Hi all, Do you what is the theory of SNR at the output of a FM demodulator (linear) with the SNR at its input ? I do measure on a real system that I made and I don't know what the theory says for a know input SNR and a measure ouput SNR (demodulated)... Best regards...
FM SNR theory
Started by ●October 26, 2006
Reply by ●October 26, 20062006-10-26
patrick.melet@dmradiocom.fr wrote:> Hi all, > > Do you what is the theory of SNR at the output of a FM demodulator > (linear) with the SNR at its input ? > > I do measure on a real system that I made and I don't know what the > theory says for a know input SNR and a measure ouput SNR > (demodulated)... > > Best regards...>From Principles of Communications, by Ziemer and Tranter:Pt = transmit carrier power A^2/2 W = output LPF bandwidth Fd = peak deviation No = input noise density m = modulating signal SNRo = 3 * mean(m^2) * (Fd / W)^2 * Pt / (No * W) Regards, John
Reply by ●October 26, 20062006-10-26
> Pt = transmit carrier power A^2/2 > W = output LPF bandwidth > Fd = peak deviation > No = input noise density > m = modulating signal > > SNRo = 3 * mean(m^2) * (Fd / W)^2 * Pt / (No * W)so if my m signal is a sinus at 250 kHz with 1 V rms then mean(m^2) = 0.5 if my Fd = 250 kHz and W = 250 kHz then (Fd / W)^2 = 1 if Pt / (No * W) = SNR input, at the input at the modulator I simulate the SNR (measure it) then SNRo = 3 * 0.5 * 1 * SNRi = 1.5 * SNRi is it exact ?
Reply by ●October 26, 20062006-10-26
patrick.melet@dmradiocom.fr wrote:>> Pt = transmit carrier power A^2/2 >> W = output LPF bandwidth >> Fd = peak deviation >> No = input noise density >> m = modulating signal >> >> SNRo = 3 * mean(m^2) * (Fd / W)^2 * Pt / (No * W) > > so if my m signal is a sinus at 250 kHz with 1 V rms then mean(m^2) = > 0.5 > if my Fd = 250 kHz and W = 250 kHz then (Fd / W)^2 = 1 > if Pt / (No * W) = SNR input, at the input at the modulator I simulate > the SNR (measure it) > > then SNRo = 3 * 0.5 * 1 * SNRi = 1.5 * SNRi > > is it exact ? >You should see SNRo > SNRi when the discriminator operates above threshold (no clicks). This is called FM improvement. I've obtained good agreement with the theory in the past. John
Reply by ●October 26, 20062006-10-26
John Sampson <johns@3db-labs.com> writes:> patrick.melet@dmradiocom.fr wrote: >>> Pt = transmit carrier power A^2/2 >>> W = output LPF bandwidth >>> Fd = peak deviation >>> No = input noise density >>> m = modulating signal >>> >>> SNRo = 3 * mean(m^2) * (Fd / W)^2 * Pt / (No * W) >> so if my m signal is a sinus at 250 kHz with 1 V rms then mean(m^2) = >> 0.5 >> if my Fd = 250 kHz and W = 250 kHz then (Fd / W)^2 = 1 >> if Pt / (No * W) = SNR input, at the input at the modulator I simulate >> the SNR (measure it) >> then SNRo = 3 * 0.5 * 1 * SNRi = 1.5 * SNRi >> is it exact ? >> > > You should see SNRo > SNRi when the discriminator operates above > threshold (no clicks). This is called FM improvement. I've obtained > good agreement with the theory in the past.Hi John, If the discriminator is just dtheta/dt where theta is the phase of the analytic baseband signal, then what is the thing you call the "threshold?" Just curious. -- % Randy Yates % "Bird, on the wing, %% Fuquay-Varina, NC % goes floating by %%% 919-577-9882 % but there's a teardrop in his eye..." %%%% <yates@ieee.org> % 'One Summer Dream', *Face The Music*, ELO http://home.earthlink.net/~yatescr
Reply by ●October 26, 20062006-10-26
patrick.melet@dmradiocom.fr wrote:> Hi all, > > Do you what is the theory of SNR at the output of a FM demodulator > (linear) with the SNR at its input ? >FM demodulator just can't be linear since it deals with the phase. Thus the SNR question is fairly complicated and I don't know of any closed form equation. It depends on the pdf of the signal. Also, the gaussian noise at the input results in non-gaussian noise at the output.> I do measure on a real system that I made and I don't know what the > theory says for a know input SNR and a measure ouput SNR > (demodulated)...Generally, this is a tg - like dependence. Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com
Reply by ●October 26, 20062006-10-26
Randy Yates wrote:> John Sampson <johns@3db-labs.com> writes: > > >>patrick.melet@dmradiocom.fr wrote: >> >>>>Pt = transmit carrier power A^2/2 >>>>W = output LPF bandwidth >>>>Fd = peak deviation >>>>No = input noise density >>>>m = modulating signal >>>> >>>>SNRo = 3 * mean(m^2) * (Fd / W)^2 * Pt / (No * W) >>> >>>so if my m signal is a sinus at 250 kHz with 1 V rms then mean(m^2) = >>>0.5 >>>if my Fd = 250 kHz and W = 250 kHz then (Fd / W)^2 = 1 >>>if Pt / (No * W) = SNR input, at the input at the modulator I simulate >>>the SNR (measure it) >>>then SNRo = 3 * 0.5 * 1 * SNRi = 1.5 * SNRi >>>is it exact ? >>> >> >>You should see SNRo > SNRi when the discriminator operates above >>threshold (no clicks). This is called FM improvement. I've obtained >>good agreement with the theory in the past. > > > Hi John, > > If the discriminator is just dtheta/dt where theta is the phase of the > analytic baseband signal, then what is the thing you call the > "threshold?" Just curious.Hello Randy, The approximation quoted by John is valid on the two assumptions: 1. SNR is high. 2. The detector is a dumb discriminator. We should distinguish the properties of the FM signal itself from the inefficiency of the particular demodulator. The discriminator goofs up when the normalized SNR falls below ~10dB. The amateurs call this a "threshold". Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com
