Bode Plot?

[fat-tony]

Yes, I admit this IS a homework assignment, but I've been trying to find any information about this, and have come back empty handed. The textbook doesn't explain this very well, and the prof is hard to follow.

Basically, I ended up with a circuit with this for a transfer function:

H(s) = [(33x10^-12) s^2 + (33x10^-6)s + 1000] / [ (33.825x10^-12)s^2 + (58x10^-6) s + 1000 ]

The problem I'm having is that the top has complex roots. How do you deal with that? Do you just take them as complex roots, and then substitute in s = jw? I understand how to draw the bode plot, it's just the complex roots are messing me up.

 

[Optikon]

Yes, I admit this IS a homework assignment, but I've been trying to find any information about this, and have come back empty handed. The textbook doesn't explain this very well, and the prof is hard to follow.

Basically, I ended up with a circuit with this for a transfer function:

H(s) = [(33x10^-12) s^2 + (33x10^-6)s + 1000] / [ (33.825x10^-12)s^2 + (58x10^-6) s + 1000 ]

The problem I'm having is that the top has complex roots. How do you deal with that? Do you just take them as complex roots, and then substitute in s = jw? I understand how to draw the bode plot, it's just the complex roots are messing me up.

Yes. Just as you draw the denominator roots as poles in the bode plot, you can draw the numerator roots as zeros.

 

[fat-tony]

Yes. Just as you draw the denominator roots as poles in the bode plot, you can draw the numerator roots as zeros.

It's the fact that they are complex that is giving me the trouble. I have no problem doing a plot of any order with all real roots, it's the complex roots that are confusing me.

For example, with this I get:

G(jw) = [ ( (w + 5.482*10^6)j - 500000) * ( (w - 5.482*10^6)j - 500000) ] / [ ( (w + 5.3659*10^6)j - 857358) * ( (w - 5.3659*10^6)j - 857358) ]

Normally, you try to get the real constant to equal one, right? So you'd (for the top) divide by -500000, and divide the w term by that, to get the frequency for that term, and to multiply the gain by -500000.

 

[fat-tony]

As it turns out, our prof explained that that question hadn't been covered yet, and now it all makes sense.

Just in case anyone else has similar problems, the "s" term describes how the curve is shaped near the cutoff frequency.