For the op amp circuit of Fig. 5.43, the op amp has an...

For the op amp circuit of Fig. $5.43,$ the op amp has an open-loop gain of 100,000 , an input resistance of $10 \mathrm{k} \Omega,$ and an output resistance of $100 \Omega$. Find the voltage gain $v_{o} / v_{i}$ using the nonideal model of the op amp.

Key Concepts

Open-Loop Gain

Open-loop gain is the amplification factor provided by the op amp without any feedback applied. Even though it is typically very high in practical op amps, its finite nature influences how well the feedback network can control the overall closed-loop gain of the circuit, and thus, it plays a vital role in determining the precision of amplification.

Feedback and Closed-Loop Gain Analysis

The process of applying negative feedback to an op amp circuit involves calculating the closed-loop gain, which relies on both the external resistor network and the inherent nonideal characteristics of the op amp. This concept is crucial in circuit design because feedback determines circuit stability, bandwidth, and the accuracy of the intended gain, making it a key focus in practical amplifier applications.

Output Resistance

Output resistance is the resistance seen by the load connected to the op amp’s output. Since real op amps do not have zero output impedance, voltage drops across this internal resistance can occur when driving loads, which affects the delivered voltage and, consequently, the overall gain of the circuit.

Nonideal Operational Amplifier Model

This concept refers to the representation of an operational amplifier that includes real-world imperfections such as finite open?loop gain, finite input resistance, and nonzero output resistance. Understanding this model is crucial when predicting how op amp circuits actually behave compared to the idealized version most often taught in basic courses.

Input Resistance

Input resistance is the effective resistance observed at the op amp’s input terminals. In a nonideal op amp, this resistance is finite, meaning that some current will be drawn from the signal source, affecting voltage levels and potentially interacting with the surrounding circuit elements, especially in high-impedance configurations.

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