WIP: Investigating Analog Multipliers - Page 1
Forum section: electronics / projects

author: c4757p
author_rank: Super Contributor
timestamp: December 29, 2014, 03:52:34 pm
content: Recent, er, discussions on transistors have got me interested in semiconductor stuff again, and I thought I'd do a short series of experiments with practical analog multipliers - circuits that might not perform quite as well as a $10 single-IC solution from ADI, but that you could build yourself and have a bit of fun poking around with.Here's my first multiplier circuit:It works by the same principle as most multipliers: varying the large-signal bias through a transistor to modify its transconductance. This circuit isn't very good (it'll likely be the worst of all the ones I'm doing here), but it has a simplicity factor: it requires only three matched transistors, which makes it probably the cheapest one I'll do as well.Here's the full documentation:PDF (412K)And a transfer curve:Next multiplier: Gilbert cell.

author: Zero999
author_rank: Super Contributor
timestamp: December 29, 2014, 05:58:03 pm
content: Have you GK's analogue multiplier design?https://www.eevblog.com/forum/projects/poor-mans-analog-multiplier/I've also seen an AD633 fairly cheap on ebay but don't know whether it's genuine or fake? Perhaps it's worth the risk?http://www.ebay.co.uk/itm/1PCS-IC-ADI-DIP-8-AD633JN-AD633JNZ-GOOD-QUALITY-LI2-/331194821678?pt=UK_BOI_Electrical_Components_Supplies_ET&hash=item4d1cbfec2e

author: c4757p
author_rank: Super Contributor
timestamp: December 29, 2014, 06:00:51 pm
content: Quote from: Hero999 on December 29, 2014, 05:58:03 pmNope - but it looks fairly similar to the one I have coming up next.QuoteProbably fine - I should buy some of those, wouldn't mind having them on hand - but that's not the point, I'm pretty much just doing this for fun. Bit of poking around in the internals of the circuits.

author: atferrari
author_rank: Frequent Contributor
timestamp: December 29, 2014, 06:15:02 pm
content: I recall using LTSpice with this circuit to actually understand how it works.At least I have an idea.It all started when I read the datasheet of an old opamp. RC4136 IIRC.I added the .txt extension.

author: c4757p
author_rank: Super Contributor
timestamp: December 29, 2014, 06:28:15 pm
content: Yup, the traditional logarithmic "slide rule" multiplierI plan to do one of those as well.

author: atferrari
author_rank: Frequent Contributor
timestamp: December 29, 2014, 06:42:06 pm
content: Quote from: c4757p on December 29, 2014, 06:28:15 pmMy interest is renewed now. Gracias.

author: miguelvp
author_rank: Super Contributor
timestamp: December 30, 2014, 02:37:22 am
content: Google for "Translinear Circuits" and "Bipolar Translinear Principle" that's what Gilbert coined it.

author: c4757p
author_rank: Super Contributor
timestamp: December 30, 2014, 02:38:50 am
content: Quote from: miguelvp on December 30, 2014, 02:37:22 amNice timing, Ijustfinished writing three pages' worth of explanation of the TLP and using it to analyze the Gilbert cell

author: GK
author_rank: Super Contributor
timestamp: December 30, 2014, 07:55:49 am
content: In the Gilbert Cell multiplier you can further linearize the long-tail-pairs to which the differential signal inputs are applied by placing each transistor into the feedback loop of an op-amp in a unity-gain configuration. If a high GBWP op-amps are used, noise gain compensation is easily applied to assure stability. An all discrete alternative is to use the Tektronix-patented "cascomp" circuit for the input LTP's.

author: c4757p
author_rank: Super Contributor
timestamp: December 30, 2014, 03:16:57 pm
content: Quote from: GK on December 30, 2014, 07:55:49 amYup, I considered using closed-loop current sources - originally decided against it out of pure laziness, not wanting to connect it all up on the breadboard, but I'll leave some space to add them if the linearity leaves something to be desired.QuoteInteresting, I've not heard of that before, thanks!

author: IconicPCB
author_rank: Super Contributor
timestamp: December 30, 2014, 09:32:50 pm
content: Is this an exercise in analog electronics or do you have some spec to meet?Consider CA3086 for match transistorsConsider CA3080 as a multiplier

author: c4757p
author_rank: Super Contributor
timestamp: December 30, 2014, 09:41:15 pm
content: Just an exercise.I've been using CA3096 (3 NPN + 2 PNP) for transistors. As for the OTA - I'll probably do one of those too, though I'll likely build it rather than buying one.

author: c4757p
author_rank: Super Contributor
timestamp: December 30, 2014, 11:37:32 pm
content: Spoiler:

author: KJDS
author_rank: Super Contributor
timestamp: December 31, 2014, 12:03:39 am
content: Quote from: c4757p on December 30, 2014, 02:38:50 amThere's a chapter written by Barrie Gilbert in Analog Circuit Design, Art science and Personalities that's well worth reading, describing the origins of Translinear amplifiers.

author: c4757p
author_rank: Super Contributor
timestamp: December 31, 2014, 05:56:34 pm
content: And here's the Gilbert cell:PDF (389 kB)This one performed quite well - better than my cobbled-together test setup could really verify. I intend to revisit this one with a circuit build and test environment that can actually do it justice.Next multiplier: log-sum-antilog.

