Analog Multiplication - Page 1
Forum section: electronics / projects

author: Daving
author_rank: Contributor
timestamp: January 16, 2013, 08:42:06 am
content: I'm somewhat interested in the dated (but perhapshttp://www.wired.com/wiredenterprise/2012/08/upside/]reviving?) art of analog computing. Along those lines, I was interested in learning how to multiply two voltages together. Of course when I asked around, one of the first responses I got was to use an ADC, do the multiplication digitally and then DAC out to get the result.I know that you can use diodes to take the logarithm of a voltage, but after adding two of the resulting logarithms together, you are most certainly going to be unable to exponentiate with another diode. So, I set about doing it my own way. I'm still hoping to find (or think of) a better general idea, but this one should work quite well.V1 is used to program a dependent current source, and V2 programs a frequency converter. The current source points into the top of a capacitor with a switch in parallel. The switch is controlled by V2's output, and V1 can have an inverter switched in if V2 is negative. Anyway, the capacitor (C1) is charged by the current source and it's peak voltage is V = I*T/C. The voltage is sampled at peak voltage and stored on another, much smaller capacitor. If the sample and hold method is too difficult, I can place a resistor in parallel with C2 and charge C2 through a diode (well, two diodes, switched based on the polarity of V1 and V2). This will insert an offset, but that could be accounted for by discharging C1 through a matched diode.Anyway, that's the idea, roughly. I don't off hand see how to attach an image (or PDF), but I had a sketch to go with this. Maybe I get the ability to attach after I post more.

author: deephaven
author_rank: Frequent Contributor
timestamp: January 16, 2013, 08:44:32 am
content: In the past I've used an MC1495.

author: Daving
author_rank: Contributor
timestamp: January 16, 2013, 09:01:47 am
content: Well, where's the fun in that?

author: penfold
author_rank: Frequent Contributor
timestamp: January 16, 2013, 09:05:18 am
content: If you do a quick google on logarithmic and exponential amplifiers (dont mean to sound patronising there).The generally accepted method is to take the antilog of the sum of two logs. Can be a bit of a pain to do it fully discrete due to temperature compensation but I've had perfectly acceptable results doing so and its a really useful experiment and an epically useful building block.I tend to use an ic for any critical work but if that's not a major concern then build it discrete.Now I did read through your method but not 100% whether or not you'd be just opening up a whole can of worms. The general method of logs and antilogs is good because its easily expandable to do all sorts of other functions and including a divide element by subtracting, don't know if your method will do that. I'll have another look later unless someone else beats me to it

author: codeboy2k
author_rank: Super Contributor
timestamp: January 16, 2013, 10:14:38 am
content: good stuff here :http://www.electronics.dit.ie/staff/ypanarin/Lecture%20Notes/DT021-4/6LogAntiLogAmplifiers.pdfAlso read the old Philbrick publications, available athttp://www.philbrickarchive.org/There is a huge archive here of publications and application notes on analog computing. Lots of tube stuff and early 50's - 60's engineering, but it's classic analog technology. Jim Williams and Bob Pease both worked at Philbrick although I don't know if their time overlapped there.

author: sorin
author_rank: Frequent Contributor
timestamp: January 16, 2013, 11:27:47 am
content: logantilog-amplifiers-to-multiply-two-voltages-from-single-supply/complete-project-constant-current-dummy-load/Two-Quadrant Analog Multiplier Project

author: jimmc
author_rank: Frequent Contributor
timestamp: January 16, 2013, 12:22:25 pm
content: A couple of other methods I can vaguely remember are...Pulse width,pulse heightUse the first voltage to set the duty cycle of a train of pulses and the second voltage to set the amplitude of the pulses.Average the pulses with a low pass filter to get the result.Quarter squaresThis is based on the the fact that X.Y can be expressed as (1/4)[(X+Y)2- (X-Y)2]Squaring can be easier than log / antilog functions.I think you might find this site interesting...http://www.philbrickarchive.org/Jim

author: GK
author_rank: Super Contributor
timestamp: January 16, 2013, 11:10:30 pm
content: The PWM idea would work, but it would be difficult to achieve a decent dynamic range, let alone bandwidth and linearity.AD make several 4 (and 2) quadrant analogue multiplier IC's.

author: ejeffrey
author_rank: Super Contributor
timestamp: January 17, 2013, 05:37:18 am
content: Quote from: GK on January 16, 2013, 11:10:30 pmThat is basically how the LT RMS-to-DC converters work (although they are sigma-delta, not plain PWM), and it appears to work extremely well. The dynamic range and linearity are much better than traditional circuits. They do suffer quite a bit in terms of bandwidth obviously, but other than that seem quite nice. The LT chips themselves are dedicated RMS to DC converters, not general purpose multipliers. However, the same technique should work for a general purpose multiplier circuit. Not sure how easy it is to make one with discrete components, but it should be OK.

