An alternative to quartz filters.

[MikeP]

 In fact, the RC chain is not the only determining factor. By the way, here you can use various combinations of timing components.

  In general, there are several important documents on the first page in my message. There are examples of frequency response.

  You can also try a simulation. I can send you a model.

  In my opinion, a fast logic diagram is a more intriguing task.

[tggzzz]

~40 years ago we needed to pick out a low level signaling 10Hz tone at >>50MHz that could be located at many different frequencies, heterodyning to an IF and crystal filters were "thought" to be the only practical solutions back then. We came up with a new type solution based upon a "Commutating Filter" originally described back in the 1960s which utilized a car distributor as a commutating switch driven by a 60Hz synchronous motor at 3600rpm which also drove another car distributor in synch. Each of the 8 "spark plug" connections on each distributor was connected by a simple RC low pass filter, series R, shunt C, resulting in an extremely narrow band filter centered around the 60Hz motor speed. Vary the speed of the motor and the narrowband filter moved to the new speed!

Hah!

In 1979 I was making a fibre optic attenuation test set, and wanted a narrowband filter to reduce the noise and hence increase the range.

I don't know how, but I found an article about N-Path filters in the September 1960 issue of the BSTJ. I used it to create a filter with a Q of ~4000 at 4kHz using 10% components. The other engineers couldn't believe its performance

I found the best way of explaining it to them was to show the baseband RC filter was transposed to the "carrier" frequency. If the baseband response was 10dB down at 10Hz, then the response at  response at 4kHz+-10Hz was also 10dB down. That very sharp rolloff was the key feature in reducing the noise when compared with a traditional filter.

I always wanted to return to the concept, feeling there was more that could be done with it. I didn't have the opportunity during my career, so after I retired I started looking again - and found the Tayloe mixer. Bugger.

[tggzzz]

Edit: BTW the origins of this Commutating Filter date back into the 1960s, but I can't remember the reference. In the paper (probably IRE) the commutators were car distributors and a synchronous motor drove the commutators as the clock, in ~1980 we replaced the distributors with fast (then) NMOS devices and the motor with a low jitter high speed programmable clock generator.

Perhaps the BSTJ September 1960 (? Vol 39 Number 5 ?). It is a 30 page article, and at 5MB is too large to upload to this site. First two pages below.

[mawyatt]

That is likely the paper I vaguely remember, thanks for showing the first two pages.

These can produce amazingly high "Q"s for something without any high "Q" components!!

I remember a very special customer coming to us and asking if we could find 10Hz signaling tones on-the-fly buried within a frequency range from DC to Daylight to go along with the new type real time Spectrum Analyzer we were developing. Fun times back then 

Tayloe was on the right path with the Tayloe Detector which was used as a demodulator, but never explored the complete mixer with the various features the PPM or N-Path Mixer offers, including better than theoretical noise figure 

Hopefully some folks will play around with these ancient commutating filters and discuss the results.

Best,

[tggzzz]

That is likely the paper I vaguely remember, thanks for showing the first two pages.

I was surprised how quickly, goven the information I'd encoded in the filename, I was able to locate https://archive.org/details/bstj39-5-1321

These can produce amazingly high "Q"s for something without any high "Q" components!!

... and without any PLL or lock-in techniques which would have been problematic in my application.

Tayloe was on the right path with the Tayloe Detector which was used as a demodulator, but never explored the complete mixer with the various features the PPM or N-Path Mixer offers, including better than theoretical noise figure 

Hopefully some folks will play around with these ancient commutating filters and discuss the results.

I haven't assimilated the PPM techniques, yet.

[RoGeorge]

That's the same 1960 paper attached here by the OP, in the first page of this thread   
https://www.eevblog.com/forum/rf-microwave/an-alternative-to-quartz-filters/msg3380028/#msg3380028

[mawyatt]

I haven't assimilated the PPM techniques, yet.

I've started a separate PPM thread here.

