Where is the 'Origin' on a Bode Plot?

[dvscrobe]

TL;DR

Discussion on Poles and Zeroes

Wasn't sure where exactly to post this. It isn't a homework problem. I am studying for my Fundamentals of Engineering exam and am struggling with control system problems. Can someone tell me where exactly the origin is on a Bode Plot? I understand the general concept of poles and zeroes but I get confused with respect to the origin.

 

[Baluncore]

Since it is a Log plot, if it has an origin, that would be at zero dB, and probably 1 Hz.
https://en.wikipedia.org/wiki/Bode_plot

 

[DaveE]

There is no origin. It goes on forever in both axes, like all log-log plots. You only draw the region you care about.

 

[Baluncore]

There is no origin. It goes on forever in both axes, like all log-log plots.

Yet the number line goes from -∞ to +∞, but still has an origin at zero.

A gain of 1 = 0 dB, in Log space.
The Log( 1 Hz ) = 0, in Log space.
So the origin of the Log-Log Bode plot is ( 0, 0 ) = ( 1 Hz, 0 dB ) = ( 1 Hz, gain 1 ).
The confusion arises because the x-axis is labelled in Hz, not the Log of hertz.

 

[DaveE]

As you can see, experienced engineers that use this plot all the time either don't agree or aren't clear on the definitions. So, IMO, the origin doesn't matter. It's the least important thing about these plots. Pick one, move along, nothing to see here...

 

[dvscrobe]

I was reading through this article. It was very good at explaining the 3rd dimension of the S-plane. The 3rd dimension is the gain. That was an eye opener for me. So, is the origin on the S-plane where the sigma axis crosses the jw axis?
Transfer Function Analysis | Basic Alternating Current (AC) Theory | Textbook (control.com)

 

[DaveE]

I was reading through this article. It was very good at explaining the 3rd dimension of the S-plane. The 3rd dimension is the gain. That was an eye opener for me. So, is the origin on the S-plane where the sigma axis crosses the jw axis?
Transfer Function Analysis | Basic Alternating Current (AC) Theory | Textbook (control.com)

yes. In the s-plane, the origin is s=0=0+j0. It's just a plot of complex numbers.

PS: just to clarify, the origin in the (horizontal) s plane is s=σ+jω=0+j0=0. In the third dimension they are plotting the magnitude of the gain, which could create the same ambiguity for the vertical axis as the bode plots if they express it in dB or not. But on this page, and in most all descriptions of this sort, it isn't a log plot and the vertical axis origin is when |G(s)|=0. They didn't label or describe that, but I know it's not a log plot because of the shape of the poles.

 

[dvscrobe]

DaveE, okay awesome! Thanks. So that definitely answers where the origin is at. I think what confused me is if a pole or zero is not at the origin, then would the bode plot shift over to that spot or remain at the origin. In the article, if you see where they trace it, it is over the origin and extend in the +jw direction. Thanks for help!

 

[DaveE]

would the bode plot shift over to that spot or remain at the origin

You can make that plot however you like. Think of it as a window in an infinite expanse in all directions of log(ω) and dB. You put your window over the areas you care about and label the axes around the edge. The origin is pretty irrelevant. For example, here is the sort of bode plot you'll see in practice: