Thevenin example with 3 two port networks

Thread Starter

Luka Kostic

Joined Nov 23, 2018
3
Hello guys, this is my first post, i really need help about this thing.
In this circuit i have 3 two port networks, given in vairus parameters. I need to calculate Thevenin equivalent between A and B.
I choosed to do it with mesh analysis, but when i write my equations i don't know what to do with Vab, is there only one closed loop or there is 3 of them?
I'm guessing there is only one, but in this case how's the current traveling in that clossed loop in the middle?

Thank you very much, i have an exam on Monday, the only thing that keeps me awake is this.
 

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The Electrician

Joined Oct 9, 2007
2,770
You have what appears to be 3 different two-ports, each specified differently:

1. Port Y1, given as admittance parameters.
2. Port T2, given as transmission parameters.
3. Port Z3, given as impedance parameters.

Assuming this is correct, show some details of how you have attempted a mesh analysis.
 

Thread Starter

Luka Kostic

Joined Nov 23, 2018
3
Converting Y1 and T1 to Z parameters. In that case i got V1 and V2 in fuction of I1 and I2 of every two-port network.
In case of Z1 i got first cloosed loop on the left and the equation would be: Es= I1R1 + Z11I1+Z12I2 and i can do that for every two-port.
The part i'm confused is how i get open loop voltage for Thevenin(Vab). I think that the whole thing in the middle is one closed loop, but i'm a bit confused with that third part that it's added. Without it i would calculate currents, then from one loop of my choice i would calculate Vab(either one from the left or from the right).
 
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The Electrician

Joined Oct 9, 2007
2,770
Converting Y1 and T1 to Z parameters. In that case i got V1 and V2 in fuction of I1 and I2 of every two-port network.
In case of Z1 i got first cloosed loop on the left and the equation would be: Es= I1R1 + Z11I1+Z12I2 and i can do that for every two-port.
The part i'm confused is how i get open loop voltage for Thevenin(Vab). I think that the whole thing in the middle is one closed loop, but i'm a bit confused with that third part that it's added. Without it i would calculate currents, then from one loop of my choice i would calculate Vab(either one from the left or from the right).
How are you dealing with the dependent source at the output of the T two-port, and the mutual inductance between the outputs of the T and Z two-ports? Do you have numerical values for the three sets of parameters, or are you expected to derive an expression for Vab using only symbolic variable names? I would expect a symbolic expression to be very complicated.

Please show the equations you have derived so far.
 
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The Electrician

Joined Oct 9, 2007
2,770
As an example of what I mean by complicated expression, here's what I get for VA if I eliminate R2 and L1:

VA Expression.png

And, I wouldn't want to bet my life on its correctness. This is one of those complicated problems where one has to be very careful to get all the signs right.
 

Thread Starter

Luka Kostic

Joined Nov 23, 2018
3
I'm sorry that i've put you through all that calculation, forgot to say that my professor doesn't require to solve the sistem, becouse he doesn't give values of the elements. So he is just asking to write all the equation and to show how we are going to come to the solution. I've realised in this case, much easier way is to use nodal analysis. Thank you for the help, and your effort!
 

The Electrician

Joined Oct 9, 2007
2,770
You have an error in your equation 5 where you have equated V3 to alpha times the current in R1. If I read the notation associated with Vs correctly, Vs is equal to alpha times the voltage across R1, not the current through R1.

Also, you might want to carefully consider equation 6. Note that the series combination of R2 and L1 is in parallel with a voltage source, Vs; therefore the voltage induced in L1 due to the current in L2 can have no effect on the voltage Vs. However the voltage induced in L2 due to the current in L1 does have an effect on the voltage V4.
 
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