author: GK
author_rank: Super Contributor
timestamp: January 17, 2013, 05:52:44 am
content: I've used the LTC1968:http://www.users.on.net/~glenk/nts/nts.htmAs far as limitations in dynamic range is concerned, I don't think the RMS converter application is analogous to an analogue multiplier. Traditional RMS converters are limited in their dynamic range by the accuracy of the precision rectifier at low input voltages.Analogue multiplication with log/exp blocks can achieve excellent accuracy in a dynamic range in excess of 6 or 7 decades - somewhat higher than any switching RMS converter; it's all relative.From memory that LT RMS converter part operates internally at a switching frequency of ~10MHz charging the external intergration capacitor via pf's of internal commutation capacitance.Matching its performance with a discrete circuit would not be trivial at all.

author: Rudolfo
author_rank: Contributor
timestamp: January 17, 2013, 08:37:52 am
content: The MC1495 is obsolete. I found a replacement with the iC-BM from iC-Haus(http://ichaus.biz/product/iC-BM).

author: deephaven
author_rank: Frequent Contributor
timestamp: January 17, 2013, 09:25:52 am
content: Quote from: Rudolfo on January 17, 2013, 08:37:52 amWow, 4 in one package! Pity the bandwidth isn't higher. I think the OP wants to roll his own though.

author: sorin
author_rank: Frequent Contributor
timestamp: January 18, 2013, 09:29:03 pm
content: Quote from: Rudolfo on January 17, 2013, 08:37:52 amhahaha $18.71 each !!!

author: w2aew
author_rank: Super Contributor
timestamp: January 18, 2013, 11:40:05 pm
content: Analog Devices has a few 4-quadrant multipliers that aren't that expensive.http://www.analog.com/en/special-linear-functions/analog-multipliersdividers/ad633/products/product.htmlas an example.Here's their table of multipliers and dividers:http://www.analog.com/en/special-linear-functions/analog-multipliersdividers/products/index.html

author: GK
author_rank: Super Contributor
timestamp: February 02, 2013, 01:16:09 pm
content: Quote from: Daving on January 16, 2013, 08:42:06 amSo did this ever make it to breadboard? circuit?Also of interest, page 40 "Time division multipliers":http://www.analogmuseum.org/library/anhyb.pdf

author: GK
author_rank: Super Contributor
timestamp: February 07, 2013, 02:17:49 am
content: Another interesting multiplier technique - integrating triangle waves. I'm going to pull out out my 12AX7, 12AU7, etc and 6AL5 stash on the weekend and make a start on giving the Figure 5 circuit a whirl (just for fun).

author: GK
author_rank: Super Contributor
timestamp: February 07, 2013, 08:40:06 am
content: Here is my initial alternate take on the triangle generator section. I probably cheated a bit in this "all tube" multiplier design by poking 3 transistors into the circuit, but it makes the performance significantly better and I have yet to find a "p-channel" tube to use insteadThe circuit topology is the standard integrator with schmitt trigger/comparator with hysteresis triangle function generator - clearly not a new concept. Twin triode V1 forms the schmitt trigger, which has a hysteresis of approximately 30V centered about 0V. Twin triodes V2 and V3 and transistors Q1 through Q3 form an op-amp compensated for unity gain operation. This op-amp makes the integrator. Capacitor C2 is the integrator capacitor.I think the concept detailed in that paper is really cool. I've got all the parts to build this all tube multiplier in my junk box(es). I think I'll fabricate a tubes-on-top display chassis for this and build it up as a complete project, complete with an on board regulated tube power supply to provided the required +/-150V.

author: robrenz
author_rank: Super Contributor
timestamp: February 07, 2013, 01:14:22 pm
content: I think there is more interest in the low noise high gain differential amplifier for a scope you sort of half volunteered for in another thread. You would sell a lot more of those boards.Just trying to help you with your priorities

author: GK
author_rank: Super Contributor
timestamp: February 07, 2013, 11:04:48 pm
content: I actually started looking at it, but differential jfet inputs with 1nV SQRT input-referred noise, high LF-HF CMRR, 20MHz bandwidth and a 1/f noise corner <=1kHz turned out to be a bit of $. A big batch of parts is scheduled to arrive next week and then I'll be busy with other stuff, back in to large scale analog computer production