# Bode Plots -Phase Graph

Discussion in 'Homework Help' started by Kayne, Oct 21, 2009.

1. ### Kayne Thread Starter Active Member

Mar 19, 2009
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Hi, I am having trouble understanding how to draw a phase graph for a bode plot. I have worked out the gain but for some reason the phase one is giving me grief.

The question i am working on is
100/(s+15)(s+27)(s+38) I know that the corner frequencies are 15, 27, 38. I have drawn the cross over freq over 2 decades from 0 to -90deg. My phase plot started on the 0deg line and traveled until i came to the first cross over freq and this is where i got stuck because i am not sure how much angle i need to travel before the next cross over freq.

Can you add the cross over freq together to find the angle?

The attachment is my attempt so far

Any help would be great.

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302 KB
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2. ### t_n_k AAC Fanatic!

Mar 6, 2009
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The total phase at any frequency will be sum of the individual phase contributions at that frequency.

So at w=10 the individual values look to be approx 39°, 26° & 19° giving a total of 84°.

Beyond w=380 the total shift would be 3x90°=270°

3. ### t_n_k AAC Fanatic!

Mar 6, 2009
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Also - Remember the phase shifts are lagging - so on your plot the phase axis should be showing -ve values.

4. ### Kayne Thread Starter Active Member

Mar 19, 2009
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T_N_K thanks for the reply, i have done what you said and went though found the sum of the individual phase contributions at that frequency and plotted them on the graph.

The attachment is the new attempt the red line is the phase plot

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293.8 KB
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29
5. ### t_n_k AAC Fanatic!

Mar 6, 2009
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Looks pretty good! Have you actually tried to draw smooth transitions around the break points or are you just assuming straight line approximations? If the latter, then the irregular bump at 6 rad/sec is a little strange. With straight line approximations I would expect a fall of around 135° per decade from w=3.8 to 150 rad/sec. But it's probably mostly due to approximation/calculation errors in the angles at your selected frequency values.

6. ### Kayne Thread Starter Active Member

Mar 19, 2009
105
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Now that I know how to draw this plot I will go into more detail and change the scale of the vertical axis to get it more accurate and get a smoother curve. Thank you for your help. I have spent a few hours looking and trying to work this out.

7. ### The Electrician AAC Fanatic!

Oct 9, 2007
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It's good to do this by hand at least once to understand how it works, but then you could use an application such as Matlab to draw the plots. If you don't have Matlab, there are free applications that should do the job. Have you considered using such an application?

8. ### Kayne Thread Starter Active Member

Mar 19, 2009
105
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I have purchased Mathlab am just waiting for the program to arrive. Like you said it is good to do it by hand first. Now i know i will use the program.

Referring to Bode plots, the frequency of gain and phase margin crossovers (Wgc&Wpc) how do you find this out when the if the gain plot start well below 0dB line eg(-44 as mine does).All the examples i have in my study book all start above the 0dB line and i can see how it all relates. With mine does this mean there is no gain margin or do i do the same as if it was over the 0dB line and say that the gain margin is -44dB.

9. ### The Electrician AAC Fanatic!

Oct 9, 2007
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I would need more details about your problem. It looks to me like the transfer function you have given does not include the effect of a gain stage.