Blog for students taking ECEN5817 Resonant and Soft Switching Techniques in Power Electronics, ECEE Department, University of Colorado at Boulder, Spring 2012
Tuesday, January 26, 2010
Calculating ||H(jw)||
Hey everyone, I need a sanity check. Can someone tell me how to go about calculating the magnitude of a transfer function?
wrich, You first write H in terms of Zo/Z1 as was done in lecture in PRC example except that now Zo=Re//1/sC//(sL/n^2) & Z1=sL/n^2. Also, H=Zo/Z1. This gives me magn(H) is the same form as eq19.31 pg 721, except that Qe=nRe*sqrt(C/L) and wo=n/sqrt(LC).
I agree with what you calculated above. What about your constant in front of H(jws) in (19.32)? I didn't get the same. I got 4/pi^2. The reasoning is because, in the text, the fourier series is obtained for a square wave form that is equally above and below the axis. However, for this problem, vs(t) is above the axis but goes to zero. The fourier series gets altered by multiplying the text fourier series by 1/2.
Brandon you are right. Thanks for pointing that out. Since vs(t) goes between +Vg and 0 the fourier series will be (2Vg/pi)*sigma(sin(nwt)/n) which then gives you a coefficient in H of 4/pi^2.
As you said, L and Cb were to be pushed to the right of xmer. That introduces the n^2 term. Also since it is given that Cb is large 1/n^2Cb << sL/n^2. Also we are not actually getting Zi to calculate H(s). If you refer to the notes H(s)=Zo/Z1, where Zo=Re//1/sC//sL/n^2 and Z1=sL/n^2. This will give you a quadratic in the denominator which you can write in standard form. Hope this helps.
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6 comments:
wrich,
You first write H in terms of Zo/Z1 as was done in lecture in PRC example except that now
Zo=Re//1/sC//(sL/n^2) & Z1=sL/n^2.
Also, H=Zo/Z1.
This gives me magn(H) is the same form as eq19.31 pg 721, except that Qe=nRe*sqrt(C/L) and
wo=n/sqrt(LC).
Another perspective: sqrt(A^2 + B^2) where A is the real component and B is imaginary. This is more general than Yusuf's comment.
Yusuf,
I agree with what you calculated above. What about your constant in front of H(jws) in (19.32)? I didn't get the same. I got 4/pi^2. The reasoning is because, in the text, the fourier series is obtained for a square wave form that is equally above and below the axis. However, for this problem, vs(t) is above the axis but goes to zero. The fourier series gets altered by multiplying the text fourier series by 1/2.
Brandon you are right. Thanks for pointing that out. Since vs(t) goes between +Vg and 0 the fourier series will be
(2Vg/pi)*sigma(sin(nwt)/n) which then gives you a coefficient in H of 4/pi^2.
Did you push the components to the right side of the transformer? What happened to Cb?
Why is Zo in parallel with 1/sC ... it looks like that is in series.
How did you get Zi ... wouldn't that be the input Z when the output is open?
Currently I am getting expression with an s^3 term and I don't know how to factor that out. Any suggestions?
Justin,
As you said, L and Cb were to be pushed to the right of xmer. That introduces the n^2 term. Also since it is given that Cb is large
1/n^2Cb << sL/n^2.
Also we are not actually getting Zi to calculate H(s). If you refer to the notes H(s)=Zo/Z1, where Zo=Re//1/sC//sL/n^2 and Z1=sL/n^2. This will give you a quadratic in the denominator which you can write in standard form. Hope this helps.
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