[time-nuts] Re: DIY Low offset Phase Noise Analyzer (Erik Kaashoek)

[Magnus Danielson]

Hi Mike,

On 7/8/22 15:34, Mike Monett via time-nuts wrote:
> You wrote:
>
>> Mike,
>> He was using an analog mixer, but your comment about XOR  mixer does
>> not apply  to  analog mixers.  Your  oversimplification  that analog
>> mixer and  XOR gates being the same thing does not  apply  here, and
>> thus the  assigned  missbehavior does not carry over  to  the analog
>> mixer case.
>> Cheers, Magnus
> Magnus,
>
> Thanks for your comment. Here are some attached files:
>
> 1. DBMS.PNG
>
> This shows the schematic of a double-balanced mixer. Note the mixer output
> is on pin U24. A low pass filter is at R1C1.
>
> 2. DBMWFM.PNG
>
> These are the waveforms in quadrature lock. The bottom waveform in red is
> the signal at pin U24. It is a square wave at twice the signal frequency.
> This signal is identical to an XOR, such as a 7486 logic ic, except the
> amplitude is much lower at only 900 mV p-p.
>
> The top waveform in green is the signal at the low pass filter. It is a
> triangle wave, the same as you would get from adding a low pass filter to
> any square wave. Thus my statement that a double-balanced mixer is an XOR
> is accurate.

No, it's not. You addresses this from the wrong side of things, 
considering that the waveform and amplitude is the only critical part, 
it's not. The way that the digital gate behaves is not providing the 
dynamics for the noise as the DBM does. A DBM has far less noise, which 
is why it is beneficial to use, as Bob pointed out.

So, while large-scale properties is similar between DBM and XOR, their 
noise behavior is quite different. Also their ability to handle signals 
of various amplitudes and the way they change behavior from it.

Also, all digital gates degrade their performance in face of higher 
amount of noise. On their way there they compress the noise. Stateful 
PFD can step state before they should, and that also compresses noise 
(and make it larger). See Gardner to cover part of this, I've done 
similar work that also reflect the same understanding.

As the goal here is to measure very low phase noise, DBM have proven to 
be the best technology until we started oversampling and digital radio 
style of processing, which is more expensive but state of art for wide 
frequency systems. More delicate systems with DBMs also achieves state 
of art, see the interferometric methods of Rubiola for instance and also 
the cross-correlator approach. I've contributed in that field myself by 
contributing the interferometric cross-correlation phase-noise setup, 
which combines the techniques to overcome a particular issue with 
cross-correlation at the thermal noise-floor.

So I continue to disagree about your generalization that DBM and XOR 
achieve the same thing, for this purpose they do not. If we where not 
looking for as deep noise floor, but only had moderate S/N needs, I 
would agreed. I've used XOR gates just fine for such applications, and 
there is plenty of such cases, it's just that this is not one of those.

>
> 3. DUBLBA01.ASC
>
> This is the double-balanced mixer schematic input for the LTspice simulator.
>
> 4. DUBLBA01.PLT
>
> This is the output waveforms from LTspice.
>
> Ordinarily, the triangle ripple output from a double balanced mixer would
> add considerable jitter to any PLL. Eric's application avoids this problem
> since his loop bandwidth is so low, at much less than 1 Hz. This makes it
> extremely difficult for him to obtain lock, which is why I proposed using a
> phase/frequency detector.

I suggested a PI loop instead. It avoids all the issues while 
maintaining the noise behavior from the DBM.

The low capture range of Eric's PLL for sure indicate the lack of loop 
gain, which also gives low bandwidth, so the end to end range of phase 
only allows for small adjustment of EFC to steer the oscillator into 
lock. A PI loop consisting of two resistors, a capacitor and an op-amp 
is a fairly good way to orthogonalize out the capture range from the 
bandwidth issue.

>
> The first block diagram I posted earlier, PNA.PNG, contained two errors. I
> corrected them in PNA2.PNG, which I will post to Eric.
>
> At first, I did not realize the significance of Eric's low loop bandwidth,
> and I erroneously assumed the triangle wave ripple output would cause
> significant jitter to his loop. It is now obvious the low loop bandwidth
> will reduce the ripple amplitude to insignificance, and I now retract my
> claim.

The ripple amplitude is also very limited to only cover a very narrow 
frequency range and those the beat note will be very low frequency. That 
take ages to lock unless one is very close at which is more the 
remaining lock-in.

Cheers,
Magnus