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What's inside an analog 4-quadrant multiplier?

The data sheets for analog 4-quadrant multiplier-on-a-chip chips are remarkably vague as to what goes on inside the chip. I'm thinking specifically of the Anaalog Devices AD633 and the Burr-Brown MPY634, which are (at my level of viewing) similar in overall function and specs (but different in some details.)

Some thoughts:

  1. One-quadrant multiplying doesn't seem too hard. Take the logs, add the logs, exponentiate the log. Basic building blocks are things I think I understand pretty well.

  1. Four-quadrant multiplying is still somewhat a mystery. The AD633 just says it has a "translinear core". I have about as much understanding of that as if they had said "dilithium crystals". The MPY634 data sheet doesn't even say that much, it just jumps right into an equation without relating it to any internal functions.

  2. Maybe a four-quadrant multiplier can be done with a one-quadrant multiplier, some absolute-value-taking circuits, and some comparators, and a final multiply-by x1 or x-1 depending on the comparators.

  1. One clue that the MPY634 and AD633 don't use the method I suggest in (3) is a lack of symmetry in the X and Y inputs. One input always has a linearity of maybe 4 times better linearity than the other. This indicates to me that internally there is some assymetry that isn't necessarily implied by my simple suggestion.

  2. Maybe the "translinear core" is something like a Gilbert cell. Or is it just a clever application of the Barrie patent that describes how things like the AD603 work? (See my thread here from September about how the AD603 works.) Even then that only gets you two quadrants... but there is an assymetry in the input such that maybe some other trick comes in.

So how many of my 5 thoughts above are completely and hopelessly wrong? All 5? :-)

If there's some Barrie patent that explains all this, I'd love to read it. When I've been pointed directly towards them in the past, they were always a joy to read. But I've got an exceptionally thick head and unless I'm pointed towards a specific one my eyes still glaze over in the claims section :-(

Tim.

Reply to
Tim Shoppa
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Bunch of Gilbert cells, usually.

This has a schematic...

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John

Reply to
John Larkin

Did you do the 1494?

John

Reply to
John Larkin

Look back thru my MC1494/95/96 threads. Particularly the linearization of the multiplier core.

...Jim Thompson

--
|  James E.Thompson, P.E.                           |    mens     |
|  Analog Innovations, Inc.                         |     et      |
|  Analog/Mixed-Signal ASIC's and Discrete Systems  |    manus    |
|  Phoenix, Arizona            Voice:(480)460-2350  |             |
|  E-mail Address at Website     Fax:(480)460-2142  |  Brass Rat  |
|       http://www.analog-innovations.com           |    1962     |
             
I love to cook with wine.      Sometimes I even put it in the food.
Reply to
Jim Thompson

Yeah, I know how to use a Gilbert cell to make a 2-quadrant multiplier. But how do they use them to make a 4-quadrant multiplier? My method would be compare-with-zeroes and absolute value circuits and a final stage of multiply by +1 or -1, but I don't think this is the "clever" way.

Hmm, I see the Gilbert cells in the multiplier section, but as for the theory they just refer to AN489, which is nowhere to be found. Can someone either explain to me (keeping in mind how slow and stupid I am) how 4-quadrant multiplication works, or point me to an online copy of AN489?

Tim.

Reply to
Tim Shoppa

I appreciate the cleverness of the linearization, but even then the MC1494 requires 4 external pots to finish the linearization and set the scale voltage.

I'm sure that the MPY634 and AD633 use laser-trimmed resistors internally to remove the need for all these pots just for external trimming. And they may have other tricks up their sleeves (especially AD, not so sure about Burr-Brown!) to make things even slicker.

But I still do not understand how to turn a Gilbert cell (a 2-quadrant multiplier) into a 4-quadrant multiplier. Maybe it's just a mental block, maybe it's just my fundamental stupidity. Can someone enlighten me?

Tim.

Reply to
Tim Shoppa

You use two. Differential X base inputs are paralleled, diff collector outputs are paralleled, and you drive the bottom current sources out of phase from the Y signal. Something like that.

John

Reply to
John Larkin

Ah, thank you. Now that I see that, I can begin to appreciate some of the finer points of linearization that Jim has talked about here in the past. It's now obvious why the X input has different linearity specs than the Y input. It's also now obvious to me why most MC1496 designs use transformer coupling :-).

If anyone wants to chime in with how Analog Devices and Burr-Brown mass-produce devices with no external trimmers, I'll gladly listen, but for now my curiosity is mostly satisfied. Maybe I'll try to build some multipliers out of CA3046's or MC1496's and see how they perform and appreciate the matching/linearization in the MPY634 and AD633.

Stupid Google Groups, and my fault for using it. I gotta get my trn working again. The good thing is that Google Groups is so frustrating that I now spend more time in the real world and less wasted time reading newsgroups...

Tim.

