Actual gain of a Tayloe mixer

[tortelsk]

Hi,

I recently started a hobby project about receiving DCF77 signals and demodulating the AM and PM bits from scratch at a minimal budget. One of the promising candidates would be using a Tayloe mixer to convert the signal down to audio frequencies as they are only 1Hz and approx. 645Hz for AM and PM, respectively. However, when simulating its behavior on LTSPICE or TINA TI I got very confusing results: the audio frequencies look just fine, but the amplitudes don't fit the calculation. I spent some time adapting the design based on multiple sources but they all behave similarly.

According to "Software-Defined Radio for the Masses", when the source resistance is 50 ohm, the default gain shown in Fig. 12 is the inverting feedback resistor divided by 4*5=200 ohm, meaning that if the feedback resistor is 200 ohm, it is of unity gain. My simulation results do show very close results. But I also noticed some other designs conducting a 100-ohm resistor on each sampling path, and this time the simulated gain doesn't follow the equation anymore (I assume the gain is now calculated as the feedback resistor divided by the sum of 200-ohm antenna equivalent impedance plus 100-ohm).

The figure below shows a 77.5KHz sine signal source with an amplitude of 10mV and an initial phase of 45 degrees, SWs are time-controlled switches with 3-ohm ON resistance. The gain shown is larger than 1, and the values of R6-R9 seem to affect the gain a lot (I got an even much higher gain when using 200-ohm resistors).

My questions are:
What is the purpose of using these resistors R6-R9 compared to the original design from Tayloe's paper and "Software-Defined Radio for the Masses"?
How to calculate the gain as a function of these resistors?

Cheers/

[mawyatt]

R6 and R7 aren't doing anything because there's no shunt element shown. Think you need to add the shunt element equivalent of the feedback resistor and capacitor to R6 and R7.

There's some discussion about the PolyPhase or N-Path Mixer that you might find useful, these mixer provide direct down conversion to I and Q at baseband, and have lots of interesting features.

https://www.eevblog.com/forum/rf-microwave/polyphase-or-n-path-mixer/

Best

[mark03]

Have you considered direct sampling at 1 MHz or so (depending on filtering and the capabilities of your ADC)?  At these frequencies it should be possible to downconvert, filter, and decimate in real-time software.

If you get this working, I'd love to see your front end design (everything before the ADC).  I have a similar project for WWVB on the back burner because I can't get that part to work.  I have 40-conductor ribbon cable in a ~ 2m diameter loop (tuned with parallel capacitance) feeding an instrumentation amplifier, but despite lots of troubleshooting I still can't see WWVB on the scope   After all the time I've put into the analog bits, I expect the DSP to be the easy part!  As usual 

[tortelsk]

Thanks for the quick response. I checked the link but not sure how it could help solve my naive question. And yes I also think there should be some sort of shunt equivalent after these resistors but they are just missing in many existing designs, say QRPLabs QCX, USDR, PICO RX, etc. I have attached some screens below, you can even see some capacitors C14-15 in PICO RX blocking the bias to the op-amp.

After doing some math I found the output voltage seems to be V_out = Vin(+) + R_feedback / (R_source*4 + R_path) * (Vin(+) -  Vin(-)), meaning that Vin(+) and Vin(-) contribute differently to the output, and the R_path somehow helps reduce the output ripple (see the last two screens). I guess this is the reason why the above designs all set the gain to be relatively high so that the second term will dominate the output?

"Software-Defined Radio for the Masses" mentions using instrumentation amplifiers so the gain won't be affected by the mixer's impedance, I will also test it but the costs are likely much higher.

Cheers/

[jwet]

This is a link to a student's MS thesis that does a pretty good job of analysing a tayloe mixer.  Its pretty interesting.  It also has a narrow bandwidth.

https://essay.utwente.nl/58276/1/scriptie_Soer.pdf

[tortelsk]

Hi there. Yes, I did consider direct sampling in the first place. However, I found it challenging to set the sampling rate to 150K (I plan to use a cheap PI PICO 2 with most of the coding being Python) and make a good LW band-pass filter. Currently, I made a simple LNA of about 40dB but since the Tayloe mixer has two audio amplifiers too and the gain seems to be at least 20dB from the equation derived above, I think I will either replace the LNA with a simple JFET + BJT follower or reduce the gain to <20dB. BTW I am using a simple ferrite rod antenna so everything has to be low noise (sadly ).

