Phase Noise measurement with Quadrature Detection - Page 1
Forum section: electronics / rf-microwave

author: MikeLogix
author_rank: Contributor
timestamp: December 05, 2017, 09:22:49 pm
content: I was reading up on Phase noise measurement. In our setup at work we have a N5500 test set. The common technique to measure phase noise is the quadrature detection method where a ref and DUT (device under test) are applied to a phase detector (like a double bal mixer). According to what I read, when the ref and DUT are 90 degree phase difference then the two signals are quadrature and the output of the mixer is zero volts (see image). This confuses me as to why 90 degree, to me it would seem that 180 degree would cause zero beat. Can anyone help me understand why it is 90 degree and not 180?Thanks

author: dmills
author_rank: Super Contributor
timestamp: December 05, 2017, 09:48:19 pm
content: Let An be (1 + the amplitude noise of signal A) and Bn be (1 plus the the amplitude noise of signal B).Then let A = An* sin wt, and B = Bn * cos wt.Multiplying these (Which is what a mixer does), you get An * Bn * sin wt * cos wtapplying the double angle identity, sin 2u = (2 sin u cos u) we get 0.5 (An * Bn) sin 2wt so for the quadrature case all of the amplitude nose ends up being mixed up to twice the carrier frequency and rejected by the measurement lowpass filter.This makes the measured nose purely that due to phase noise and does not include the amplitude noise, providing the phase noise is small compared to the oscillator power (If it is not then the two can no longer be meaningfully said to be in quadrature!).Regards, Dan.

author: MikeLogix
author_rank: Contributor
timestamp: December 05, 2017, 10:09:47 pm
content: Quote from: dmills on December 05, 2017, 09:48:19 pmHi Dan, thanks for replying. Just to clear some of my confusion. You say let A and B, be 1 + amplitude of noise. Would not that be the main carrier amplitude so A = (1+signal) that we want to cancel out. What I mean, two signals say 10 MHz, would we not want to zero beat the 10 MHz so what remains is the noise to measure?Also in your formula, you use wt, would that be w= 2piF, and t= time? Just want to make sure I put in the correct numbers.Thanks

author: rfeecs
author_rank: Frequent Contributor
timestamp: December 05, 2017, 10:17:41 pm
content: Here are some references on using a double balanced mixer as a phase detector. When the RF is in phase with the LO, you get a maximum (say -1), and when RF is 180 degrees out of phase you get a negative maximum (say +1). In between, at 90 degrees, the output passes through zero:https://www.jlab.org/uspas11/Reading/RF/Mixers%20-%20phase%20detectors.pdfhttp://www.markimicrowave.com/blog/2015/02/all-about-mixers-as-phase-detectors/

author: rfeecs
author_rank: Frequent Contributor
timestamp: December 06, 2017, 12:04:46 am
content: Quote from: dmills on December 05, 2017, 09:48:19 pmThe upper sideband is at twice the frequency, the lower sideband is at baseband so it is not rejected by the lowpass filter. I don't see that this rejects AM.My impression is that the AM is rejected by saturating the mixer with both inputs:Quotehttps://www.minicircuits.com/app/AN41-001.pdf

author: Kire Pûdsje
author_rank: Regular Contributor
timestamp: December 06, 2017, 02:18:02 am
content: Another way of looking at it is with phasor diagrams.If we mix two signals, we get the difference of the frequencies.A*exp(jwa+j phia)*B*exp(-jwb -j phib) = AB exp(j(wa-wb+phia-phib))If both are at the same frequency:AB exp(j(phia-phib))If both signals are in phase, the phasor will point at +1.If both signals are 90 deg out of phase, the phasor will point at +jIf both signals are 180 deg out of phase, the phasor will point at -1Since we can 'only' measure real signals, we measure the projection on the real axis.Now imagine what a perturbation will do to the projectionin phase, then only the length of the phasor (AM noise) will influence the projection90 degrees, then only the angel of the phasor (PM noise) will influence the projection180 degrees, then only the length of the phasor (AM noise) will influence the projection

author: dmills
author_rank: Super Contributor
timestamp: December 06, 2017, 04:34:36 pm
content: Thats what I was getting at, in quadrature the AM noise cancels and all ends up around the sum term, only the PN remains, which is why this measurement is made in quadrature.Modulation is one of those places where a good feel for polar form and phasor diagrams is really useful.Regards, Dan.

author: Kire Pûdsje
author_rank: Regular Contributor
timestamp: December 06, 2017, 06:36:08 pm
content: Sorry, I was not implying your view was invalid.You gave the example based on sine/cosines. I do agree that my example is exactly the same as yours. The 'other' view is more about thinking of it as phasors. Mathematically it is exactly equivalent, but visualizing the concept with phasors might help the OP, since he still did not grasp the idea. By 'projecting' on the real axis, the phasors degrade to the sine/cosines as described in your post.

author: rfeecs
author_rank: Frequent Contributor
timestamp: December 06, 2017, 06:38:59 pm
content: If you had a full IQ mixer you could separate the magnitude and phase.Here you are just mixing the test signal with a quadrature reference signal.This gives you an output that is proportional to the phase.But it is also proportional to the amplitude. Your mixer output is still AM modulated. You haven't removed the AM noise.Of course there is one point where the two signals are exactly 90 degrees out of phase where you have zero AM. That's just because the output is zero at that point.As I mentioned, one way to suppress the AM is the saturate the mixer.

author: Kire Pûdsje
author_rank: Regular Contributor
timestamp: December 06, 2017, 06:50:30 pm
content: Yes, the output is dependant on amplitude. For phase noise measurement, compensating for the amplitude itself is usually not the hardest problem. For the measurements, in general you are not looking to the last dB. (unless you are just over the design limit).AM and FM/PM noise are two orthogonal properties. by not having exactly the 90 degrees, you are measuring a combination of the two, as you state. Finding the right point where AM cancels is exactly the whole the point of a phase noise measurement setup.Compression/saturation could also cause al kinds of other effects like for example AM/PM conversion, etc. and is in general not a good idea. I have seen a lot of cases, where the 1/f noise of the mixers due to the rectifying effect of the mixer was the major cause of AM noise. With saturation, you are really pushing the rectifying effect.

author: dmills
author_rank: Super Contributor
timestamp: December 06, 2017, 07:02:46 pm
content: Thats a reasonable perspective, you can always use a limiting amplifier to remove AM, no so with PN.Remember that both AM and PM are small at any reasonable offset, so for the purpose of first order analysis you can consider whichever one you don't care about to be zero providing your detection arrangements do not gratuitously amplify whichever one you are trying to cancel.Consider, that while the measured amplitude of the PN in a quadrature measurement depends on the level of the measured signal, and so is really the product PN * (1 + AN) where the nominal carrier level is 1, AN the amplitude noise component will generally be very much smaller then the carrier level, so unless you have a spur at a really silly level or something the AN component can be ignored, similarly the in phase measurement of amplitude noise is really AN * (1 + PN) where providing PN is much smaller then 1 it can be ignored.Regards, Dan.