CHAPTER 6 Frequency Response, Bode Plots, and Resonance

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CHAPTER 6 Frequency Response, Bode

Plots, and Resonance

1. State the fundamental concepts of Fourier

analysis.

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Principles and Applications SE OND EDITION Chapter 6

Frequency Response, Bode Plots, and Resonance

3. Use circuit analysis to determine the

transfer functions of simple circuits.

4. Draw first-order lowpass or highpass filter

circuits and sketch their transfer functions.

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Fourier Analysis

All real-world signals are sums of sinusoidal

components having various frequencies,

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Filters

Filters process the sinusoid components of an input

signal differently depending of the frequency of

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Transfer Functions

The transfer function H(f ) of the two-port filter

is defined to be the ratio of the phasor output

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The magnitude of the transfer function shows

how the amplitude of each frequency component

is affected by the filter. Similarly, the phase of

the transfer function shows how the phase of each

frequency component is affected by the filter.

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Determining

the output of a filter

for an input with multiple

components:

1. Determine the frequency and phasor

representation for each input component.

2. Determine the (complex) value of the transfer

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3. Obtain the phasor for each output

component by multiplying the phasor for each

input component by the corresponding

transfer-function value.

4. Convert the phasors for the output

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Linear circuits behave as if they:

1. Separate the input signal into components

having various frequencies.

2. Alter the amplitude and phase of each

component depending on its frequency.

3. Add the altered components to produce

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DECIBELS, THE CASCADE

CONNECTION, AND LOGARITHMIC

FREQUENCY SCALES

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Cascaded Two-Port Networks

( )

f

H

( )

f

H

( )

f

H

=

₁

×

₂

( )

f

_dB

H

1

( )

f

_dB

H

2

( )

f

_dB

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Logarithmic Frequency Scales

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A decade is a range of frequencies for which

the ratio of the highest frequency to the

lowest is 10.









=

1

2 log

decades

of

number

f

An octave is a two-to-one change in frequency.

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BODE PLOTS

A Bode plot shows the magnitude of a network

function in decibels versus frequency using a

logarithmic scale for frequency.

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1. A horizontal line at zero for f < f

_B

/10.

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SERIES RESONANCE

Resonance is a phenomenon that can be

observed in mechanical systems and

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Conversion of Signals from

Analog to Digital Form

If a signal contains no components with

frequencies higher than f

_H

, the signal can be

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Digital Lowpass Filter

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