INC 342 Lecture 5: Bode plot Dr. Benjamas Panomruttanarug - - PowerPoint PPT Presentation

INC 342

Lecture 5: Bode plot

• Dr. Benjamas Panomruttanarug

Benjamas.pan@kmutt.ac.th

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Starts from a sinusoidal signal, , which can be rewritten as

• Polar form (showing magnitude and phase shift):

) / ( tan 1

2 2

A B B A M

i i 

    

 

) / ( tan cos

1 2 2

A B t B A



  

3 expressions of sinusoidal signal

) sin( ) cos( t B t A   

i i

M  

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• Rectangular form (complex number):
• Euler’s formula (exponential):

) sin( ) sin( ) cos( ) cos( ) cos( ) sin( ) sin( ) cos( ) cos( ) cos( t M t M t M t t t

B i i A i i i i

                           

i

j ie

M



2 expressions of sinusoidal signal (cont.)

jB A

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• Magnitude response:

– ratio of output mag. To input mag.

• Phase response:

– difference in output phase angle and input phase angle

• Frequency response:

) ( 

Frequency response of system

) ( M

) ( ) (     M

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Basic property of frequency Response

) ( 

‘mechanical system’ input = force

• utput = distance

sinusoidal input gives sinusoidal output with same damped frequency shifted by ,

• mag. expanded by

) ( M

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) ( 

The HP 35670A Dynamic Signal Analyzer obtains frequency response data from a physical system.

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• Get transfer function
• Set
• Write
• Then the output is composed of

) ( ) ( ) ( ) ( ) ( ) (         

i

• i
• M

M M   

Finding frequency response from differential equation

 j s 

) (s T

) ( ) ( ) ( ) ( s T s T M      

)] ( ) ( [ ) ( ) ( ) ( ) (             

i i

• M

M M

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 j

Finding frequency response from transfer function

s

) 2 ( 1 ) 2 ( 1 ) ( ) 2 ( 1 ) (    j j j G s s G      

ω = 0, G = 0.5 0.5∟0 ω = 2, G = 0.25 – j0.25 0.35 ∟‐45 ω = 5, G = 0.07 ‐ 0.17i 0.19 ∟‐68.2 ω = 10, G =0.019 ‐ j0.096 0.01∟‐78.7 ω = ∞, G = 0 0 ∟‐90 Substitute with

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What’s next?

After getting magnitude and phase of the system, we need to plot them but how???

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Types of frequency response plots

• Polar plot (Nyquist plot): real and

imaginary part of open‐loop system.

• Bode plot: magnitude and phase of open‐

loop system (begin with this one!!).

• Nichols chart: magnitude and phase of
• pen‐loop system in a different manner

(not covered in the class).

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) 2 ( 1 ) (   s s G

Polar plot of

so called ‘Nyquist plot’

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Bode plot

Note: log frequency and log magnitude Magnitude Phase

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It’s convenient for calculation to plot magnitude in log scale!!!

What about ???

• plot each term separately and sum

them up

• log magnitude (s+2) added with log

magnitude (s+3)

• phase (s+2) added with phase (s+3)

) 3 )( 2 ( 1 ) (    s s s G

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Example

sketch bode plot of

) 2 )( 1 ( ) 3 ( ) (     s s s s s G

break frequency at 1,2,3

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sketch bode plot of

• Set then
• At DC, set s=0,
• Break frequency at 2, 3, (or 5)

) 25 ) ( 2 ) )(( 2 ) (( ) 3 ( ) (

2

          j j j j j G

Example

 j s 

) 25 2 )( 2 ( ) 3 ( ) (

2

     s s s s s G

50 3 ) (  G

25

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Drawing Bode plot

• Get transfer function
• Set
• Evaluate the break frequency
• Approximate mag. and phase at low and high

frequencies, and also at the break frequency

– Mag. plot: slope changes for 1st order, for 2nd order (at break frequency) – Phase plot: slope changes for 1st order, for 2nd order dec dB / 20 

Conclusions

 j s 

) (s T

dec dB / 40  dec / 45 

dec / 90 

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