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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:

Using the Low-pass filter example:

Drops at 20 db

per decade

A zero at the origin

A pole at jw1

A zero at jw1

A pole at jw2

A pole at

the origin

- 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.

- 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.

A zero at the origin

A pole at jw1

A zero at jw1

A pole at jw2

A pole at

the origin

Zero at origin

Two poles

at half power

Take square and

reciprocal of both sides

Need both solutions for

positive values of w

Positive w for -1

Positive w for +1

Bandwidth for a series

resonant bandpass

filter