Question 1

What is a capacitance multiplier circuit and why is it used?

Accepted Answer

A capacitance multiplier circuit produces a larger capacitance value when a small physical capacitance is insufficient for integrated circuit applications. The circuit multiplies capacitance by factors up to 1000, allowing a 10-pF capacitor to replicate the performance of a 100-nF capacitor. This efficient solution generates larger capacitances without increasing physical component size.

Question 2

How do the two op-amps function in a capacitance multiplier circuit?

Accepted Answer

The first op-amp operates as a voltage follower to isolate the multiplied capacitance from loading effects imposed by the second op-amp. The second op-amp functions as an inverting amplifier. Since no current enters op-amp input terminals, the feedback capacitor carries all input current, enabling the circuit to generate effective capacitance through this configuration.

Question 3

How is effective capacitance calculated in a multiplier circuit?

Accepted Answer

By applying Kirchhoff's Current Law, a relationship between input and output voltage with respect to resistances is established. This relationship is substituted into the current expression and rearranged to determine input impedance. By selecting appropriate resistance values, an effective capacitance between the input terminal and ground is generated as a multiple of the physical capacitance.

Question 4

What limits the maximum capacitance multiplication factor?

Accepted Answer

Op-amp saturation limits the effective capacitance by constraining the inverted output voltage. As capacitance multiplication increases, the maximum allowable input voltage must decrease to prevent saturation. This inverse relationship between multiplication factor and input voltage represents a fundamental design constraint in capacitance multiplier circuits.

Question 5

Why does the voltage follower isolate the capacitance in this circuit?

Accepted Answer

The voltage follower isolates the multiplied capacitance from the loading imposed by the inverting amplifier stage. This isolation is critical because no current enters the op-amp's input terminals, forcing all input current through the feedback capacitor. Without this isolation, the inverting amplifier would load the capacitance and degrade circuit performance.

Question 6

What role does the feedback capacitor play in the circuit?

Accepted Answer

The feedback capacitor carries all input current since no current enters the op-amp input terminals. This capacitor is fundamental to the circuit's operation, as the current flowing through it, combined with appropriate resistance values, creates the effective multiplied capacitance. The feedback network design directly determines the multiplication factor achieved.

Question 7

How do resistance values affect the capacitance multiplication factor?

Accepted Answer

Selecting appropriate resistance values determines the effective capacitance generated between the input terminal and ground. The relationship between input and output voltage depends on these resistances, which are substituted into current expressions to calculate input impedance. Resistance selection directly controls the multiplication factor and overall circuit performance.

设计示例：电容倍增器