Electronic Design

# What's All This Multiplication Stuff, Anyhow? (Part IV)

When I'm out on the road, preaching at Linear Seminars, I run into guys with good questions, every day. Some I can answer, some I can't, and others just take a long while for me to figure out a good answer. One question that I carried for at least 70,000 miles was, "I would like to have a voltage-controlled 'pot,' similar to the 'digitally controlled pot,' so the output will be a function of a normalized control voltage Vk (where Vk/VREF = k), and:

VOUT = VA × k + VB × (1 − k)."

The "wiper" moves proportionally from VA to VB.

I thought about this a long time and kept the question in my wallet. I pulled it out and mulled over it many random times. Finally, I had a Eureka! moment and wrote to the guy: "Hey, Jim, you asked me why couldn't I invent an 'analog pot'. After I thought about this for a long time, I figured out that the reason is because somebody already invented it. It's called the analog multiplier.

"The good news: You can go to Analog Devices' Web site (www.analog.com) and look up the AD534 analog multiplier. You want to connect the VA and VB to the differential input pins at VX(+) and VX(−). Then you also connect VA to the VZ output offset pin. As you move VY up and down from 0 to 10.0 V, you get the ANALOG pot that you said you wanted.

"The bad news: These things cost \$16 and up (even the cheapest grade, even in 100s) and I don't think you're prepared to pay that price for an audio pot. I'd love to design you an analog multiplier using the LM13600, but that's now obsolete, and we ain't got any more to sell."

Jim agreed that it was a neat solution, but much more pricey than he would pay. He plans to try out the true analog multiplier, but at low priority.

I thought about it some more. I was mentioning this trick solution the other day to a colleague. He said, "Great solution, but the LM13600 isn't completely obsolete because you can still buy the LM13700, which is the same function." I was astonished. "They told me that the LM13600 and LM13700s were all discontinued," I said. He then replied, "You go look it up." He was right.

So here I'll give you the good cook-book circuit for this "analog-controlled pot" using the LM13700 as a multiplier/modulator (see the figure). This circuit has one additional advantage: If you move the Vk a little too far, the analog multiplier causes the unwanted channel to feed through a little. In my approach, no feedthrough occurs.

If you want this "pot" to provide a precision output with no offset, you can use any suitable op amp to buffer the output. Then you'd keep the 1-kΩ pots and trim for low output offset. If you're just going to need it for audio, use the Darlington output. Use two 499-Ω resistors to replace a 1-kΩ pot. No op amps or pots necessary—costing 1/10 the price of a store-bought multiplier.

What's good about this circuit? You can implement it with rich current biases and get better bandwidth and noise. If you don't mind a little extra noise, you can run the whole circuit on less than a milliampere. Store-bought multipliers won't do that. The bandwidth will still be over 12 kHz, and you can design it to run on just about any supplies, such as ± 5, 6, 8, or 15 V.

What's not so good? This circuit isn't perfect in linearity, but it's better than 1/2% THD. The noise for a 10-kHz bandwidth is only about 70-dB down. (But the analog multiplier may even be better at some settings.) The crosstalk from an unwanted channel is just −85 dB.

After I built it, what did I see? It worked as designed. Have fun!

All for now. / Comments invited!
RAP / Robert A. Pease / Engineer
[email protected]—or:

Mail Stop D2597A
National Semiconductor
P.O. Box 58090
Santa Clara, CA 95052-8090