CHAPTER 6: BODE PLOT

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CHAPTER 6 BODE PLOT
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Bode plot procedure

• There is 4 basic forms in an open-loop transfer
  function G(j?)H(j?).
• Gain factor, K
• (j?)p factor pole and zero at origin
• (1j?T)q factor
• Quadratic factor

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The magnitude and phase plots for some typical
factors
20logK
0dB
0º
20log?
90º
45º
0dB
20 dB/decade
0º
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The magnitude and phase plots for some typical
factors (cont)
40log?
180º
90º
0dB
40 dB/decade
0º
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-20log?
0º
-45º
0dB
-20 dB/decade
-90º
1
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The magnitude and phase plots for some typical
factors (cont)
-40log?
0º
-90º
0dB
-40 dB/decade
-180º
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20log(1?2T2)0.5
90º
45º
0dB
20 dB/decade
0º
1/T
0.1/T
1/T
10/T
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The magnitude and phase plots for some typical
factors (cont)
0º
-20 dB/decade
-45º
0dB
-90º
1/T
10/T
1/T
0.1/T
-20log(1?2T2)0.5
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The magnitude and phase plots for some typical
factors (cont)
180º
90º
0dB
40 dB/decade
0º
0º
-40 dB/decade
-90º
0dB
-180º
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EXAMPLE

• Sketch the bode plot for the system with the
  open-loop transfer function as follow
• a)
• b)

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Gain margin and Phase margin

• Gain margin
• The gain margin is the number of dB that is
  below 0 dB at the phase crossover frequency
  (ø-180º). It can also be increased before the
  closed-loop system becomes unstable.
• Phase margin
• The phase margin is the number of degrees the
  phase of that is above -180º at the gain
  crossover frequency. It can also be defined as
  the angle where the phase can be increased before
  the closed loop system becomes unstable.

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Gain margin and Phase margin
Magnitude (dB)
20dB
0dB
-20dB
Gain margin
Gain Crossover with 0dB line
-40dB
-60dB
Magnitude curve
Phase curve
0º
Phase Crossover with -180º line
Phase margin
-90º
-180º
-270º
Log ?
Phase (Degree)
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Matlab

• systf(200,1 12 20 0)
• bodeplot(sys)

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