[mawyatt]

This is a link to a student's MS thesis that does a pretty good job of analysing a tayloe mixer.  Its pretty interesting.  It also has a narrow bandwidth.

https://essay.utwente.nl/58276/1/scriptie_Soer.pdf

That's a good find. Believe the author went on to get his PhD and with Professors Nauta and Kumpernik got involved with the N-Path or PolyPhase Mixer (PPM) later after the 1st public papers presented by Cornell's Andrews and Molar at the ISSCC mentioned here again.

https://www.eevblog.com/forum/rf-microwave/polyphase-or-n-path-mixer/

The Tayloe Detector and 4 phase version of the PPM are similar in appearance, however the Tayloe doesn't create/address the bidirectional nature of the PPM which allows impedance matching at the input port that tracks the LO, or the sub 4dB Noise figures achieved for example. Nor does it address the higher order effects/advantages of having more clock phases (8 being a sweet spot).

Best

[RoGeorge]

But I also noticed some other designs conducting a 100-ohm resistor on each sampling path

Have you seen this paper by Tayloe?
http://norcalqrp.org/files/Tayloe_mixer_x3a.pdf

I think the fig.3 has a typo, because the author says those opamps are differential summers, yet they are missing a resistor from in+ to GND.  However, in the later schematics, the missing resistor on the in+ of the opamp appears correctly (as a 22k tied to Vcc, it's AC coupled so either to Vcc or to GND, the differential summing for AC remains the same).

Then, later the differential summing opamps are simplified further, by eliminating the resistors (and their implicit thermal noise).  So, the version without series resistors should have less noise according to the Tayloe paper.

Note that a Tayloe mixer can be seen as a particular case of the generic N-path filter.

One of the advantages of N-path filters is that they act as a steep bandpass, AND they can be put right after the antenna.  So, you'll have a narrow filter (narrow band means less noise) right after antenna, and a mixer all in one.  The best theory + demo I could find about N-path filter are these 2 videos:

N-path filters explained
icdutwentenl


N path filters: basics & demo
icdutwentenl


Highly recommended videos if you are curious how, or why the N-path filter (or the Tayloe) works at all.

Another thing, if you have the LTspice version of the schematic (I don't have TINA-TI), please attach the LTspice schematic here (the .asc file from LTspice).  I suspect the switches might not go in the right order.

[mawyatt]

An often overlooked feature of the Commutating or N-Path Filter besides the remarkable "Q" one can achieve with simple "jelly bean" passive components, is the ability to tune the center frequency with an accuracy dictated by the clock accuracy. Creating a highly variable clock over many decades of frequency is trivial with the cheap clock generation chips available, and the clock frequency accuracy is dictated by the supporting quartz crystal with its' inherent precision/stability.

The N-Path (PPM) Mixer utilized this powerful feature to its' fullest by effectively creating a narrowband "preselector" input filter that tracked the Mixer LO without need for conventional tunable elements.

The N-Path Filter/Mixer or if one prefers Commutating Filters/PPM, are such interesting circuit technologies employing Discrete Time Continuous Amplitude (DTCA) signal processing, we're surprised that others haven't been involved. We started this journey back in ~1980 with a Chirp-Z-Transform based handheld RTSA based upon custom CCD chips that operated in the DTCA Domain.

DTCA is indeed a highly useful Domain, wish others would discover and delve into this more

Best

[tggzzz]

DTCA is indeed a highly useful Domain, wish others would discover and delve into this more

Just so.

While a DCTA circuit might be sufficient on its own, there's nothing preventing a DCTA+DSP implementation. But a pure DSP guy is less likely to realise that; if you know how to wield a hammer, everything looks like a nail.

[tortelsk]

Thanks for the videos, yes I understand how the first part of the Tayloe mixer works, but I'm trying to understand the behavior of the second part (detector output to op-amp), say, the formula of gain. Although in Tayloe's paper, the resistors in the filtered path are removed, several existing SDRs still have them for unknown reasons. I use the attached file for LTSPICE simulation, the input signal has an amplitude of 1mV but somehow the detector output is 40mV for in-phase, where I expected to see an identity gain based on the formula.

The master thesis from jwet's post says no closing form for the Tayloe mixer's response in the time domain as it is related to the sampling cap's voltage from the t(n-1) stage, I am not sure if this is the answer to my simulated results but I still doubt that something is missing in analyzing the op-amps.

