(a) Determine the voltage gain of the inverting amplifier...

(a) Determine the voltage gain of the inverting amplifier circuit shown in Figure P9.47 using the op amp model of Figure 9.3. Assume $A_v=50, R_2=10 \mathrm{k} \Omega, R_1=1 \mathrm{k} \Omega$. (b) Repeat (a) with $A_v=500$. (c) Repeat (a) taking the limit as $A_v \rightarrow \infty$. Figure P9.47 can't copy

Key Concepts

Finite Open-Loop Gain

Real-world op amps have a finite open-loop gain, which impacts the accuracy of the amplification in feedback configurations. When the open-loop gain is not infinite, the assumptions leading to the simple -R2/R1 gain expression are not perfectly met. Instead, corrections must be made to account for the finite value, and the actual voltage gain of the inverting amplifier will slightly differ from the ideal case, particularly when the magnitude of the open-loop gain is relatively low.

Closed-Loop Gain Calculation

The closed-loop gain of an inverting amplifier is determined by the ratio of the feedback resistor to the input resistor, typically given by -R2/R1 under the assumption of an ideal op amp (with infinite open-loop gain). This ideal relationship is modified when taking into account the finite open-loop gain, which introduces error terms and slightly alters the effective closed-loop gain compared to the ideal case.

Virtual Ground Concept

In the inverting amplifier setup, the negative input of the op amp is held at a potential very close to the positive input (which is at ground) because of the high open-loop gain of the op amp. This condition, known as the virtual ground, simplifies analysis since the voltage at the inverting terminal can be assumed to be approximately zero volts, even though it is not directly connected to ground.

Inverting Amplifier Configuration

An inverting amplifier is an operational amplifier circuit where the input signal is applied to the inverting (-) terminal while the non-inverting (+) terminal is typically connected to ground. The circuit uses a resistor network to feed a portion of the output back to the inverting terminal, resulting in a signal that is inverted (180 degrees out of phase) relative to the input. This configuration is widely used because it allows for precise control of the gain through the resistor values.

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