Reply to
Tim Shoppa

Tim, This may give you the enlightenment you need:

formatting link

The algebra in the appendix isn't as elegant as it could be, but from memory, there is nothing fundamentally wrong with it, it's just a little clumsy. It also looks very similar to that in AN-489, but I haven't checked that it is literally the same. (To get AN-489, Motorola or OnSemi - can't remember which - had to fax it to me, so I doubt you'll find it on the web).

Tim

(neither of the 2 ways I access s.e.d shows me the full thread, so apologies if this is slightly out of place...)

--
__________________________________________________________
Tim Stinchcombe

Cheltenham, Glos, UK
Reply to
Tim Stinchcombe

I'll see if I can find some publicly disclosable information about this next week when I return to work (we're shut this week).

Steve ADI employee by day...

Reply to
Stephan Goldstein

The real precision multipliers are duty-cycle modulators. But slow.

Or, um, motor-driven pots.

John

Reply to
John Larkin

There's a classic approach from the analog computer world, the "quarter square" multiplier. This is symmetrical in X and Y.

Recall that

A*B = ((A+B)^2 - (A-B)^2) / 4

Op-amps can do sum and difference. Logarithmic amps can do squaring. So this is quite buildable.

This approach goes back to the tube era. NEC revived it in 1994. It's not seen often any more, but if you want a instrument-grade analog multiplier, it's the way to go.

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John Nagle

Reply to
John Nagle

The '96 doesn't have the linearization of the core... does it?

It is simpler and is the only one of the series available anymore, as far as I know.

Reply to
gwhite

Another way the log function was done was witha Diode Function generator (DFG). Using the analog computer, one can set-up a sweep of the error (sweep one input, plot against error) and see a "sawtooth" ripple on top of the "slow" errors which usually look like a 2nd or 3rd order error curve from end to end. At least with the dynamic display, it was easier and faster to adjust for minimum overall errors. The textbook method used constants and sucked in over all useability results.

Reply to
Robert Baer

Motor driven MaryJane? To get away from the Feds?

Reply to
Robert Baer

I don't know those specific chips offhand. However in answer to the core question, there was some in-depth exchange on sci.electronics.design recently about "translinear" circuits (under a "Square-root" subject) in which I cited the seminal papers by Gilbert that popularized the standard BJT four-quadrant multiplication technique. (By the way, I worked under Barrie Gilbert, some time ago.) A bit of patient searching and reading under "translinear" -- with some patience for the lame after-the-fact cobbled-together explanations that tend to be numerous on Web sites -- should reveal much.

(It has little to do with "log-antilog," except implicitly.)

--
Now a trivia question for the analog hotshots here, the real hot shots,
about analog multiplication.  Not serving Tim Shoppa's question, but of
historical interest.  (Later I'll post answer and classic references.)
I assume this wasn't covered recently; if it was, never mind.  The
question concerns basic _mathematical_ identities that can (by various
practical means) be harnessed to build a multiplication out of other
kinds of mathematical operations.  There are _three_ classic ones.
Everybody (who is an analog hotshot anyway, or reads textbooks) knows
_two_ of them: the log-antilog identity, and the quarter-square
identity (given recently in this thread).  What is the third?
Cheers --     Max
Reply to
Max

If you can, I would advise doing the math in software. Log amps are a continual sore spot in the equipment that uses them.

--
Nicholas O. Lindan, Cleveland, Ohio
Consulting Engineer:  Electronics; Informatics; Photonics.
Remove spaces etc. to reply: n o lindan at net com dot com
psst.. want to buy an f-stop timer? nolindan.com/da/fstop/
Reply to
Nicholas O. Lindan

I looked around in my files yesterday and couldn't find anything specific to the innards of the AD633. But the basic principles of a 4-quadrant multiplier are in ADI's _Nonlinear Circuits Handbook_ -- basically, make two 2-quadrant multipliers and tie them together. It's a little more than this, of course, but that's the general idea.

These multipliers are translinear circuits, not logarithmic ones, so the thermal issues that always arise with loggers are not a problem.

Steve

Reply to
Stephan Goldstein

There's lots of good detail in Barrie Gilbert's patents, including his very effective linearizer secrets, with schematics and full math.

4,156,283 - Multiplier Circuit 4,586,155 - High-Accuracy Four-Quadrant Multiplier Which is Capable of Four-Quadrant Division 6,074,082 - Single-Supply Analog Multiplier

Another good info source is Barrie's two lengthy chapters in the book, "Analogue IC Design: The Current-Mode Approach," edited by C. Toumazou.

--
 Thanks,
    - Win
Reply to
Winfield Hill

And Barrie's original 1970 patent (continuation of a Jan 1968 filing) on the subject (granted Sept, 1972 and assigned to Tektronix),

3,689,752 - Four-Quadrant Multiplier Circuit 
--
 Thanks,
    - Win
Reply to
Winfield Hill

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