70938

Charging a finite length linę through a resistor

In the first example we will consider what happens when an initially uncharged linę is suddenly connected to an excitation voltage source through a resistance which it is common to cali Zs but which might have been morę properly known as Rs. This situation

is depicted in Figurę 2.7

Because we have not considered any relation between the source resistance Zs, the load resistance Zi.and the characteristic impedance Zo, the situation we are studying has

considerable generality. Its study will lead to the powerful concept of the lattice diagram,

which is an orderly way of kccping track of multiple reflections up and down the linę which occur aftcr the excitation is first applied.

In the above Circuit we close the switch t = 0 and let T = 1/c be the timc for a one-way propagation down the linę.

We cxpcct that the closing of the switch will first launch, at the source end, a forward wave, which will travel over a time T to the load end, where it will be reflected, travel back over a time T to the source end, where it will be reflected forward again. Consider first the sending end. At z = S we have at all times