EEE 302 Electrical Networks II

Dr. Keith E. Holbert Summer 2001 Lecture 23 1

Filter Networks

• Filters pass, reject, and attenuate signals at various frequencies • Common types of filters:

Low-pass

: pass low frequencies and reject high frequencies

High-pass

: pass high frequencies and reject low frequencies

Band-pass

: pass some particular range of frequencies, reject other frequencies outside that band

Band-rejection

: reject a range of frequencies and pass all other frequencies (e.g., a special case is a

notch

filter) Lecture 23 2

Common Filter Bode Plots

Low Pass Frequency Band Pass Frequency Lecture 23 High Pass Frequency Band Reject Frequency 3

Passive Filters

•

Passive filters

desired filter use

R

,

L

,

C

elements to achieve the • The

half-power frequency

is the same as the

break frequency

(or

corner frequency

) and is located at the frequency where the magnitude is 1/  2 of its maximum value • The resonance frequency,  0 , is also referred to as the

center frequency

• We will need

active filters

than unity to achieve a gain greater Lecture 23 4

Class Examples

• Extension Exercise E12.16

• Extension Exercise E12.17

• Extension Exercise E12.18

Lecture 23 5

V

S + –

First-Order Filter Circuits

High Pass Low Pass R C Low Pass

V

S + – R L High Pass

G

R = R / (R + 1/

sC

)

G C

= (1/

s

C) / (R + 1/

sC

)

H

R = R / (R +

s

L)

H

L =

s

L / (R +

s

L) Lecture 23 6

Second-Order Filter Circuits

Band Pass

V

S + – R Low Pass High Pass C Band Reject L

Z =

R + 1/

s

C +

s

L

H

BP = R /

Z H

LP = (1/

s

C) /

Z H

HP =

s

L /

Z H

BR =

H

LP +

H

HP Lecture 23 7

Frequency & Time Domain Connections

• First order circuit break frequency:  break = 1/ • Second order circuit characteristic equation  s 2 + 2  0 (j  ) 2 + 2 s +  0 2  (j  ) + 1 s 2 + BW s +  0 2 [  [  = 1/(2

Q

) ] = 1/  0 ] s 2 + R/L s + 1/(LC) [series RLC]

Q

value also determines damping and pole types

Q

< ½ (  > 1) overdamped, real & unequal roots

Q Q

= ½ (  > ½ (  = 1) critically damped, real & equal roots < 1) underdamped, complex conjugate pair Lecture 23 8

PSpice Design Example

• Repeat E12.18 using Pspice – Plot the resistor voltage in DBs – Use goal function “BPBW” to determine the band-pass filter bandwidth: BPBW(VDB(#),3)) – Use goal function “CenterFreq(VDB(#),0?)” • Bandwidth design – Design circuit to achieve a bandwidth of 300 Hz • Center frequency design – Design circuit for a center frequency of 100 Hz Lecture 23 9