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To draw a Bode diagram

for a transfer function there are three steps:

1. Rewrite the transfer function in proper form.

2. Separate the transfer function into its constituent parts.

3. Draw the Bode diagram for each part.

4. Draw the overall Bode diagram by adding up the results from

part 3.

http://www.swarthmore.edu/NatSci/echeeve1/Ref/Bode/Bode.html

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1. Rewrite the transfer function in proper form.

A transfer function is normally of the form:

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we would like to rewrite this so the lowest order term

in the numerator and denominator are both unity.

Example:

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2. Separate the transfer function into its constituent parts.

The next step is to split up the function into its constituentparts. There are seven types of parts:

1. A constant

2. Poles at the origin

3. Zeros at the origin

4. Real Poles

5. Real Zeros

6. Complex conjugate poles

7. Complex conjugate zeros

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This function has

a constant of 2,

a zero at s=-10, and

poles at s=-3 and s=-50.

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3. Draw the Bode diagram for each part

Term Magnitude Phase

Constant:K

1020 log

0 : 0

0: 180

"

s

$

$

Real Pole:

0

1

s1

[

y Low freq. asymptote at 0 dB

y High freq. asymptote at -20 dB/dec

y Connect lines at break freq.

y Low freq. asymptote at 0o

y High freq. asymptote at

90o

y Connect with straight line

from 0.1[0 to 10[0

Real Zero*:

0

s1

[

y Low freq. asymptote at 0 dB

y High freq. asymptote at +20 dB/dec.

y Connect lines at break freq

y Low freq. asymptote at 0o

y High freq. asymptote at

+90o

y Connect with line from

0.1[0 to 10[0

Pole at Origin:1

s -20 dB/dec; through 0 dB at [=1 90

$

Zero at Origin*:s +20 dB/dec; through 0 dB at [=1 90 $

Underdamped Poles:

2

0 0

1

s s2 1

^ [ [

y Low freq. asymptote at 0 dB

y High freq. asymptote at -40 dB/dec.

y Draw peak at freq.

2

r 01 2[ ! [ ^

with amplitude

y 2r 10H j 20 log 2 1[ ! ^ ^ y Connect lines

y Low freq. asymptote at 0o

y High freq. asymptote at -

180o

y Connect with straight line

from

10

0 0

10

2log

2to

2 2log

^ [ ! [ [ ! [

^

Underdamped Zeros*:

2

0 0

s s2 1

^

[ [

y Draw low freq. asymptote at 0 dB

y Draw high freq. asymptote at +40

dB/dec.

y Draw dip at freq. 0r 21 2

[[ !

^with

amplitude

2r 10H j 20 log 2 1[ ! ^ ^ y Connect lines

y Low freq. asymptote at 0o

y Draw high freq. asymptote

at -180oy Connect with a straight

line from

10

0 0

10

2log

2to

2 2log

^

[ ! [ [ ! [

^

Notes:

*Rules for drawing zeros create the mirror image (around 0 dB) of those for a pole with the same break freq

For underdamped poles and zeros peak exists for 10 0.7072

^ ! and peak freq. is typically very near the break freq

For underdamped poles and zeros If

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4. Draw the overall Bode diagram by adding up the results

from part 3.

After the individual terms are drawn, it is a simple matter to

add them together.