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Description of the Variable Capacitance Multiplier
The circuit shown is a variable capacitance multiplier, also known as an active capacitance simulator. From the point of view of the input node, the network behaves as if a much larger capacitor were connected to ground, even though the physical capacitor used is relatively small. The effective capacitance can be continuously adjusted by means of a resistive control network.
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1. Basic operating concept
A capacitance multiplier uses an operational amplifier to scale up the apparent value of a capacitor. Instead of increasing capacitance by adding large or electrolytic components, the circuit uses gain and feedback to make a small, stable capacitor appear electrically much larger.
Seen from the input node, the circuit draws current in the same way a large capacitor would, producing the same low-frequency filtering effect.
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2. Role of the operational amplifier
The operational amplifier, shown with very high open-loop gain, acts as a buffer and active feedback element.
Its functions are
to isolate the capacitor from the load
to reproduce the voltage variations at its input at the output
to force additional current through the capacitor via feedback
Because of this action, the current drawn from the input node is multiplied, which is perceived as an increase in capacitance.
The 100 ohm resistor at the output
improves stability
limits output current
isolates the amplifier from the capacitive load
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3. Capacitor multiplication mechanism
The real capacitor in the circuit is the 1 nF capacitor connected from the inverting input to ground. On its own, this capacitor is very small and would have little effect at low frequencies.
However, the operational amplifier senses voltage changes at its input and drives its output so that the voltage across the capacitor follows these changes with gain. As a result, the capacitor draws a proportionally larger current, exactly as if its value had been increased.
From the input node perspective, this looks like a much larger capacitor connected to ground.
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4. Variable gain and tuning network
The chain of resistors consisting of
two 5 kΩ resistors
a 1 kΩ resistor
and the adjustable tap between the two 5 kΩ resistors
forms a variable gain network.
By moving the adjustment point, the effective feedback factor of the operational amplifier is changed. This directly controls how strongly the capacitor current is multiplied.
As the gain increases
the effective capacitance increases
As the gain decreases
the effective capacitance decreases
This makes the apparent capacitance continuously adjustable.
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5. Input and output behavior
The 10 kΩ resistor at the input isolates the source and defines the interaction between the signal source and the multiplied capacitance.
At the right side of the circuit, the multiplied capacitance appears in series with a 100 ohm resistor and a 220 microfarad capacitor, which together provide additional filtering and stabilization. The large capacitor ensures low-frequency stability and reduces noise, while the resistor prevents oscillation.
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6. Frequency response and limitations
At low and mid frequencies, the circuit behaves very closely to an ideal large capacitor.
At higher frequencies, the behavior departs from ideal due to
finite op amp bandwidth
slew rate limitations
phase shift in the feedback loop
For correct operation, the op amp must have sufficient gain-bandwidth product relative to the highest frequency of interest.
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7. Typical applications
Power supply ripple reduction without large electrolytic capacitors
Active low-pass filters with tunable cutoff frequency
Signal conditioning in audio and instrumentation circuits
Laboratory demonstrations of active impedance scaling
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Summary
This circuit uses an operational amplifier and a small physical capacitor to simulate a large, adjustable capacitance. The effective capacitance is controlled by a resistive tuning network, allowing smooth adjustment without changing the actual capacitor. It is particularly useful where large capacitors are undesirable, unstable, or impractical.
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