Realisation Of Low Distortion Multiplier

[Samuel Groner]

Hi

I started some research on low distortion/low noise multipliers but didnt' find too much information. Intended use would be to provide amplitude and frequency control of a state-variable filter for a oszillator and/or THD+N auto tune notch filter.

Let's start with a known implementation based on JFETs by Cordell: thd_analyzer.pdf

Now I could think of an easy way to replace the JFETs with a LDR. How would distortion and noise compare to the original solution? I guess at least VCAs would provide lower THD+N, but they are less convenient to use with this circuit as we need negativ multiplication as well.

Thanks for your input!

Samuel

 

[JohnRoberts]

I recall Cordell's article and it was some nice work.

To control amplitude of a state variable oscillator with low distortion will be much easier than varying it's tuning frequency since to sustain oscillation you only need to inject a small incremental amount of signal. Cordell kept the distortion low by keeping the working voltage low and first order linearization with the common variable JFET shunt circuit. Besides the linearity of the multiplier, distortion in sine wave generators is strongly influenced by rectifier ripple controlling this AGC loop. Common downside to excessive filtering is long settling time, and Cordell uses diode threshold dual rate to somewhat speed settling time.

Cordell full wave rectifiies the LPF output. In the state variable topology you have three 90' offset phases available to potentially further reduce ripple. In a recent thread on this topic, Brad pointed out a published design that used the trig identity (SIN^2 + COS^2=1) to make a ripple free rectifier. I played around with this same idea myself years ago using a different technique to perform the trig math but never reduced my design to a working prototype.

To control frequency fully with some low distortion VCA, you will be hard pressed to get a distortion floor low enough to measure low distortion VCAs with. There are sundry tricks like adding passive poles after the generator but this is beyond your specific question. Most common multipliers (like VCA) are often designed with a sharp pencil so some "cost is no object" benefit is a vailable from paralleling them, but this benefit diminishes quickly beyond a few.

JR

 

[Samuel Groner]

Thanks for your answers.

Analog Devices makes a great precision multiplier...

Which one--AD534 or AD632? I'm a bit concerned about noise--the specs don't look too promising. In addition to this, I don't remember having seen a THD plot for those. Precision doesn't need to mean low distortion I think. But I might be wrong.

Besides the linearity of the multiplier, distortion in sine wave generators is strongly influenced by rectifier ripple controlling this AGC loop.

I'm well aware of this distortion mechanism and I'm planning to go the sin/cos route you mentioned. I wonder if you could post the schematic suggestion by Brad (IIRC) for this part of the circuit?

To control frequency fully with some low distortion VCA, you will be hard pressed to get a distortion floor low enough to measure low distortion VCAs with.

I don't need full frequency control, just a few % to catch drift and oscillator/notch mismatch. Resistively dividing the multiplier/VCA output should take care of the noise I guess.

Thinking about it I came up with a circuit using two VCAs fed with inverting polarity and opposite controll voltages which could be used as full multiplier after summing the outputs. The SSM2018 looks especially promising for this application with its differential input. Need to think more about it though.

Any ideas on the linearity of LDRs?

Samuel

PS: 1k5 posts!

 

[JohnRoberts]

Brad was generous enough to scan and send the schematic to me off list since it was likely protected IP, I can pass it along but am reluctant to publish it. PM me with a real e-mail addy and I'll try to dig it up this weekend.

I could probably generate a schematic for my alternate approach, where I used base-emitter junctions to perform the math in log domain, but it is not a debugged circuit so I am reluctant to offer it as anything more than a possible approach. I am not inclined to build and debug myself, then or now.

If I were inclined to roll a serious sine wave source these days it might include a high bit rate d/a driven by calculated sine values and followed by a few passive poles. Settling time could be mSec, frequency tweaking including relative phase could be pretty precise using high enough clock rates.

Different strokes, I'm an old analog dog but digital has it's utility. Given my druthers, i'd use a complex not sine wave test source. A precision digital file, with results compared to the source file. Of course this is limited by the digital media and will show all deviation from perfect, not just distortion products, so YMMV.


JR

 

[JohnRoberts]

I did some investigation of LDRs for possible VCA use years ago and they seemed pretty low distortion. I found them expensive to linearize control (required center tapped units, used with center tap grounded) and so abandoned my investigation. FWIW the distortion floor of my bench at the time (mid '70s) was not very low.

Probably OK in minor parallel path inside closed loop application where there is no need to control precisely.

JR

 

[bcarso]

That's a nice article series---I don't think I ever saw it. Reminds one of the often high quality of what was a fairly popular magazine in its day.

