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Design an integrator as shown in figure 2 to be operated with an AC signal of 5 kHz and to give a closed loop voltage gain of Af = 10 at w=1 rad/s.

Design an integrator as shown in figure 2 to be operated with an AC signal of 5 kHz and to give a closed loop voltage gain of Af = 10 at w=1 rad/s.

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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Solve Figure 2, 3, and 4. Please do it step by step without jumping any mathematical steps -for example, if you have to factor out dont just write the result of the factorization, but show the process-. And explain what is heppening in relevant steps. Thank you.

**Educational Explanation of Two Amplifier Circuits** **Figure 1: Difference Amplifier** The difference amplifier in Figure 1 is characterized by the following values: - Open-loop gain \( A_0 = 5 \times 10^5 \) - Resistors: - \( R_1 = 5 \, \text{k}\Omega \) - \( R_F = 50 \, \text{k}\Omega \) - \( R_a = 2 \, \text{k}\Omega \) - \( R_x = 20 \, \text{k}\Omega \) The input voltages are: - \( v_b = 5 \, \text{mV} \) - \( v_a = -15 \, \text{mV} \) The task is to find the output voltage \( v_o \). The diagram shows an operational amplifier (op-amp) used in a difference amplifier configuration. It processes two input voltages and amplifies the difference between these inputs. The circuit includes feedback and input resistors to define its gain and input impedance. **Figure 2: Integrator Design** Figure 2 illustrates a design for an integrator circuit. This design is intended to be operated with: - An AC signal of 5 kHz - A closed-loop voltage gain \( A_f = 10 \) at \( \omega = 1 \, \text{rad/s} \) The components involved are: - Resistors: \( R_1 \) and \( R_F \) - Capacitor: \( C_F \) - Power supply voltages: \( +V_{CC} \) and \( -V_{EE} \) This circuit setup uses an op-amp with a feedback capacitor to integrate the input signal over time, providing an output proportional to the integral of the input voltage. The resistor \( R_x \) is set as the parallel combination of \( R_1 \) and \( R_F \). The diagrams contain multiple circuit notations including: - Inverting and non-inverting inputs (\(+\) and \(-\) terminals) - Feedback paths - Input and output points marked with voltages (\(v_i, v_o\)) This explanation aims to provide insight into the workings of amplifier and integrator circuits through practical configurations and component specifications.
Transcribed Image Text:**Educational Explanation of Two Amplifier Circuits** **Figure 1: Difference Amplifier** The difference amplifier in Figure 1 is characterized by the following values: - Open-loop gain \( A_0 = 5 \times 10^5 \) - Resistors: - \( R_1 = 5 \, \text{k}\Omega \) - \( R_F = 50 \, \text{k}\Omega \) - \( R_a = 2 \, \text{k}\Omega \) - \( R_x = 20 \, \text{k}\Omega \) The input voltages are: - \( v_b = 5 \, \text{mV} \) - \( v_a = -15 \, \text{mV} \) The task is to find the output voltage \( v_o \). The diagram shows an operational amplifier (op-amp) used in a difference amplifier configuration. It processes two input voltages and amplifies the difference between these inputs. The circuit includes feedback and input resistors to define its gain and input impedance. **Figure 2: Integrator Design** Figure 2 illustrates a design for an integrator circuit. This design is intended to be operated with: - An AC signal of 5 kHz - A closed-loop voltage gain \( A_f = 10 \) at \( \omega = 1 \, \text{rad/s} \) The components involved are: - Resistors: \( R_1 \) and \( R_F \) - Capacitor: \( C_F \) - Power supply voltages: \( +V_{CC} \) and \( -V_{EE} \) This circuit setup uses an op-amp with a feedback capacitor to integrate the input signal over time, providing an output proportional to the integral of the input voltage. The resistor \( R_x \) is set as the parallel combination of \( R_1 \) and \( R_F \). The diagrams contain multiple circuit notations including: - Inverting and non-inverting inputs (\(+\) and \(-\) terminals) - Feedback paths - Input and output points marked with voltages (\(v_i, v_o\)) This explanation aims to provide insight into the workings of amplifier and integrator circuits through practical configurations and component specifications.
**Design a Differentiator Circuit** **Objective:** Design a differentiator circuit as shown in **Figure 3** to achieve \( f_L = 5 \text{kHz} \) and \( f_H = 10 \text{kHz} \). The pass band gain is \(|A_{PB}| = 20\). Use PSpice/Multisim to verify your answer. Upload a snapshot of the PSpice/Multisim output. **Figure 3: Differentiator Circuit Diagram** - **Components and Notations:** - \( C_1 \): Capacitor - \( R_1, R_F \): Resistors - \( R_x = R_F \): Feedback resistor - \( A = \infty \): Operational amplifier with infinite open-loop gain - \( v_s \): Input voltage - \( v_o \): Output voltage **Two Inverting Op-Amps Cascaded** **Objective:** Explore the circuit shown in **Figure 4**, consisting of two cascaded inverting op-amps. The unity-gain bandwidth of the op-amps is \( f_u = 1 \text{MHz} \), and the slew rate is \( SR = 6 \text{V/ms} \). 1. **Analysis:** a. Given: - \( R_1 = 20 \text{k}\Omega \) - \( R_2 = 100 \text{k}\Omega \) - \( R_3 = 150 \text{k}\Omega \) - \( R_4 = 520 \text{k}\Omega \) - \( R_5 = 160 \text{k}\Omega \) Determine the voltage gain \( A_f = \frac{v_o}{v_1} \). 2. **Verification:** b. Use PSpice/Multisim to verify your results. Upload a snapshot of the PSpice/Multisim output. **Figure 4: Cascaded Inverting Op-Amps Diagram** - **Components and Notations:** - \( R_1, R_2, R_3, R_4, R_5 \): Resistors - \( v_1 \): Input voltage - \( v_{o1} \): Intermediate voltage output of the first op-amp - \( v_o \): Final output
Transcribed Image Text:**Design a Differentiator Circuit** **Objective:** Design a differentiator circuit as shown in **Figure 3** to achieve \( f_L = 5 \text{kHz} \) and \( f_H = 10 \text{kHz} \). The pass band gain is \(|A_{PB}| = 20\). Use PSpice/Multisim to verify your answer. Upload a snapshot of the PSpice/Multisim output. **Figure 3: Differentiator Circuit Diagram** - **Components and Notations:** - \( C_1 \): Capacitor - \( R_1, R_F \): Resistors - \( R_x = R_F \): Feedback resistor - \( A = \infty \): Operational amplifier with infinite open-loop gain - \( v_s \): Input voltage - \( v_o \): Output voltage **Two Inverting Op-Amps Cascaded** **Objective:** Explore the circuit shown in **Figure 4**, consisting of two cascaded inverting op-amps. The unity-gain bandwidth of the op-amps is \( f_u = 1 \text{MHz} \), and the slew rate is \( SR = 6 \text{V/ms} \). 1. **Analysis:** a. Given: - \( R_1 = 20 \text{k}\Omega \) - \( R_2 = 100 \text{k}\Omega \) - \( R_3 = 150 \text{k}\Omega \) - \( R_4 = 520 \text{k}\Omega \) - \( R_5 = 160 \text{k}\Omega \) Determine the voltage gain \( A_f = \frac{v_o}{v_1} \). 2. **Verification:** b. Use PSpice/Multisim to verify your results. Upload a snapshot of the PSpice/Multisim output. **Figure 4: Cascaded Inverting Op-Amps Diagram** - **Components and Notations:** - \( R_1, R_2, R_3, R_4, R_5 \): Resistors - \( v_1 \): Input voltage - \( v_{o1} \): Intermediate voltage output of the first op-amp - \( v_o \): Final output
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