Download EEE 302 Lecture 23 - Arizona State University

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
High Pass
Frequency
Frequency
Band Reject
Band Pass
Frequency
Frequency
Lecture 23
3
Passive Filters
• Passive filters use R, L, C elements to achieve the
desired filter
• 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 to achieve a gain greater
than unity
Lecture 23
4
Class Examples
• Extension Exercise E12.16
• Extension Exercise E12.17
• Extension Exercise E12.18
Lecture 23
5
First-Order Filter Circuits
High Pass
VS
+
–
R
C
Low Pass
Low
Pass
VS
+
–
R
L
GR = R / (R + 1/sC)
HR = R / (R + sL)
GC = (1/sC) / (R + 1/sC)
HL = sL / (R + sL)
Lecture 23
High
Pass
6
Second-Order Filter Circuits
Band Pass
R
VS
+
–
Low
Pass
High
Pass
Z = R + 1/sC + sL
HBP = R / Z
C
Band
Reject
L
HLP = (1/sC) / Z
HHP = sL / Z
HBR = HLP + HHP
Lecture 23
7
Frequency & Time Domain Connections
• First order circuit break frequency: break = 1/
• Second order circuit characteristic equation
s2 + 20 s + 02
[  = 1/(2Q) ]
(j)2 + 2(j) + 1
[  = 1/0 ]
s2 + BW s + 02
s2 + R/L s + 1/(LC)
[series RLC]
Q value also determines damping and pole types
Q < ½ ( > 1) overdamped, real & unequal roots
Q = ½ ( = 1) critically damped, real & equal roots
Q > ½ ( < 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