Understanding the Relationship Between Poles, Zeros, and Bode Plots

[perplexabot]

Hello all. I have two questions.

1] How do poles and zeros relate to bode plots? What happens at a pole or zero?

2] Can you come up with a rough sketch of a bode plot if you know the following (without having to use the transfer function)?:
- Zeros
- Poles
- H(s -> 0) Low frequency gain
- H(s -> infinity) High frequency gain

Thank you.

 

[berkeman]

Hello all. I have two questions.

1] How do poles and zeros relate to bode plots? What happens at a pole or zero?

2] Can you come up with a rough sketch of a bode plot if you know the following (without having to use the transfer function)?:
- Zeros
- Poles
- H(s -> 0) Low frequency gain
- H(s -> infinity) High frequency gain

Thank you.

This should help:

http://en.wikipedia.org/wiki/Bode_plot

 

[perplexabot]

Hahaha. Good ol' wikipedia. Thanks I guess.

EDIT: Just read almost all of that wikipedia article you referred me to, It has a good explanation on how to do bode plots the standard way (using the 20log rule and so on) but I was wondering if there is anyway we can bypass all that work assuming we have the variables shown in my original post. The reason I ask this is because I currently have a somewhat complicated transfer function. Also, the article did have a part about poles and zeros but I still don't understand what they mean on the bode plot. I guess I need to do way more reading.

 

[milesyoung]

... but I was wondering if there is anyway we can bypass all that work assuming we have the variables shown in my original post.

You could just have a computer evaluate the magnitude and phase of your transfer function for s = jω, 0 ≤ ω < ∞. MATLAB is a good tool for this.

Being able to draw a Bode plot using the asymptotic approximations is a good way to learn how to use them for control design, same with root locus analysis, but for the most part, I don't do it by hand any more.

Also, the article did have a part about poles and zeros but I still don't understand what they mean on the bode plot.

I think their effect will become clear to you with some practice. You could try drawing Bode plots for some simple transfer functions.

Edit:
Zeros, poles and DC gain uniquely determines your transfer function.

 

[rbj]

Zeros, poles and DC gain uniquely determines your transfer function.

the gain at DC might be zero (like for a high-pass filter or even a band-pass filter). you might say that the loci of the zeros and the poles and the constant gain factor is what fully determines the transfer function and that fully determines the frequency response.

 

[perplexabot]

Thank you so much for the informative responses. So I am assuming from your answers that one CAN plot the bode plots from the given information. I will do a bit more reading. Thank you all once again.

 

[jim hardy]

it's basically adjusting the slope at each pole or zero.

[STRIKE]a Pole directs it up 20 db/decade, a Zero down 20.[/STRIKE]

OOPS ! I got it backward ---- See following posts

 

[milesyoung]

the gain at DC might be zero (like for a high-pass filter or even a band-pass filter). you might say that the loci of the zeros and the poles and the constant gain factor is what fully determines the transfer function and that fully determines the frequency response.

Sorry I should have mentioned that it won't hold for a system with a zero or pole at the origin.

 

[jrive]

I think Jim Hardy's response was incorrect. Every pole increases the slope -20db/decade (downward). Every zero increases the slope +20dB/decade (upward).

 

[psparky]

I think Jim Hardy's response was incorrect. Every pole increases the slope -20db/decade (downward). Every zero increases the slope +20dB/decade (upward).

Agreed. Jim is human after all:)

 

[jim hardy]

Agreed. Jim is human after all:)

(OOPS! icon)
Thanks guys - late night, typed quickly --- something told me to wait 'till morning.

Humble apologies . No excuses - it was a direct miss.

It just seemed to me the simple mechanics of making the Bode plot hadn't been mentioned.

Here's a little tutorial with examples
http://lpsa.swarthmore.edu/Bode/BodeExamples.html

old jim

 

[perplexabot]

hey. Sorry for the late reply. Just want to say that your feedback has helped me so much. Poles dec. the slope by 20db/dec and zeros inc. slope by 20db/dec. That makes so much sense. Thank you everyone for your precious help, and a special thanks to Jim Hardy for the very useful information.