Chapter 6Chapter 6

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The sinusoidal frequency response (or, simply, frequency response) of a circuit provides a measure of how the circuit responds to sinusoidal inputs of arbitrary frequency.

The frequency response of a circuit is a The frequency response of a circuit is a measure of the variation of a load-related measure of the variation of a load-related voltage or current as a function of the voltage or current as a function of the frequency of the excitation signal.frequency of the excitation signal.

A circuit model

Thévenin equivalent source circuit

Complete equivalent circuit

VL( jω) is a phase-shifted and amplitude-scaled version of VS( jω).

Filters

Low-Pass Filters

A simple RC filter

Magnitude and phase response plots for RC filter

High-pass filter

High-Pass Filters

Frequency response of a high-pass filter

Bandpass Filters, Resonance, and Quality FactorBandpass Filters, Resonance, and Quality Factor

RLC bandpass filter

Frequency responses of RLC bandpass filter

Resonance and Bandwidth

(a) Normalized magnitude response of second-order bandpass filter; (b) normalized phase response of second-order bandpass filter

Bode PlotsBode Plots

Frequency response plots of linear systems are often Frequency response plots of linear systems are often displayed in the form of logarithmic plots, called Bode displayed in the form of logarithmic plots, called Bode plots, where the horizontal axis represents frequency on plots, where the horizontal axis represents frequency on a logarithmic scale (base 10) and the vertical axis a logarithmic scale (base 10) and the vertical axis represents the amplitude ration or phase of the represents the amplitude ration or phase of the frequency response function. In Bode plots the frequency response function. In Bode plots the amplitude ratio is expressed in units of decibels (dB), amplitude ratio is expressed in units of decibels (dB), wherewhere

Bode plots for low-pass RC filter; the frequency variable is normalized to ω/ωο. (a) Magnitude response; (b) phase response

Bode plots for high-pass RC filter. (a) Magnitude response; (b) phase response