Name: capacitance multiplier circuit for larger capacitance
Uploaded: 2025-05-22T09:06:15.000Z
Duration: 1 min 20 s
Channel: JoVE

Capacitance multiplier circuits are used in integrated circuits to produce a multiple of a small physical capacitance when a high-value capacitance is required.
These circuits are designed using a combination of op-amps, resistors, and capacitors.
The first op-amp in the circuit functions as a voltage follower, while the second op-amp acts as an inverting amplifier.
The voltage follower isolates the capacitance formed by the circuit from the loading imposed by the inverting amplifier.
As no current enters the input terminals of the op-amp, the input current flows through the feedback capacitor.
By applying KCL, a relationship between input and output voltage in terms of resistances is obtained, which can be substituted into the current expression.
Rearranging the expressions further helps determine the input impedance.
By selecting appropriate resistance values, an effective capacitance between the input terminal and ground can be generated, which is a multiple of the physical capacitance.
To prevent op-amps from saturating, the effective capacitance is limited by the inverted output voltage. As capacitance multiplication increases, the maximum allowable input voltage must decrease.

design example: capacitance multiplier circuit

In integrated circuit technology, a capacitance multiplier is often utilized to produce a larger capacitance value when a small physical capacitance falls short. This is achieved by a circuit that multiplies capacitance values by a factor of up to 1000, such that a 10-pF capacitor can replicate the performance of a 100-nF capacitor.
The circuit illustrated in Figure 1 below incorporates two op-amps, with the first operating as a voltage follower and the second acting as an inverting amplifier.
<img alt="Operational amplifier circuit diagram, voltage input Vi, feedback loop, resistors R1, R2, capacitor C." src="/files/ftp_upload/15176/15176_PT_Figure_1.svg" style="text-align: center; height: 200px;" data-altupdatedat="1754904545000" data-alt="RC circuit diagram with op-amps A1, A2; resistor R1=2, capacitor C; analyzing feedback network." />
Figure 1: Capacitance Multiplier
The voltage follower functions to isolate the capacitance created by the circuit from the loading incurred by the inverting amplifier. Since no current enters the op amp's input terminals, the feedback capacitor carries the input current.
By applying Kirchhoff's Current Law (KCL), a relation between input and output voltage with respect to resistances can be established, which can be further substituted into the current expression. Rearranging the expressions aids in determining the input impedance. By selecting appropriate resistance values, an effective capacitance can be generated between the input terminal and ground that is a multiple of the physical capacitance.
To prevent op-amps from saturating, the effective capacitance must be limited by the inverted output voltage. As the capacitance multiplication increases, the maximum allowable input voltage must decrease. Capacitance multiplier circuits such as this one provide an efficient solution for generating larger capacitances without increasing the physical capacitance.

Design Example: Capacitance Multiplier Circuit

In integrated circuit technology, a capacitance multiplier is often utilized to produce a larger capacitance value when a small physical capacitance falls ...

design-example-capacitance-multiplier-circuit

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Electrical Engineering

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AC Circuit Analysis

KEY TERMS AND CONCEPTS

capacitance multiplier circuit for larger capacitance

A capacitance multiplier circuit creates a larger effective capacitance from a small physical capacitor. In integrated circuit technology, this approach is useful when a small capacitor is not enough. The circuit can multiply capacitance by as much as 1000, so a 10-pF capacitor can act like a 100-nF capacitor.

The design uses two op-amps. The first op-amp works as a voltage follower, which helps isolate the generated capacitance from the loading caused by the second stage. The second op-amp works as an inverting amplifier.

No current enters the op amp input terminals, so the feedback capacitor carries the input current. Kirchhoff’s Current Law, or KCL, is then used to relate the input and output voltages through the resistances. That relationship can be placed into the current expression and rearranged to find the input impedance.

By choosing the resistance values, the circuit produces an effective capacitance between the input terminal and ground. This effective capacitance is a multiple of the actual capacitor value. The multiplication is limited by the inverted output voltage, so the op-amps do not saturate. As the multiplication factor increases, the maximum input voltage must decrease. Capacitance multiplier circuits provide an efficient way to generate larger capacitances without using a larger physical capacitor.

Capacitance Multiplier Circuit for Larger Capacitance

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A capacitance multiplier circuit creates a larger effective capacitance from a small physical capacitor. In integrated circuit technology, this approach is useful when a small capacitor is not enough. The circuit can multiply capacitance by as much as 1000, so a 10-pF capacitor can act like a 100-nF capacitor. The design uses two op-amps. The first op-amp works as a voltage follower, which helps isolate the generated capacitance from the loading caused by the second stage. The second op-amp...

key terms and concepts

Learn how a capacitance multiplier circuit uses two op-amps, KCL, and resistor choices to create a larger effective capacitance from a small capacitor.

Capacitance Multiplier Circuit for Larger Capacitance | JoVE K12

JoVE Core Electrical Engineering offers easy-to-understand animated videos that cover fundamental concepts of electric circuits along with circuit analysis techniques. It incorporates first-order and second-order circuits using operational amplifiers and circuit transformation concepts. The inclusion of practical design examples and real-world applications through scientist-in-action videos adds significant educational value, making complex concepts accessible.

electrical engineering

Capacitance Multiplier Circuit for Larger Capacitance

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