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

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 j  1 A zero at j  1 A pole at j  2 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 j  1

Examples: (2/3) A zero at j  1 A pole at j  2 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 

Bandwidth of Resonant Bandpass (2/2) Positive  for -1 Positive  for +1 Bandwidth for a series resonant bandpass filter