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Now much is said regarding the measured signal sensitivity of a new radio design and the Receivers signal noise floor. However, in this scenario the RF signal generator is connected to the radio under test by a coax cable, and thus the
external noise floor of the radio attached to an antenna is not measured as a whole radio signal sensitivity measurement.
The reason of this article is that the low level signal performance listed in the magazine tests and manual for the radio does not mention the story, not the fault of the magazine or the manufacturer, but I believe there is more that can be accomplished to provide a more real world test set of measurements.
Now consider the circuit diagram below:
The Balum transformer type circuit is just a ruff guide, but you may have noticed that the although the signal generator and the radio under test ( D.U.T. Rx ) are connected to each other via the balum, so is also antenna loading. The antenna loading is there to expose the Radio receiver to the a real world test, not an off air signal test, but the antenna loading to there to provide the white noise signal of the etha ( picked up by the antenna loading ) to the radio receiver front end circuit RF bandwidth..
Now depending of the size of the antenna loading will depend upon the etha signal noise level. A 1/4 wave antenna would be 25% efficient upon the etha signal level pick up, while a 50ohm stub is not more than 10% efficient, a full wave antenna would collect a full etha noise level signal for the radio receivers low level signal performance, hence the on air sensitivity noise floor test by filling the front end of the radio bandwidth with the etha noise signal the radio would experienced while on air in use.
Now please refer to the tabled results below:
The label "RF_Bw" relates to the RF Bandwidth of the front end amplifier of the radio under test. The next label "max_temp" relates the noise floor temperature required of the radio as a whole to resolve a 1uV signal. The label "dB_margin" relates the overall space of signal performance the radio has in the face of losses to resolve the 1uV signal. Please note that if the front end noise temperature was 353Kelvin, then the front end RF bandwidth could be as large as 4MHz, which at the 2m or 70cm band is perhaps more likely, but these conditions of radio design would resolve a better than a 1uV signal. When the radio set front end RF bandwidth is a low as 100KHz, then the radio base line signal is around the 0·14uV, that is a 16dB margin of performance over a 1uV signal test line for the radio best performance weak signal test. The "max_temp" number of 14482 Kelvins is the degree of the noise temperature the front end can emit for the radio receiver to still pick up the 1uV signal, in short a very noise front end device.
Now the way I believe to view this overall data ( referring to the 353K noise temperature calculation ) from the table below is the RF noise floor experienced on air,. The first part of additional data to add to noise floor sensitivity is the required s/n ( signa to noise ratio ) of the intended required signal, say 10dB s/n to adequately resolve the signal, which would put the minimum signal then from the 0·8dB "dB_margin" back up to the -8·1dB "dB_margin", in theory equating to a minimum signal performance of 2.53uV. The next bit of addition data to add to this is the noise floor signal performance is that of the front end, say 2dB noise ( a good circuit design) , then the minimum signal is then up to the -10·1dB "db_margin" level, hence a minimum signal sensitivity of some 3uV in signal level. If the front end signal amplifier is much more noise than 2dB, one can see from the a greater input signal than 3uV would be required by the radio set.
Now not included on the tabled below is the antenna efficiency, a 1/4 wave would be 25% efficient in a space of a 3uV / sq metre field strength, so a 3uV input to the radio terminal would be thus a 12uV in practice. out of the 12uV sq metre signal magnetic field strength, the 25% efficient 1/4 wave antenna, relative to a full wave antenna, out of the 12uV sq metre signal picked up by the full wave antenna, only 3uV would be induced or picked up by the 1/4 wave antenna. Thus the radio set sensitivity would be 12uV sq metre magnetic field strength for a 3uV signal input at the radio set antenna terminal socket.
There is another side to this, in that although a full wave wire would pick the whole collective etha noise exposed to the front end filter, hence noise floor limits, the fullwave would also pick up the full intended signal. That is to say if the test was measured with a 50ohm stub antenna loading, then the minimum signal generator signal level measurement would while showing the etha noise floor, the 50ohm stub antenna is only barely 10% efficient, thus the etha intended signal would in anycase 10dB down from a fullwave.
Therefore the minimum signal level using a 50ohm stub loaded measurement, the signal generator test would only show the signal generator level, for while using the 50ohm stub antenna, to induce the 1uV signal from the stub antenna would require a 10uV etha intended signal to give the radio terminal 1uV signal from the etha intended signal. The effective on air noise floor level would then be 10dB worse off than measured. For the on air noise floor measured test with a 1/4 wave antenna, the correct noise floor level would be 6dB worse off, while for the fullwave antenna, the signal generator measurement would be correct.
