( SWR dummy load)

The reciprocal of the measured "SWR = 1:0·50", equates the SWR transmitter = 2:1, which would put the transmitter output impedance as "2 * 50Ω = 100Ω" source transmission line impedance with an inductance load value.

Consequently, if the "SWR dummy load" is measured as "SWR = 1:1·50", hence as higher than 50Ω the dummy load seems as an inductive load, by virtue of the same above equation, the transmitter SWR output would be uncovered as "SWR = 1:0·66", or a 33Ω transmitter source transmission line impedance with a capacitance load value.

Once the new source impedance is known, the quarter wave matching section can be redesigned, by replace line 20 within the first listed BBC basic program shown above at the top of this particular posting, i.e. R_source = 50, can be changed to in the first example of a 100Ω transmitter output impedance to "R_source = 100", or in the second case found transmitter output impedance, "R_source = 33". The BBC Basic program would in both cases recalculated the new quarter wave matching section component values.

The same trick can be used to determine output impedances of RF mixers, RF filters and even perhaps if the forward and reflected voltage measurements are sensitive enough, an RF pre-amplifier.

However to measure the input impedance measurement of a device or unit under test, would be to measure the forward and reflective voltages of the unit under test as a dummy load. By using a reference 50Ω RF signal source generator, the input SWR value of the unit under test would be referenced to the 50Ω RF signal source generator as the RF signal source was the RF transmitter, then the input SWR value of the unit under test would be revealed. From this the SWR measurement, the input impedance of the unit under test can be determined as transmission line input impedance and the associated reactive component of inductance or capacitance.

One additional thought, if your auto ATU uses the forward and reflected voltages from the SWR sensor bridge, then it is quite possible that the antenna load would be matched your radio even it has a construction fault and it is not quite to a 50Ω specification. That is to say not 50Ω but higher or lower than 50Ω. As the ATU measures the forward and reflected voltages to a base line reference, in this regard to the radio set output impedance ( the source impedance ), any error within the radio set output impedance would be compensated for by the auto ATU antenna matching. If the radio set is 40Ω, then the auto ATU antenna would match the antenna load to a 40Ω source impedance, and so would the case if the radio set output impedance, thus the source impedance was 70Ω.

One this point, an auto ATU purchase may safe your bank balance, that is to say not upset the emotions of your banks branch manager. If one is a home builder of RF amplifiers in the QRP to legal limit, then an auto ATU purchase would help with any design construction errors of the terminal impedance that is hopefully 50Ω, within the final build. Mind you, it would help the main line equipment manufactures and small scale companies should any constructional error creep in, fully in the knowledge that the auto ATU would compensated for any manufacturing errors.

Actually that is a point, as in the days of HF final stage tube or valve amplifiers, the output matching circuit of the tube amplifier would have two adjustment controls, a "plate" and "load" or an "anode" or "load". Sometimes labelled as "tune". The tube or valve output circuit thus matched to a 50Ω dummy load. From this point on, the antenna load was matched to the radio set, a radio set that had been tuned to indicate a 50Ω RF source output. The auto ATU would in effect accomplish the "load" process of a legal limit amplifier, while the "plate" would manually or automatically be adjusted to set the "plate" or "anode" to the RF band plan setting.

The reason for the "plate" adjustment is made as the amplifying device travels up and down the radio spectrum, the RF impedance match requirements of the amplifying device change. Many RF amplifier designs tend to use a wide band RF transformer couplings, using a balam, but even here it is perhaps at best a compromise. It is perhaps possible that over the HF spectrum, even a solid stage amplifier output impedance may vary around the 50Ω mark. If this is true, then an auto ATU would possibly overcome any difficulties along these lines.

Balanced Transmission lines.

Many radio ham may be perhaps using a balanced transmission lines system. A balanced 300Ω line system is not uncommon, but a 50Ω version is different. A balanced line system is said to be more resistant to EMF interference, and perhaps may radio hams have found that to use a counter-poise ground has in some cases reduced the Electro-magnetic interference pickup. From this prospective, I am wondering if the below diagram would help in the reduction of EMI noise.

The above diagram illustrates the 50Ω balanced line approach. Essentially the method entails a 1:1 balum fed to and from a standard unbalanced 50Ω co-axial line. The counter-poise is used to provide a counter-poise 50Ω grounding, turning the unbalanced co-axial line into a 50Ω balanced line system. The HF radio would provide a 50ohm source, the auto ATU while impedance matching the antenna load, would in itself provide a 50Ω load to the balanced line structure of the transmission line system. The plan is for the counter-poise to not only provide the 5Ω balanced line but also help reduce the EMI pickup by virtue of the now in use 50Ω balanced line system. The components used to create the counter-poise load, are the same values used for the HF mobile vertical antenna's matching stub tune line circuit, so would then provide the antenna counter-poise impedance across the HF band.

The signal end "the co-axial line central core", is connected to the top side of the 1:1 balum. The lower termination end of the balum, is connected to the top end of the counter-poise. The bottom unconnected end of the counter-poise must stay as a high impedance connection, that is to say left unconnected and not earthed or grounded. By leaving unconnected, the counter-poise will reflect a 50ohm load as the balanced antenna load into the 1:1 balum, thus creating the 50Ω balanced line application.

Food for thought.