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ELECTRIC CIRCUITS EIGHTH EDITION
JAMES W. NILSSON & SUSAN A. RIEDEL ELECTRIC CIRCUITS EIGHTH EDITION
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INTRODUCTION TO FREQUENCY SELECTIVE CIRCUITS
CHAPTER 14 INTRODUCTION TO FREQUENCY SELECTIVE CIRCUITS © 2008 Pearson Education
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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
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14.1 Some Preliminaries Input signal Output signal Filter
The action of a filter on an input signal results in an output signal © 2008 Pearson Education
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14.1 Some Preliminaries A circuit with voltage input and output
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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
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14.1 Some Preliminaries (a) An ideal low-pass filter
(b) An ideal high-pass filter (c) An ideal bandpass filter (d) An ideal bandreject filter Ideal frequency response plots of the four types of filter circuits © 2008 Pearson Education
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14.2 Low-Pass Filters A series RL low-pass filter.
The equivalent circuit at ω = 0. The equivalent circuit at ω = ∞. © 2008 Pearson Education
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14.2 Low-Pass Filters The frequency response plot for the series RL circuit. © 2008 Pearson Education
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14.2 Low-Pass Filters The cutoff frequency, ωc , 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) Hmax. © 2008 Pearson Education
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14.2 Low-Pass Filters Cutoff frequency for RL filters
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14.2 Low-Pass Filters Example: Designing a Series RC Low-Pass Filter
For the series RC circuit in the figure above: Find the transfer function between the source voltage and the output voltage. Determine an equation for the cutoff frequency in the series RC circuit. Choose values for R and C that will yield a low-pass filter with a cutoff frequency of 3kHz. © 2008 Pearson Education
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14.2 Low-Pass Filters A low-pass filter passes voltages at frequencies below ωc and attenuates frequencies above ωc. Any circuit with the transfer function Transfer function for a low-pass filter © 2008 Pearson Education
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14.2 Low-Pass Filters Two low-pass filters, the series RL and the series RC, together with their transfer functions and cutoff frequencies © 2008 Pearson Education
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14.3 High-Pass Filters A series RC high-pass filter
The equivalent circuit at ω = 0 The equivalent circuit at ω = ∞ © 2008 Pearson Education
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14.3 High-Pass Filters The frequency response plot for the series RC circuit © 2008 Pearson Education
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14.3 High-Pass Filters 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: Derive an expression for the circuit’s transfer function. Use the result from (a) to determine an equation for the cutoff frequency in the series RL circuit. Choose values for R and L that will yield a high-pass filter with a cutoff frequency of 15kHz. © 2008 Pearson Education
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14.3 High-Pass Filters A high-pass filter passes voltages at frequencies above ωc and attenuates voltages at frequencies below ωc . Any circuit with the transfer function Transfer function for a high-pass filter © 2008 Pearson Education
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14.3 High-Pass Filters Two high-pass filters, the series RC and the series RL, together with their transfer functions and cutoff frequencies © 2008 Pearson Education
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14.4 Bandpass Filters Bandpass filters and bandreject filters each have two cutoff frequencies, ωc1 and ωc2. These filters are further characterized by their center frequency (ω0), bandwidth (β), and quality factor (Q). © 2008 Pearson Education
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14.4 Bandpass Filters Center frequency © 2008 Pearson Education
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14.4 Bandpass Filters Cutoff frequencies, series RLC filters
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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
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14.4 Bandpass Filters A bandpass filter passes voltages at frequencies within the passband, which is between ωc1 and ωc2. It attenuates frequencies outside of the passband. Transfer function for RLC bandpass filter © 2008 Pearson Education
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14.4 Bandpass Filters Two RLC bandpass filters, together with equations for the transfer function, center frequency, and bandwidth of each © 2008 Pearson Education
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14.5 Bandreject Filters A bandreject filter attenuates voltages at frequencies within the stopband, which is between ωc1 and ωc2. It passes frequencies outside of the stopband. © 2008 Pearson Education
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14.5 Bandreject Filters Transfer function for RLC bandreject filter
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14.5 Bandreject Filters Two RLC bandreject filters, together with equations for the transfer function, center frequency, and bandwidth of each © 2008 Pearson Education
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THE END © 2008 Pearson Education
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