Reply by ●October 26, 20062006-10-26
Randy Yates wrote:> John Sampson <johns@3db-labs.com> writes: > > >>patrick.melet@dmradiocom.fr wrote: >> >>>>Pt = transmit carrier power A^2/2 >>>>W = output LPF bandwidth >>>>Fd = peak deviation >>>>No = input noise density >>>>m = modulating signal >>>> >>>>SNRo = 3 * mean(m^2) * (Fd / W)^2 * Pt / (No * W) >>> >>>so if my m signal is a sinus at 250 kHz with 1 V rms then mean(m^2) = >>>0.5 >>>if my Fd = 250 kHz and W = 250 kHz then (Fd / W)^2 = 1 >>>if Pt / (No * W) = SNR input, at the input at the modulator I simulate >>>the SNR (measure it) >>>then SNRo = 3 * 0.5 * 1 * SNRi = 1.5 * SNRi >>>is it exact ? >>> >> >>You should see SNRo > SNRi when the discriminator operates above >>threshold (no clicks). This is called FM improvement. I've obtained >>good agreement with the theory in the past. > > > Hi John, > > If the discriminator is just dtheta/dt where theta is the phase of the > analytic baseband signal, then what is the thing you call the > "threshold?" Just curious.Hello Randy, The approximation quoted by John is valid on the two assumptions: 1. SNR is high. 2. The detector is a simple discriminator. We should distinguish the properties of the FM signal itself from the inefficiency of the particular demodulator. The discriminator fails when the normalized SNR falls below ~10dB. The popular word for this is a "threshold". Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com
Reply by ●October 26, 20062006-10-26
Randy Yates wrote:> John Sampson <johns@3db-labs.com> writes: > >> patrick.melet@dmradiocom.fr wrote: >>>> Pt = transmit carrier power A^2/2 >>>> W = output LPF bandwidth >>>> Fd = peak deviation >>>> No = input noise density >>>> m = modulating signal >>>> >>>> SNRo = 3 * mean(m^2) * (Fd / W)^2 * Pt / (No * W) >>> so if my m signal is a sinus at 250 kHz with 1 V rms then mean(m^2) = >>> 0.5 >>> if my Fd = 250 kHz and W = 250 kHz then (Fd / W)^2 = 1 >>> if Pt / (No * W) = SNR input, at the input at the modulator I simulate >>> the SNR (measure it) >>> then SNRo = 3 * 0.5 * 1 * SNRi = 1.5 * SNRi >>> is it exact ? >>> >> You should see SNRo > SNRi when the discriminator operates above >> threshold (no clicks). This is called FM improvement. I've obtained >> good agreement with the theory in the past. > > Hi John, > > If the discriminator is just dtheta/dt where theta is the phase of the > analytic baseband signal, then what is the thing you call the > "threshold?" Just curious.I'd have to pull out the books (Schwartz?) to provide equations, but there's an intuitive (to me, anyway) explanation. Wideband FM uses excess bandwidth to buy better S/N. The receiver's wide front end lets in more noise than a narrow one would. Below some threshold* input level, the extra noise from the wide-open front end overwhelms FM's inherent noise improvement. Above that level, the output S/N improves rapidly. The effect is that for an unmodulated carrier, the background noise -- "FM hiss" drops precipitously as the threshold is exceeded. This phenomenon is known as "quieting", and a typical receiver spec might be "30 dB quieting at 5 microvolts" at the antenna input. Jerry ______________________________ * How is that "thresh hold" (the raised sill that keeps the threshed grain from spilling out)? I read it either "thresh old" or "thres hold". I guess dropped aitches are common in English. -- "The rights of the best of men are secured only as the rights of the vilest and most abhorrent are protected." - Chief Justice Charles Evans Hughes, 1927 ���������������������������������������������������������������������
Reply by ●October 26, 20062006-10-26
Vladimir Vassilevsky wrote:> > > patrick.melet@dmradiocom.fr wrote: > >> Hi all, >> >> Do you what is the theory of SNR at the output of a FM demodulator >> (linear) with the SNR at its input ? >> > > FM demodulator just can't be linear since it deals with the phase. Thus > the SNR question is fairly complicated and I don't know of any closed > form equation. It depends on the pdf of the signal. Also, the gaussian > noise at the input results in non-gaussian noise at the output. >Also, if I recall the analysis correctly, you can't find an "optimum" FM demodulator the way that you can with AM modulation and Gaussian noise. This means that you have to start by assuming a demodulation scheme, then analyze it's performance -- but someone may come by tomorrow with a better demodulator, that'll outperform yours by a few dB. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Posting from Google? See http://cfaj.freeshell.org/google/ "Applied Control Theory for Embedded Systems" came out in April. See details at http://www.wescottdesign.com/actfes/actfes.html