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

Be careful this is a total deep dive into what is usually thought "you can't do that" territory, from NF, to TIO, to tracking impedance matching and so on. Prefect example of what Discrete Time Continuous Amplitude (DTCA) processing circuitry can achieve without DSP!! Reminiscent of our ~1980s Special Purpose Reconfigurable Real Time Spectrum Analyzer done with DTCA Chirp Z ++ methods that had folks saying "you can't do that" because two well known and respected corporate institutions had attempted and failed, and it took the equivalent of 1/3 Cray Supercomputer to keep up! The DSP folks were in awe that we pulled it off, and couldn't believe it only consumed ~4 watts and was a textbook size solution 

True be told, we had the DSP guru from modems back then that came over to the Dark Side of DTCA signal processing, and found the fatal flaw in what others had attempted! We also used RF subsampling (using aliasing to our advantage), reactive clocking (nearly lossless), current-mode amplification, custom CCD devices, custom CMOS and so on. Even had to design our own specialized test equipment like an RF AWG (and synchronized Spectrum Analyzer) that produced spectral outputs with specific "signature" characteristics rather than the in the usual time domain, even a custom Digital Scope that could observe & record multiple CCD channels simultaneously including the "Chirp" coefficients. More technology innovations in that project than I've ever encountered, fun times indeed

This began the whole concept of "you can't do that" systems and processing for us, because if everyone thinks this, including your adversaries, well then   

Best,

[mawyatt]

That's the same 1960 paper attached here by the OP, in the first page of this thread   
https://www.eevblog.com/forum/rf-microwave/an-alternative-to-quartz-filters/msg3380028/#msg3380028

How did I miss that reference, my bad 

Geeze getting old sucks, I can't even remember how old I've become

Anyway, thanks for this pointing this out and my apology to OP MikeP for not spotting this reference he found.

Best,

[RoGeorge]

To me the easiest way to understand all the ups and down at one look, was to think about it in frequency domain:

• I think of the switch like it's a normal analog multiplier, just that the local oscillator here is made of rectangular pulses instead of a single sinusoidal signal.
• a rectangular signal (here the LO) is nothing but a bunch of synchronous sinusoidal signals (if we think at the spectrum of the rectangular signal)
• therefore, assuming linearity and time invariance of the circuit, it's like mixing the input signal with more than one LO frequency at once

At this point it's clear that we will have to deal with a lot of harmonics and spectrum foldings.

Keeping the same idea of filtering at low frequency, I think the same performance should be possible with only one path and one filter, by just downconverting, filtering, then upconverting again, except we can do that with two normal analog multipliers and a sinusoidal LO.

That way all the very nasty harmonics and spectrum foldings can be avoided from the start.

Which one to prefer, analogous or switched multipliers, it all depends of the available technology and the final application.

LATER EDIT:
Sorry for the previous message.

Now it looks like that was meant to only say about that attachment.  I hit enter to soon.  By the time I was pressing send with this whole reply, there were already two more answers so I moved the rest of it here, and then read the answers and, yeah, my bad, I apologize, sorry, didn't meant that.      

Will continue with the questions in the dedicated thread, thank you for opening one.

[mawyatt]

Keeping the same idea of filtering at low frequency, I think the same performance should be possible with only one path and one filter, by just downconverting, filtering, then upconverting again, except we can do that with two normal analog multipliers and a sinusoidal LO.

Quickly thinking about this, upon downconversion with just one conventional mixer and LO, the USB and LSB land on top each other at baseband. You need two LOs & two mixers as well as two baseband filters ( I and Q) since you want to create a bandpass at the output LO frequency. One Sine and one Cosine mixer, LO and two identical baseband filters. Think this is correct?

Best,

[ejeffrey]

That is likely the paper I vaguely remember, thanks for showing the first two pages.

These can produce amazingly high "Q"s for something without any high "Q" components!!

Well of course they have one "high Q component", the oscillator driving the commutation.  Which is presumably the other reason (other than raw speed) for using ECL -- its exceptionally low jitter.  Clock jitter will cause spurious response just like clock jitter in a DAC or LO phase noise in a mixer.  Luckily high Q oscillators and low jitter ECL logic are quite available while high Q inductors are not so much.

[ejeffrey]

I was late for an interesting conversation.

 16 bit ADCs were mentioned above due to the need to have a range of 80 dB. In reality, this will not happen even with 16 bits. The sampling rate for 10 MHz cannot be 25MS or even 65MS. The filter we are talking about will sample at a frequency of up to 100 MHz. And this is not enough.

