PolyPhase or N-Path Mixer

[mawyatt]

There has been lots of discussions on this subject over on another thread which is about filters not mixers, so please take a quick view there first. In respect for the OP and the filter thread, I decided to start a new thread on these new type passive mixers.

https://www.eevblog.com/forum/rf-microwave/an-alternative-to-quartz-filters/

I've attached a couple of the earliest public domain publications on the subject from Drs Molnar and Andrews from Cornell in the IEEE SSJ and CAS publications. Our first public discussions were in 2009 at the IEEE ISSCC where Molnar and Andrews gave a presentation. Today there are 100's of papers on the subject and it's derivatives and I believe a few of the PPM (PolyPhase Mixers) have made it to the commercial world in some SDRs I've been told.

Anyway, happy viewing.

Best,

 

[mawyatt]

Here's a couple low resolution images of an early wide-band tuning receiver based on the PolyPhase Mixer (PPM). Created by Cornell in 65nm CMOS, and photographed with a developing technique utilizing custom lenses and precision camera/lens control.

Here's a brief list of the proprieties of the PPM I can think of, some of which are quite unique and make this device a fascinating subject.

1} Better than theoretical passive Bi-Phase Mixer noise figure! Less than 2dB measured NF without LNA, you can't do that
2} Very high input referred TOI without preselector filter, even for passive mixer. ~30dBm!!
3} Wide tuning range over decades in frequency!
4} Narrowband passive impedance match at antenna port without inductors or transmission lines!
5} Input match follows effective mixer LO over multiple decades without varactors or other tunable impedance!
6} Complex input antenna port +-j impedances achieved from baseband without inductors or transmission lines!
7} Direct I and Q downconversion! Basis for wide tuning range Direct Down Conversion Mixer First Receiver (see images)!
8} Compatible with small feature CMOS, performance scales with 1/feature size!
9} Bi-linear transformation from baseband to antenna (tracks LO)! Directly allows higher order bandpass filtering at antenna port with baseband low pass transfer functions without inductors!

Best,

[RoGeorge]

This trick (the PolyPhase Mixer) is new to me, thank you for opening a thread for it.

Didn't parsed yet the 2 attached PDF from here, will look at them, but first I want to ask why the switched approach and many paths of the signal was preferred, instead of a single path with one analog multiplier -> analog filter -> analog multiplier and sinusoidal LO?

Is this some technological choice, like for example preferring a switch over a Gilbert cell, or is it something else about the topology of PolyPhase mixer that I missed entirely?

[mawyatt]

This trick (the PolyPhase Mixer) is new to me, thank you for opening a thread for it.

Didn't parsed yet the 2 attached PDF from here, will look at them, but first I want to ask why the switched approach and many paths of the signal was preferred, instead of a single path with one analog multiplier -> analog filter -> analog multiplier and sinusoidal LO?

Is this some technological choice, like for example preferring a switch over a Gilbert cell, or is it something else about the topology of PolyPhase mixer that I missed entirely?

The many paths are fundamentally why the PPM can achieve a better than theoretical NF (2/pi) for a passive Bi-Phase Mixer. The PPM can approach a 0dB NF as the n-paths approach infinity. The many paths also push the harmonic response upwards generally well out of the region of interest.

By up converting the baseband LPF due to the bi-laterial transformation PPM properties this allows a very large shunt capacitor as "seen" from the antenna port with Out-of-Band signals. This large capacitor attenuates these OoB signals before they have a chance to enter the mixing process because of the low mixer input  impedance (S11~0dB) for OoB signals. In effect the PPM has pushed a baseband integrating capacitor LPF directly to the antenna port symmetrical around the LO. From a system design perspective this is exactly what you want for high dynamic range, force the signal filtering process directly upon the input signal at the very input before any active signal processing (gain). OoB signals get attenuated just like a preselector filter before any amplification, except this PPM filter is the baseband signal filter, or a major part of such, and tracks with the LO unlike the usual fixed frequency preselctor filter. We came up with a way that allowed doubling of the bandwidth of the receiver without effecting the bandwidth of the PPM input and TOI, and effecting the NF by <0.1dB

The Gilbert Mixer suffers from shot noise due to the active switching of bias currents, this imposes a NF limit that is higher than conventional passive mixers, and much higher than the PPM. The MicroMixer is another brilliant mixer from Barrie Gilbert that has a theoretical infinite DR, due to the unlimited current handling capability, of course real transistors have current limits. Another unique attribute of this mixer is that the gain increases with the input signal level! We've utilized these in many applications with SiGe bipolar devices and they work very well, but still suffer the same noise issues as the classic Gilbert Mixer.

