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## BODE PLOT

*What is bode plot? Why it is used?*

#### Some Important points about Bode plot:

Bode plot is a plot which is often used in control
engineering to find out the stability of the system. The graph plotted by bode
plot gives two plots.

One is the magnitude plot with respect to frequency.

Second is the phase plot with respect to frequency.

Bode plot is drawn from the transfer functions given in s
domain form. The numerators in the s domain provide the number of zeros and
denominator provides the number of poles.

The zeros of bode plot provides the gain of 20db/decade.

The poles of bode plot provides the gain of -20db/decade.

If there are two zeros at the same point than the gain will
be 40db/decade, if there are three zeros at same point on s plane than gain
will be 60db/decade.

Similarly for poles if there are two poles the decrement
will be -40db/decade.

## The Bode Plot graph paper:

How to bode plot? Phase and frequency plot wrt frequency in Bode plot graph paper |

The graph paper used to plot the bode plot is known as
semilog graph paper. In this graph paper the y axis can be used to show the gain
of the function. The x axis is not linear, it is a decade based x axis. Each
block in the x axis increases in a pattern like (10 20 30 40 50 60 70 80 90 100
200 300 400 500 600 … and so on.). This is the way of writing the frequency on
the x axis of bode plot.

## Bode plot example:

Suppose a simple transfer function for bode plot is given:
Transfer Function = s/[(s+1)(s+2)]

In this transfer function,

Zero is at s=0 from numerator.

Poles are s = -1 and s = -2

## Cutt off frequencies for the bode plot:

for zero, s = 0 [take the coefficient reciprocal of s as
corner frequency, here 1.s therefore corner frequency from zero is 1]

for pole, take 2 out of the denominator factor (s+2) than
transfer function become s/[2(s+1)(s/2+1)]

corner frequencies from pole is 1 and 2. [coefficients of s
in denominator are considered]

## Gain Margin and Phase Margin from bode plot:

Gain margin is the gain away from the 0 magnitude when phase
plot crosses the -180 degree axis in phase plot of bode plot.

Phase margin is the phase difference between the phase
reference -180 and the phase plotted when gain magnitude plot of bode plot
crosses the zero magnitude.