[SOLVED] Basic question about poles and zeros (Bode plot)

Hi guys,

Please, consider the transfer function below and its Bode plot.



(a) There are poles in s = - 10² rad/s and one in s = - 10⁵ rad/s. Their values are negative. So why, the pole location in the graph is positive?
(b) What is the physical meaning of a negative pole frequency?

Thanks and best regards.

Hi Palmeiras,

You can plot the absolute value of a transfer function, abs( T(s) ), in a three-dimensional space, for example, assume that the x axis is sigma, the y axis is j*omega and the z axis is abs( T(s) ). (where s = sigma + j * omega). From a mathematical point of view, wherever, there is a pole, this 3_D plot will go to minus infinity as if we have a deep valley at this point; however, when plotting the magnitude response, we put sigma = 0 and we consider a projection of this valley on the j*omega axis (now we have a 2-dimensional graph). Based on the location of the valley, we will have the -20 dB/dec roll-off in either the positive or the negative part of the j*omega axis.

Physically, if we restrict our discussion to circuits, a pole can be somehow attributed to a node of the circuit. When we increase the frequency, we get to the point that the abs of ( the impedance of the capacitors connected to the node ) becomes equal to the equivalent value of the resistors connected to that node. At this point, the capacitors start to bypass the node to ground. So the voltage swing reduces and we get a smaller gain which is why we see the -20dB/dec roll-off in the frequency response.

-Mahdi