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According to the following lecture https://www.youtube.com/watch?v=1dgdiws3Kl8&t=817s. A two-port network such as the following

two-port network

can be expressed as the following simultaneous equation $$a_{1}V_{1} + a_{2}V_{2} + b_{1}I_{1} + b_{2}I_{2} = 0 $$ $$a_{3}V_{1} + a_{4}V_{2} + b_{3}I_{1} + b_{4}I_{2} = 0 $$

However, this implies two degrees of freedom so two independent variables but I struggle to understand why, given when I apply an input voltage it is the only independent factor and all else is dependent on the input voltage?

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I apply an input voltage it is the only independent factor and all else is dependent on the input voltage?

You have to also consider what you connected to port 2. If you connected a voltage or current source, that obviously also sets one of the variables on port 2. If you connected nothing at all, that means you set \$I_2=0\$. If you connected a short, then you set \$V_2=0\$.

If you connected a resistor, you set \$I_2 = -V_2/R\$, which doesn't force either variable to anything in particular, but it does remove one degree of freedom from your original equations.

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  • \$\begingroup\$ I now understand why there can be two independent variables as it is possible to attach an independent voltage/current source to both ports hence two independent variables. However, how do you get the two equations stated above? \$\endgroup\$ – dilinex Nov 23 '19 at 3:00
  • \$\begingroup\$ Which two equations? \$\endgroup\$ – The Photon Nov 23 '19 at 3:12
  • \$\begingroup\$ Apologies, the equations I mentioned in my question \$\endgroup\$ – dilinex Nov 23 '19 at 3:14
  • \$\begingroup\$ @dilinex, Watching the video, he just says it's the right number of equations to leave the right number of degrees of freedom to allow for the external connections, which is true, but isn't really a proof of any kind. And I don't know what the proof is (and it would depend what you consider axioms of circuit theory). I can say that once you start defining real linear 2-ports, the equations generally come out with only 3 terms each (or with S-parameters you define new linear combinations of the port variables to simplify them to 3 variables each). \$\endgroup\$ – The Photon Nov 23 '19 at 3:23

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