Hello:
I am having major trouble with the algebra for problem 2A. There must be something that I am missing.
The voltage equation is fine and okay to put into the model. However, when solving for i2, I cannot isolate (d'/d)*<i1> and when solving for i1, I cannot isolate (d/d')*<i2>. Therefore I cannot solve the transformer.
The approach I am taking is to solve for Ion and then plug into the other current equation. This leaves the currents multiplied by a factor of 1/(d+(tr/Ts)). I can combine all of the terms by taking the common denominator, but this leaves a very messy numerator term which does not help much.
Also, if I add the two current equations, I can eliminate a lot of variables. This results in <i1>+<i2> = Ion which is not much help.
Any assistance will be much appreciated! Just some small hint will probably help me get to the next step so that I can proceed with the assignment.
If anyone is having similar problems, let's put our heads together to solve this. I can email you what I have so far and then we can go from there. I also am available for email, gchat, fb, or cell phone.
Thank you,
Alex
hi alex. you can mail me what you have at vincent.din@colorado.edu
ReplyDeletei'm workin through this, too. i can email you once i figure something out.
i used
ReplyDelete= Ion(d+tr/Ts) + Qr/Ts
before plugging this into my expression, i distributed the Ion term. i did not end up with any d+tr/Ts factors.
hope this helps
sorry that is an expression for i1, average value
Deletei ended up with an Ion factor in my i2 expression. reworking it now...
DeleteAfter eliminating Ion, I get the following equation:
ReplyDelete(d'-tr/Ts) = (d+tr/Ts) + Qr/Ts
The equation seems consistent. You can see that the tr/Ts terms simply shift the duty cycle and hence the transformer ratio a bit. If this equation is fine, is there a way to contruct the equivalent circuit with dependent current sources on both sides, similar to page 20 in the lecture 4 notes? In other words, can we build it with a dependent source on the primary and a dependent source in the secondary? Would it model the equation correctly? Any thoughts would be greatly appreciated.
Hi Drew,
ReplyDeleteI reworked the algebra. Not sure if your formatting got messed up, but this is the equation I got (looks the same):
i1_avg = i2_avg * (d+tr/Ts)/(d'-tr/Ts) + Qr/Ts
It would appear that constructing the circuit with additional dependent sources would make sense, though the professor answered another blog post in a way that suggested we should not have dependent sources, so I am unsure.
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ReplyDeleteHi Alex,
ReplyDeleteI used the fact that (1-d)>tr/Ts and found avg.ion to be (+Qr/Ts)/d'. I used this to solve for avg.i1. i ended up with avg.i1 =(d/d'+tr/Tsd')+Qr/Tsd'. This made it easy to build the model with d':d transformer.
Hi praSANTA:
DeleteThank you for the idea. I solved the circuit differently though. I solved both current equations for Ion and then set the two Ion values equal to each other.
I think this does the job.
My only concern is that I have two dependent current sources in the circuit (similar to fig 7.56). Since the example shown in fig 7.56 has these type of current sources, I am leaving my circuit this way.
Thanks everyone for the input.
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ReplyDelete