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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.png

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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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