The 'Nauta' circuit

[RoGeorge]

Please excuse the surrounding tale in the video, it was not in particular about the circuit I want to ask, it was about its author.

The circuit description starts at minute 3:20, and the working of the circuit is detailed at minute 6:00, but I didn't understand how it works.  It's made out of CMOS digital gates, but the circuit is exploiting the analog (linear) behavior, and it is used in RF, so I'm posting in this forum section.  (also, he's the same guy that is very nicely explaining the N-path filters in one of his videos on the same channel)



What I don't get is what "A circuit without internal nodes, so theoretically infinitely fast..." means in this context.  Later at minute 6:45 he's saying "and every part is connected to either input or output... so there is no parasitic capacitance and no bandwidth limitation", but I don't see how the internal parasitic capacitance will vanish in this situation.

- What is the relation between the bandwidth of a circuit and the "no internal nodes", at what theoryetical part is he hinting with that remark?
- Why does the circuit has to have two short-circuited gates?
- What filter is he talking about at minute 7:00, when saying the parasitic output capacitance is "useful and needed for my filter" (though the parasitic capacitance at input will still reduce the bandwidth)?
- Any clues how this circuit works, or what am I missing here?   

[RoGeorge]

My questions are about the circuit in this pic, which I assumed is what is called "Nauta Circuit".



I'm not very sure how to use that in an N-path filter, but even so, I still don't get how the input parasitic capacitance vanishes in theory, or why two inverters at the output are short-circuited.  Why not replacing them with just a wire?

[mawyatt]

I thought this was about another video he did, which was the PolyPhase Mixer, or N-Path. I removed my note since it's not related.

Need to think about this later, I had not seen this before.

Best,

[RoGeorge]

I think I've found the original paper:

IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 27, NO. 2. FEBRUARY 1992
A CMOS Transconductance-C Filter Technique for Very High Frequencies
DOI: 10.1109/4.127337
https://ris.utwente.nl/ws/portalfiles/portal/6771395/cmos_transconductance.pdf

[mawyatt]

Couldn't get the paper yesterday, so tried again this morning and part of the paper was available. Not sure whats going on with the site, but did get enough to recognize the paper from back in 92.

This technique Nauta employed of using CMOS digital inverters to realize a classic analog gmC integrator is the main point. Using the cross coupled concept realizes a positive feedback to raise the output impedance. A similar technique was used in the Caprio Cell back in ~70 to equalized and cancel distortion in a differential circuit, also employing some positive feedback is a cross coupling method.

The mention of "infinite bandwidth" is somewhat misleading, sure the transconductor has infinite bandwidth without any capacitance, however any transconductor does the same....so nothing new here. Many folks use a simpler scheme to realize a somewhat high intrinsic bandwidth transconductor by tying the MOS gate to drain terminal (diode connection), this realizes a gmC with a shunt C or the parasitic, but the technique by Nauta of using a digital CMOS inverter has better overall characteristics, and with the cross coupled technique the performance is even better. Just about any linear filter transfer function can be created by gmC means, and became very popular because of the direct integration afforded by digital CMOS processes.

We began using CMOS digital inverters back when RCA introduced the CD4000 series CMOS logic ~70, they made nice single ended inverting amplifiers with a simple feedback resistor and a smooth "S" transfer characteristic which we employed for soft signal limiting. Think Nauta is credited with utilizing CMOS inverters for the gmC filter use tho.

Remember folks looking at our designs and somewhat perplexed asking "what the heck were all the logic gates doing scattered around in a purely analog signal processing section of the systems"

Another interesting integrator technique arose with the Log Domain Filters originally implemented with bipolar transistors. These filters were highly non-linear on purpose, and compressed the input signal with the natural log characteristics of bipolar transistors. The filtering action took place with integrators on the compressed signal, and then the signal was expanded utilizing the exponential bipolar characteristic. Back around 2000 we did an experimental 9th order inverse Chebyshev low pass in IBM 8HP SiGe BiCMOS that tuned ~5 decades (300MHz to 3KHz). The achilles heal of these Log Domain Filters was the noise was higher than conventional filters because the noise created in the compressed filtering domain became expanded with the signal expansion at the output.

Believe the earliest use of Log Filtering techniques was the 1st order Log filter employed by Dolby, where the signal was compressed, then recorded to tape, later expanded with the bipolar exponential characteristic on playback.

Anyway, many clever techniques were employed long ago before the digital revolution took over.

Best,

[RoGeorge]

It all starts to make sense now, thank you very much for taking the time to explain.
I'll have to read again and lookup the other things I didn't know, like for example the Caprio Cell.



My bad for posting a sci-hub link that might not be available worldwide, sorry.  Meanwhile I've searched again and found the same paper on his university website, and edited the previously posted link accordingly.

[mawyatt]

Yep, the Caprio Cell is a relatively unknown jewel of a circuit. Was used to cancel out distortion by passing the emitter/collector currents of each side of a differential amplifier thru equal base emitter junctions where the sum of the applied base-emitter voltages are identical. This cancels the distortion when the output is differential.

We employed this inside a Cherry-Hooper differential amplifiers and adapted to Gilbert style mixers with very large BWs and high linearity.

Best,