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1.1 Find the relationship between V and V in circuits a and b of figure 1 assuming b) a) R R mmm Vout - Vout ideal op-amps Figure 1: a) Op-amp with capacitor and b) op-amp with an inductor. 1.2 AssumeV (t) = A sin(20ft). Using the formula in part 1.1, simplify Vand report the maximum value of V out °Ţ₁

1.1 Find the relationship between V and V in circuits a and b of figure 1 assuming b) a) R R mmm Vout - Vout ideal op-amps Figure 1: a) Op-amp with capacitor and b) op-amp with an inductor. 1.2 AssumeV (t) = A sin(20ft). Using the formula in part 1.1, simplify Vand report the maximum value of V out °Ţ₁

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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### Understanding Op-Amp Circuits #### 1.1 Analysis We aim to find the relationship between \( V_{out} \) and \( V_{in} \) in circuits a and b shown in Figure 1, assuming ideal operational amplifiers (op-amps). - **Figure 1a: Op-Amp with Capacitor** This circuit includes: - A resistor \( R \) connected in series after an input voltage \( V_{in} \). - A capacitor \( C \) connected in parallel with the op-amp. - The output voltage \( V_{out} \) is taken from the op-amp. - **Figure 1b: Op-Amp with Inductor** This circuit includes: - A resistor \( R \) connected in series after an input voltage \( V_{in} \). - An inductor \( L \) connected in parallel with the op-amp. - The output voltage \( V_{out} \) is taken from the op-amp. #### Figure Description - **Ideal op-amps**: The op-amps are assumed to be ideal in this problem. #### 1.2 AC Signal Analysis Given: \[ V_{in} (t) = A_{in} \sin(2\pi ft) \] Using the formula derived in part 1.1, we will: 1. Simplify \( V_{out} \). 2. Report the maximum value of \( V_{out} \). This problem involves applying AC analysis, where the input voltage is a sinusoidal function. The detailed steps would involve solving the differential equations governing the circuits and applying the properties of ideal op-amps to determine \( V_{out} \). The maximum value of \( V_{out} \) would generally correspond to the amplitude of the resultant output sine wave derived from the analysis. The exact calculations and results depend on the specific relationships found from part 1.1.
Transcribed Image Text:### Understanding Op-Amp Circuits #### 1.1 Analysis We aim to find the relationship between \( V_{out} \) and \( V_{in} \) in circuits a and b shown in Figure 1, assuming ideal operational amplifiers (op-amps). - **Figure 1a: Op-Amp with Capacitor** This circuit includes: - A resistor \( R \) connected in series after an input voltage \( V_{in} \). - A capacitor \( C \) connected in parallel with the op-amp. - The output voltage \( V_{out} \) is taken from the op-amp. - **Figure 1b: Op-Amp with Inductor** This circuit includes: - A resistor \( R \) connected in series after an input voltage \( V_{in} \). - An inductor \( L \) connected in parallel with the op-amp. - The output voltage \( V_{out} \) is taken from the op-amp. #### Figure Description - **Ideal op-amps**: The op-amps are assumed to be ideal in this problem. #### 1.2 AC Signal Analysis Given: \[ V_{in} (t) = A_{in} \sin(2\pi ft) \] Using the formula derived in part 1.1, we will: 1. Simplify \( V_{out} \). 2. Report the maximum value of \( V_{out} \). This problem involves applying AC analysis, where the input voltage is a sinusoidal function. The detailed steps would involve solving the differential equations governing the circuits and applying the properties of ideal op-amps to determine \( V_{out} \). The maximum value of \( V_{out} \) would generally correspond to the amplitude of the resultant output sine wave derived from the analysis. The exact calculations and results depend on the specific relationships found from part 1.1.
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