# Bode Plot

• It is used to draw the frequency response of an open loop & a closed loop system. It is also called corner plot & asymptotic plot.
• The representation of logarithm of  & phase angle of , both plotted against frequency in logarithmic scale & these plots are called Bode plots.
• Here we determine gain margin & phase margin.
• The gain margin is determined by:

where is the phase cross frequency where line crosses the frequency axis.

- When  < 1, the G..M. in decibel comes out to be positive indicating a stable system.

- When  = 1, the G..M. in decibel comes out to be zero indicating a marginally stable system.

- When  > 1, the G..M. in decibel comes out to be negative indicating an unstable system.

• The phase margin is given by:

where is measured clockwise & is the gain crossover frequency at which  line crosses the frequency axis.
• For a stable system, phase margin should be positive and the gain cross over frequency should be less than the phase cross over frequency.
• For unstable systems: the gain cross over frequency > phase cross over frequency.
• For marginally stable systems: the gain cross over frequency should be equal to the phase cross over frequency.