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Electric CircuitsEighth Edition
Appendix E
James W. NilssonProfessor Emeritus
Iowa State University
Susan A. RiedelMarquette University
HW 0
(a) Use semi-log graph paper (in the last page of this note) to sketch the
(approximate) Bode plots for the magnitude and phase of the transfer function;
(b) Plot the exact magnitude and phase using the computer (use any software).
(Appendix E, Sidra and Smith, Problem E.10, 5th):
4 5
3 4
10 (1 /10 )( )
(1 /10 )(1 /10 )
sH s
s s
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Bode Plots
Hendrik Wade Bode
(pronounced Boh-dee in English ),
(1905 1982) was an American engineer,
researcher, inventor, author and scientist.
A Bode plot is a graph of the logarithm of the transfer function
versus frequency, plotted with a log-frequency axis, to show thesystem's frequency response. It is usually a combination of a
Bode magnitude plot and a Bode phase plot.
http://en.wikipedia.org/wiki/File:Hbode.png8/12/2019 Bode Plots Nilson Sidra App E Student
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1
1
( )( )( )
K s zH ss s p
where z1 = z1 and p1= p1
To draw the Bode diagrams we must put H(j) in a standard form
1
1
1
1
1 1
1
1
( 1)
( )( 1)
(1 )
( )
( )(1 )
sKz
zH s s
spp
jKz z
H jp
j j
p
Straight-Line (Approximate) Bode Plot
Nilsson and Riedel, Appendix E
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1
1 11 1
11
1 1 1
1 1 1
1 1
1
1
1
1 1
1 1
1 tan(1 )
( )
( )(1 ) 90 1 tan
1
tan 90 tan ( ) ( )
1
1
( )
1
( ) tan 90 tan
o
o
o
jjz zK z z
H j Kp
j j jp p p
K jz
H jz p
j
p
K jz
H j
jp
z p
Straight-Line (Approximate) Bode Plot
Nilsson and Riedel, Appendix E
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1
1
dB
1 1
1
( )
1
20 log ( )
20 log 20 log 1 20 log 20 log 1
o
o
K jz
H j
j p
A H j
K j jz p
Straight-Line (Approximate) Magnitude Bode Plot
Nilsson and Riedel, Appendix E
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dB
1
1
20log
20 log 1
20log
1
20 log 1
oA K
j z
jp
Assume; Ko
= 10, z1 = 4 rad/s, p1 = 4 rad/s
Straight-Line (Approximate) Magnitude Bode plot
1
1
1( )
1
oK j zH j
jp
This is why crossing x-axesat 1
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Assume; Ko
= 10, z1 = 0.1 rad/s, p1 = 5 rad/s
10
1
(1 )
( )
( )(1 )
jz
H j K
j jp
Straight-Line (Approximate) Magnitude Bode Plot
Nilsson and Riedel, Appendix E
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Example E.1
Construct the straight-line (approximate) of the Bode Magnitudeplot.
dB 20 log ( )
20 log 0.11 20 log 20 log 1 20 log 1
10 100
A H j
j j j
-19.2 dB
Nilsson and Riedel, Appendix E
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(Actual ) Magnitude Bode Plot
( ) 20 log 1 1
20 log 2
3 dB
cH j j
When = cwhere c
is either p
or z
( ) 20 log 1
20 log 1
z
p
H j j
or
j
Nilsson and Riedel, Appendix E
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Assume;
Ko
= 10
z1 = 0.1 rad/sp1 = 5 rad/s
Straight-Line (approximate) Phase Angle plot
Nilsson and Riedel, Appendix E
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(Actual) Phase Bode Plot
5.7
in Sidra 5th edition, Appendix-E, page E-5
Nilsson and Riedel, Appendix E
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s-Domain Analysis: Poles,
Zeros, and Bode Plots
Sidra Appendix D4-D5
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Exercise E.1
Find the H(s) = Vo
/Vi
Sidra Appendix D4-D5
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Figure E.2 Bode plots for Example E.1.
Example E.1
An amplifier has the following transfer function
Sketch the Bode plot for the magnitude of the transfer function.2 5
10( )
(1 /10 )(1 /10 )
sH s
s s
Sidra Appendix D4-D5
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Low-pass filter (LPF)
Sidra Appendix D4-D5
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High-pass filter (HPF)
Sidra Appendix D4-D5
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