Revisit the exact analysis of the inverting amplifier in...

Revisit the exact analysis of the inverting amplifier in Section 4.3. (a) Find an expression for the voltage gain if $R_{\text {in }} \neq \infty$ $R_{\mathrm{out}}=0, A_{o} \neq \infty$ (b) For $R_{2}=27 \mathrm{k} \Omega$ and $R_{1}=3 \mathrm{k} \Omega,$ plot the ratio of the actual gain to the ideal gain for $A_{e}=1000$ and $1 \mathrm{k} \Omega \leq R_{\mathrm{in}} \leq 100 \mathrm{k} \Omega$ (c) From your plot, does the ratio approach unity as $R_{\text {in }}$ increases or decreases? (d) From your plot in (b), what is the minimum value of $R_{\text {in }}$ if the gain ratio is to be at least $0.98 ?$

Revisit the exact analysis of the inverting amplifier in Section 4.3.
(a) Find an expression for the voltage gain if $R_{\text {in }} \neq \infty$ $R_{\mathrm{out}}=0, A_{o} \neq \infty$
(b) For $R_{2}=27 \mathrm{k} \Omega$ and $R_{1}=3 \mathrm{k} \Omega,$ plot the ratio of the actual gain to the ideal gain for $A_{e}=1000$ and $1 \mathrm{k} \Omega \leq R_{\mathrm{in}} \leq 100 \mathrm{k} \Omega$
(c) From your plot, does the ratio approach unity as $R_{\text {in }}$ increases or decreases?
(d) From your plot in (b), what is the minimum value of $R_{\text {in }}$ if the gain ratio is to be at least $0.98 ?$

Key Concepts

Inverting Amplifier Configuration

This concept involves understanding the classical inverting amplifier circuit, where an input signal is applied through a resistor to the inverting terminal of an operational amplifier, and a feedback resistor connects the output to the same inverting terminal. The noninverting terminal is typically grounded. The circuit is designed such that the gain is determined by the ratio of the feedback resistor to the input resistor, leading to an ideal voltage gain of -R2/R1 when the op?amp is assumed to be ideal.

Op-Amp Nonidealities

Real operational amplifiers deviate from the ideal behavior, especially in terms of finite open-loop gain (A_o) and non-infinite input impedance (R_in). Finite open-loop gain means that the amplifier cannot drive the differential voltage exactly to zero, and a finite input impedance implies that the amplifier draws some input current, therefore altering node voltages. These nonideal characteristics must be included in the analysis for accurate performance prediction of the circuit.

Feedback Network and Closed-Loop Gain Analysis

Deriving the closed-loop gain involves analyzing the amplifier with its feedback network while taking into account the nonideal parameters. The analysis incorporates the voltage divider effect created by R_in and the resistors in the network, along with the finite open-loop gain A_o. The resulting expression for voltage gain will show correction factors to the ideal gain of -R2/R1, indicating the influence of the noninfinite input impedance and finite gain on the amplifier’s performance.

Gain Ratio and Tolerance in Practical Design

In practical circuit design, it is important to quantify how close the actual gain of a nonideal amplifier approaches the ideal value. This is typically done by plotting the ratio of the actual gain to the ideal gain as a function of the finite parameters, such as R_in. The analysis then involves identifying conditions (for example, a minimum R_in) under which the gain error stays within acceptable tolerances (such as a ratio of at least 0.98). This approach is crucial in ensuring reliable circuit function within specified design margins.

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