Bode Plot Question: Homework Statement & Solution Analysis

[Melawrghk]

Homework Statement

I'm doing a question that requires a Bode plot (magnitude and phase).

The Attempt at a Solution

I got a transfer function of
$$H(\omega)=\frac{1+\frac{j*\omega}{3}}{1-0.1667(\omega)^{2}+0.4167j*\omega}$$

So there is a simple zero at 3 rad/s; complex pole at 2.45 rad/s; and no DC gain.
I am able to plot the magnitude plot correctly, however my phase isn't exactly right.

For phase I have essentially two contributions from the zero and the pole:
From zero: 0.3<omega<30 rad/s with a slope of 45 degrees/decade
From pole: 0.245<omega<24.5 rad/s with a slope of -90 degrees/decade

So combining the two, I get (w==omega, I'm too lazy to write it out):
0<w<0.245: 0 degrees,
0.245<w<0.3: slope of -90 degrees/decade
0.3<w<24.5: slope of -45 degrees/decade
24.5<w<30: slope of 45 degrees/decade
w>30: slope of 0

However the solution my prof provided says:
0<w<0.245: 0 degrees,
0.245<w<0.3: slope of -90 degrees/decade
0.3<w<24.5: slope of -45 degrees/decade
w>24.5: slope of 0, flattens out at -90 degrees.

Am I wrong? If so, why?

 

[berkeman]

Homework Statement

I'm doing a question that requires a Bode plot (magnitude and phase).

The Attempt at a Solution

I got a transfer function of
$$H(\omega)=\frac{1+\frac{j*\omega}{3}}{1-0.1667(\omega)^{2}+0.4167j*\omega}$$

So there is a simple zero at 3 rad/s; complex pole at 2.45 rad/s; and no DC gain.
I am able to plot the magnitude plot correctly, however my phase isn't exactly right.

For phase I have essentially two contributions from the zero and the pole:
From zero: 0.3<omega<30 rad/s with a slope of 45 degrees/decade
From pole: 0.245<omega<24.5 rad/s with a slope of -90 degrees/decade

So combining the two, I get (w==omega, I'm too lazy to write it out):
0<w<0.245: 0 degrees,
0.245<w<0.3: slope of -90 degrees/decade
0.3<w<24.5: slope of -45 degrees/decade
24.5<w<30: slope of 45 degrees/decade
w>30: slope of 0

However the solution my prof provided says:
0<w<0.245: 0 degrees,
0.245<w<0.3: slope of -90 degrees/decade
0.3<w<24.5: slope of -45 degrees/decade
w>24.5: slope of 0, flattens out at -90 degrees.

Am I wrong? If so, why?

The zero is at -3 rad/s. Does that make a difference, or was that just a simple typo?

 

[Melawrghk]

Uh, neither. We're only dealing with positive frequencies (actually, absolute values, I suppose). We're calling them poles and zeros, but the values we're interested in is just the corner frequencies.

 

[berkeman]

Uh, neither. We're only dealing with positive frequencies (actually, absolute values, I suppose). We're calling them poles and zeros, but the values we're interested in is just the corner frequencies.

Sorry, then why do you say you have a zero at 3 rad/s?

 

[Melawrghk]

Sorry, then why do you say you have a zero at 3 rad/s?

It's just the terminology used. Corner frequency is like absolute value of zero/pole.