# Two-ports question ABCD parameters

I am trying to find the ABCD parameters of the two port network in this circuit (where $R = 1\Omega$ and $x = 1$):

simulate this circuit – Schematic created using CircuitLab

To determine A and C, we leave the output port open so that $I_2=0$ and place a voltage source $V_1$ at the input port. We have

$V_1 = (j10 + 1)I_1$

and

$V_2 = I_1 *$ what?

Should I do this with nodal analysis instead?

Using the definition:

$$A = \frac{v_i}{v_0}\mid i_0=0$$ $$B = \frac{v_i}{i_0}\mid v_0=0$$ $$C = \frac{i_i}{v_0}\mid i_0=0$$ $$D = \frac{i_i}{i_0}\mid v_0=0$$

Output voltage is voltage over R $$A: v_0 = \frac{R}{R+jx}v_i \Rightarrow A = \frac{R+jx}{R} \\$$ Input voltage is voltage over jx + voltage over R $$B: v_i = i_ijx + (50+1)*i_iR = i_0\frac{jx}{50} + i_0\frac{51}{50}R$$ $$v_i = \frac{jx+51R}{50}i_0 \Rightarrow B = \frac{jx+51R}{50}$$ Output voltage is voltage over R $$C: v_0 = i_iR \Rightarrow C = \frac{1}{R}$$ Relation is already given $$D: i_0 = 50i_i \Rightarrow D = \frac{1}{50}$$

Assuming that when $$i_0 = 0$$ the current source cannot deliver any current.

You can not leave the terminals of a current source open.

A current source will always try to develop a voltage across its terminals so as to supply a constant current to the load. When the terminals are left open, the voltage that should be developed by the current source becomes infinity.

If that is possible, then $V_2 = -\infty$