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с 5. Consider the circuit on the left with two resistors, a capacitor and an ideal OP-AMP. You may make simplifying assumptions about the OP-AMP but you must state your assumptions clearly. R₁ R₂ VI (a) By making a suitable assumption for the capacitor, find the DC gain of this circuit, namely, (vo/VI)DC (Hint: How does the capacitor behave for steady- state DC voltages?) VO (b) Write down a general expression that relates vi to vo. You do not have to solve the equation yet. (c) Assuming the input voltage is a step function that is zero before t<0 and vi after t>0, obtain an expression for the output voltage assuming vo=0 at t=0. (d) Sketch the output voltage as a function of time using your result from (c). t> 0

с 5. Consider the circuit on the left with two resistors, a capacitor and an ideal OP-AMP. You may make simplifying assumptions about the OP-AMP but you must state your assumptions clearly. R₁ R₂ VI (a) By making a suitable assumption for the capacitor, find the DC gain of this circuit, namely, (vo/VI)DC (Hint: How does the capacitor behave for steady- state DC voltages?) VO (b) Write down a general expression that relates vi to vo. You do not have to solve the equation yet. (c) Assuming the input voltage is a step function that is zero before t<0 and vi after t>0, obtain an expression for the output voltage assuming vo=0 at t=0. (d) Sketch the output voltage as a function of time using your result from (c). t> 0

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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### Operational Amplifier Circuit Analysis #### Circuit Description Consider the circuit on the left with two resistors, a capacitor, and an ideal operational amplifier (OP-AMP). The input voltage \(v_I\) is a step function that is zero before \(t < 0\) and \(v_I\) for \(t > 0\). The circuit consists of the following components: - \(R_1\): Resistor - \(R_2\): Resistor - \(C\): Capacitor - Ideal OP-AMP #### Questions and Steps for Analysis 1. **DC Gain Calculation (a)**: By making a suitable assumption for the capacitor, find the DC gain of this circuit, namely, \((v_O/v_I)_{DC}\). (Hint: How does the capacitor behave for steady-state DC voltages?) 2. **General Expression (b)**: Write down a general expression that relates \(v_I\) to \(v_O\). You do not have to solve the equation yet. 3. **Step Function Input (c)**: Assuming the input voltage is a step function that is zero before \(t < 0\) and \(v_I\) after \(t > 0\), obtain an expression for the output voltage assuming \(v_O = 0\) at \(t = 0\). 4. **Output Voltage Sketch (d)**: Sketch the output voltage as a function of time using your result from (c). #### Explanation of Graphs and Diagrams - **Input Voltage Graph**: The input voltage graph shows a step function where \(v_I = 0\) for \(t < 0\) and \(v_I\) for \(t > 0\). This step function acts as an input to the OP-AMP circuit. - **Circuit Diagram**: The circuit diagram includes an ideal OP-AMP with the non-inverting input grounded. Resistor \(R_2\) connects the inverting input of the OP-AMP to the ground, while resistor \(R_1\) and capacitor \(C\) are connected in series between the input voltage \(v_I\) and the inverting input of the OP-AMP. The output voltage \(v_O\) is taken from the OP-AMP output. Through these steps and diagrams, the objective is to understand and analyze the behavior of the
Transcribed Image Text:### Operational Amplifier Circuit Analysis #### Circuit Description Consider the circuit on the left with two resistors, a capacitor, and an ideal operational amplifier (OP-AMP). The input voltage \(v_I\) is a step function that is zero before \(t < 0\) and \(v_I\) for \(t > 0\). The circuit consists of the following components: - \(R_1\): Resistor - \(R_2\): Resistor - \(C\): Capacitor - Ideal OP-AMP #### Questions and Steps for Analysis 1. **DC Gain Calculation (a)**: By making a suitable assumption for the capacitor, find the DC gain of this circuit, namely, \((v_O/v_I)_{DC}\). (Hint: How does the capacitor behave for steady-state DC voltages?) 2. **General Expression (b)**: Write down a general expression that relates \(v_I\) to \(v_O\). You do not have to solve the equation yet. 3. **Step Function Input (c)**: Assuming the input voltage is a step function that is zero before \(t < 0\) and \(v_I\) after \(t > 0\), obtain an expression for the output voltage assuming \(v_O = 0\) at \(t = 0\). 4. **Output Voltage Sketch (d)**: Sketch the output voltage as a function of time using your result from (c). #### Explanation of Graphs and Diagrams - **Input Voltage Graph**: The input voltage graph shows a step function where \(v_I = 0\) for \(t < 0\) and \(v_I\) for \(t > 0\). This step function acts as an input to the OP-AMP circuit. - **Circuit Diagram**: The circuit diagram includes an ideal OP-AMP with the non-inverting input grounded. Resistor \(R_2\) connects the inverting input of the OP-AMP to the ground, while resistor \(R_1\) and capacitor \(C\) are connected in series between the input voltage \(v_I\) and the inverting input of the OP-AMP. The output voltage \(v_O\) is taken from the OP-AMP output. Through these steps and diagrams, the objective is to understand and analyze the behavior of the
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