Where is the 'Origin' on a Bode Plot?

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Discussion Overview

The discussion revolves around the concept of the 'origin' on a Bode Plot, particularly in the context of control systems. Participants explore the implications of the logarithmic nature of Bode Plots and how poles and zeros relate to the concept of an origin.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • One participant seeks clarification on the location of the origin on a Bode Plot, expressing confusion regarding poles and zeros.
  • Another participant suggests that the origin could be considered at zero dB and 1 Hz, referencing the logarithmic scale of the plot.
  • Some participants argue that there is no true origin on a Bode Plot, as it extends infinitely in both axes, but acknowledge that the number line has a point at zero.
  • A participant explains that a gain of 1 corresponds to 0 dB and that the confusion arises from the x-axis being labeled in Hz rather than its logarithmic value.
  • One participant expresses the opinion that the concept of the origin is not significant in practical use of Bode Plots, suggesting that users can choose their own reference point.
  • Another participant discusses the S-plane and questions whether the origin is where the sigma axis crosses the jw axis, confirming that it is at s=0.
  • A later reply clarifies that the origin in the S-plane is at s=0 and discusses the potential ambiguity in representing gain on the vertical axis.
  • One participant questions whether the Bode Plot would shift if a pole or zero is not at the origin, indicating that the plot can be adjusted based on the area of interest.

Areas of Agreement / Disagreement

Participants do not reach a consensus regarding the definition and significance of the origin on a Bode Plot. Multiple competing views are presented, with some arguing for its relevance and others deeming it unimportant.

Contextual Notes

The discussion highlights the ambiguity in defining the origin due to the logarithmic nature of Bode Plots and the varying interpretations of poles and zeros. There are unresolved questions about how these elements affect the representation on the plot.

dvscrobe
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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.
 
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There is no origin. It goes on forever in both axes, like all log-log plots. You only draw the region you care about.
 
DaveE said:
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.
 
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 said:
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.
 
Last edited:
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!
 
dvscrobe said:
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:

1709328453059.png
 
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