Bode Plot Tutorial
Contents
1 Introduction
1
2 Bode Plots Basics
1
2.1
Magnitude
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
2.2
Phase
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
3 Combining Poles and Zeroes
4
1
Introduction
Although you should have learned about Bode plots in previous courses, this tutorial will give you a brief
review of the material in case your memory is fuzzy.
2
Bode Plots Basics
Making the Bode plots for a transfer function involves drawing both the magnitude and phase plots. The
magnitude is plotted in decibels (dB) while the phase is plotted in degrees (
◦
). For both plots, the horizontal
axis is either frequency (
f
) or angular frequency (
ω
), measured in Hz and rad
/
s respectively. In addition,
the horizontal axis should be logarithmic (i.e. increasing by factors of 10).
Most of the transfer functions we will encounter in this lab manual can be rearranged into the general
form:
H
(
jω
) =
A
·
jω/ω
z
1
(1 +
jω/ω
z
2
) (1 +
jω/ω
z
3
)
...
jω/ω
p
1
(1 +
jω/ω
p
2
) (1 +
jω/ω
p
3
)
...
,
(1)
where
A
is an arbitrary constant and
j
is
√
−
1. Besides the exception of
jω/ω
c
, the basic component of this
transfer function is 1 +
jω/ω
c
, where
ω
c
is some numerical constant. Let us analyze this basic component
first before we analyze the transfer function as a whole.
2.1
Magnitude
Recall the definition of magnitude (measured in dB):

H
(
jω
)

dB
= 20 log

H
(
jω
)

= 20 log
radicalBig
(
ℜ
[
H
(
jω
)])
2
+ (
ℑ
[
H
(
jω
)])
2
(2)
Let us apply this definition to our basic component (1 +
jω/ω
c
), which is also called a
zero
when it appears
in the numerator of the transfer function:

1 +
jω/ω
c

dB
= 20 log

1 +
jω/ω
c

= 20 log
radicalBig
1 + (
ω/ω
c
)
2
(3)
For small values of
ω
, we have 20 log

1 +
jω/ω
c
 ≈
0 dB.
For large values of
ω
, 20 log

1 +
jω/ω
c
 → ∞
.
When
ω
=
ω
c
, the magnitude of the transfer function is approximately 3 dB.
Since there is little change in the magnitude of the transfer function from
ω
= 0 to
ω
=
ω
c
, we can
approximate the magnitude expression as equal to 0 dB within this interval. As for the
ω > ω
c
interval, the
(
ω/ω
c
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 Spring '08
 MonaHella
 Decibel, ωc, Bode Plots

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