ELECTRIC CIRCUITS EIGHTH EDITION JAMES W. NILSSON & SUSAN A. RIEDEL

CHAPTER 14 INTRODUCTION TO FREQUENCY SELECTIVE CIRCUITS © 2008 Pearson Education

CONTENTS 14.1 Some Preliminaries 14.2 Low-Pass Filters 14.3 High-Pass Filters 14.4 Bandpass Filters 14.5 Bandreject Filters © 2008 Pearson Education

14.1 Some Preliminaries © 2008 Pearson Education Input signal Filter Output signal The action of a filter on an input signal results in an output signal

14.1 Some Preliminaries © 2008 Pearson Education A circuit with voltage input and output

14.1 Some Preliminaries   A frequency selective circuit, or filter, enables signals at certain frequencies to reach the output, and it attenuates signal at other frequencies to prevent them from reaching the output.   The passband contains the frequencies of those signals that are passed; the stopband contains the frequencies of those signals that are attenuated. © 2008 Pearson Education

Ideal frequency response plots of the four types of filter circuits (a) An ideal low-pass filter (b) An ideal high-pass filter (c) An ideal bandpass filter (d) An ideal bandreject filter © 2008 Pearson Education 14.1 Some Preliminaries

14.2 Low-Pass Filters © 2008 Pearson Education A series RL low-pass filter. The equivalent circuit at ω = 0. The equivalent circuit at ω = ∞.

14.2 Low-Pass Filters © 2008 Pearson Education The frequency response plot for the series RL circuit.

14.2 Low-Pass Filters   The cutoff frequency, ω c, identifies the location on the frequency axis that separates the stopband from the passband.   At the cutoff frequency, the magnitude of the transfer function equals (1 / √2) H max. © 2008 Pearson Education

14.2 Low-Pass Filters © 2008 Pearson Education Cutoff frequency for RL filters

14.2 Low-Pass Filters © 2008 Pearson Education Example: Designing a Series RC Low-Pass Filter For the series RC circuit in the figure above: a)Find the transfer function between the source voltage and the output voltage. b)Determine an equation for the cutoff frequency in the series RC circuit. c)Choose values for R and C that will yield a low-pass filter with a cutoff frequency of 3kHz.

14.2 Low-Pass Filters   A low-pass filter passes voltages at frequencies below ω c and attenuates frequencies above ω c.   Any circuit with the transfer function Transfer function for a low-pass filter © 2008 Pearson Education

Two low-pass filters, the series RL and the series RC, together with their transfer functions and cutoff frequencies © 2008 Pearson Education 14.2 Low-Pass Filters

14.3 High-Pass Filters A series RC high-pass filter © 2008 Pearson Education The equivalent circuit at ω = 0 The equivalent circuit at ω = ∞

14.3 High-Pass Filters © 2008 Pearson Education The frequency response plot for the series RC circuit

14.3 High-Pass Filters © 2008 Pearson Education Example: Designing a Series RL High-Pass Filter. Show that the series RL circuit in the figure below also acts like a high-pass filter: a)Derive an expression for the circuit’s transfer function. b)Use the result from (a) to determine an equation for the cutoff frequency in the series RL circuit. c)Choose values for R and L that will yield a high-pass filter with a cutoff frequency of 15kHz.

14.3 High-Pass Filters   A high-pass filter passes voltages at frequencies above ω c and attenuates voltages at frequencies below ω c. Any circuit with the transfer function Transfer function for a high-pass filter © 2008 Pearson Education

Two high-pass filters, the series RC and the series RL, together with their transfer functions and cutoff frequencies © 2008 Pearson Education 14.3 High-Pass Filters

14.4 Bandpass Filters   Bandpass filters and bandreject filters each have two cutoff frequencies, ω c1 and ω c2.   These filters are further characterized by their center frequency (ω 0 ), bandwidth (β), and quality factor ( Q ). © 2008 Pearson Education

14.4 Bandpass Filters © 2008 Pearson Education Center frequency

14.4 Bandpass Filters © 2008 Pearson Education Cutoff frequencies, series RLC filters

14.4 Bandpass Filters These quantities are defined as Relationship between center frequency and cutoff frequencies Relationship between bandwidth and cutoff frequencies Quality factor © 2008 Pearson Education

14.4 Bandpass Filters   A bandpass filter passes voltages at frequencies within the passband, which is between ω c1 and ω c2.   It attenuates frequencies outside of the passband. Transfer function for RLC bandpass filter © 2008 Pearson Education

Two RLC bandpass filters, together with equations for the transfer function, center frequency, and bandwidth of each © 2008 Pearson Education 14.4 Bandpass Filters

14.5 Bandreject Filters   A bandreject filter attenuates voltages at frequencies within the stopband, which is between ω c1 and ω c2.   It passes frequencies outside of the stopband. © 2008 Pearson Education

14.5 Bandreject Filters Transfer function for RLC bandreject filter © 2008 Pearson Education

Two RLC bandreject filters, together with equations for the transfer function, center frequency, and bandwidth of each © 2008 Pearson Education 14.5 Bandreject Filters

THE END © 2008 Pearson Education