No, this isn't correct.  14 bit ADC is needed to get 80 dB SNR over the full bandwidth, but you get to include the processing gain for your filter, which is like 40 dB for a 3 kHz filter with a 20 MHz nyquist zone.  In principle -- just based on quantization noise -- you could get by with a 7 bit ADC or something silly like that and still have 80 dB dynamic range in each 3 kHz channel.  In reality this won't work as the linearity of a 7 bit ADC will likely be rather poor and would cause distortion spurs that could degrade your SNR, so you want an ADC with an SFDR of 80 dB at 10 MHz.  I quickly browsed through some ADCs from TI and analog devices and it seems that most 10 bit ADCs can't quite meet this but there are plenty of 12 bit / 40 or 65 MHz ADCs that would appear to fit the bill here.

  It's hard for me to explain this, and I'm probably grossly mistaken, but with heterodyning we introduce a number of undesirable factors. As a result, it will be even more difficult to select the desired bands. Correct me please. Finally, the bands are not 2000, there are less than ten. Among other things, the phase that can be lost is important here. Unfortunately, this moment is still not very clear to me.

Heterodyning does have some challenges as mixers generate all sorts of harmonic and mixing products you don't want and you have to do careful frequency planning and analog filtering to keep them out of your signal.  That appears to be part of what the polyphase mixer solves as discussed by the posts above.  You also *can* loose the phase although that is not required.

Anyway, 10 channels is not too much and a polyphase filter does sound like it can be done reasonably effectively, but I don't think DSP is to outrageously expensive if done properly, especially since I guess it sounds like you want the analog signals at the end, so for DSP you would need a bank of moderate speed DACs to reproduce the output waveform.

That said, there is still one area of concern that gf brought up: do you actually need to have a -3 dB BW of 3 kHz and an -80 dB bandwidth of 7.5 kHz?  That is pretty incredible.  The simple way to implement a polyphase / N path filter will give you high Q (ratio of center frequency to 3 dB bandwidth) but will not give you such a high order filter.  I suspect implementing a 10th order polyphase filter with good performance is not going to be trivial.

[MikeP]

 

No, this isn't correct...

  Thanks for your thoughts. When I talked about 16 bits, 80 dB was the result of ENOB. I firmly believe in the impossibility of 100% for this parameter.
  Please do not take my words as an axiom or statement. Unfortunately my qualifications are nil in the context of this conversation. Therefore, I ask for leniency.
  I also ask you to assume: what is the delay time of the digital filter we get after the signal heterodyning? To any frequency convenient for you.

  Regarding the required characteristics. It may not be achieved. But this characteristic is really inherent in quartz filters. Nevertheless, the experiment must be carried out.

[gf]

I also ask you to assume: what is the delay time of the digital filter we get after the signal heterodyning? To any frequency convenient for you.

Heterodyning is just a multiplication, so its delay is rather negligible.

An analog 10th order Butterworth lowpass with 1.5kHz cut-off (corresponding to a 3kHz BW bandpass) has about 0.7-1.3ms group delay, in the 150Hz...1.5kHz range (i.e. for the baseband signal which is modulated onto the carrier of your band). See Figure 8.15 in https://www.analog.com/media/en/training-seminars/design-handbooks/Basic-Linear-Design/Chapter8.pdf. The diagrams are normalized to 1Hz cut-off. An analog Butterworth is a minimum phase filter, AFAIK.

In the digital domain you can design a filter having almost the same impulse response as this analog filter.
There will be some extra delays in the DSP chain, but IMO the filter itself still dominates the overall group delay.

Regarding the required characteristics. It may not be achieved.

Why not? It is a matter of the design, though. A high-order filter is a must, in order that you can achieve it.
You can never ever achieve it with a first order filter, though, regardless how hard you try.

But this characteristic is really inherent in quartz filters.

IMO nobody here denied that quartz filters can achieve that. But again, then they need to have a sufficient number of poles, so I assume that your filters contain rather a handfull of crystals each, and not just a single one?

Btw, Google found these quartz filters (up to 16 poles). Yet another proof that they are obviously feasible and do exist. I've no idea what's their price, and even less idea what they would cost when tailored for custom frequencies/bandwidths. What do your filters cost? What is actually the price per filter you need to beat with an alternative solution? Is it worth the efforts?

