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E E 2415 - PowerPoint PPT Presentation

E E 2415. Lecture 15 Introduction to Frequency Response, Poles &amp; 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 E2415

Lecture 15

Introduction to Frequency Response, Poles & Zeroes, Resonant Circuit

Gain in Decibels

Using the Low-pass filter example:

Drops at 20 db

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

Resonant BandPass Poles & Zeroes

Zero at origin

Two poles

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