Complex Frequencies and the s-Plane

We will now consider s-plane techniques. Not because we will use them, but more to understand some of the common electronics terminology.

We can enhance the usefulness of the transfer function by transforming to a complex frequency. Define the complex variable such that

where is an inverse time constant.

Our exponential function now becomes

and we have a rich set of cases

So we can not only describe oscillatory behavior but transient responses as well.

 
• Poles and Zeros of H