Transmission and Y parameters with dependent current source

Transmission parameters: V1 = A V2 − B I2, I1 = C V2 − D I2. Admittance parameters: I1 = y11V1 + y12V2, I2 = y21V1 + y22V2.

Reading the figure. At port 1 side a dependent current source 0.5 I3 (arrow downward, to the bottom wire) is in shunt; then a 10 Ω series resistor carrying I3 (I3 flows from the port 1 node into the 10 Ω); and a 6 Ω shunt resistor across port 2. Since nothing lies between port 1 and the source, the port 1 node voltage is V1.

Equations

I3 = (V1 − V2)/10
KCL at port 1 node:   I1 = I3 + 0.5 I3 = 1.5 I3
KCL at port 2 node:   I2 + I3 = V2/6

Y-parameters

I1 = 1.5 (V1 − V2)/10 = 0.15 V1 − 0.15 V2
I2 = V2/6 − (V1 − V2)/10 = −0.1 V1 + (1/6 + 1/10) V2 = −0.1 V1 + 0.2667 V2

y11 = 0.15 S = 3/20     y12 = −0.15 S = −3/20
y21 = −0.1 S = −1/10    y22 = 4/15 S = 0.2667 S

Transmission parameters

From the I2 equation: V1 = (0.2667 V2 − I2)/0.1 = 2.667 V2 − 10 I2, so A = 8/3, B = 10 Ω. Then I1 = 0.15 V1 − 0.15 V2 = 0.15(2.667 V2 − 10 I2) − 0.15 V2 = 0.25 V2 − 1.5 I2, so C = 0.25 S, D = 1.5.

A = 8/3 = 2.667     B = 10 Ω
C = 0.25 S          D = 1.5
Check: AD − BC = 4 − 2.5 = 1.5 ≠ 1  → network is not reciprocal (y12 ≠ y21).

Answer: Y = [0.15 −0.15; −0.1 0.2667] S; T = [2.667 10 Ω; 0.25 S 1.5].