Hi! My task is to find z parameters of individual networks and z parameters of whole network (z=zN1+zN2). Here is what I have done:
I will echo t_n_k's comment. However, I was able to save the images and increase the contrast, but you shouldn't post hard to read images when you're asking for help. If you make it too hard for those who would help you to read your work, they may just decide it isn't worth it. Your result for the Z matrix of N2 is correct, but the Z matrix for network N1 isn't correct. Why does the Z matrix for N1 involve V1' and V2? I think you haven't dealt with the dependent source correctly. The Z matrix should not involve V1' and V2.
Sorry for poor quality of images, at the time of writing post I have not been able to put better images. @The Electrician, I know that Z matrix should not involve V1' and V2 but I don't know how to get rid of them
Yes, but I have no ideat what to do here I expressed V2 in terms of V' and V'' (image in post #2) and substituted it in zN1 but it didn't give me result...
Just to mention that I analysed whole circuit without using rule for series connection and I got: z11=((3*s+2+3/s)*(1-m)+m*(2+3/s))/(1-m); z21=(2+3/s)/(1-m); z12=(2*s+4*s*m+3+m)/(s*(1-m)); z22=(4/s+6)/(1-m);
First, I'm posting a redrawn version of your circuit with a reference node selected, and the other nodes indicated in red. I'll be doing all my work with respect to this circuit. It would probably be helpful for all involved to reference this image. I'll be doing a nodal analysis. I'm going to designate the voltages at the various nodes as e1, e2, e3, e4, e5 and e6. Thus, V1 is the same as e1, V2 is equal to e3-e6 and so forth.
Now you need to write 6 nodal equations, some of which must deal with the dependent source. For example, the equation for node 2 is:
This appears to be correct, but now I'm puzzled. How are you able to get this result for the whole circuit, which means you had to deal with the dependent source, but you can't get the result for the N1 subcircuit?
When you're working on ZN1, use the fact that V1'' and V2'' are zero. In other words, V1' = V1 and V2' = V2. This should help you eliminate the unwanted voltages.
I can't be sure I'm reading your final result correctly. Would you please type the result from page 5 into a post, transcribing very carefully? I find that with the result I get, it's not true that Z = ZN1 + ZN2. Do you get that result also?
Here are parameters for N1: z11=(2*s+2)*(s+1-s*m)/(s+1-s*m-m); z12=(2*(1-m)+m*(1/s+2))/(1-m); z21=(2*s+2)/(s+1-s*m-m); z22=(1/s+2)/(1-m); N2: z11=3/s+s; z12=3/s; z21=3/s; z22=3s+4; It should be: z11(N1) + z11(N2) = ((3*s+2+3/s)*(1-m)+m*(2+3/s))/(1-m), z12(N1) + z12(N2) = (2*s+4*s*m+3+m)/(s*(1-m)), z21(N1) + z21(N2) = (2+3/s)/(1-m), z22(N1) + z22(N2) = (4/s+6)/(1-m), but these relations are not satisfied.
Here's what I get: With some algebra, your results can be shown to be identical to mine. The reason that Z ≠ ZN1+ZN2 is that the dependent source value is m V, not m V'. The Z parameters for N1 can't even be calculated without N2 in place, so N1 and N2 aren't independent. I assume that one purpose of this exercise is to show that you can't always get the Z parameters of the overall network by adding the parameters of the sub-networks. You had the same problem in your earlier thread about two-port parameters. The networks they want you to solve just get more complicated. You'll notice that the presence of the dependent source also had the effect of making the network non-bilateral--Z12 doesn't equal Z21.
Thanks a lot for all your help! Since method we tried is not working, I think that only way to find ZN1 is: 1) find Z parameters for whole circuit, 2) find Z parameters for N2, 3) Z=ZN1+ZN2 => ZN1=Z-ZN2
What do you mean, the method we tried is not working? It worked fine. Are you thinking that the parameters you derived for N1 are incorrect? You got the same thing I did, and they are correct. The point is to realize that using the formula Z=ZN1+ZN2 doesn't always work, even if the parameters for N1 and for N2 are correct. If you do this: 1) find Z parameters for whole circuit, 2) find Z parameters for N2, 3) Z=ZN1+ZN2 => ZN1=Z-ZN2 for this network you will get incorrect ZN1.