[iMo]

Do not forget the "Softrock" series of pretty successful sdr radios (the kits) from around 2005-7.
The mixers and opamps are wired differently, the amplification is typically around 500 (like 10ohm and 5k in the feedback of the opamp).
They worked well, I built several various versions from those kits, the receive params comparable with big ham radios at 80/40/20m bands.

http://www.wb5rvz.com/sdr/New_SR_Lite/
http://www.wb5rvz.com/sdr/RX_V9_0/

[RoGeorge]

I still doubt that something is missing in analyzing the op-amps.

Tayloe has 4 switches, so a full period is split in 4 time segments, one for each capacitor.  Now, if we align the phase of Vin just right around the max peak,



such that one capacitor will charge during the 1/4 period of the topmost peak of the Vin (sinusoidal signal), that capacitor will charge (over many, many periods) almost as high as the Vin peak, more precise, to the integral of voltage between V at the moment Tpeak minus 1/8 of a period, and Tpeak plus 1/8 of a period. (1.41*Vpeak/(pi/2))= about 0.9*Vpeak

Same for the 180 degree capacitor, but with minus.  The opamp is supposed to do the difference between the two capacitors' voltage, so at most the gain will be almost 2, but in fact it will be less than 2.  That is in theory, and neglecting the opamps input impedances.

In practice, one can make the differential opamps to sum with a gain, or without, as in the second formula from https://www.analog.com/en/resources/analog-dialogue/articles/deeper-look-into-difference-amplifiers.html

Now, looking at the values from the LTspice schematic, 200 ohms seems too low (because that value will shunt the sampling capacitor).  I might be wrong (it's early AM hours) will take a closer look tomorrow.

[tortelsk]

I think I solved it! From https://files.tapr.org/meetings/DCC_2020/2020DCC_KL7NA.pdf, I realized that the op-amp configuration imposes different gains on the inverting and non-inverting paths. The input impedances of the two paths also differ, so the sampling capacitors will not function similarly. This results in the gain not following the math. By replacing the op-amp with the instrumentation amp, the gain can be correctly set and the sampling caps are no longer affected by the following amplifiers.

Upon closer simulation, I also realized that the differential output could be sqrt(2)*Vpp, but a biased ins amp will map this output to V_ref + gain*sqrt(2)*Vpp, so the output dynamic will be only a quarter of the full Vcc. I'm thinking of just keeping the non-unity gain buffers while removing the differential stage from the ins amp, this gives me two symmetric paths for I or Q. The new simulation is well-aligned with my calculation, so the dynamic range won't be compressed and all I need to do is sample these two signals sequentially and do the math in the software. As the output BW is only <1KHz this should be fairly easy to achieve. What do you think?

[jwet]

These videos and references that you all have provided are just great!  I told Mike Wyatt that I studied some of this while I was at Maxim- kind of semi sponsored research the CTO of my company instituted- I was on his staff as apps expert but the program was mostly for designers that felt that were just grinding out designs and couldn't stop and smell the roses.  I've since retired but I thought this was a neat program.  It was called "IQ" = "innovation quest" and they were 40 to 400 hours at the CTO's disgression.  Some cool work came out of them and they improved morale.  That paper that I provided was something I dug up in my lit search way back when.

My proposal was to study the effect of good CMOS switches in these applications.  I did a lot of work on our analog switch line mainly because I couldn't find Apps Engineers to work on them.  I love switch apps and these sort of synchronous detectors,  correlated samplers and mixers- its all really fascinating.  Its hard slogging going through the math in the academic papers but some of what you've posted here is very approachable.  My Maxim research showed moderate improvements especially in some balance type effects since they have symmetrical conductance versus N only switches.  The gains were interesting but not enough to make up for the loss in area of PMOS, etc (as MW attested from his experience). 

This discussion has me fired up again- I think I'll reproduce the circuit in Nauta's video.  I'd like to see the effect of inverting polarity etc in the second bank, etc.  Just FYI, Maxim (now ADI) make a pin compatible 4052 type switch with really premium specs - Ron <= 18 ohms and good flatness.  Maxim is still the king of samples if you need some.  There are lots of good switches out there.

Have fun and thanks for the interesting thread.

[RoGeorge]

This discussion has me fired up again- I think I'll reproduce the circuit in Nauta's video.  I'd like to see the effect of inverting polarity etc in the second bank, etc.

Funny thing, got the exact same feeling after rewatching those 2 videos.  In fact, I still have some untested ideas to try from a couple of years ago, when mawyatt brought the n-path filters to attention (at least for me, he was the initiator, thank you Mr. mawyatt for the very interesting topic).

