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A) Write down the characteristics B) Find vo and i, in the following circuit. of an ideal op-amp.

A) Write down the characteristics B) Find vo and i, in the following circuit. of an ideal op-amp.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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### Ideal Operational Amplifier Characteristics and Circuit Analysis #### A) Characteristics of an Ideal Operational Amplifier (Op-Amp) 1. **Infinite Open-Loop Gain**: The gain, A, of an ideal op-amp is infinite when no feedback is applied. 2. **Infinite Input Impedance**: The input impedance is infinite, meaning no current flows into the input terminals. 3. **Zero Output Impedance**: The output impedance is zero, meaning it can supply any amount of current without affecting the output voltage. 4. **Infinite Bandwidth**: The ideal op-amp amplifies any frequency with equal gain. 5. **Zero Offset Voltage**: The output is zero when the input is zero; there is no inherent voltage difference between the inverting and non-inverting inputs. 6. **Infinite Common-Mode Rejection Ratio (CMRR)**: It can perfectly reject any voltage common to both input terminals. 7. **Infinite Power Supply Rejection Ratio (PSRR)**: Changes in power supply voltage do not affect the output. #### B) Finding \( v_o \) and \( i_o \) in the Following Circuit Consider the given circuit diagram: - The circuit features two operational amplifiers (Op-Amps) in a configuration. - \( V_{\text{in}} \) is a 20mV DC source applied to the circuit. - The resistors are labeled as follows: - A 12 kΩ resistor and a 3 kΩ resistor connected to the first op-amp. - The second op-amp has a 10 kΩ resistor and a 4 kΩ resistor. The steps to analyze the circuit typically include: 1. **Node Voltage Analysis**: Determining the voltages at critical nodes (such as nodes "a" and "b"). 2. **Applying Ideal Op-Amp Rules**: - **Voltage at Inverting and Non-Inverting Inputs are the Same** due to infinite gain. - **Input Currents are Zero** due to infinite input impedance. The detailed solution usually requires solving the governing equations based on Kirchhoff's laws and the characteristics of an ideal op-amp. This process includes setting up and solving simultaneous equations that dictate the behavior of the voltages and currents in the circuit, particularly at nodes "a" and "b". ### Circuit Description The circuit diagram illustrates two operational amplifiers connected in a cascaded configuration with associated resistances and a DC
Transcribed Image Text:### Ideal Operational Amplifier Characteristics and Circuit Analysis #### A) Characteristics of an Ideal Operational Amplifier (Op-Amp) 1. **Infinite Open-Loop Gain**: The gain, A, of an ideal op-amp is infinite when no feedback is applied. 2. **Infinite Input Impedance**: The input impedance is infinite, meaning no current flows into the input terminals. 3. **Zero Output Impedance**: The output impedance is zero, meaning it can supply any amount of current without affecting the output voltage. 4. **Infinite Bandwidth**: The ideal op-amp amplifies any frequency with equal gain. 5. **Zero Offset Voltage**: The output is zero when the input is zero; there is no inherent voltage difference between the inverting and non-inverting inputs. 6. **Infinite Common-Mode Rejection Ratio (CMRR)**: It can perfectly reject any voltage common to both input terminals. 7. **Infinite Power Supply Rejection Ratio (PSRR)**: Changes in power supply voltage do not affect the output. #### B) Finding \( v_o \) and \( i_o \) in the Following Circuit Consider the given circuit diagram: - The circuit features two operational amplifiers (Op-Amps) in a configuration. - \( V_{\text{in}} \) is a 20mV DC source applied to the circuit. - The resistors are labeled as follows: - A 12 kΩ resistor and a 3 kΩ resistor connected to the first op-amp. - The second op-amp has a 10 kΩ resistor and a 4 kΩ resistor. The steps to analyze the circuit typically include: 1. **Node Voltage Analysis**: Determining the voltages at critical nodes (such as nodes "a" and "b"). 2. **Applying Ideal Op-Amp Rules**: - **Voltage at Inverting and Non-Inverting Inputs are the Same** due to infinite gain. - **Input Currents are Zero** due to infinite input impedance. The detailed solution usually requires solving the governing equations based on Kirchhoff's laws and the characteristics of an ideal op-amp. This process includes setting up and solving simultaneous equations that dictate the behavior of the voltages and currents in the circuit, particularly at nodes "a" and "b". ### Circuit Description The circuit diagram illustrates two operational amplifiers connected in a cascaded configuration with associated resistances and a DC
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