Bode plot

Content covered:Introduction to bode plot, basics of bode plot, construction of bode plot and its example.

1. Basic Bode Plot
by -Prof. Mrunal Deshkar

2. The Bode plot or the Bode diagram consists of
two plots −
1. Magnitude plot
2. Phase plot
•The
 
magnitude 
of the open loop transfer
function in dB is -
•The
 
phase angle 
of the open loop transfer
function in degrees is -
Bode plot

3. Basic of Bode Plots

5. Consider the open loop transfer function
 
G(s)H(s)=K
Magnitude
 
M=20logK
Phase angle
 
ϕ=0 
degrees
If
 
K=1, then magnitude is 0 dB.
If
 
K>1, then magnitude will be positive.
If
 
K<1, then magnitude will be negative.

6. Consider the open loop transfer function
 
G(s)H(s)=s.
Magnitude
 
M=20logω
Phase angle
 
ϕ=90
At
 
ω=0.1 
rad/sec, the magnitude is -20 dB.
At
 
ω=1 
rad/sec, the magnitude is 0 dB.
At
 
ω=10 
rad/sec, the magnitude is 20 dB.

7. Consider the open loop transfer function
 
G(s)H(s)=1+sτ

8. Construction of Bode Plots

9. Stability Analysis using Bode Plots
Phase Cross over Frequency
The frequency at which the phase plot is having the phase of -
180
0
 
is known as 
phase cross over frequency. It is denoted
by
 ωpc. The unit of phase cross over frequency is 
rad/sec.
Gain Cross over Frequency
The frequency at which the magnitude plot is having the
magnitude of zero dB is known as
 
gain cross over frequency.
It is denoted by
 ωgc. The unit of gain cross over frequency
is
 
rad/sec. If ωpc>ωgc : control system is
 
stable.
 If ωpc=ωgc : control system is 
marginally
stable.
 If ωpc<ωgc : control system is
 
unstable.

11. GM & PM 
are +ve : the control system is 
stable.
 GM & PM 
are zero : the control system is 
marginally stable.
GM & PM 
are -ve : the control system is 
unstable.

12. The procedure of drawing a Bode plot:
1. Substitute the s = jω in the open loop transfer function G(s) × H(s).
2. Find the corresponding corner frequencies and tabulate them.
3. Now we are required one semi-log graph chooses a frequency range such that
the plot should start with the frequency which is lower than the lowest corner
frequency. Mark angular frequencies on the x-axis, mark slopes on the left hand
side of the y-axis by marking a zero slope in the middle and on the right hand side
mark phase angle by taking -180
o
 
in the middle.
4. Calculate the gain factor and the type or order of the system.
5. Now calculate slope corresponding to each factor.

13. For drawing the Bode magnitude plot:
•Mark the corner frequency on the semi-log graph paper.
•Tabulate these factors moving from top to bottom in the given sequence.
1.Constant term K.
2.Integral factor
 
3.First order factor
 
4.First order factor (1+jωT).
5.Second order or quadratic factor:
•Now sketch the line with the help of the corresponding slope of the given factor.
Change the slope at every corner frequency by adding the slope of the next factor.
You will get the magnitude plot.
•Calculate the gain margin.
For drawing the Bode phase plot:
1.Calculate the phase function adding all the phases of factors.
2.Substitute various values to the above function in order to find out the phase at
different points and plot a curve. You will get a phase curve.
3.Calculate the phase margin.

20. Thank you