E e 2415
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E E 2415. Lecture 15 Introduction to Frequency Response, Poles & Zeroes, Resonant Circuit. Low-Pass Filter Example: (1/2). Low-pass Filter:. Low-Pass Filter Example: (2/2). Gain in Decibels. Using the Low-pass filter example:. Drops at 20 db per decade. Bode Plot of Low-Pass Filter.

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E E 2415

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E E2415

Lecture 15

Introduction to Frequency Response, Poles & Zeroes, Resonant Circuit


Low-Pass Filter Example: (1/2)

Low-pass Filter:


Low-Pass Filter Example: (2/2)


Gain in Decibels

Using the Low-pass filter example:

Drops at 20 db

per decade


Bode Plot of Low-Pass Filter


Phase Plot of Low-Pass Filter


High-Pass Filter Example: (1/2)


High-Pass Filter Example: (2/2)


High-Pass Gain in Decibels


Bode Plot of High-Pass Filter


Phase Plot of High-Pass Filter


Definition: Poles & Zeroes

A zero at the origin

A pole at jw1

A zero at jw1

A pole at jw2

A pole at

the origin


Effect of a Pole on the Bode Plot

  • A pole causes the asymptotic slope to decrease by 20 db/decade.

  • A pole at the origin causes the slope to start at –20 db/decade.

  • A pole not at the origin causes a corner to appear at the pole’s frequency; then the slope is 20 db/decade less for frequencies greater than the pole’s frequency.


Effect of a Zero on the Bode Plot

  • A zero causes the asymptotic slope to increase by 20 db/decade.

  • A zero at the origin causes the slope to start at +20 db/decade.

  • A zero not at the origin causes a corner to appear at the pole’s frequency; then the slope is 20 db/decade more for frequencies greater than the zero’s frequency.


Examples: (1/3)

A zero at the origin

A pole at jw1


Examples: (2/3)

A zero at jw1

A pole at jw2

A pole at

the origin


Examples: (3/3)


Resonant Bandpass Filter (1/2)


Resonant Bandpass Filter (2/2)


Resonant BandPass Poles & Zeroes

Zero at origin

Two poles


Bode Plot for Resonant Bandpass


Phase Plot for Resonant Bandpass


Bandwidth of Resonant Bandpass (1/2)

at half power

Take square and

reciprocal of both sides

Need both solutions for

positive values of w


Bandwidth of Resonant Bandpass (2/2)

Positive w for -1

Positive w for +1

Bandwidth for a series

resonant bandpass

filter


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