Now one thing that comes to mind is the magnetic field strength measured as per metre. If a 40 metre long wire antenna used for the "40m band" ( 7MHz ) is to induce a 12uV sq metre signal, over a 40m long wire, would induce a 480uV signal ( 12uV * 40m long wire ). Is it then possible that the 12uV magnetic field strength for the 40m band a measurement of a 12uV over a square area of one wavelength per side, which then a full wave 40m long wire would induce a 12uV signal. A 1/4 wave antenna ( 10metres physical long wire antenna ) would then induce the 3uV signal, a 1/4 wave being 25% efficient.
A similar theory would be other radio bands. For the field strength meter to accurately portray a magnetic field strength reading, the meters antenna calibration would have to relevant to the band in use.
Do focus on the point that although the required s/n ratio required in a signal gen test would also included the noise signal performance of the front end device circuit, as the signal sensitivity measurement would include the noise performance of the front end, but in the table below the two values are added to give the overall hopefully measured results with a signal gen.
By adding the antenna loading connection to the overall signal performance test, the on air signal sensitivity is found, as the etha antenna signal is added to the bench test measurement results.
Below is a copy of the BBC Basic test program to calculate the tabled results. The code is a text window so that it maybe copied and pasted into the BBC Basic IDE program.
Text Box
10 REM calculation of noise floor relative to rf bandwidth of front end
20 REM boltzmans constant
30 Kb = 1.381E-23
40 REM power of a 1uV signal
50 Pn = 2E-14
60
70
80 FOR Bw = 50.1E6 TO 100E3 STEP -2E6
90 PROC_room_noise
100 PROC_temp
110 PROC_dB_diff
120 PRINT TAB(10);"RF_Bw = ";Bw/1E6;" MHz";TAB(29);"max_temp = "; INT(Kt * 1 )/1;TAB(48);" dB _margin = ";INT(Margin * 10 )/10;TAB(72);" V_floor = ";INT(V_floor * 1E6 * 100 )/ 100;" uV "
130 NEXT
140 END
150
160 DEF PROC_room_noise
170 Pn_room = Kb * 290 * Bw
180 V_floor = SQR(Pn_room * 50)
190 ENDPROC
200
210
220
230 DEF PROC_temp
240 Kt = (Pn/Bw)*(1/Kb)
250 ENDPROC
260
270
280 DEF PROC_dB_diff
290 Margin = 10*LOG(2E-14/Pn_room)
300 ENDPROC
Maximum Sensitivity of radio to front BPF Bandwidth.
The tabulated list result below, illustrates an interesting thought regarding our radio for todays purchase.
The Yeasu FT980 as many radios of that era, all have front end BPF for the radio bands we all use. However I have heard either rightly or wrongly, that some radio of the DSP era just have a lowpass filter to limit the top end frequency response. However if this is true, then for a 50MHz top end filter, the minimum electron noise using Boltzman's constant, of 1·38*10^-23, means that for a 50MHz front end top limited signal into the 1st amp then to the A/D chip for DSP work, the accumulated voltage is 3·16uV, however not assuming any antenna type. Now add then a signal to noise ratio for the audio at the speaker end of the radio, then this looks like a near 18uV signal. If however a front end filtering was used, even a tuneable pre-selector is used, and if the bandwidth was a good 250KHz, then the noise level could perhaps be 220nV or 0·22uV, then for a 15dB s/n ratio for the recovered audio, a radio sensitivity of 1·2uV is perhaps found. Now looking at the Noise figure listing, with a RF front end bandwidth of 250KHz, the complete radio receiver could posses and noise figure of some 13dB and still pick up a 1uV signal. However the Boltzman's constant mentions a max sensitivity of 220nV or 0·22uV, which would mean a radio noise figure of much less than 13dB, in other words much lower in value than 13dB.
A look at the computer code below, please look at the lines listed below here:
420 DEF PROC_room_noise
430 Pn_room = Kb * 290 * Bw
440 V_floor = SQR(Pn_room * 50)
450 floor_noise = INT(V_floor * 1E6 * 100 )/ 100
460 ENDPROC
Line 430, illustrates the noise equation set to room temperature in Kelvins, and the Bw for the for the radio 1st stage front end filtering. Line 440, then square roots "Pn_room" with the radio terminal impedance. Now I know this may look wrong, I did to, but however, Boltzmans constant is measured as "1·38*10^-23 J/K", note the "J/K", in other words "Joules per Kelvin". Now one "Joule per second" equates to "one watt of power per second", which means therefore that "line 430", Pn_room = Kb * 290 * Bw , is a power equation not a voltage equation. Hence thus "line 440", V_floor = SQR(Pn_room * 50) , is correct to calculate the voltage for a 50ohm terminal impedance. Thus the use of the Blotzman's constant is multiplied up by virtue of the device temperature and the bandwidth of the radio spectrum included for the power noise equation.