Same feeling as you about the synchronous detection/n-path filters/lock-in amplifier/SDR/etc.  These topics are so entangled that they almost overlap.  And yes, I am sooo tempted to solder an n-path filter right now. 

I think I solved it! From https://files.tapr.org/meetings/DCC_2020/2020DCC_KL7NA.pdf

To be honest, spent all day with preparations for the tomorrow's new year, I didn't read that pdf.  At a first look, the result you found seems different than what I thought it should be yesterday night (didn't have the time to double check that one either), but since I don't know the exact context of that pdf, and as long as it clarified your question, then that's great.

[tortelsk]

I will probably build a prototype soon and keep things updated in this thread. Happy New Year!

[RoGeorge]

There's no bigger fun, and no bigger learning than when building something.  Don't hesitate to do that.

Good luck with it, and happy new year to everybody!  🥳

[tggzzz]

And yes, I am sooo tempted to solder an n-path filter right now. 

If you have the components, it should take about an hour using manhattan techniques. And then a very long time to understand all the theory, variants, and practice.

In other words: it is a good topic

There's no bigger fun, and no bigger learning than when building something.  Don't hesitate to do that.

Oooh, there is - at least for me. Learning and understanding the theory plus seeing it realised in practice.

[Kleinstein]

The DCF77 and similar signals are often quite weak. So one would still want amplification and some LC filtering (e.g. a resonant antenna and possibly one more LC filter stage) before the mixer. Similar it may be a good idea to have some filter and amplifier between the mixer and ADCs. This is espcially the case with a relatively low resolution ADC (e.g. µC internal 12 bit). One may get away without when using a high resolution ADC (e.g. 16 bit audio card).
As the signal strength can vary quite a bit depending on the position of the antenna one may also want to have a way to adjust the gain.

[mawyatt]

Funny thing, got the exact same feeling after rewatching those 2 videos.  In fact, I still have some untested ideas to try from a couple of years ago, when mawyatt brought the n-path filters to attention (at least for me, he was the initiator, thank you Mr. mawyatt for the very interesting topic).

You are quite welcome, hope others would find this DTCA N-Path/PP/Mixer/Filter interesting 

We certainly did way back starting in ~1980 with CZT RTSA and Commutating Filter (another name for N-Path), then in ~2000 with PolyPhase Mixer (N-Path Mixer).

Fun stuff indeed 

Happy New Year ,

Best

[coppice]

DTCA is indeed a highly useful Domain, wish others would discover and delve into this more

Just so.

While a DCTA circuit might be sufficient on its own, there's nothing preventing a DCTA+DSP implementation. But a pure DSP guy Matlab monkey is less likely to realise that; if you know how to wield a hammer, everything looks like a nail.

There. Fixed that for you.

[mawyatt]

WRT to general Signal Processing and System Design. The best case one can achieve the important parameters of SNR, Interference Rejection and DR is by placing the BW defining Filter right at the input before anything.

Early on we starting doing this even at low frequencies (under 1Hz while trying to detect certain nanovolt level signals in the presence of enormous interference), while the RF community has done this forever by utilizing "preselector filters" before the LNA and Mixer.

In our case of the low frequency, we shoved an integrator right up to the input, so the 1st low-noise amplifier became a signal integrator, after some gain to isolate the later amplifiers/filters noise, we did the frequency band selectivity with integration compensation. This worked beautifully and was the signal processing chain for the Miles Signal Processor (MSP) based upon Magnetostriction Cable Intrusion Detection back in 70s.

The PPM or N-Path Mixer performs a similar function that shoves the baseband integrating LPF right up to the antenna port by means of the unique bilateral transfer characteristics of the PPM. Very powerful technique that creates a large impedance mismatch as "seen" from the antenna port by the shunt capacitive baseband integrating LPF. Out-of-Band signals get reflected at the antenna port before entering the signal processing stage, while In-Band signals "see" a good impedance match at the antenna and are absorbed and passed along for post signal processing. This effect tracks the LO and because of the unique low noise characteristic (better than theoretical Bi-Phase Mixer NF) there's no need for an LNA, while simultaneously imposing harmonic rejection techniques to it's fullest!!

Just a few features of this unique Mixer that is deceptively simple in appearance but quite complex in behavior and why once becoming public became an intellectual whirlwind throughout academia and the advanced research community.

We can't stress enough for interested folks to study the various IEEE papers mentioned staring with the 1st public releases from Cornell. 

