[EMAIL PROTECTED] wrote: > Bruce Griffiths wrote: > >> After low pass filtering >> >> Vo(t) = (A2/2)*sin((w1-w2)t) >> >> >> Thus the amplitude of the discrete spur related component in the low >> pass filtered phase detector output is 1/2 (6dB) the amplitude of the >> discrete spur itself. >> >> >> This result is independent of any additional calculations that may be >> done to derive L(f) from the observed spectrum. >> >> > > I agree completely that the phase detector output amplitude > of your ideal multiplier is half the input spur amplitude. > > But I believe that particular 0.5 drops out later along the > way in the computation of S_phi(f) and L(f), as converting > from voltage to phase requires division by the phase detector > constant Kd, which is also 1/2 for your ideal multiplier. > Yes I realised that as I fell asleep and I was going to comment on it but I thought that I would gather it all together in pdf file for easier reference. To generate a beat frequency signal for calibration requires one to use an RF signal which is offset from the LO frequency, so naturally their is no difference between this and Martyn's case. > > Here's my attempt at continuing on to calculate S_phi(f) and L(f) > for your example phase detector ( somewhat simpler than a real > world calculation requiring gain and calibration corrections ) : > > > S_phi is defined as the square of the RMS phase > : > : S_phi = phase_rms ^ 2 > : > > RMS phase is the RMS voltage over the phase detector constant: > : > : phase_rms = Vrms / Kd > : > > Substituting to get S_phi in terms of Vrms and Kd: > : > : S_phi = [ Vrms / Kd ] ^ 2 > : > > Given your earlier calculation: > : > : Vphase_detector_out = 0.5 * Vspur > : > > The rms voltage at your ideal phase detector output is therefore: > : > : Vrms = 0.707 * Vphase_detector_out > : = 0.707 * 0.5 * Vspur > : > > The phase detector constant, Kd, is 0.5 for your ideal multiplier: > : > : Kd = 0.5 > : > > Plugging in, we get: > : > : S_phi = [ Vrms / Kd ] ^ 2 > : = [ 0.707 * 0.5 * Vspur / 0.5 ] ^ 2 > : = [ 0.707 * Vspur ] ^ 2 > : = 0.5 * Vspur^2 > : > : L = 0.5 * S_phi ( small angle approximation L ~= S_phi/2 ) > : = 0.5 * 0.5 * Vspur^2 > : = 0.25 * Vspur^2 > : > > As these are powers, S_phi(f) is -3 dB, and L(f) is -6 dB > > Which is exactly what Martyn's 3048A has been telling him ! > > > Brian > > > p.s. > > One interesting detail of the calculation of S_phi > is that the phase detector constant Kd depends upon > the _peak_ value of the phase detector output. > > This is the Achilles heel of that system, real phase detectors may not have a sinusoidal response to the phase difference. This is why NIST developed a phase angle modulator to calibrate phase measurement systems without switching amplifier gains or disabling PLLs etc. > In an actual system with the phase detector constant > calibrated by a beat note measurement, if the system > instrumentation measuring the beat note amplitude > returns an RMS value, that tosses another 1.414 into > the calculation of Kd to convert from RMS to peak. > > This is the source of the 'mystery' 3dB correction > John Miles mentioned elsewhere in the recent discussions: > >> According to the notes written by the guy whose office >> door the 3048A authors would have knocked on for advice >> (see _www.ke5fx.com/Scherer_Art_of_PN_measurement.pdf_ >> > (http://www.ke5fx.com/Scherer_Art_of_PN_measurement.pdf) page 12), > >> you need to subtract 6 dB from the noise trace for two reasons. >> 3 dB of it comes from a mysterious "Accounts for RMS value of >> beat signal (3 dB)" clause in Scherer's app note. >> >> > > The top of page 35 ( original page numbering ) of the following > HP app note describes the beatnote correction : > > _http://www.home.agilent.com/upload/cmc_upload/All/5952-8286E.pdf_ > (http://www.home.agilent.com/upload/cmc_upload/All/5952-8286E.pdf) > The above analysis accurately describes the origin of the 6dB reduction in the relative amplitude of the spur as seen by the phase measurement.
Bruce _______________________________________________ time-nuts mailing list -- [email protected] To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there.
