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Y and g parameters with dependent source 4V1

Short answer

y = [−8/(3s) 0; −8s (6s²+1)/(3s)]. g-parameters: g11 = −8/(3s), g12 = 0, g21 = 24s²/(6s²+1), g22 = 3s/(6s²+1). The network is non-reciprocal because y12 = 0 and y21 ≠ 0.

Find the y and g-parameters of the circuit in figure below and also find whether the network is reciprocal or not. [Figure: port 1 (V1, I1) followed by a 1 H inductor and a 2 F capacitor in series arm; a 3 H inductor as a shunt at port 1 side; a dependent voltage source 4V1 as a middle shunt branch; a 3 H inductor as a shunt at port 2 (V2)]

Reading the figure (assumption). From port 1: a 3 H shunt inductor, a 1 H series inductor, then a middle shunt branch that is the dependent voltage source 4V1 (+ at the top), then a 2 F series capacitor, and a 3 H shunt inductor across port 2.

The middle node M is held at VM = 4V1 by the voltage source.

y-parameters

Port 1:  I1 = V1/(3s) + (V1 − VM)/s = V1/(3s) + (V1 − 4V1)/s = (1/(3s) − 3/s) V1
         I1 = −(8/(3s)) V1
Port 2:  the current into port 2 node from M through the 2 F is (4V1 − V2)(2s).
         I2 + (4V1 − V2)(2s) = V2/(3s)
         I2 = −8s V1 + (2s + 1/(3s)) V2

y11 = −8/(3s)       y12 = 0
y21 = −8s           y22 = 2s + 1/(3s) = (6s² + 1)/(3s)

g-parameters (I1 = g11 V1 + g12 I2, V2 = g21 V1 + g22 I2)

Solve the second y-equation for V2 and substitute:

g11 = I1/V1 |I2=0 = y11 − y12 y21/y22 = −8/(3s)
g12 = I1/I2 |V1=0 = y12/y22 = 0
g21 = V2/V1 |I2=0 = −y21/y22 = 8s·3s/(6s² + 1) = 24s²/(6s² + 1)
g22 = V2/I2 |V1=0 = 1/y22 = 3s/(6s² + 1)

Reciprocity

A network is reciprocal if y12 = y21. Here y12 = 0 but y21 = −8s ≠ 0, so the network is not reciprocal (the controlled source makes it active/non-reciprocal). Equivalently g12 = 0 ≠ −g21.

Answer: y = [−8/(3s) 0; −8s (6s²+1)/(3s)]; g = [−8/(3s) 0; 24s²/(6s²+1) 3s/(6s²+1)]; not reciprocal.

✓ Answer checked by Claude Opus 5.5 (high effort)

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