Happy New Year,

Best

[jwet]

The Softrock receiver was mentioned, I built many variations with DSP back ends  to make HF receivers.  They work well but have one funny habit explained by some of this discussion.  When you're looking at a waterfall type display for tuning, the high Q of the front end makes the signal peak go away as you get closer to it.  On a spectrum analyzer display, you don't have this- it is flat as you move a marker on a peak.  I guess you could setup the Tayloe so it had low Q but the standard circuits and a lot of benefit come from this Q.  Is this effect my imagination or real?

[mawyatt]

If I understand the question (don't know anything about the Softrock Rx), this seems to indicate that the signal amplitude peak drops as it approaches tuned frequency of the high Q receiver? If this is the proper understanding, the input signal "sees" a poor impedance match which gradually get better as the Rx tuned frequency is approached. The input signal is reflected until approaching the Rx frequency, then becomes gradually absorbed by the Rx input match showing a dip in magnitude as the signal gets closer to the tuned Rx as "Seen Looking Towards the Rx Front End from the Outside", or as "Seen from Looking Towards the Antenna Port".

Of course if one looks towards the Antenna Port from "Inside the Rx", or how the Rx responds, as the typical case, then the result is the usual narrow band high Q response.

Not sure if this is what is being asked, but an attempt to answer such!!

Happy New Year,

Best

[jwet]

Thanks Mike- yes I believe that's my observation and its explained by the selectivity.

I noted that the Tiny SA doesn't do this.  It has a pair of Gilbert Cell type mixers (SA612 type) up front driven by a quadrature LO and so you don't have selectivity.  If you see a signal on a spectrum plot and move your quadrature LO over to center it, it doesn't change.  I might have to make a short video of how a Tayloe type front end works on a waterfall display- its very confusing.  I think another artifiact of this is that the harmonic sensitivity gives you a lot of artifical signal on the spectrum.  Most superhets have some birdies but these artifacts are really odd.

The fact that the Tayloe also has this selectivity quality makes it useful in a receiver but less so in SA type app.

[mawyatt]

....I think another artifiact of this is that the harmonic sensitivity gives you a lot of artifical signal on the spectrum.  Most superhets have some birdies but these artifacts are really odd....

WRT the harmonic response, not sure about the Tayloe Detector, however the 8 phase PPM has a harmonic response that employs harmonic rejection mixer concepts which pushes the harmonic responses above the center frequency out to believe the 7th or 9th harmonic. We've mentioned this somewhere discussing the PPM, and it's also discussed in the Cornell IEEE papers.

This is another remarkable feature of the PPM that's not usually observed/appreciated but one quickly becomes aware when building actual sensitive Rxs based upon the PPM where conventional mixers have multiple low order harmonic responses that must be dealt with by means of some form of preselect filtering.

An important observation with the Tayloe Detector as shown earlier and here:

https://www.norcalqrp.org/files/Tayloe_mixer_x3a.pdf

Is the discontinuous nature of the input dynamic impedance as "seen" from outside the input looking in. This is caused by the non-symmetrical switching load impedance at the switching outputs which gets "reflected" to the input by means of the bilateral transform of the switching process. This creates large switching artifacts as well as harmonic responses at the input which causes issue if not filtered before hand. Thus the Tayloe Detector requires preselect filtering of some sort as shown in Dan Tayloe's reference and related schematics.

Way back in 2000s this was addressed with the PPM, as one application was for EW use and LO radiation from the antenna port was a major concern as any type of LO radiation or dynamic impedance effects are discoverable. Since the PPM has a completely balanced input from LO phase to phase, dynamic impedance effects are minimized as are harmonic responses. Later in one of the Cornell IEEE papers discussed a means to reduce the effective LO radiation of the PPM to acceptable levels (vaguely recall less than -90dBm as seen directly from the antenna port without any filtering). 

Best

[mark03]

I've been following this conversation with interest.  I remember skimming some of the papers the last time PPM mixers came up in a forum thread, and I sense I need to go back now and re-read them!

One thing I have wondered, is how many of the benefits mentioned here are achievable using the readily available analog switches / bus switches which are the standard thing for amateur Tayloe designs.  The academic papers, obviously, are written by folks doing their own advanced CMOS designs.  Can the amateur throw together an 8-phase PPM from off-the-shelf parts and still do clever things like integrated antenna impedance matching?  Or do you really need to design at the transistor level for that?

[mawyatt]

You can certainly do a lot of things with off-the-self components. The only limitation is the upper frequency limit since a sweet spot for the PPM is with 8 clock phases, so the logic generating the 8 phases becomes the limiting factor.

You are bound to have loads of fun with the PPM

Best