Bode plot.pptx

Bode plot is a graph of the frequency response of a system. It is usually a combination of a Bode magnitude plot, expressing the magnitude of the frequency response, and a Bode phase plot, expressing the phase shift.

1. Frequency Response Bode Plot

2. The response of the system when a sinusoidal input is provided to it. is the frequency response. If a sinusoidal signal is applied as an input to a Linear Time-Invariant (LTI) system, then it produces the steady state output, which is also a sinusoidal signal. The input and output sinusoidal signals have the same frequency, but different amplitudes and phase angles. Frequency response

3. Let us consider a stable LTI causal SISO dynamic system whose transfer function is P(s). Let us consider an input sinusoidal function as:  

4. i.e All the poles of P(s) lies in the left half plane

5. Representation of Sinusoidal transfer function: putting s= Steady state output equation: If we give sinusoidal input of frequency then, The steady state output will be sinusoidal signal of the same frequency as that of the input, but scaled in magnitude by and shifted in phase by Both magnitude and phase depend upon This is a property of Linear time invariant system.  

6. How we get P( )  

7. P( ) is a complex valued function how would we visualize it when is varied? With the help of the following plotting methods  

8. BODE PLOT We use logarithmic scale for plotting bode plots instead of linear scale It can cover wide range of frequencies 2. Low frequency range can be expanded Product and ratio can easily be converted into addition and subtraction.

9. Building blocks of a Transfer Function Factors which make a transfer function in numerator and denominator Constant ( k ) Integral (1/s) Derivative term (s) First order term (1/Ts+1) First order term (Ts+1) Let them plot individually:

10. . 1. Bode Plot of Constant (K) Magnitude plot Phase plot

11. 2. Bode Plot of Integral Term (1/s) Magnitude plot Phase plot Put w=0.1, 1 , 10

12. 3. Bode plot of Derivative Term (s)

13. 4. Bode plot of First order ( )   Log of 1 to the base 10=0 conjugate

14. Phase plot

15. 5

16. How to add them? At w=0.1 plot of (0.1) and (S)= -40db At w=1 plot of (0.1) and (S)= -20db At w=1 plot of (1/s+1) starts contributing At w=10 plot of (1/0.1s+1) starts contributing