What's inside an analog 4-quadrant multiplier?

[Tim Shoppa]

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.

2. 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.

3. 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.

4. 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.

5. 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.

 

[Jim Thompson]

On 29 Dec 2004 17:03:49 -0800, "Tim Shoppa" <shoppa@trailing-edge.com>
wrote:

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.

2. 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.

3. 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.

4. 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.

5. 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.

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 Voice480)460-2350 | |
| E-mail Address at Website Fax480)460-2142 | Brass Rat |
| http://www.analog-innovations.com | 1962 |

I love to cook with wine. Sometimes I even put it in the food.

 

[Tim Shoppa]

John Larkin wrote:

Bunch of Gilbert cells, usually.

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.

This has a schematic...
http://www.onsemi.com/pub/Collateral/MC1494-D.PDF

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.

 

[Tim Shoppa]

Jim Thompson wrote:

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

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.

 

[John Larkin]

On 29 Dec 2004 18:38:46 -0800, "Tim Shoppa" <shoppa@trailing-edge.com>
wrote:

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

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.

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

 

[Tim Stinchcombe]

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,
This may give you the enlightenment you need:

http://www.onsemi.com/pub/Collateral/AN531-D.PDF

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

 

[Tim Shoppa]

This may give you the enlightenment you need:
http://www.onsemi.com/pub/Collateral/AN531-D.PDF

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.

(neither of the 2 ways I access s.e.d shows me the full thread

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.

 

[Stephan Goldstein]

In article <1104415043.759776.229360@z14g2000cwz.googlegroups.com>, "Tim Shoppa" <shoppa@trailing-edge.com> wrote:

This may give you the enlightenment you need:
http://www.onsemi.com/pub/Collateral/AN531-D.PDF

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.

<snip remainder>

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...

 

[John Nagle]

Tim Shoppa wrote:

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 Analog 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.)

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.

http://ieeexplore.ieee.org/xpl/abs_free.jsp?arNumber=272093

John Nagle

 

[John Larkin]

On Mon, 03 Jan 2005 03:18:04 GMT, John Nagle <nagle@animats.com>
wrote:

Tim Shoppa wrote:

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 Analog 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.)

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.

http://ieeexplore.ieee.org/xpl/abs_free.jsp?arNumber=272093

John Nagle

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

Or, um, motor-driven pots.

John

 

[Robert Baer]

John Nagle wrote:

Tim Shoppa wrote:

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 Analog 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.)

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.

http://ieeexplore.ieee.org/xpl/abs_free.jsp?arNumber=272093

John Nagle

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.

 

[Robert Baer]

John Larkin wrote:

On Mon, 03 Jan 2005 03:18:04 GMT, John Nagle <nagle@animats.com
wrote:

Tim Shoppa wrote:

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 Analog 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.)

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.

http://ieeexplore.ieee.org/xpl/abs_free.jsp?arNumber=272093

John Nagle

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

Or, um, motor-driven pots.

John

Motor driven MaryJane? To get away from the Feds?

 

[Richard the Dreaded Liber]

On Mon, 03 Jan 2005 08:59:41 +0000, Robert Baer wrote:

John Larkin wrote:

On Mon, 03 Jan 2005 03:18:04 GMT, John Nagle <nagle@animats.com
wrote:

Tim Shoppa wrote:

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 Analog 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.)

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.

http://ieeexplore.ieee.org/xpl/abs_free.jsp?arNumber=272093

John Nagle

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

Or, um, motor-driven pots.

John

Motor driven MaryJane? To get away from the Feds?

For lazy heads. %-}

Cheers!
Rich

 

[Nicholas O. Lindan]

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 Analog Devices AD633 and the Burr-Brown MPY634,

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/

 

[Max]

Tim Shoppa wrote:

are remarkably vague as to what goes on inside...
I'm thinking specifically of the Anaalog Devices
AD633 and the Burr-Brown MPY634 ...

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

 

[Stephan Goldstein]

In article <p5mCd.629$vP1.567@newsread3.news.atl.earthlink.net>, "Nicholas O. Lindan" <see@sig.com> wrote:

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 Analog Devices AD633 and the Burr-Brown MPY634,

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

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

 

[Robert Baer]

Stephan Goldstein wrote:

In article <p5mCd.629$vP1.567@newsread3.news.atl.earthlink.net>, "Nicholas O. Lindan" <see@sig.com> wrote:
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 Analog Devices AD633 and the Burr-Brown MPY634,

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


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

If one designs those loggers properly, there will be no thermal
issues.

 

[Stephan Goldstein]

In article <crgpuj01s3o@drn.newsguy.com>, Winfield Hill <hill_a@t_rowland-dotties-harvard-dot.s-edu> wrote:

Stephan Goldstein wrote...

Tim Shoppa wrote:

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 Analog Devices AD633 and the Burr-Brown MPY634,

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.

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.

I was going to check the Tomazou book, but I loaned it to a colleague who
saw fit to read it at home

I did find a few pages that are OK for public consumption (i.e. not proprietary)
and have contacted Tim by email about faxing them. If anyone else is
interested please post here and I'll contact you. I don't have a scanner so
fax or mail are the only ways.

Steve

 

[Winfield Hill]

Stephan Goldstein wrote...

Winfield Hill wrote:

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.

I was going to check the Tomazou book, but I loaned it to a colleague
who saw fit to read it at home

Get it back, or submit a bill. :&gt

I did find a few pages that are OK for public consumption ...

Ahem, a few pages may not do it. Barrie wrote 81 pages in Chapter 2,
a translinear tutorial, and 58 pages in Chapter 6, a current-mirror
masterpiece. That's 139 world-class pages in this 640-page book, and
arguable the best pages. They are among his best writings, SFAICT.


--
Thanks,
- Win

 

[Jim Thompson]

On 14 Jan 2005 07:19:39 -0800, "Tim Shoppa" <shoppa@trailing-edge.com>
wrote:

[Tungsten filaments, CdSe photocells, MOV resistor with exponential
curves]

Those are all interesting implementations, but they aren't a new
mathematical identity like Max was asking for. They're just varying
implementations of the exponent/logarithmic circuit.

One interesting thing about the CdSe photocells is that they're very
linear in electrical response while being nonlinear in optical
response. That has very real advantages in many applications.

Tim.

CdSe? I've heard of CdS, although I can recall, as a kid, dismantling
Selenium rectifiers and using a single plate as a photocell.

...Jim Thompson
--
| James E.Thompson, P.E. | mens |
| Analog Innovations, Inc. | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| Phoenix, Arizona Voice480)460-2350 | |
| E-mail Address at Website Fax480)460-2142 | Brass Rat |
| http://www.analog-innovations.com | 1962 |

I love to cook with wine. Sometimes I even put it in the food.