# What information Bode plot does NOT present?

The classic Bode plot (2D Bode) represent value of the transfer function (a complex number) evaluated at $$\j\omega\$$ (imaginary axis). It provides information on system closed-loop stability margins and also some means to estimate pole/zero of the transfer function, if not available (for experimental data).

Still, given that the classic Bode plot (2D Bode) provides transfer function values only on the $$\j\omega\$$-axis (i.e. only the Sinusoidal pieces of system characteristics), what information of the system characteristics (as far as modes and stability) are missing by not looking at the 3D Bode plot (Sinusoidal ($$\j\omega\$$) + Exponential ($$\\sigma\$$) information)?

In other words, what useful/practical information does the 3D Bode add to the 2D Bode?

Also, found this question useful but not enough to address my question.: What does a Bode plot represent and what is a pole and zero of a Bode plot?

• Bode plot plot is providing the full information - the amplitude and the phase versus the frequency. It is a 3D plot, just divided into two separate plots. – Eugene Sh. Oct 20 '20 at 14:17
• Most signals of interest can be decomposed into sinusoids. So, the plot along $j\omega$ axis is enough to get info about the system. Moreover, one can reconstruct the pole zero locations if the plot along the $j\omega$ axis is available. So IMO, there is no information lost. – AJN Oct 20 '20 at 14:30
• Well, you didn't explicitly specify a linear system. Often we take bode plots of non-linear systems with a small-signal disturbance so you get the needed information at a single bias point, but you don't know what the response will be at a different operating point. – John D Oct 20 '20 at 15:38
• @EugeneSh. I think OP's point was that if you consider the Laplace domain, the Bode plot doesn't directly show the behavior for s off the imaginary axis. I think if you consider only systems defined by a finite number of poles and zeros, all the information is still there. But if you consider systems (which I don't know how you would build) with other functional dependency ($H(s) = \exp{[-a(s-s_0)^2]}$, for example) then only knowing about the imaginary axis might lose some information. – The Photon Oct 20 '20 at 15:54
• @ThePhoton But Bode plot is not providing the data from imaginary axis only. It is providing the amplitude of the complex value. And it is providing its phase. These two values are fully describing this number. – Eugene Sh. Oct 20 '20 at 16:22

## 1 Answer

This pole zero diagram: - Tells you everything about the transfer function and it also tells you everything about what the bode plot will look like. It's just a plan view of this: - You cannot always (or even accurately) reverse the bode plot i.e. this: - Into the pole zero diagram (top picture in this answer).

• As I mentioned in comments to the question, this assumes you have a TF that can be defined by a finite set of poles and zeros. – The Photon Oct 20 '20 at 16:34
• @ThePhoton explanations were the most useful for me. Appreciate it. – Alborz Oct 20 '20 at 16:38