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

Wed Feb 10 07:10:38 UTC 2021

Hi,  I wonder if you could achieve this easier with a "brute force"
approach and digitize directly at the mixing frequency?  Then do the rest
with math in an FPGA.  --mike

On Wed, Feb 10, 2021 at 1:20 AM Magnus Danielson <magnus at rubidium.se> wrote:

> Attila,
>
> On 2021-02-09 21:15, Attila Kinali wrote:
> > 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)
>
> There is more methods available than Gilbert cell mixers. For many
> purposes you do not need to go full Gilbert cell, which is a 4-quadrant
> mixer, but can satisfy with a simpler 2-quadrant mixer. Both kinds is
> really a transistor pair and they do indeed to proper multiply.
> Additionally linearizing diodes can be used to reduce the distorsion
> from the arctanh distorsion (by letting the diodes perform logarithm),
> and thus one can push them to higher ampiltude without too much
> distorsion, but higher still remains relatively low, which remains the
> fundamental SNR issue. The main claim to fame of these is really that
> you can do them on silicon as integrated chip without any transformers
> involved. That has it's uses, but really not what brings you best
> performance.
>
> A better approach is the Drawmer VCA, which has way better SNR than
> Gilbert cell type, but they typically do only lend themselves to
> 2-quadrant as the control is exponential. For mixers with very good
> dynamics and big signal support, the H-bridge mixers seems to be the
> king of the hill these days.
>
>
> >
> > First thing to note, a diode mixer does not multiply. It only
> > multiplies the signs of the signals, but adds the amplitudes.
>
> Actually, it's a bit more complex than that, if you do not have high
> drive-level. It actually is able to do a multiplication, but it is not a
> very good one. It ends up doing the logarithm of the two input sources,
> add them and then do the exponential, all through the same NP junction
> exponential response, as it finds it's balance-point in the setup. It
> might sound mind-boggling, but if one comes from the right direction on
> it, it would make kind of sense. To improve things, you can increase the
> drive-level and well, there is a reason we do that. Then you can
> consider the simplified model you advocate.
>
> Any NP junction will to the mixing, and this is a major issue in mobile
> towers, causing passive intermodulation (PIM).
>
> > 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.
> For DMTD a problem is that the two different beat-cycles integrate only
> partly the same noise from the common source, and hence there is a
> decorrelation loss occurring which raises the leakage of the transfer
> oscillator noise into the noise-floor. When the beat is near each other,
> that problematic effect ends being minimized, but so would the time
> difference, which may or may not be what you want.
> > 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.
> The cancellation of even harmonics comes because the main wish to cancel
> the input terms, as the unbalanced mixer lets both through, the balanced
> mixer blocks one and the double-balanced mixer blocks both inputs.
> >
> > 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
> >
>
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