Best, 

[mawyatt]

This trick (the PolyPhase Mixer) is new to me, thank you for opening a thread for it.

You are welcome. BTW the PPM is more that just a trick circuit, it employs DTCA signal processing to it's fullest as your soon to discover with the reference papers attached above which just scratch the surface....thus my reference to a "deep dive" in the other filter thread

There's a reason why Apple acquired a small startup Passif and made a bright young PhD student Dr. Caroline Andrews a multi-millionaire a year after graduating

Best,

[MikeP]

  Mike, thank you so much for posting these documents! 

[mawyatt]

You are quite welcome.

Have fun with this PPM, it's beyond an intellectual curiosity that challenges conventional thinking, but a highly useful and practical circuit that lends itself to modern CMOS scaling

Best,

[ejeffrey]

This trick (the PolyPhase Mixer) is new to me, thank you for opening a thread for it.

Didn't parsed yet the 2 attached PDF from here, will look at them, but first I want to ask why the switched approach and many paths of the signal was preferred, instead of a single path with one analog multiplier -> analog filter -> analog multiplier and sinusoidal LO?

An analog multiplier has a NF limit because when the LO is zero you are throwing away signal.  A switched mixer appears at first glance to avoid this as one switch is always on  but in fact has exactly the same limit only the "lost" signal goes into LO harmonic products.  The multipath mixer always has one phase on like the biphase switched mixer but phase shifts each to combine to the output .  This it both avoids (or reduces for finite phases) the harmonic products and puts that power in the signal band.

In principle a quadrature pair of analog multipliers could get the same effect, but it's hard to make lossless noiseless continously variable couplings.

Interestingly you can also build active circulators with a similar technique where the symmetry is broken not by a magnetic material but by the rotation of the switch pulse.

[mawyatt]

An analog multiplier has a NF limit because when the LO is zero you are throwing away signal.  A switched mixer appears at first glance to avoid this as one switch is always on  but in fact has exactly the same limit only the "lost" signal goes into LO harmonic products.  The multipath mixer always has one phase on like the biphase switched mixer but phase shifts each to combine to the output .  This it both avoids (or reduces for finite phases) the harmonic products and puts that power in the signal band.

This is incorrect!! The NF limit is based upon a full mixer/multiplier usage in all 4 quadrants, not limited to just 2 quadrants! A little analysis will show that with a perfect Bi-Phase multiplication (+-1) results in 2/pi loss, and thus a NF of 3.92dB. With using only 2 quadrants the resulting loss with be twice as much and 1/pi or 9.94dB NF.

Edit: There are many references for where this 3.92dB theoretical NF limit comes from, some highly theoretical and some like this "What is a Mixer" video that are very practical.
https://youtu.be/WwJKxvz7qbs?t=129

Research will show the PPM, N-Path Mixer, Mixer First has achieved a measured NF below 2dB some time ago, and likely much lower today with the available smaller feature CMOS.

In principle a quadrature pair of analog multipliers could get the same effect, but it's hard to make lossless noiseless continously variable couplings.

And how would a pair of analog multipliers achieve this below 3.92dB NF using whatever kind of couplings (?) you chose?? Please elaborate!!

Interestingly you can also build active circulators with a similar technique where the symmetry is broken not by a magnetic material but by the rotation of the switch pulse.

Yes, low frequency magnetic-material-less circulator variants have been around for some time.

