# Y matrix (admittance parameters) and Transfer function

I have the following two port network:

for which the Y matrix elements are:

• $$\y11(s): (2+3s)\$$
• $$\y12(s): -1\$$
• $$\y21(s): -1\$$
• $$\y22(s): 1.5\$$

I need to get the value of $$\ZL\$$ in order for the transfer function of the circuit to corresopnd to the following Bode plot:

From the two port network: Based on the equations of the network,

and the fact that $$\V_2 = -I_2*Z_L\$$, writing the following equations system:

I get the transfer function $$\H(s)=\frac{2*Z_L}{2+3*Z_L}\$$

On the other hand, to find the Transfer function of the given Bode, I proposed:

• num. of decades between two frequencies: $$log\frac{\omega_x}{10} = \frac{4}{20} \implies \omega_x = 10^\frac{4}{20}$$
• In $$\\omega_0\$$ there is a single pole.
• In $$\\omega_x\$$ theres a single zero.

Therefore: $$\H(s)=k\frac{(\frac{s}{\omega_x} + 1)}{\frac{s}{10} + 1}\$$

Where $$\k=0.5\$$

With all that, I get the following value for $$\Z_L\$$:

which has absurd numbers, and therefore I suspect I'm doing something wrong, although I'm not seeing where.