The end two columns relate to the noise figure or noise temperature required by a radio receiver design to take advantage of the front end bandwidth filtering. Strangely enough, a 3dB Noise figure or a 290K noise temperature radio receiver will do fine. So as long as your radio has a 3dB noise figure on its receiver, then hopefully you should experience the best signal performance your radio can provide on Rx mode.
Please bare in mind, that the signal strength required for a 15dB signal to noise ratio on your receiver is antenna depended. The figure below relates to a full wave antenna, that being for a full wave electromagnetic antenna coupling to the etha radio signal for that wave length, or for full signal electromagnetic induction into the full wave antenna. If a 1/4 wave antenna is used, then only 25% of the etha radio signal will be induced into the 1/4 wave antenna. Thus so, the best performance one can experience is a signal input requirement of four times the full wave etha signal requirement of a full wave antenna. Hence for a 1/4 wave antenna, a 250KHz front end bandwidth 1st stage will require a 4·8uV etha signal for the 15dB signal to noise audio output, not a 1·2uV as for a full wave antenna.
One thing comes to mind, if the Transmitter noise figure is no greater than 3dB, then the transmitted signal will have now more added to reduce the signal reception at the receiver end. That is to say, transmitter noise will add to the over all noise floor measurement, thus adding to the Boltzman's figures for the "Boltz uV (Bw)" calculations at the receiver end for the signal path, due to the transmitter noise irrespective the receivers front end bandwidth. Mind you that is bar any other noise signal source due to QRM and the like.
Now lets say one is a NASA deep space project design engineer, designing perhaps ground base radio telescopes, or even space probes, and wish to cool the radio receiver from 290 Kelvins down to 150 Kelvins, that is from 17 degrees "C" down to -123 degrees "C", a 140 Kelvin ( 140 degrees "C" ) drop in temperature from room temperature. To include this calculation alternative answer, just replace the 290 with 150 within this program line, from line 430 "Pn_room = Kb * 290 * Bw" , to new line 430 of " Pn_room = Kb * 150 * Bw" , or to any other device noise temperature design spec. To match the radio receiver to the radio transmitter, the transmitter would also have to be cooled down to the same cool temperature.
Strangely enough, although the new 150 Kelvin temperature is used, the first set of figure to receive a 1uV signal irrespective the front end bandwidth remain the same or unaltered, however, the "RX max sens" set of figures on the right hand side do alter in value, revealing a more sensitivity radio design due to the cooling effect of temperature noise, from a temperature cooling equipment. The "Boltz uv (Bw)" calculated values show that the 250KHz signal performance drops from 0·22uV to a new lower 0·16uV, that is a 2·7dB improvement, which would reduce the additional path loss of signal propagation by 2·7dB, equating to a increased signal propagation path distance of some 1·89 times..
It may be the case that a 1st stage RF amplifier with a lower noise temperature, say 150Kelvins or a Noise figure of 1·8dB, would bring the signal advantages of the lower signal value while still operating at room temperature. However, the noise temperature of a low noise 1st stage amplifier, such a noise figure of such a device may well be made at room temperature ( 290 Kelvins ). Th equation below, Friss equation for cascade amplifiers:
would thus go to show that a lower noise temperature or noise figure amplifier as the 1st stage amplifier would go to reduce the required signal level, the 1st stage amplifier "F1" signal gain "G1" would reduce the otherwise 3dB noise figure "F2" of the radio, by virtue of using the lower noise 1st stage receiver amplifier or a masthead pre-amplifier, "F1".
Now if the is new amplifier of a noise temperature of 150Kelvins ( 1·8dB NF ) operating at room temperature of 290Kelvins, if it was itself reduce by 140Kelvins to a new 150Kelvins, the effect upon the new amplifier device of a 1·8dB noise figure ( 150 K noise temperature ), would to then reduce the new amplifiers specs to just 10Kelvins ( 0·14dB NF ) in comparison.