Some related research at Cornell has produced a CMOS chip Duplexer from IEEE SSJ May 2015 Abstract:
"A fully integrated wideband active duplexing transceiver with baseband noise-cancelling duplexing LNAs is presented. The circuit allows in-band full duplex operation with concurrent reception and transmission in the same band or closely-spaced channels. A passive mixer-first architecture is applied here, sharing a single passive mixer to perform simultaneous up-conversion and down-conversion. The bi-directional transparency of the passive mixer allows the duplexing function to be implemented at baseband instead of RF front end. Under the same condition as required for noise cancellation, the baseband duplexing LNAs buffer the transmitter input signals to the mixer while canceling those signals in receive path. Measurements from the transceiver implemented in 65 nm CMOS show a frequency tuning range of 0.1-1.5 GHz with 20 dB, NF as low as 5.5 dB and transmitted power up to -7.1 dBm. A 30 dB linear isolation between receive and transmit is generally maintained across both LO frequency and in-band transmit/receive frequency separation. Significant suppression of transmit-induced noise and nonlinear intermodulation between received and transmitted signals are also achieved."

from 2014
“A widely tunable active duplexing transceiver with same-channel concurrent RX/TX and 30dB RX/TX isolation,” IEEE RFIC, 2014.
http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=6851731&url=http%3A%2F%2Fieeexplore.ieee.org%2Fiel7%2F6844558%2F6851613%2F06851731.pdf%3Farnumber%3D6851731


You can find all sorts of interesting research on the PPM, Duplexers and related topics here.
https://molnargroup.ece.cornell.edu/publications/

Notes in blue.


Best,

[RoGeorge]

Meanwhile browsed the two paper and the thesis attached in the other thread.  It all starting to make sense, very clever indeed, especially as an antenna filter.

However, I still don't get how to avoid overlapping all the multiple of LO bands down to zero.

My reasoning is like this (thinking first only about one phase/path and one low pass filter):
- a switch is a multiplier of Vin with either 0 or 1, therefore we can think about it as a normal mixer
- a normal mixer fed with f1 at one input and f2 at the other will produce two distinct tones f1+f2 and f1-f2 at output
- we plan to tune our LO such as f1-f2 will be zero
- the other tone, f1+f2, will be cut out anyway by the low pass filter following after multiplier
- since a square wave is not a pure tone, but a bunch of many harmonics, we can take the spectrum of the 0/1 waveform tone by tone and multiply each frequency with Vin
- since any 2 distinct frequencies are orthogonal to each other (doesn't "influence" or mix to each other in a linear circuit) we can just apply them all at once
- the spectrum of a pulsed square waveform is an infinite series of multiples of the base frequency, the amplitudes for each harmonic varies, but the overall envelope is a sin(x)/x with the same period as the width of one pulses

The spectrum for a square wave signal with duty cycle 50%, 25%, 12.5% and 6.125% (that will correspond to 2, 4, 8 and 16 phases/paths) will look like in the attached animated gif (made with real signals from the soundcard).



The first plot is the signal waveform at 4 different duty factors (from 50% to 6.125%), and the following two plots are the corresponding spectrum for these duty factors.  Both spectrum plots are the same, just that one is with the spectral lines in Volts, and the other with the spectral lines in dB.

We see that the case for n=2 (50%) is the only one that has the most spaced apart harmonics, because it has only odd harmonics.  All other duty factors will have both odd and even harmonics, and the bigger the n, the more equal in amplitude these harmonics will be.  We note that all the harmonics are equally space at an f_LO distance, and comparable in power (except for the missing one at each n^th of LO multiple, where n is the number of paths/phases).

This is a concern because our multiplier will shift to zero not only the frequency of interest, LO, but any other multiple of LO frequency will be shifted to zero.  Once we do that, there is no way to distinguish what signal came from which multiple of the LO frequency.  So, this is a rather a comb pass any-LO-multiple-shifted-to-zero type of filter.

In other words, once we see a signal at the output, we have no clue from which frequency that signal came.  It can be from any multiple of the LO.  I am not sure yet how to get rid of all the other teeth of the comb and keep only the first one.

Is this type of filter used only where it doesn't matter from what multiple of the f_LO our signal of interest is coming?

[mawyatt]

Remember the PPM is a completely different type of mixer which has sampled memory and the bi-linear transformation property allows simultaneous down and up conversion, this property is responsible for the nulling of the harmonic responses at the antenna port. Fourier analysis shows that N +-1 do not get nulled and thus in the 8 phase PPM the 7th and 9th harmonics are not suppressed. Later work has shown the nulled harmonics attenuated over 60dB.

