Variable Capacitance Multiplier Design with Op Amp

Implementation and analysis of a variable capacitance multiplier circuit are presented in this video. This circuit is useful in applications where a large adjustable capacitance is needed. This Analog circuit is implemented with two operational amplifiers and one potentiometer. In an alternative implementation we can use a digital potentiometer or RDAC. How does capacitor multiplier work is intuitively discussed in this video. This circuit is utilizing a combination of positive feedback and more dominant negative feedback. The positive feedback is enabling the larger than one scaling of the value of the internal 100 nano Farad capacitor in this circuit. The first Op Amp stage is wired as a buffer (unity-gain amplifier) and the second OpAmp stage is effectively an inverting amplifier in the frequency range of interest for this circuit. Both Op Amps are assumed to be stable and operating in linear region (not saturated) enforced by the dominant negative feedback that also enforces virtual short between positive and negative input terminals of op amp (virtual short). To find input impedance of this programmable capacitor multiplier circuit, a test voltage is applied at the input of the circuit and then the resulting input current is found. It is then shown that the input impedance is purely simulating an scaled capacitor whose value is adjustable by the potentiometer in the circuit. For more circuit design videos please see the analog circuit and signal processing video playlist • Electrical Engineering... .

[@mr1enrollment]

So prof,... this is a ground connected C on one side.
If + input of Amp2 were un:grounded - could the circuit topology support a floating G*Cap1?
Imagine using two of these circuits in a Wien Bridge Oscillator.
I suspect so, but also imagine some challenges with the result.
Comment?

[@STEMprof]

Thanks for watching and sharing your thoughts. I am afraid we can't un-ground the positive (non-inverting) input terminal of the second Op Amp as it destabilizes the circuit. But to your point, simulated floating impedance (capacitor or inductor) has practical applications. Few examples of such circuits and applications are: Simulated floating inductor realized by converting a Capacitance to inductance ua-cam.com/video/weIHG45G6Pg/v-deo.html
and Butterworth Filter Design with Capacitor Multiplier, Op Amp and Transistor ua-cam.com/video/9CFPe76vAtg/v-deo.html
I hope these videos are helpful and interesting.

[@mr1enrollment]

I believe then, in principal using a transformer at the input will provide a "floating" capacitive reactance --- at least over a useful frequency range. @@STEMprof
???
It works in Spice but yeah spice is spice, not real circuits.

[@STEMprof]

Implementation and analysis of a variable capacitance multiplier circuit are presented in this video. This circuit is useful in applications where a large adjustable capacitance is needed. This Analog circuit is implemented with two operational amplifiers and one potentiometer. For more circuit design videos please see the analog circuit and signal processing video playlist ua-cam.com/play/PLrwXF7N522y4c7c-8KBjrwd7IyaZfWxyt.html
And Digital Circuits and DSP playlist ua-cam.com/play/PLrwXF7N522y6cSKr0FmEPP_zQl011VvLr.html
Thanks for watching.

[@TomLeg]

What is "S"?

[@STEMprof]

In S domain circuit Analysis, the circuit is transformed from time domain to Laplace domain where derivativative of variable is represented by multiplying variable with S and integrating a variable is represented by dividing it by S. I hope this is helpful.

[@TomLeg]

@@STEMprof I'm afraid you might as well have been speaking Chinese. Is there somewhere I can learn about this?

[@STEMprof]

@@TomLeg Please watch the video: Analog Computer that solves Differential Equation ua-cam.com/video/ENq39EesfPw/v-deo.html . I hope it helps with explaining what I meant by S domain circuit analysis.