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Design >> Analog Design >> multiply two dc voltages
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Message started by msaut on Feb 6^th, 2014, 8:51am

Title: multiply two dc voltages
Post by msaut on Feb 6^th, 2014, 8:51am

Hi guys,

I would like to know if there is a smart way to multiply two dc voltages.

I'm trying to obtain a voltage proportional to (Vodp+Vodn)/(Vodp*Vodn) where Vod is the overdrive of a N or P-MOS.

Thanks in advance.

Regards.

Title: Re: multiply two dc voltages
Post by RobG on Feb 6^th, 2014, 9:12am

Barrie Gilbert did this a long time ago with bipolar transistors, although you should be able to do it with CMOS in weak inversion. It is done in the current domain. http://en.wikipedia.org/wiki/Translinear_circuit

Title: Re: multiply two dc voltages
Post by RobG on Feb 6^th, 2014, 9:26am

The unit of your desired result is 1/Volts. Best I can think of for voltage will get you Vref^2*(1/Vodp + 1/Vodn) by using two Vref/R currents and one (Vodn+Vodp)/R currrent.

Please let us know if you come up with anything better.

Title: Re: multiply two dc voltages
Post by msaut on Feb 7^th, 2014, 12:54am

Thank you!
I think this is exactly what I was looking for...

Title: Re: multiply two dc voltages
Post by loose-electron on Feb 7^th, 2014, 6:35pm

DC voltages?

It's called an ADC and some digital logic.

Gilbert multiplier for RF type frequencies for sure, but there are times it is a lot smarter to take it over to the digital side of the device.

Title: Re: multiply two dc voltages
Post by msaut on Feb 8^th, 2014, 1:42am

Quote:

It's called an ADC and some digital logic.

I agree with you but I'm trying to do a self calibrated analog circuit.

However, these circuits are different from the Gilbert cell and very interesting.

Quote:

Best I can think of for voltage will get you Vref^2*(1/Vodp + 1/Vodn) by using two Vref/R currents and one (Vodn+Vodp)/R currrent.

I think this is not correct, the result is proportional to 1/(Vodp+Vodn) and not to (1/Vodp + 1/Vodn). Am I wrong?
I will try to extract the two overdrive voltages using a diode connected MOS cascaded with a source follower, this is possible only if the overdrive voltage isn't too low.

Title: Re: multiply two dc voltages
Post by RobG on Feb 8^th, 2014, 8:48am

No, you are correct - I was trying to cut corners and use one translinear circuit and made a silly math error. You should be able to do it with two circuits: The first would output Vref^2/Vod1/R and the second Vref^2/Vod2/R and then you connect the outputs together to get the sum.

I think you have the right idea for getting a Vod/R current. If your circuit doesn't give you what you need then the classic bootstrapped bias might:

Note that this needs a startup circuit.

Simply thinking, the current in R0 is (Vod9-Vod8)/R0, so if you wanted a current Voda/R0 you could (for example) make Vod9=1.5*Voda and Vod8=0.5*Voda.

And I'll also note to Jerry that the translinear circuits I referenced aren't the RF Gilbert multiplier and are intended for operation down to DC.