If you study both the IEEE papers attached above by Molnar and Andrews, this harmonic response is discussed and in the 8 phase version of the PPM the "Specifically, the 8-phase passive mixer eliminates content at the 3rd, 5th, 11th, 13th harmonics and so on" from SSJ paper C. Benefits of 8-Phase Mixing pg 2699 and from C. Harmonic Suppression, pg 2705, "For the 8-phase case, which actively rejects these harmonics, the output due to the 3rd harmonic was 35.4 dB less than the fundamental and that due to the 5th harmonic was 42.6 dB less...... However, recent works have presented harmonic rejection
schemes which provide 60–80 dB of rejection (depending on implementation) [29], [36]. These techniques could easily be applied to our design as well, providing a similar degree of rejection". pg 2705.

In CAS paper "One such structure is the 8-phase passive mixer shown in Fig. 16, driven by eight nonoverlapping LO signals similar in concept to “harmonic suppression mixers” recently discussed in the literature [1], [13], [18], [20]..... Thus , which takes the form shown in Fig. 17, has a Fourier series which only contains half of all odd harmonics, driving the terms corresponding to n=3,5,11,13,... to zero." pg 3101

Be sure and follow up with the references mentioned in these 2 IEEE papers, as well as later works using A. Molnar, C. Andrews, N-Path, Mixer 1st and Polyphase Mixer searches on the IEEE site, as there was a flurry of activity after these 2 IEEE papers were published. I recall a paper reporting a measured NF of ~1.8dB over 8 years ago, but can't recall the paper name or authors.

As mentioned the PPM is a very very deep dive, and takes considerable time and effort to truly get an understanding of what's going on. I would forgo the simulations until you get a firm grip on what's really going on, simulations can easily mislead, obscure the details, and send you down the wrong path.

After some time studying the PPM I think you'll agree that this is one of the most amazing circuits I've ever come across, deceptively simple, frustratingly complex in behavior, many unique useful properties, and outstanding performance.

Best & Happy Holidays,

[mawyatt]

Is this type of filter used only where it doesn't matter from what multiple of the f_LO our signal of interest is coming?

Please remember this PPM (PolyPhase Mixer {PPM} or N-Path Mixer or Mixer First, which I refer all as PPM) is a Mixer that imposes a filter like function at the antenna port rather than just a filter. The PPM does frequency translation to baseband I and Q, thus is a Mixer, whereas a basic filter has no frequency translation.

This mixer can be used in most places because the first harmonic response is the 7th, and second harmonic response is the 9th harmonic for the 8 phase PPM version. The other harmonics of the LO clock are suppressed and effectively nulled by the unique behavior of this mixer.

BTW nice graphs, how do you create those with a sound card?

Best & Happy Holidays,

[RoGeorge]

Indeed, mixer, I was incorrectly using the term filter (thinking mostly about what I wanted to use it for, instead of what it is).

That was just a sloppy usage of words, sorry for that, but I am still very bamboozled by the whole circuit, because apparently it shouldn't work.  That is why I was detailing so much each step of my reasoning.  I like to think based on intuition and visual elements, rather than based on math and formulas.  I know this habit can easily lead to wrong conclusions, but has its advantages, too.

Since the circuit works in practice, yet it looks to me like it shouldn't, I'm certainly loosing some very important aspect here.  Will read again, and pay more attention to the referred bibliography papers, thank you for pointing them.


About the animated picture, I did that because I was not very sure about the theory.  I only vaguely recalled from the uni days that the envelope for the spectrum of a square wave is sinc(x).  But I like visual representations rather than formulas, so I started to tinker some theoretical spectrum plots with Python and Matplotlib.  Since I'm not a software developer, formatting the plots and eventually adding some sliders to change the duty factor, soon turned into a programming chore.

I would have very much preferred to touch some real knobs and buttons instead of Python simulations, but I have no spectrum analyzer.  Then, I remember about an old oscillocope/generator free tool for controlling the sound card, a tool that was already having all the required features I was looking for ( https://www.zeitnitz.eu/scope_en made by Christian Zeitnitz )
- can plot the spectrum or the waveform
- can generate square waves with a given duty factor
- can save the plots on disk

The "Scope" program was made for Windows (its look tells it was made with NI's LabVIEW).  Luckily "Scope" still works under Linux, too, with Wine.  So I made a few plots at different duty factors and saved them.  Since they were way too many to attach them all, I stitched them together (the oscilloscope view and the 2 spectrum views) with Gimp in 4 images, one image for each duty factor (I was wanting to see the spectrum up to n=16, because it happens that I have some old 16:1 analog switches mux/demux ICs - MMC4067 - from the CMOS 4000 series).

