# Help graphing Bode Plot

Discussion in 'Homework Help' started by TripleDeuce, Jan 31, 2011.

1. ### TripleDeuce Thread Starter New Member

Sep 20, 2010
26
0
I need to graph a bode plot of this transfer function

H(jω) = (1.5 x 10^-3 *(1+jω/10)) / ((1+jω/100)(1+jω/500))

and I have no idea how to do so. I'm trying to follow an example my professor did in his notes. I replace jω with an "s" so the equation looks like this

H(s) = (1.5 x 10^-3 *(1+s/10)) / ((1+s/100)(1+s/500))

It seems he graphed each component of a transfer function separately, so I'll try to do the same

Gain of 1.5 x 10^-3 is 20log(1.5 x 10^-3) = -56.5db.

It's graph is just a horizontal line at height -56.5db for all ω. The x axis is where ω is.

(1+s/10) has corner frequency at ω = 10. So it contributes 20db/decade asymptote started at ω=10.

(1+s/100) has corner frequency at ω = 100. Since it is in the denominator, it contributes -20db/decade asymptote started at ω=100.

(1+s/500) has corner frequency at ω = 500. Since it is in the denominator, it contributes -20db/decade asymptote started at ω=500.

Now how do I physically add all the plots to give me an overall bode plot?

2. ### thatoneguy AAC Fanatic!

Feb 19, 2009
6,357
718
I think you are over-complicating it a bit.

The X axis is frequency
The Y axis is amplitude (dB/Volts/Power/etc)

Calculate the Y for several values of X, most concentrating on the corner frequency(/ies) area(s). Then connect the dots.

The 20dB/decade numbers are what can be read from the bode plot by the steepness of the amplitude curve, dB/octave or dB/decade do not need to be calculated for each sample, only the actual amplitude value from the top formula.

Does that make sense?

3. ### TripleDeuce Thread Starter New Member

Sep 20, 2010
26
0
You're saying that to indicate a slope of 20db/decade, I would just go up an amplitude of 20db and go across one decade? What do you mean by

I'm graphing this on a semilog plot by the way.

Oh, and since I was going to start a thread to ask this question, do you also know how to graph a bode asymptotic phase angle plot of the function?

4. ### Georacer Moderator

Nov 25, 2009
5,151
1,266
If I was asked to draw that plot in Uni, they would require me to do pretty much what the OP did.

First calculate the DC gain (@ ω=0). Then go level until you find a pole or zero that will add or subtract inclination to your plot. You don't have to plot more that two or three decades after the final pole/zero.

Also take a moment to visit this very useful site:
http://www.williamsonic.com/BodePlot/