Next: Root locus of Second Up: Evaluation of Fourier Transform Previous: First order system

## Second order system

As discussed before, the transfer function of a second order system is

where can be either , , or , and and are the two roots of the denominator:

Note that when , the poles are a complex conjugate pair which can be written in polar form as well as in Cartesian form:

where

How the magnitude of the frequency response changes as a function of frequency can be qualitatively determined from the pole-zero plot of . For convenience, we define these vectors in the s-plane:

• , has no zeros and two poles and

As is some constant when and approaches 0 when , the system is a low-pass filter.

• , has one zero and two poles and

As when or but it is greater than 0 in between, the system is a band-pass filter.

• , has two repeated zeros and two poles and

As when , but it approaches a constant when , the system is a high-pass filter.

Next: Root locus of Second Up: Evaluation of Fourier Transform Previous: First order system
Ruye Wang 2012-01-28