To illustrate even better how the spectrum evolves with doubling n each step, the 4 stitched pics from Gimp were grouped together in an animated gif, with these few lines of Python:

Code: [Select]

#!/usr/bin/env python3
# -*- coding: utf-8 -*-

from PIL import Image
import glob
 
# Create the frames
frames = []
imgs = sorted(glob.glob('*.png'), reverse=True)   # sorted by name

for i in imgs:
    new_frame = Image.open(i)
    frames.append(new_frame)
 
# Save into a GIF file that loops forever
frames[0].save('png_to_gif.gif', format='GIF',
               append_images=frames[:], #frames[0] is twice
               save_all=True,
               duration=500, loop=0)


[mawyatt]

I agree about the math, it's the intuitive understanding that is what comes first, then the math follows to have a proof that the intuition is right. Just about every break-thru was by intuition, or by accident-then intuition, then the math.

You are approaching the PPM in the right way IMO, get a seat-of-the-pants understanding and then the math will make more sense. Your initial assessment is likely from experience and what to expect, this simple circuit with a few switches , resistors and capacitors can't work as described, yet it does work and works incredibly well indeed

The key to understanding the PPM is to realize this is not a simple switch with a shunt capacitor and "bleed" resistor, or what one might expect of a sample and hold with a leak path resistor. Using superposition think of this as a means for the signal at the antenna to experience effects of what's on the other side of the switch, so as the input signal is experiencing down-conversion it is simultaneously experiencing up-conversion from the baseband. Once you get a feel for this then consider that using multiple switches time sequenced can create a somewhat continuous effect as "seen" from the antenna port due to one switch is always on.

Because of the up conversion the baseband can influence what's "seen" at the antenna port and this is how the impedance matching takes place, and since this follows the switching process it follows the effective LO or frequency of the clock divided by the number of switches. The matching network tunes with the center frequency, with no inductors, transmission lines, varactor diodes, or active circuitry required, just passive switches, Rs and Cs!!! Complex R +-jX impedance matches can be created at the antenna port by manipulating the baseband impedance magnitude and phase.

The noise properties are another fascinating effect, defying conventional thinking just like the impedance matching. The 2/pi theoretical limit is bypassed because the mixer has memory and allows the RF signal to correlate with the clock/N period. As the RF signal approaches the center frequency the correlation gets stronger reaching a peak when the RF signal period equals the N cycle period of the mixer, at this point the correction effectively becomes the auto-correlation function. So the input RF waveform is cycling over and over again thru the switches and synchronously stored on the shunt capacitors and experiences a noise reduction effect as predicted by correlation.

For signals that are far out of band the PPM antenna port "looks" like a huge shunt capacitor with the switch on resistance is series. With a switch resistance of an ohm or less, this produces a significant mismatch for the out of band signals and they don't couple to the antenna port. It's only when the input signal gets close to the center frequency does it begin to see a decent impedance match and begin to couple to the port and experience the downconversion to baseband. This is a massive benefit for the PPM based system as the out of band signals that cause problems with desensitization and blocking experience a large attenuation right at the antenna input before any active circuitry, just like a preselector filter, but without a dedicated preselect filter and all the issues that brings! Another not so obvious benefit of the PPM that is likely not observed with initial review and study.

There is much much more but I'll leave this for starters

That's interesting about the use of the sound card, thanks.

Best & Happy Holidays,

[KE5FX]

That's a nice way to put it -- to the extent the signal from the antenna 'agrees' with the charge already on the capacitor that is connected to it at the moment, less current will flow into or out of that capacitor.  As the RF and LO frequencies start to diverge, the capacitors draw more current as they try to follow the resulting voltage fluctuations from one LO cycle to the next, and the shunt impedance drops.

I think someone mentioned Dan Tayloe's work with a similar approach on the other thread.  Googling for info on the "Tayloe mixer" may give newcomers a better introduction than wading through a bunch of IEEE or BSTJ papers full of math, because Tayloe's work introduced the technique to amateur radio circles.  It's interesting stuff. 

I'd point out, however, that the main reasons for the post-2010 renaissance of interest in commutating RF circuits are VLSI-friendliness and power consumption.  This topology doesn't give you any magical new capabilities, or open up corners of the performance envelope that were previously forbidden.  If you aren't building cell phones or otherwise obsessing over getting the most IP3 per mAh, then multipath mixers and filters are just new rabbit holes that eventually lead to the same places where the existing ones do, but with less literature and prior art to guide the way.

