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I am trying to derive the open circuit impedance of half circuit [i.e \$Z_{och}\$ ] and short circuit impedance of half circuit [i.e \$Z_{sch}\$ ] of symmetric lattice two port network (which is shown below in the diagram) is given as: $$Z_{och}= Z_2$$ $$Z_{sch}= Z_1$$

schematic

simulate this circuit – Schematic created using CircuitLab

My Approach:
In order to derive \$ Z_{och} \$ & \$ Z_{sch} \$ , we must divide the given two port network into two equal parts as stated by Bartlett's Bisection Theorem

so,for \$ Z_{sch} \$ :

schematic

simulate this circuit

where red line representing the shorted line to find short circuit half circuit impedance

Now taking \$ 11'\$ port
we get: $$Z_{sch}= \frac{Z_1}{2} + \frac{Z_1}{2}=Z_1$$ Thus,we derived for \$ Z_{sch} \$

Similarly,for \$ Z_{och} \$

schematic

simulate this circuit
Now taking \$ 11'\$ port
we get, \$ Z_{och}= \infty \quad [ \because \$ we don't get any closed path from 1 to 1']

,but we know \$ Z_{och} = Z_2\$ ; so did i missed any concept? , please help anyone...

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enter image description here

Don't forget to multiply the normalized results by 50 Ohm for S11.

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    \$\begingroup\$ What will i do after finding \$S_{11} \$ ? I need to find \$Z_{och} \$ not \$S_{11} \$ ! \$\endgroup\$ – Suresh Mar 1 at 12:57

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