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Negative Capacitance

05/11/2015 7:07 PM

For RF circuit analysis, I sometimes use RFSIM99. It has a neat feature called "automatch." If you have a known load whose schematic is expressed in some combination of Rs, Ls & Cs the system can generate either a high pass or a low pass network that will match the load at a specific frequency. It also can show a Smith Chart over a swept frequency range.

I recently encountered a circuit for which the Matching network consisted of a parallel small inductance and a series *negative capacitance* of -15pF.

Obviously I can't rush down to Radio Shack (If I can Find One!) and buy some.

But it got me thinking:

What would be the characteristics of Negative Capacitance?

Could such a thing be simulated using something like a gyrator circuit?

Thanks! Bill

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#1

Re: Negative Capacitance

05/11/2015 7:28 PM

What would be the characteristics of Negative Capacitance?

Looks to me like a special capacitor circuit configuration used to cancel out specific other capacitive effects.

http://www.cpes.vt.edu/public/showcase/negativecancellation.php

Could such a thing be simulated using something like a gyrator circuit?

Yea I am sure you could model it and use capacitors with a negative value.

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#2

Re: Negative Capacitance

05/11/2015 7:39 PM

You have to do some magic with op amps...

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#3
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Re: Negative Capacitance

05/11/2015 10:09 PM

That's the correct fundamental circuit. However, the problems with nearly all Negative Impedance Circuit (NIC) designs are stability from the positive feedback and complications from all of the non-ideal attributes of real versus ideal operational amplifiers.

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#4
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Re: Negative Capacitance

05/11/2015 10:20 PM

But but but....the design I built in the computer modelling program clearly proves........

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#5
In reply to #3

Re: Negative Capacitance

05/12/2015 1:03 PM

Thanks to all for their info!

In a network, where is the op amp connected?

Are there op-amps that might work at RF? Say up to 15 MHz?

Is this a low-power-only (milliwatts) approach, or could it be used at power levels up to, say, 10s of watts?

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#6

Re: Negative Capacitance

05/13/2015 2:40 AM

A capacitor between input and output is positive capacitance , a capacitor between input and ground is negative capacitance, as viewed from the output. Correct?

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#8
In reply to #6

Re: Negative Capacitance

05/13/2015 7:16 AM

No, the input impedance of the whole circuit (op=amp, capacitor, resistors and op-amp supply) that Rixter posted has an input impedance of -C.

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#7

Re: Negative Capacitance

05/13/2015 3:45 AM

Negative capacitance is a new term for me. Capacitance is not a vector.

Parasitic capacitance cancellation is usually done with inductors and a trim cap.

Is an inductor a negative capacitance?

Negative capacitance is a functional concept not an electrical parameter.

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#9
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Re: Negative Capacitance

05/13/2015 7:34 AM

Negative Impedance Converters are atypical circuits in the Gyrator family. (The Wikibooks link gives a very nice derivation of this analog circuit.) An inductor and capacitor can produce a non-reactive load at a particular frequency when properly tuned. A capacitor canceled by a capacitive negative impedance circuit will only have a frequency dependence of the linear bandwidth of the op-amp.

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#10

Re: Negative Capacitance

05/13/2015 8:17 AM

You should be able to find circuits called "negative impedance converter" [NIC] and "general impedance converter" [GIC] on the web. I did some work some years ago in electrically small antenna matching using negative impedances in matching networks. They are pretty simple, if you can build an active filter you can build an NIC/GIC.

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#12
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Re: Negative Capacitance

05/13/2015 11:18 AM

With a GIC one can (and I have) also build an impedance of 100 Henry in the size of a small postage stamp. If one desires one can even construct an impedance that otherwise does not exist, like the squared capacitor impedance of 1/(s^2*Xc).

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#13
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Re: Negative Capacitance

05/13/2015 2:07 PM

Electrically Small antennas are just what I am interested in. Did you publish any work? Anything you might share offline? --

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#14
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Re: Negative Capacitance

05/13/2015 2:36 PM

As a recent college graduate, I worked with Stephen E Sussman Fort [AB2EW]. Steve has published papers relative to this topic. My greatest contribution was the derivation that the required gain for the gain blocks needed to be > 4000 for minimum acceptable performance. Efficiency is horrible to some power but we were working around 10W using cascode MOSFET gain blocks I believe.

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#11

Re: Negative Capacitance

05/13/2015 10:00 AM

This is a completely new concept for me, If I had a set of calculations that said I needed a negative capacitance, negative inductance, or negative resistance. My first thought would be to double-check the math by hand, as the formula may not be right. Then I'd look for every point where roots are taken, because the nth root of Xn is ±X, when n is even, and polarities may get flipped there. Finally I'd conclude that the circuit needs to have some of its values adjusted, as some section is WAY out of bounds to drive another into negative fundamental values to balance things out.

Remember, computers are wonderful tools, they allow humans to make thousands more mistakes per minute than they could on their own. In other words, don't trust computer simulations implicitly, whether an RF circuit design program or a GPS-based navigation system. All it takes is one bit to flop when it should have flipped, and suddenly you're looking for a capacitor with negative farads, or driving down a runway to get to the airport because the navigation map has incorrectly identified it as a drivable street.

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#15
In reply to #11

Re: Negative Capacitance

05/14/2015 12:52 AM

Yes.

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