[time-nuts] PM-to-AM noise conversion (was RE: New Question on HP3048A Phase Noise Test Set)

[Bruce Griffiths]

John Miles wrote:
> That '6 dB' part is probably what is bothering you.  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 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.  Second, the AM noise at baseband contains
> energy from both conversion sidebands.  You're trying to measure SSB noise,
> so there's the other 3 dB.
>
> I will confess I don't completely follow his reasoning.  First, subtracting
> the first 3 dB from the noise trace implies that there's something different
> about the "RMS-ness" of SA-measured spur levels versus SA-measured noise
> levels.  I don't see the mathematical justification for that.  If nothing
> else, the difference between the crest factors of discrete spurs and
> Gaussian noise is much greater than a 3-dB correction would account for.
>
>   
Actually the explanation is relatively straight forward.
If (in the case where the RF port isnt saturated as in the 3048) the
phase detector output is the cosine of the phase difference between the
LO and RF inputs:

i.e. Vo = Vb*cos(theta)
then the slope (volts/radian) is
slope = -Vb sin(theta)
at the zero crossing the slope is
Vb (volts/radian).

Where Vb is the beat signal amplitude.
When the rms amplitude(Vb/SRT(2)) of the beat signal is measured then if
this rms value is used in the formula for L(f) instead of the peak
amplitude(Vb) then one has to subtract 20log(SRT) = 3dB from the
calculated value of L(f) to obtain the correct value.
> Second, the two mixing products that are folded into the baseband spectrum
> by the mixer are identical, since the IF spectrum is symmetrical.  Given 50R
> impedance at all three mixer ports, wouldn't the DSB output voltage be 2x (6
> dB) the equivalent SSB value, not 1.414x (3 dB) as Scherer indicates?  -3 dB
> is what you use to correct for addition of dissimilar sources, -6 dB for
> in-phase ones.
>
>   
The Scherer analysis only applies to noise components.
For coherent spurs the 6dB correction (plus an additional 3dB if the rms
beat signal amplitude is used instead of the peak amplitude in the
Formula for L(f)) is correct.
> So my thinking is that while Scherer has the right figure for AM-to-PM noise
> conversion (-6 dB), he may have reached it for the wrong reasons.  I do not
> believe that any RMS correction needs to be applied for the calibration
> beat-note amplitude versus that of the sample-detected AM values that will
> eventually be interpreted as either phase noise values *or* discrete spurs.
> And I believe that the proper correction value for baseband downconversion
> is 6 dB rather than 3 dB, regardless of whether the spectrum is full of
> noise, spurs, or both.
>
> >From what you are saying, it sounds like the 3048A system software is going
> out of its way to avoid applying the -6 dB part of the gain correction
> factor to discrete spurs.  In my opinion they should be treated identically.
>
>   
No, noise and discrete spurs should be treated differently.
> Disclaimer: Dieter knows what he is talking about.  I don't.  Caveat lector.
>
> -- john, KE5FX
>
>   
The problem with the Scherer analysis is that real DBM phase detectors
don't necessarily have a sinusoidal phase detection characteristic.
Although with a sufficiently low RF input ths phase detector response
will be sinusoidal.
However this approach raises the system phase noise floor above that
achieved when the RF port is also saturated.
Wenzel gets around this by actually measuring the beat frequency slope
at the zero crossing.
NIST use a calibrated phase modulator to measure the system phase angle
transfer function.
Both these methods allow the RF port to be saturated for lowest system
noise floor and increased AM rejection.
Adding white noise to the OCXO output adds white PM noise raising the
noise floor so that the system phase transfer function can be determine.

Bruce