# what does the s-plane response of a system's transfer function describe?

I am having trouble understanding the s-plane and not sure if I have grasped it from reading the standard signals and systems texts, so hopefully you guys can help me!

Does the z-axis on the s-plane plot the amplitude response of the system's transfer function to the input values of σ+jω (x+jy)? or does it plot the complex-frequency response (output of the system in terms of σ+jω) of a system to an impulse input signal?

EDIT: Z-axis = axis showing amplitude

• It's the S-plane. There is no Z axis. Sep 26, 2016 at 11:00
• thank you, yes you are right but it is a 3d space when the response is included and I was trying to describe the 3rd axis..what is the proper term for this? Sep 26, 2016 at 11:08

This picture might help: - Bottom left is an attempt at showing a 3D view of the pole zero diagram with the s-plane being flat to the floor so to speak. The example used is for a 2nd order low pass filter.

Note that the bode-plot (amplitude) and pole zero diagram are really parts of the same thing hence it's the complex frequency response that it covers.

• Thank you this does help! but can you please answer my question more directly? Sep 26, 2016 at 11:12
• I think you need to state what you mean by z-axis (maybe refer to my diagram?). Also you mention "transfer function" in the question and this is unrelated to the stimulus (impulse or otherwise). Sep 26, 2016 at 11:32
• with reference to your diagram, the amplitude vs frequency plot (top-left), by z-axis I mean the Amplitude axis. I have rephrased the question to make it easier to understand Sep 26, 2016 at 12:12
• OK that's the bode-plot amplitude and, on my picture it's any of the top three diagrams AND on the 3D view it's the view looking to the left shown by the bog arrow and the words "bode plot view". What is your question that I haven't answered - I'm unsure where you think it hasn't been answered. Sep 26, 2016 at 12:51
• as always Andy, nice illustrations. Sep 26, 2016 at 13:00