Phase Response 

The phase response plot is phase of given transfer function in degrees or radians versus the logarithm of frequency, ω in rad/s.

• For the constant gain, K, phase response is the constant 0⁰ horizontal line.
• For the zero of order 1, phase angle is 0⁰ until 0.1/T, then rises at rate of 450/decade and settles at 90⁰ for ω ≥ 10/T.
• For simple zero of order n, the phase is 0⁰ till 0.1/T , then increases at the rate of 450 × n/decade and settles down at 900 × n for ω ≥ 10/T .
• For a simple pole having order 1, the phase is 00 until 0.1/T , then falls at rate of -450 /decade and settles down at -900 for ω ≥ 10/T.
•  For the simple pole of order n, the phase is 00 until 0.1/T , then drop-off at rate of -450 × n /decade and settles down at -900 × n for ω ≥ 10/T .
• For a differentiator of order n that is H (jω) = (jωT )n, phase plot is the constant line of 900 × n.
• For an integrator of order n, phase response is the horizontal line of -90⁰ × n (see Fig- ure 5.13(b) for a first order integrator). In the Equation stated above, the 1800 term in phase angle is because of the 2nd order integrator.

   

Asymptotic Bode plots of the constant gain.
 

Asymptotic Bode plots of the zero of order 1.
 
Asymptotic Bode plots of the pole of order 1.
 
Figure--Asymptotic Bode plots of 1st order differentiator.
  
Asymptotic Bode plots of a 1st order integrator

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