# Derivation of $Z_{och}$ & $Z_{sch}$ for a symmetrical lattice two port network

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: $$Z_{och}= Z_2$$ $$Z_{sch}= Z_1$$

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} \$$ :

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} \$$

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...

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