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

schematic

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?

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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.

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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\$

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