Design Example: Capacitance Multiplier Circuit

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.

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.

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.

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.

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.

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.

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.