Zero and pole physical significance

For the transfer function, the zero makes the output to be zero, and the pole makes the output to be infinite.

From the bode plot, however, the gain drops when there is a pole and rises when there is a zero, which is a conflict with the above zero/pole definition.

Could you please explain? Thanks.

For the transfer function, the zero makes the output to be zero, and the pole makes the output to be infinite.

Click to expand...

Poles and zeros are located in a complex plane, the above consideration applies to poles and zeros on the imaginary (or jω) axis. A common case is an ideal integrator with a pole in the origin, which has actually infinite gain for ω=0.

OK, there two definitions of pole.

For example, H=1/(s+2):

1st definition, the denominator is 0, s+2=0, s=-2, which makes H to be infinite, now the pole frequency is a negative value at the complex plane, a negative pole makes the system stable.

2nd definition, the gain drops to -3dB of the H, which means s=2, a positive frequency on the frequency domain, so this pole, unlike the 1st definiton pole, makes the gain H to drops to H/2 (3dB).


Then for the 1st definition of pole, which is on the left plane, with a negative value, while it is positive on the frequency domain in the 2nd definition. right? Thanks.

- - - Updated - - -

A positive pole in the 2nd definition, for example, changing its sign, it becomes to a negative pole in the 1st definition at the s plane, which is easy to transfer to the exponential part presenting as a time domain signal to analysis.