Magnitude and Phase Bode Plot Help

[NHLspl09]

Hi all, on a current homework I have been given a transfer function and asked to draw the straight-line (asymptotic) magnitude (dB) and phase (degrees) Bode plot. I first learned Bode plots roughly a year ago, and while being on spring break and my notebook from last year is at school, I'm having difficulty remembering some techniques. I do know how to plot these when given a zero frequency, but in this specific problem, this transfer function has no zeros and has three poles. Judging from my notes from this class, I tried my best to dictate what to do for the magnitude, but was posting here to check and make sure I plotted the magnitude properly. My handwork to show the breakpoints and slopes is in Attachment 2 - Handwork, and the magnitude plot can be seen through Attachment 3 - Magnitude Plot.

My question though is for the phase plot. As seen in my handwork, I think that because the numerator is second order, it's slope should be +90°/decade, but am I supposed to include that in the phase plot because there is no zero frequency? Also, I'm a little fuzzy as to how I find out where I begin my plot in degrees - I have been taught that you begin with a slope of 0°/decade and end with a slope of 0°/decade, but how do I know where to begin my plot for phase?

Any help on this topic would be greatly appreciated!

Homework Statement

(Attachment 1 - Problem)

Homework Equations

None.

The Attempt at a Solution

(Attachment 2 - Handwork)

(Attachment 3 - Magnitude Plot)

 

[gneill]

Hi all, on a current homework I have been given a transfer function and asked to draw the straight-line (asymptotic) magnitude (dB) and phase (degrees) Bode plot. I first learned Bode plots roughly a year ago, and while being on spring break and my notebook from last year is at school, I'm having difficulty remembering some techniques. I do know how to plot these when given a zero frequency, but in this specific problem, this transfer function has no zeros and has three poles. Judging from my notes from this class, I tried my best to dictate what to do for the magnitude, but was posting here to check and make sure I plotted the magnitude properly. My handwork to show the breakpoints and slopes is in Attachment 2 - Handwork, and the magnitude plot can be seen through Attachment 3 - Magnitude Plot.

My question though is for the phase plot. As seen in my handwork, I think that because the numerator is second order, it's slope should be +90°/decade, but am I supposed to include that in the phase plot because there is no zero frequency? Also, I'm a little fuzzy as to how I find out where I begin my plot in degrees - I have been taught that you begin with a slope of 0°/decade and end with a slope of 0°/decade, but how do I know where to begin my plot for phase?

Any help on this topic would be greatly appreciated!

Hi NHLspl09. I took a quick look at your transfer function and plot. If I'm not mistaken I think that the magnitude plot should probably peak at about 80dB in the neighborhood of 10⁴ Hz.

The phase plot looks to be an interesting beast. Sort of a water-slide ride from 180° down to about -90° with a plateau of near zero phase shift coinciding with that of the magnitude plot. Does this sound like what you're getting?

 

[NHLspl09]

Hi NHLspl09. I took a quick look at your transfer function and plot. If I'm not mistaken I think that the magnitude plot should probably peak at about 80dB in the neighborhood of 10⁴ Hz.

The phase plot looks to be an interesting beast. Sort of a water-slide ride from 180° down to about -90° with a plateau of near zero phase shift coinciding with that of the magnitude plot. Does this sound like what you're getting?

Interesting, if you don't mind me asking, how did you come up with a peak at around 80dB around 10⁴ Hz? I didn't think that could be possible if my break frequencies aren't within that bound of 10⁴ Hz?

And my main problem with the phase plot is I can't remember for the life of me on how to find where I start my plot. Looking at my notes is it: j(2∏T_m)f? Although I could be entirely wrong about that.

 

[gneill]

Interesting, if you don't mind me asking, how did you come up with a peak at around 80dB around 10⁴ Hz? I didn't think that could be possible if my break frequencies aren't within that bound of 10⁴ Hz?

Well, I cheated, of course I used MathCad to plot the magnitude. You should be able to verify by plugging in the corresponding jω value for that frequency and finding the magnitude.

And my main problem with the phase plot is I can't remember for the life of me on how to find where I start my plot. Looking at my notes is it: j(2∏T_m)f? Although I could be entirely wrong about that.

I'm not sure about a rule of thumb for this; I usually just find the angle for a very low frequency far from any critical frequencies (ideally in the limit as f → 0) and begin there.

 

[NHLspl09]

Well, I cheated, of course I used MathCad to plot the magnitude. You should be able to verify by plugging in the corresponding jω value for that frequency and finding the magnitude.

I'm not sure about a rule of thumb for this; I usually just find the angle for a very low frequency far from any critical frequencies (ideally in the limit as f → 0) and begin there.

Wish I could use that and call it a day I'm interested to see which is correct - which yours is I'm sure because of MathCad, but using the methods my professor taught I'm interested to see what I did wrong. I suppose I'll find out tomorrow!