# Design a circuit whose impedance is 1/(omega*C)

#### shivashankar_p

Joined Nov 10, 2015
50
Hi,

I want to realize an impedance which is 1/(omega*C). Basically, a capacitor without any phase shift (or a resistor whose resistance varies inversely with frequency). How can I realize this? Is there any circuit (Op-Amp based) that can be used to realize this? I am thinking of a simple phase-shifter in series with a capacitor.

Thanks

#### Wolframore

Joined Jan 21, 2019
2,610
You’re over complicating

$Xc = 1/\omega C$ what happens when $\omega$ goes to 0, and what happens when it goes to infinity? Now design the circuit.

#### Papabravo

Joined Feb 24, 2006
21,264
Hi,

I want to realize an impedance which is 1/(omega*C). Basically, a capacitor without any phase shift (or a resistor whose resistance varies inversely with frequency). How can I realize this? Is there any circuit (Op-Amp based) that can be used to realize this? I am thinking of a simple phase-shifter in series with a capacitor.

Thanks
Do you mean in simulation or in a real circuit?
You certainly know the formula for the magnitude of a complex impedance. If you know anything about complex numbers then you know they can be expressed in polar form. To express something in polar form you need a magnitude and and an angle. This angle will the inverse tangent of the ratio of the imaginary part to the real part. We know the magnitude of the imaginary part, but the real part is the ever present ESR (Equivalent Series Resistance). So we end up with a magnitude of omega*C and an angle of very close to -90°. If you have ever watched the sweep of a capacitor on a VNA you will see that the complex impedance will circle the origin. Truly a freakish site!

So for a real part the answer is no. How about a combination of parts? If we are limited to passive components, I think it is unlikely. For an opamp circuit, I have never seen or heard of one that would do this. There are circuits that can be used to provide lead and lag over narrow frequency ranges, but nothing that is true over a wide range. There is also the allpass filter that has a gain of 1 (or 0dB) but changes the phase as a function of frequency, and there is the Bessel filter that has constant group delay in the passband.

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#### shivashankar_p

Joined Nov 10, 2015
50
Thanks for the reply. I want to build a real circuit, perhaps with opamps. Maybe operating near a narrow band of frequency.

#### Papabravo

Joined Feb 24, 2006
21,264
Thanks for the reply. I want to build a real circuit, perhaps with opamps. Maybe operating near a narrow band of frequency.
Good luck, but I think you're going to have a hard time of it.

#### Wolframore

Joined Jan 21, 2019
2,610
Ah, I missed the part about not having phase change.. have a look at gyrator.

#### shivashankar_p

Joined Nov 10, 2015
50
Good luck, but I think you're going to have a hard time of it.
Isn't there any standard circuit for this (like that of an frequency dependent negative resistance or so)?

#### Papabravo

Joined Feb 24, 2006
21,264
Isn't there any standard circuit for this (like that of an frequency dependent negative resistance or so)?
Not that I am aware of. Maybe you know something that I don't. It could happen.

#### MisterBill2

Joined Jan 23, 2018
19,069
Creating a capacitor whose leakage resistance approaches infinity is a challenge all in itself, and then using that capacitor burdens the action with unfortunate reality.
Bob Pease presented a few articles about reducing leakage, and they would be worth reading. And there is little use for a perfect capacitor becauseas soon as it is in a real circuit the actual situation is much farther from ideal.