Poles, zeros and bode plots.

1. Apr 20, 2013

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.

2. Apr 21, 2013

Staff: Mentor

This should help:

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

3. Apr 21, 2013

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.

Last edited: Apr 21, 2013
4. Apr 21, 2013

milesyoung

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.

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.

Last edited: Apr 21, 2013
5. Apr 21, 2013

rbj

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.

6. Apr 21, 2013

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.

7. Apr 21, 2013

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

Last edited: Apr 22, 2013
8. Apr 22, 2013

milesyoung

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

9. Apr 22, 2013

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).

10. Apr 22, 2013

psparky

Agreed. Jim is human after all:)

11. Apr 22, 2013

jim hardy

(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

Last edited: Apr 22, 2013
12. Apr 28, 2013

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.