Whatâ€™s All This Multiplier-Divider Stuff, Anyhow?

A few weeks ago, an engineer knocked on the front of my cubicle and asked, â€śCan you recommend a good design for a multiplier-divider?â€ť I just happened to have my Linear Apps book open to AN-31, so I said, â€śLike this one?â€ť (see http://cds.linear.com/docs/Application%20Note/an31.pdf)

She said, â€śNo, not exactly. That runs on Â±15-V supplies, and I need one to run on +4 V.â€ť Oh. So the engineer showed me the specs she needed: IOut = (I1/I2) Ă— I3. The I1 and I2 would cover barely an octave, and I2 could be bigger than or smaller than I1. And I3 would be just a few ÂµA.

After pinning down the process and a few more details, I told her, â€śGo away, and see what I got for you tomorrow.â€ť

Time to design

Anyhow, I cobbled together this basic idea. It was still adding and subtracting logs, but it didnâ€™t need so many op ampsâ€”like one instead of four. A week later, I asked her how it was coming. She replied, â€śOh, we decided we didnâ€™t really need that....â€ť I explained, â€śWell, I gave that to you, and if you arenâ€™t going to use it, I want it back.â€ť So I took it back. And here it is (see the figure).

To take a ratio of I1 to I2, we just need to put those currents through a pair of well-matched NPNs, such as Q1 and Q2. I put in a servo amplifier A1 to establish a control voltage, VC, which will be 18 mV per octave at room temp. VC can be positive if I1 is bigger than I2â€”or smaller if vice versa. This VC is also applied to Q3 and Q4. The ratio factor established by VC will scale IOut as needed. Piece of cake.

Normally we would like to use the National LM394 for the matched pairs. But since some foolish people obsoleted them, weâ€™ll just the next best thing, the MAT-12.

Now, this multiplier as shown is designed around some tightly matched transistors and one real op amp. If this was being constructed in a biCMOS IC process, the discrete matched NPNs could easily be replaced by some well-matched common-centroid NPNs with (presumably) low offset, and the op amp could be replaced by a P-channel matched pair, running as a differential amplifier. Still, the idea is the same: A simple servo, to generate VC....

Have I built this? Not yet. But thatâ€™s not a big deal. Circuits like this are very easy to test out with back-of-envelope Spice. It will work perfectly.

Bobâ€™s Mailbox: Steering Lock-Ups

Hi Bob,

I have a 1991 Chevy S-10 pickup truck with automatic transmission that locks up. When one turns the key all the way toward off and does not pull the key out, the steering wheel will still lock up. I tried this while driving and learned quickly how it behaves. Just to be sure, I went out and tried it in my driveway and it indeed locks up.

Full disclosure: the test while driving was with me driving and my daughter as a passenger. I wanted to demonstrate and make the point to her that if the engine stalls, you will lose power steering. But even though the steering wheel is harder to turn, it still works. To my surprise, it locked while doing 45 mph. I quickly turned it back on before I got into real trouble.

-Jim Sylivant

That was a first-class demonstration! I think your daughter got a fine education. One of the best.

But if you only turned it 20Â°, until the engine died, it wouldnâ€™t lock up, right? In a stick shift, just kick it out of gear when you turn off the key, and when you turn the key back, youâ€™ll be safe.

Beast regrds. /rap

Â

carl@cipher.com
on Sep 12, 2011
With a little spare time, I entered the schematic into LTspice. After correcting some of my minor connection errors, I was still getting an oscillation. After I changed the .001uF cap to connect between the opamp in and output terminals, all worked quite well. Bob was awfully good at these simple, yet elegant circuits. I hope he will forgive me for using SPICE . . .
DaleM
on Sep 12, 2011
I would imagine Bob would welcome the URL pointing to his good freind, Jim Williams, app note 31; However, the more likely one he is referencing is this one: http://www.national.com/an/AN/AN-31.pdf
which just so happens to have the multiplier he mentions . . .
whit3rd
on Sep 13, 2011
There's more on this kind of circuit in the Raytheon RC4200 spec sheets, though their old unit wasn't intended for a low DC supply. My own back-of-envelope efforts make the 32kOhm resistors a bit of a puzzle; at
microamps of collector current, there's only a few score nanoamps
there, and a millivolt of collector voltage result. Does that
accomplish some useful filtering, with the Miller effect? Or, is it
maybe a way to accomplish an easy wire-cross in a process like
the old TTL, where some small-value resistors were just jumper
wires in a single-metal-layer circuit layout?

Commentaries and Blogs
A 5G wireless cell phone is in your future.
Posted 5 days ago
\$45 Million Dollar Bank Heist Fades Into Obscurity
Posted 5 days ago
in alt.embedded
LinkedIn. Is it trustworthy? Is it safe?
Posted 1 week ago
in London Calling
Forums

Lead Bending: "Thereâ€™s more to it than just
making the heatsink fit!"