BTW I'd love to get my hands on the Hofer preprint listed at the end of part one. Bruce doesn't publish that often and when he does it's worth seeking out.

Where do you want to use the LDR? Its distortion will be low, generally---a bit of third IIRC. However the control law is not particularly stable from part to part or from one day to the next, and they are slow.

I don't recall the exact reference I cited but it was a fairly recent audioXpress piece about an oscillator project. IIRC the guy used a 13700-style OTA hooked up in a tricky way (one example is in the National Semi datasheet I think) to get four-quadrant multiplication for the trig identity amplitude stabilization manoeuvre. Maybe that approach could be adapted using a better two-quadrant multiplier (i.e., VCA); however, bear in mind that audio VCAs are usually set up to do a dB versus control variable gain change, and for the trig math you want linear.

A roll-your-own transconductance multiplier with THAT transistor arrays would probably beat most everything out there if done right.

 

[bcarso]

[quote author="JohnRoberts"]Brad was generous enough to scan and send the schematic to me off list since it was likely protected IP, I can pass it along but am reluctant to publish it. PM me with a real e-mail addy and I'll try to dig it up this weekend.


If I were inclined to roll a serious sine wave source these days it might include a high bit rate d/a driven by calculated sine values and followed by a few passive poles. Settling time could be mSec, frequency tweaking including relative phase could be pretty precise using high enough clock rates.

JR[/quote]

I'll bet all of the article is on the aXp website.

I've not seen what Ap does in the System One and successors, but I believe it is a combination of digital and analog techniques.

 

[Samuel Groner]

Where do you want to use the LDR?

Let me illustrate the three possibilities I consider at the moment: multiplier_ideas.gif

(a) is just the FET-based multiplier copy-pasted from the Cordell article. (b) replaces the FET with a LDR and (c) is my "complementary VCA"-idea.

I guess the VCA-approach is best with respect to distortion, while the other two are much better with respect to noise.

Its distortion will be low, generally--a bit of third IIRC.

So you'd say the LDR is a significant improvement over the FET in the circuits linked above?

However the control law is not particularly stable from part to part or from one day to the next, and they are slow.

The control law doesn't matter if we drop this multiplier into the Cordell oscillator (fig. 9, page 39 in the first article), right? But would the speed cause stability problems here?

Samuel

 

[Samuel Groner]

Found some distortion plots for LDRs: http://www1.silonex.com/audiohm/constants.html

Looks like a NSL-32SR3 would work well if run at suitably low levels.

Samuel

 

[JohnRoberts]

The slower speed of LDR would just look like another LPF in control chain so might impact settling time slightly but that control path will be slow to deliver low distortion anyhow.

While the LDR will benefit from the reduced voltage level in Cordell's JFET multiplier, keep in mind that topology has some other very important characteristics useful in linearizing the JFET, namely it's terminal voltage is predictable and independent of it's conductance, so control signal can utilize common linearizing technique. It might be worth looking at other topologies for the relatively simple task of nudging the loop into oscillation. It may not even require throwing a dedicated opamp at it.

JR

 

[bcarso]

[quote author="Samuel Groner"]Found some distortion plots for LDRs: http://www1.silonex.com/audiohm/constants.html

Samuel[/quote]

Ah yes Silonex. I remember when they were getting going years ago and pitched to Harman, who were using optocouplers in an amplifier Plunkett designed for Ford. Although they sounded good the QA people were bedeviled by them due to the various aging/history/temperature effects. About the time Silonex was being considered as a supplier, that amplifier was phased out, and poorer audio quality but more predictable limiters, designed by David McCorkle, based on OTAs, eventually replaced them.

Silonex provides a lot of good data there. I wonder if they would give me the time of day with regard to the actual typical reverse breakdown voltage of their specially matched LEDs, unlike the cold shoulder I got from the Vactrol folks?

I wish they showed the spectrum of the distortion. It's a bit higher in magnitude than I had thought as well.

One concern would be the somewhat higher Z of a circuit using the optos and the consequent noise, but if the corrective effects needed from it are small then perhaps it would be fine.

 

[Samuel Groner]

Another article on the topic of THD analysers: EPSG085898.pdf

Samuel

 

[JohnRoberts]

8903 was a great workhorse bench unit.

JR

 

[clintrubber]

[quote author="Samuel Groner"]Another article on the topic of THD analysers: EPSG085898.pdf

Samuel[/quote]
Hey, that's close to home :thumb: (I'm the happy owner of an -A & -B).
If relevant for this thread and if not already known, note that for further details the full service doc of the 8903B can be found on the Agilent website (as two pdfs IIRIC) and there's some for the -A as well.

Regards,

Peter