Opamp-circuits van de tweede orde

Consider an audio system that utilizes a second-order low-pass filter to eliminate the undesirable high-frequency noise in the audio signal.

This setup includes a second-order op-amp circuit with a voltage follower configuration and two nodes comprising of two storage elements.

Applying Kirchhoff's current law at these nodes yields two differential equations.

Additionally, the voltage across the feedback capacitor equals the resistor's voltage minus the other capacitor's voltage.

These equations can be utilized to eliminate the capacitor voltages from the KCL equation at the first node.

The result is a second-order characteristic differential equation.

The solution to this differential equation encompasses both transient and steady-state responses.

The transient response dissipates over time and resembles the solution for source-free circuits in overdamped, underdamped, and critically damped scenarios.

When the circuit reaches a steady state, no current flows through the capacitors or resistors, and the input terminals of the ideal opamp prevent current inflow. As a result, the steady-state response matches the source voltage.

Eliminating the input source voltage leads to a purely transient response.