author: miguelvp
author_rank: Super Contributor
timestamp: December 31, 2014, 06:06:51 pm
content: Nice, You could get one of these chips and compare the resultshttp://www.analog.com/en/special-linear-functions/analog-multipliersdividers/products/index.htmlThey have in there an old app note as well:http://www.analog.com/static/imported-files/tech_docs/ADI_Multiplier_Applications_Guide.pdfnote: the pdf is a scan, and very slow to navigate through.

author: c4757p
author_rank: Super Contributor
timestamp: December 31, 2014, 06:13:25 pm
content: Quote from: miguelvp on December 31, 2014, 06:06:51 pmQuoteQuote

author: miguelvp
author_rank: Super Contributor
timestamp: December 31, 2014, 06:29:59 pm
content: told you it was old

author: G0HZU
author_rank: Super Contributor
timestamp: December 31, 2014, 06:51:07 pm
content: If you want to see a very elegant use of a precision multiplier (using transistors) then download the maintenance manual for the Racal 9300 true rms voltmeter.This is a really nice old meter made sometime about 1980 and I've been using one of these at work and at home pretty much all of my design career. It works up to about 20MHz and the ICs with the transistors inside are 'matched' at IC manufacture and then the best of these ICs are very carefully matched together by Racal in order to get very high performance in the multiplier section.The maintenance manual gives lots of equations to explain how it all works in Appendix 1 about halfway through the manualhttp://www.ko4bb.com/manuals/109.146.241.59/Racal_9300_Maintenance_Manual_4-5-85.pdfThe way it is designed to measure true rms is very elegant and it can measure down to a few uV.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: January 01, 2015, 01:24:24 am
content: Great stuff!Also, nice formatting (LaTeX never disappoints). What are you using for the schematics and plots?Tim

author: c4757p
author_rank: Super Contributor
timestamp: January 01, 2015, 01:43:38 am
content: Thanks! Yeah, I'm obviously using LaTeX for the main document - schematics are XCircuit, and the plots are done with NumPy+matplotlib (with the exception of a single plot in the first one, which was done with gnuplot).

author: T3sl4co1l
author_rank: Super Contributor
timestamp: August 27, 2015, 01:54:24 am
content: The long awaited continuation!Suppose we generate a PWM square wave, with duty cycle reasonably proportional to an input voltage. If we filter this (removing the AC components, leaving just the average DC value), we get the original voltage back ... but not exactly, because PWM is a digital function, and digital signals are a matter of definition. Namely, the '1' and '0' voltages are defined by what the logic puts out. So the output is actually proportional to the digital logic levels.Hmm...Suppose we use our digital PWM signal as one input to a one-bit DAC, and set the reference level of that DAC from another voltage. Ahah, now we have an output (after filtering) that's jointly proportional to two signals: a product!(And yes, a "one bit DAC" is not a useless concept -- semantically, we're translating from an abstract digital signal (which might have unstable voltage levels, ratty rising and falling edges, lots of noise, etc.), to an analog signal that's supposed to be precise and stable. For many purposes, a CMOS logic gate actually does a fine job of this, which is seen from time to time. We can't use a logic gate here though, because of the voltage range required.)Such a circuit might look like attached (see PDF). The top half is a ramp oscillator (Fo = 191kHz) and PWM comparator. (A 555 timer could be used for the oscillator just as well, perhaps saving a few resistors, but the current source is important, otherwise you get a sloppy waveform, and poor linearity along one axis. More on that later. This entire section could be replaced by an LT TimerBlox IC, but wouldn't handle the supply voltage, and would still cost more. Although it would save considerable board area.)The bottom half buffers the input, drives a MOSFET pair, then filters it (3rd order ~Butterworth, Fc = 3.6kHz) to give a stable "DC" output. The magic part is the MOSFET pair, which acts as a one-bit DAC, switching between the buffered signal, and the ground reference (VGND comes from a voltage divider, so is about 6V; all the input and output measurements are relative to this net). As long as the digital voltage swing is much greater than the reference voltages, this works well. The analog voltages are 6-9V (relative to GND), and the digital signal is 0.4V/11.6V, so this gives plenty of headroom to turn on the MOSFETs.The main drawback, as shown, is the considerable capacitance of these transistors. This necessitates R9-C2 to mitigate the charge injection (otherwise there is a pronounced spike in the waveform, and much more error, at low duty cycles). Very much smaller devices should be used, preferably a monolithic analog switch, like 1/3 CD4066.Results:The bi-linearity is pretty good. Modeling the data as a 2nd order bi-variate polynomial, the error is:RMS 1.03% FSPeak 1.64% FSSetting the quadratic terms to zero (i.e., only linear offset/gain corrections required to get a pure product result), the errors are,RMS 1.15% FSPeak 1.67% FSSome plots are provided for flavor. The first simply shows the data series; this isn't very illustrative, aside from seeing the nonzero intercept. The second shows three "slices" through the data, along the Vin1 = const axis, Vin2 = const, and along Vin1 = Vin2 (which is, ideally, the simple product). The third shows the "error bars" as a function of coordinate.You'll notice the error seems to be biased along vertical columns: this suggests the Vin1 port has worse error. Which seems to suggest an error in the voltage-to-PWM conversion. There would be a pronounced curve here (something like flexing a sheet) if I had used an RC timer instead of the current source ramp generator. Probably, contributing factors are capacitance variation (Y5P disc cap, transistor Ccb), current source stability (should be pretty good actually), comparator speed and output voltage stability, and so on.Tim