6.15:
Op Amp AC Circuits
In an audio system, the filter circuit processes the amplified audio signal from an amplifier, strongly attenuating the signal components with low frequencies.
Consider the simplest filter circuit consisting of an op-amp in an inverting configuration coupled with resistors R1 and R2 and capacitor C1. What is the resultant output signal for a known input signal?
The capacitor's impedance is calculated using the angular frequency derived from the time domain expression for input voltage.
The frequency domain equivalent circuit represents the input signal in polar form and impedances Z1 and Z2. The impedance Z2 corresponds to the parallel combination of capacitor C1 and resistor R2.
Applying Kirchoff's current law and Ohm's law at the node yields a nodal equation for an ideal op-amp. This equation, when rearranged, indicates that the ratio of the output to the input voltage equals the negative ratio of the impedances.
By substituting the known and calculated values into this equation, the output voltage is determined in polar form, which is then converted into the time domain.
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.