Is the output stringently analog, and still modulated? What happen actually with the signal after the filter? For instance, a subsequent demodulator could possibly be directly integrated into a DSP chain.

[ejeffrey]

 

No, this isn't correct...

  Thanks for your thoughts. When I talked about 16 bits, 80 dB was the result of ENOB. I firmly believe in the impossibility of 100% for this parameter.
  Please do not take my words as an axiom or statement. Unfortunately my qualifications are nil in the context of this conversation. Therefore, I ask for
leniency.

I'm not sure I understand.  You don't believe a 16 bit ADC is practical for your system?  You don't think you can get away with less and preserve your dynamic range?  You don't think you can meet 80 dB dynamic range? 
 
Anyway I can give a brief rundown of how to think about SNR in a quantized system.  The RMS quantization noise of an ideal digitizer is LSB/sqrt(12).  If you take that as your noise and assume a full-scale sinusoidal signal you can calculate the SNR and you get the standard formula: SNR =  6.02*bits + 1.76 dB.  Real ADCs have more noise so we flip this around use the actual SNR to calculate an "effective" number of bits: ENOB.

But the quantization noise is (under certain assumptions) uncorrelated white noise.  The noise spectral density is just the mean-squared noise (LSB^2/12) divided by the nyquist bandwidth.  When you apply a narrow-band digital filter to the data stream you ideally keep 100% of your signal but remove all of the noise outside your filter band.  This improves your signal to noise dramatically.  This is how you can get very good dynamic range with a DAC that only has 10 or 12 bits.

Really this isn't that surprising.  A narrow filter is averaging thousands of points to produce an output -- averaging is good at reducing noise, that's why we do it.

One thing you do need to account for is extra channels.  If you have multiple channels they each can't have a full-scale sine wave simultaneously or you will get clipping. A proper analysis has to take this into account based on your signal.

  I also ask you to assume: what is the delay time of the digital filter we get after the signal heterodyning? To any frequency convenient for you.

Basically the group delay of your requested filter function is so great that nothing else you are going to do will make a meaningful difference.  Mixers have negligible delay.  DSP has some delay: ADCs and DACs have latency, and DSP pipelines may have some excess delay, but for a system operating at 50 MHz, that won't be more than a few microseconds.  The transfer function itself is going to require hundreds of microseconds or over a millisecond of delay to implement.  Other analog filters in the system such as image reject filter or anti-aliasing filters also have some delay but they are going to be small compared to a 3 kHz 8th order filter or whatever you end up needing.

Note that you can use mixing either in conjunction with DSP or just with analog filters.

[gf]

Basically the group delay of your requested filter function is so great that nothing else you are going to do will make a meaningful difference.

Indeed. And this applies to a corresponding anlog filter as well. When the quartz filters do have the specified frequency response, then they are supposed to have a similar amount of group delay either. A minimum phase filter for a given amplitude response has the shortest achievable group delay. It is not possible to achieve shorter group delays without renouncing some characteristics of the amplitude response.

[ For some use cases phase distortion matters, though, so that a linear phase response (i.e. a constant delay - at least for a particular frequency range) may more important than minimizing group delay at each frequency. ]

Note that you can use mixing either in conjunction with DSP or just with analog filters.

And a special case of "in conjunction with DSP", which is IMO worth to be mentioned explicitly, is digital down conversion, where even the LO and the mixer run digitally in the DSP, eliminating the need for an LO and analog mixer for each channel, and avoiding flaws of analog mixers, like LO harmonics, non-linearities, I/Q imbalance. Unlike in the analog domain, the digital LO sinewave and the mixer multiplication can be calculated by the DSP up to the desired numerical precision. The input signal needs to be digitized only once in this case, at a fixed sampling rate, i.e. N filter channels can share a single ADC, and only a single clock generator is required.

[radiolistener]

The RMS quantization noise of an ideal digitizer is LSB/sqrt(12).  If you take that as your noise and assume a full-scale sinusoidal signal you can calculate the SNR and you get the standard formula: SNR =  6.02*bits + 4.77 dB.

why 4.77?

SNR = 20*log(2^N) + 20*log(sqrt(3/2)) = 6.02 * N + 1.76 dB isn't it? 

