As we have been discussing, we can simply use Figure 19.22 for our analysis. However, the tank network is a parallel L and C. This will lead into a Transfer function problem of H(s) = 1........since all voltages are in parallel........which should not be the case.
Am I misinterpreting something?
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H(s)=1 is true.
Figure 19.22 can not be used entirely in pb19.3:
- rectifier network model from 19.22 can be applied to pb19.3
- switch network model from 19.22 can not be applied to pb19.3:
Fig 19.22 switch network has voltage source vs1(t)=4Vg/pi)*sin(ws*t) that feeds the resonant tank(voltage-fed), and pb19.3 has current source that feeds the resonant tank(current-fed): is(t)=square wave with amplitude Ig; is(t)_fundamental=is1(t)=(4*Ig/pi)*sin(ws*t)
Fig 19.22 switch network has current source ig_avg=(2Is1/pi)*cos(phi_s) on the Vg side and pb19.3 has the voltage source vg_avg=(2Vs1/pi)*cos(phi_s) on the Vg and Lf1 side(v(Lf1)_avg=0). (2Vs1/pi)*cos(phi_s) is obtained the same way as in chapter 19.1.1 equation 19.4 when ig(t) is replaced by voltage.
Switch network from 19.22 is dual to pb19.3 switch network.
pb19.3 switch operation:
0<t<Ts/2: D1, Q1, D4 and Q4 are on; D2, Q2, D3 and Q3 are off: is=Ig=constant
Ts/2<t<Ts: D1, Q1, D4 and Q4 are off; D2, Q2, D3 and Q3 are on: is=-Ig=constant
Hello All,
I found out H(s) = 1 too, given Vr and Vs is equal. Then, I think H(s) can't be part of equation to figure out M=V/Vg.
So, I take slightly different path.
From observation of tank resonance circuit with
Re, I conclude that Ir(t) (current output from resonant tank) is in phase with Vs(t). So, I can directly relate Vs and Ir by writing Re = Vs/Ir.
My final expression for V/Vg (M) then:
M = (V/I) * (I/Ir1) * (Ir1/Vs) * (Vs/Vg)
After doing some math cancellation, I get:
M = 1/cos(phi_s)
where phi_s is phase angle of tank resonance input impedance.
I don't have confidence yet with my answer.
It's completely different than the textbook.
Thank You
But if we write V/Vg=V/ir1*ir1/is1*is1/Vg then ir1/is1 = Re/(Re+(sL//1/sC))=H(s). The other terms will give some constant. In this case we cannot say H(s)=1
Yusuf,
I think your current divider is wrong......I think ir1/is1 = (sL//1/sC)/(Re+(sL//(1/sc))
I got the current divider mixed up. Brandon has given the correct formula. But the point is H(s) is not 1. It is represented by the current division expression above. Correct??
Yeah that's correct......I think we are just getting mixed up with terminology. H(s) for the voltages is 1 BUT the transfer function (i.e. H(s) regarding I) for the currents is NOT 1 but a function of jw...
Yusuf -- How did you come up with the ratio for Is1/Vg? Once I get this I'm home free.
I have been pzzling over is1/Vg as well. That seems like its not going to be very straight forward.
I agree with Tanto's answer...but you can't leave it in that form. You have to find a relationship for cos(phi)....any suggestions?
Has anyone been able to calculate M for prob.19.3 that accounts for Qe and F? I've been struggling with relating the variables in the switch network. Any hints?
Here is what I did.....based on my explanation above I took V/Vg=V/ir1*ir1/is1*is1/Vg. I expressed this as (some constant)*ir1/is1 where ir1/is1 is H(s) and it evaluates as (sL//1/sC)/(Re+(sL//(1/sc)) the magnitude of which evaluates to (F/Qe)/sqrt((1-F^2)^2+(Qe/F)^2). The hitch is I have been unable to find the constant because I have had no luck evaluating the is1/Vg term.
19.3c M=M(Qe,F)=?
M=(V/Vr1)*(Vr1/Vs1)*(Vs1/Vg)=1/cos(phi_s)
V/Vr1=2/pi for PRC
Vr1/Vs1=1 from the circuit
Vs1/Vg=pi/(2*cos(phi_s)) from v(Lf)_avg=0
M=1/cos(phi_s)
phi_s=phase(Zin(jws))=
=tan^-1(Im(Zin(jws))/Re(Zin(jws))),
Using trig identity: cos(tan^-1(x))=1/[sqrt(1+x^2)]
M=1/cos(phi_s)=sqrt(1+(Im(Zin(jws))/Re(Zin(jws)))^2)
Zin(s)=Re||1/(sC)||sL
Next is to find the:
Im(Zin(at s=jws)) and Re(Zin(at s=jws)),
find the ratio between the two Im/Re and plug it into the M=sqrt(1+(Im/Re)^2)
Vojkan,
You are a power point in our homework.
Thank you.
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