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What is H(jw)?

What is H(jw)?

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
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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What is H(jw)? 

This image depicts an electrical circuit diagram alongside a mathematical expression for the transfer function of the system. ### Circuit Diagram 1. **Component Z1:** - In the left part of the circuit, there is a parallel configuration of a resistor \( R_1 \) and a capacitor \( C_1 \). - This parallel configuration is labeled as \( Z_1 \). 2. **Component Z2:** - The right part of the circuit includes another parallel configuration, consisting of a resistor \( R_2 \) and a capacitor \( C_2 \). - This is labeled as \( Z_2 \). ### Mathematical Expression The transfer function \( H(s) \) is given by: \[ H(s) = H(j\omega) = \frac{Z_2}{Z_1 + Z_2} \] - This represents the frequency response of the circuit, where \( s = j\omega \) is the complex frequency variable in the Laplace transform domain. - \( Z_1 \) and \( Z_2 \) are impedances corresponding to the parallel resistor-capacitor combinations in the circuit. This formulation suggests the calculation of the transfer function in terms of the impedances of the two parallel branches.
Transcribed Image Text:This image depicts an electrical circuit diagram alongside a mathematical expression for the transfer function of the system. ### Circuit Diagram 1. **Component Z1:** - In the left part of the circuit, there is a parallel configuration of a resistor \( R_1 \) and a capacitor \( C_1 \). - This parallel configuration is labeled as \( Z_1 \). 2. **Component Z2:** - The right part of the circuit includes another parallel configuration, consisting of a resistor \( R_2 \) and a capacitor \( C_2 \). - This is labeled as \( Z_2 \). ### Mathematical Expression The transfer function \( H(s) \) is given by: \[ H(s) = H(j\omega) = \frac{Z_2}{Z_1 + Z_2} \] - This represents the frequency response of the circuit, where \( s = j\omega \) is the complex frequency variable in the Laplace transform domain. - \( Z_1 \) and \( Z_2 \) are impedances corresponding to the parallel resistor-capacitor combinations in the circuit. This formulation suggests the calculation of the transfer function in terms of the impedances of the two parallel branches.
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