6.15 : Op Amp AC Circuits

Within an audio system, the filter circuit plays a pivotal role in processing the amplified audio signal from an amplifier. Its primary function is significantly attenuating signal components with lower frequencies, thereby shaping the audio output. This circuit's operations are examined, focusing on the fundamental filter configuration. This configuration involves an operational amplifier arranged in an inverting setup coupled with resistors (R₁ and R₂) and a capacitor (C₁).

When faced with a known input signal, the challenge lies in determining the resultant output signal. The first step involves calculating the capacitor's impedance, which is achieved by employing the angular frequency derived from the time-domain expression of the input voltage.

As a result, the analysis transitions into the frequency domain, where the input signal is represented in polar form alongside the impedance components Z₁ and Z₂. Z₂ relates explicitly to the parallel combination of capacitor C₁ and resistor R₂. The core of the analysis rests on applying Kirchhoff's current law and Ohm's law at a specific node in the circuit, thereby formulating a nodal equation for an ideal op-amp. This equation, when rearranged, reveals a critical insight: the ratio of the output to the input voltage is inversely proportional to the ratio of impedances.

The known and calculated values are skillfully substituted into this equation to unveil the output voltage in polar form. The outcome, representing the output voltage, can then be transformed into the time domain, providing a comprehensive understanding of the filter circuit's response to the input signal. For the analysis, ideal op-amp properties are often assumed, including the principle that no current enters either of its input terminals and that the voltage across its input terminals remains zero.