[mawyatt]

That's a nice way to put it -- to the extent the signal from the antenna 'agrees' with the charge already on the capacitor that is connected to it at the moment, less current will flow into or out of that capacitor.  As the RF and LO frequencies start to diverge, the capacitors draw more current as they try to follow the resulting voltage fluctuations from one LO cycle to the next, and the shunt impedance drops.

I think someone mentioned Dan Tayloe's work with a similar approach on the other thread.  Googling for info on the "Tayloe mixer" may give newcomers a better introduction than wading through a bunch of IEEE or BSTJ papers full of math, because Tayloe's work introduced the technique to amateur radio circles.  It's interesting stuff. 

I'd point out, however, that the main reasons for the post-2010 renaissance of interest in commutating RF circuits are VLSI-friendliness and power consumption.  This topology doesn't give you any magical new capabilities, or open up corners of the performance envelope that were previously forbidden.  If you aren't building cell phones or otherwise obsessing over getting the most IP3 per mAh, then multipath mixers and filters are just new rabbit holes that eventually lead to the same places where the existing ones do, but with less literature and prior art to guide the way.

I'm not aware of any prior art before 2009 in the public domain that addresses these features, if you have references/papers please provide those. Dan Tayloe's work is the closest I'm aware of before 2009 but his patents don't address these features either. I never seen any reference before 2009 that discusses a passive mixer with a sub 3.92dB noise figure, nor a baseband passive inductor-less matching network that is used to track an LO and match an antenna port with a complex impedance. There was prior work on the harmonic rejection mixers tho, with references in the IEEE papers attached earlier.

I've never seen DARPA create a workshop specifically for a circuit concept, and they did so with the Mixer First workshop which was entirely dedicated to this topic. DARPA wouldn't be wasting time with just another RF circuit if this wasn't some new and undiscovered capability lurking behind the commutating concepts that future radios could benefit from. Soon after the workshop others got involved adding more credibility to this new type mixer.

Having the small CMOS available today has certainly helped fuel these types of commutating RF circuits recently and bring them into the public view. 20 years ago ~200GHz devices were available tho and we were doing commutating RF circuits back in ~1980 (Chirp Z based real time SA), so this technology has been available lurking in the background for many decades. I think the real reason for the post-2010 renaissance are more folks are involved, more $, and wireless technology is now an everyday discussion.

Best & Happy Holidays, 

[KE5FX]

I'm not aware of any prior art before 2009 in the public domain that addresses these features, if you have references/papers please provide those. Dan Tayloe's work is the closest I'm aware of before 2009 but his patents don't address these features either. I never seen any reference before 2009 that discusses a passive mixer with a sub 3.92dB noise figure, nor a baseband passive inductor-less matching network that is used to track an LO and match an antenna port with a complex impedance. There was prior work on the harmonic rejection mixers tho, with references in the IEEE papers attached earlier.

Point being, those goals are all achievable with traditional filter/LNA/mixer and ADC+DSP signal paths.  Commutation is mainly useful if you're trying to shrink size and power consumption, which is always of keen interest to DARPA.  Otherwise, it's technically very interesting, but not a game-changer. 

Nobody here is designing their own chips... and you can bet that the ones that are being designed are patented out the yin-yang.  This sort of thing gets really interesting when I can buy it off the shelf from Mouser.

[RoGeorge]

I found my mistake!   

The very first assumption I made, the one that a switch is the same as an analog multiplier is wrong.  They might be considered the same, but only for a pure rezistive load, and not when a capacitor or an inductor is present in the load.

For an analog multiplier, when an input is zero volts the output is also forced to zero volts, and that will forcefully start to discharge any energy stored in the load.  For a switch, when the switch is open the output is disconnected from the load, and any energy already present in the load stays there.  So, the voltage is undefined (in regards to the inputs) and depends of the load only when the switch is disconnected.  Here, in the case of a capacitor as a load, the output remains at the same voltage until the switch connects the Vin again.

This changes everything, the essential thing I was missing is the behavior of a switched capacitor, which is not the same as a permanently connected capacitor to a pulsed source.

Some very interesting things happen in a circuit containing switched capacitors!