[mawyatt]

The RMS quantization noise of an ideal digitizer is LSB/sqrt(12).  If you take that as your noise and assume a full-scale sinusoidal signal you can calculate the SNR and you get the standard formula: SNR =  6.02*bits + 4.77 dB.

why 4.77?

SNR = 20*log(2^N) + 20*log(sqrt(3/2)) = 6.02 * N + 1.76 dB isn't it? 

Yes, that's the standard definition, ENOB is then (SNR -1.76)/6.02 or more precisely ENOB = (SINAD-1.76)/6.02 including ADC distortion.

Have no idea where ejeffrey came up with SNR =  6.02*bits + 4.77 dB 

Best and Happy Holidays,

[ejeffrey]

Fixed.  Forgot to actually include the full scale signal amplitude.

[MikeP]

 Friends, thanks for the analysis and answers to my questions. This information is not obvious to me. And I missed the relationship between filtering and noise.

 With Mike's help and the documents provided, I'm almost ready to start experimenting. Indeed, a switch filter is not a trivial task. Hopefully CMOS will provide the required jitter and phase purity.

 I do not know the cost of a quartz filter; there is a question about providing such characteristics.

 I ask for clarification. If 10-12 bits are enough for analysis, then there is no need for preliminary heterodyning?

[radiolistener]

I ask for clarification. If 10-12 bits are enough for analysis, then there is no need for preliminary heterodyning?

it depends on different factors.
10 bit ADC provide you with about 60 dB SNR.
12 bit ADC provide you with about 69 dB SNR.
14 bit ADC provide you with about 75 dB SNR.
16 bit ADC provide you with about 80 dB SNR.

As previously said, you can improve noise floor with processing gain by using filter.
How you can use it depends on your needs and signal source properties.

Usually 12 bit ADC is good enough for usual radio receiver performance.
Anyway performance is limited with phase noise of cheap TCXO.

But if you want to achieve professional grade receiver performance, you're needs to use 16 bit ADC with a low phase noise VCXO oscillator.

[gf]

I ask for clarification. If 10-12 bits are enough for analysis, then there is no need for preliminary heterodyning?

The reason for considering heterodyning an option is, that down-mixing prior to the DSP chain (and up-mixing again after the DSP chain) enables the DSP chain to operate at a lower sampling rate. Without heterodyning, the lowest possible sampling rate is dicated by the highest frequency in your input signal (which is 10MHz).

A FIR bandpass with the required characteristics would need to have 100000+ taps when running at (say) 25MSa/s. That's not feasible. A corresponding IIR filter, decomposed into 10 biquad stages still requires 40 multiplications and 40 additions per sample (not counting multiplications by 1), which implies 1,000,000,000 multiplications and 1,000,000,000 additions per second (when running at 25MSa/s).

At lower sampling rates, a FIR filter could have a lower number of taps, and the number of multiplications and additions per second for an IIR filter were proportionally lower as well. Numerical precision of the IIR filter can be lower, too, then.

Anyway, I'm not a FPGA expert, but I think it is not really a problem to realize 10 pipelined biquad IIR stages running @25MSa/s on a FPGA. So IMO heterodyning can still be renounced here. The required fixed point precision needs to be determined (with single precision float it appears to be stable when I applied such a filter in Octave).

[SilverSolder]

[...]
16 bit ADC provide you with about 80 dB SNR.
[...]

How is that derived, just out of interest?   16 bits is theoretically 96dB dynamic range, right?

[radiolistener]

How is that derived, just out of interest?

from datasheets 

16 bits is theoretically 96dB dynamic range, right?

this is for ideal ADC, but real world ADC has worse dynamic range. Especially 16 bit high speed one.
80 dB is the best result for 16 bit ADC.

[MikeP]

 Once I was a little involved in the analysis of information from acceleration sensors. The system used the AD8552 and AD7767 - 24 bit ADCs. The least significant eight bits were ALWAYS noise without a signal source. That is, I have a slightly biased attitude.

  I understand that 10-12-14 bits are applicable. But only with averaging and filtering. These operations require time and computational resources. What I do not understand - what is happening with the noise in the target band?

 Unfortunately, there is nothing in my country for a REAL switch-filter experiment. The corresponding order will be made later. Now I will do a crude experiment with a 74HC4017 counter and 2N7002 transistors. I think we'll get a general idea soon.