# What is the definition of characteristic impedance of a lattice network?

We were being taught about Lattice networks in class, today, and our professor mentioned that the characteristic impedance of a symmetrical lattice network like

is given by:

$$Z_0=\sqrt{Z_aZ_b}$$

I'm not sure what characteristic impedance means in this context. I searched around the net a bit and found that the term is generally used in the context of transmission lines. However, I'm not sure how it applies to a lattice network or perhaps more generally to a two-port network.

Basically, my question is: What is the definition of characteristic impedance of a lattice network (or a two-port network)?

I'm not sure what characteristic impedance means in this context.

If you "placed" an impedance on the output (on the right of the network) and looked at the impedance into the network (from the left) then the input impedance (looking in from the left) will equal the "placed" impedance when that placed impedance equals the characteristic impedance of the network.

You could go through the math and calculate the input impedance when an unknown impedance is placed on the output then equate the input impedance to that unknown impedance and it would turn out to be $Z_0$.

The impact of this is that you can cascade an infinite number of sections and the input impedance would remain constant.

• The formula for iterative/characteristic impedance of a two-port network is given in my notes as $Z_0=\sqrt{Z_{11}^2-Z_{12}^2}$. Any idea how to derive it directly?
– user193992
Jul 23 '18 at 1:16
• I have done the derivation of standard t-lines but not this. Maybe raise a new question to gain a potentially bigger audience. Jul 23 '18 at 9:25

When you connect the characteristic impedance at the output port, the circuit will reduce to a balanced wheatstone bridge(as the circuit given is a symmetrical lattice network) and the the input impedance which itself is characteristic will reduce to the average of impedance's Za and Zb.