The gain from the a low noise figure amplifier ( 1·8dB NF ), and to cooling down the noise temperature of the low noise amplifier ( 1·8dB NF ) by 140Kelvins to a simulated 10Kelvins noise temperature ( 0·14dB NF ), the 250KHz front end bandwidth, may perhaps equate to a 12dB signal improvement on reducing the additional path loss, 12dB = 20 * LOG( 0·16uV / 0·04uV ). This equates to perhaps a 16 times advantage, that may gave a 16 times increase in propagation signal path distance.
Just a note, it transpires that with the 10Kelvin ( 0·14dB NF ) of the low noise 1st stage amplifier, the maximum bandwidth that a radio front end can have, to allow a maximum of 1uV of "Boltz_uV" noise signal to pass through is 150MHz. At this point, the required noise figure of the 1st stage amplifier needs to be 0·14dB in value, thus matching the 1st stage amplifiers low noise figure. For a 3dB noise figure for a radio design, the matching front end bandwidth for a 1uV "Blotz_uV" noise floor is 5MHz, while for a 1·8dB noise figure radio design, the matching bandwidth for a 1uV "Boltz_uV" noise floor is 10MHz.
However even though due to the difference of radio design noise figure, for an audio quality of audio signal set at the 15dB s/n mark, referencing the "Boltz_uV" set to 1uV, the required signal for reception with a full wave antenna is around the 6uV in strength.
Text Box
10 REM calculation of noise floor relative to rf bandwidth of front end
20 REM boltzmans constant
30 Kb = 1.381E-23
40 REM power of a 1uV signal
50 Pn = 2E-14
60 s_n = 15
70 PRINT TAB(37);"Noise spec for 1uV Rx to front end Bw";TAB(100);"Rx max sens for Boltz front end Bw, full wave antenna"
80 PRINT
90 PRINT TAB(6);"front End BPF (Bw)";TAB(39);"Noise Temp";TAB(59);"Noise Figure";TAB(90);"Boltz uV (Bw)";TAB(115);"AF o/p @ ";s_n;"dB s/n";TAB(140);"Rx temp ";TAB(160);"Rx NF"
100 PRINT
110 PRINT
120
130 FOR Bw = 75E6 TO 100E3 STEP -5E6
140 PROC_process
150 NEXT
160 Bw = 2500E3
170 PROC_process
180
190 Bw = 1000E3
200 PROC_process
210
220 Bw = 500E3
230 PROC_process
240
250 Bw = 250E3
260 PROC_process
270
280 Bw = 100E3
290 PROC_process
300
310 END
320 DEF PROC_process
330 PROC_room_noise
340 PROC_temp
350 PROC_dB_boltz_noise_floor
360 PROC_boltz_s_n_signal_AF
370 PROC_radio_max_sens_temp_NF
380
390 PRINT TAB(4);"front_RF_Bw = ";Bw/1E6;" MHz";TAB(39);"temp = ";Kt_dec;" K";TAB(59);"NF = ";Nt;" dB";TAB(90);"Boltz_uV = ";floor_noise;" uV ";TAB(115);"sig + s/n = ";sig_s_n_uV;" uV";TAB(140);"temp = ";Kt_floor;" K";TAB(160);"NF = ";noise_floor;" dB"
400 ENDPROC
410
420 DEF PROC_room_noise
430 Pn_room = Kb * 290 * Bw
440 V_floor = SQR(Pn_room * 50)
450 floor_noise = INT(V_floor * 1E6 * 100 )/ 100
460 ENDPROC
470
480
490
500 DEF PROC_temp
510 Kt = (Pn/Bw)*(1/Kb)
520 Kt_dec = INT(Kt*1)/1
530 ENDPROC
540
550
560 DEF PROC_dB_boltz_noise_floor
570 front_noise = 10*LOG((Kt/290)+1)
580 Nt_floor = front_noise
590 Nt = INT(Nt_floor*100)/100
600 REM Nt = 290*(10^(front_noise/10)-1)
610 ENDPROC
620
630
640 DEF PROC_boltz_s_n_signal_AF
650 sig_noise_floor_db = (20*LOG(V_floor/1E-6))
660 noise_sig_hear = sig_noise_floor_db + s_n
670 sig_s_n_uV = INT(10^(noise_sig_hear/20)*10)/10
680 ENDPROC
690
700 DEF PROC_radio_max_sens_temp_NF
710 boltz_power_floor = (V_floor^2)/50
720 Kt_floor = INT(((boltz_power_floor / Bw)*(1/Kb))*10)/10
730 noise_floor = INT(10*LOG((Kt_floor/290)+1)*10)/10
740 ENDPROC
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