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

Wed Feb 10 10:41:54 UTC 2021

Hi Mike,

On 2021-02-10 08:10, Mike Ingle wrote:
> 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

You can, and that is more or less what the modern instruments are doing,
even if they do not have the sampling frequency tuned in exactly that manor.

It's the key to the modern deep noise floor tools.

Cheers,
Magnus

>
> 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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