[time-nuts] AM/PM conversion on mixer, DMTD

[Attila Kinali]

Ciao Mattia!


On Tue, 9 Feb 2021 10:58:20 +0100
Mattia Rizzi <mattia.rizzi at gmail.com> wrote:

> I had a look at the literature and I found a paper [1] that put an
> upperbound between AM/PM and OIP3. Therefore I am looking for triple
> balanced mixers or DBM with high IP3.
> My question is: in your experience is that all or there's something else?

Uh.. this is a difficult question. 
First of, let me start with a few questions: what is the general
circuit you are working with? What are you trying to synchronize?
Is it synchronization or syntonization? Will you steer the phase
difference to zero?

Next: Forget everything you think you learned about diode mixers.
All texts I've read on them are strong simplifications of what
is going on, in order to make the problem of describing them
tractable. 
(I have not looked at Gilbert cell mixers yet, so I cant's say
anything about their analysis)

First thing to note, a diode mixer does not multiply. It only
multiplies the signs of the signals, but adds the amplitudes.
This fact alone, while not invalidating the general principle,
makes the used description hard to use for precision applications. 
Add to that, that diodes are not ideal switches. Even a "slow, but
symmetric switching" description does not capture them properly.
Switching is asymmetric, due to the space charge zone and it
bounces like a mechanical switch due to parasitic inductances
and diffusion time constants. The non-linearity in the switching
behaviour  will cause headaches once you try to get to a good model
of phase linearity in mixers.

With that in mind, it becomes obvious that a diode DBM is
pretty aweful (in the nutty time-nut sense) when it comes
to phase linearity. But, a lot of the non-idealities cancel
out or become insignificant, once you steer the phase such,
that you are at certain sweet spots (e.g. 90°).

But, from what you wrote, you are not concerned about using
a mixer as a phase detector, but as a frequency translation
device in two parallel branches. There things change a bit.
Foremost: DC offsets are of no consequence. This simplifies
a lot in the analysis. But it also causes problems: now
you have shifting phases, hence you can't stay at a sweet spot.
But with this, all you care about is noise, of any form, ending
up in the IF signal band. To analyze this you can look at the
frequency domain behaviour of the mixer, like I did in [1] for
the sine-to-square wave converter.

The lessons are also pretty similar: Avoid even order
harmonics. All even order harmonics will lead to (correlated)
noise and signal being brought into the signal band, which will
lead to phase offsets (including AM to PM conversion).
The above is also the reason why high IP3 seems to help: All
devices that have high IP3 (relative to the operation point,
or to the 1dB compression point) have also a high IP2, This
means, that high IP3 devices are low in even harmonics.
And it also explains why a double balanced mixer has less noise
than a single balanced mixer: The two paths, that are driven
180° out of phase, lead to the cancelation of even order harmonics,
thus get less (sub-harmonic) down conversion of noise into the
IF band.

I wanted actually to sit down and repeat the analysis of [1]
for the diode DBM, but never got around it. If you are interested
in doing that, we could work together.

An additional note, as you care about sub-0.1° phase differences:
To achieve this, you will need to either control or compensate
the temperature dependent phase shift of mixers. 1-5ps/°C is
what I have seen in various papers. For two similar paths,
you can expect a 1:10 to 1:20 matching. If not controlled,
this will lead to a phase shift in the order of 0.01-0.03°/°C
of differntial phase shift between the paths at 3GHz.

			Attila Kinali

[1] "A Physical Sine-to-Square Converter Noise Model", IFCS 2018
http://people.mpi-inf.mpg.de/~adogan/pubs/IFCS2018_comparator_noise.pdf

-- 
The driving force behind research is the question: "Why?"
There are things we don't understand and things we always 
wonder about. And that's why we do research.
		-- Kobayashi Makoto