Doh, I never thought before about switches that way, as connecting/disconnecting energy storage components to a circuit.  Usually all the parts are permanently connected.  Switching is somehow similar with changing a circuit's topology on the fly.

Need to experiment a little with that in order to build an intuition, and think more about the consequences of switching.

[gf]

Doh, I never thought before about switches that way, as connecting/disconnecting energy storage components to a circuit.

Off-topic here, but that's exactly what the switches in a SMPS do as well - connecting/disconnecting energy storage components, or re-connecting them in a different way

Another point is IMO, it is not sufficient to consider a single path alone. The interaction of the paths matters. If this were not the case, there were no reason to use N paths instead of a single one. Cancellation of particular harmonics eventually happens at the summing node.

[mawyatt]

Point being, those goals are all achievable with traditional filter/LNA/mixer and ADC+DSP signal paths.  Commutation is mainly useful if you're trying to shrink size and power consumption, which is always of keen interest to DARPA.  Otherwise, it's technically very interesting, but not a game-changer. 

But everything electronic is pursuing shrinking the size, power, and cost, so this is a potential game-changer!! I have a "hint" that the PPM is in the Apple AirPods, Watch, and a few commercial SDRs, no verification (yet), just a "hint"

Edit: I would like to see what a "traditional filter/LNA/mixer and ADC+DSP signal paths" that can cover over ~2 decades in frequency, have a ~2dB Noise Figure, ~30dBm TOI, and direct downconversion to I & Q would look like? Likely large, complex, expensive, and consume a few watts

Nobody here is designing their own chips... and you can bet that the ones that are being designed are patented out the yin-yang.  This sort of thing gets really interesting when I can buy it off the shelf from Mouser.

Not advocating folks design their own chips, but you can buy the components at Mouser for a moderate frequency PPM. A few resistors, capacitors, a CMOS bi-lateral (or discrete NMOS) switch (CD4016 or 66) and a shift register (74-594, 595) is all that's required for < $2. Certainly within the capability of most folks that can play around to get a "feel" for what's going on with the PPM

Best,

[mawyatt]

I found my mistake!   

The very first assumption I made, the one that a switch is the same as an analog multiplier is wrong.  They might be considered the same, but only for a pure rezistive load, and not when a capacitor or an inductor is present in the load.

For an analog multiplier, when an input is zero volts the output is also forced to zero volts, and that will forcefully start to discharge any energy stored in the load.  For a switch, when the switch is open the output is disconnected from the load, and any energy already present in the load stays there.  So, the voltage is undefined (in regards to the inputs) and depends of the load only when the switch is disconnected.  Here, in the case of a capacitor as a load, the output remains at the same voltage until the switch connects the Vin again.

The shunt resistor called Rb in the PPM is to "bleed" off charge from the capacitor between the switch phases. This causes a bi-directional charge flow from the antenna input that follows the signal which is responsible for creating the impedance effect as seen from the input. For example without Rb, if the RF signal were at the LO frequency then the charge distribution stored on each capacitor would be fixed and no significant change in charge would occur at the input during or between clock phases, thus the impedance "seen" would appear very high. Rb causes a charge change and the impedance "seen" as Vinput/dQ/dT, where dQ/dT is the charge change and Input is the RF input voltage.

Best,

[mawyatt]

Another point is IMO, it is not sufficient to consider a single path alone. The interaction of the paths matters. If this were not the case, there were no reason to use N paths instead of a single one. Cancellation of particular harmonics eventually happens at the summing node.

Another reason for using N paths is the impedance "seen" at the input would be highly discontinuous with just one path since the baseband would be disconnected half the time. With N paths greater than 1, then the baseband is always connected by one switch.

Of course the summing node just happens to be the antenna port

Best,

[gf]

Of course the summing node just happens to be the antenna port

One summing node is the antenna port of course, and the other one is obviously the "Harmonic Recombination" stage (from the 2nd attached PDF), where appropriate weighting of each path seems to be important for the harmonic suppression.

[R_G_B_]

Interesting discussion.

See this link this should help some better understand what's happening:
https://youtu.be/MP7m5OjXWUg

Thanks for the interesting post

[mawyatt]

You are welcome.

BTW great find, excellent discussion by Dr Nauta!!

He and a few others in Europe became involved after the initial discussions and papers at the ISSCC in ~2009.

Best,