INPUT AND TRANSFER IMPEDANCE:
If the load impedance is not equal to the source impedance, then all the power that are transmitted from the source will not reach the load end and hence some power is wasted. This is represented as impedance mismatch condition. So for proper maximum power transfer, the impedances in the sending and receiving end are matched. This is called impedance matching.
Stepped transmission line
A simple example of stepped transmission line consisting of three segments.
Stepped transmission line is used for broad range impedance matching. It can be considered as multiple transmission line segments connected in serial, with the characteristic impedance of each individual element to be, Z0,i .
And the input impedance can be obtained from the successive application of the chain relation.
where βi is the wave number of the ith transmission line segment and li is the length of this segment, and Zi is the front-end impedance that loads the ith segment.
The impedance transformation circle along a transmission line whose characteristic impedance Z0,i is smaller than that of the input cable Z0.
Conversely, if Z0,i > Z0, the impedance curve should be off-centered towards the +x axis.
And as a result, the impedance curve is off-centered towards the -x axis.
Because the characteristic impedance of each transmission line segment Z0,i is often different from that of the input cable Z0, the impedance transformation circle is off centered along the x axis of the Smith Chart whose impedance representation is usually normalized against Z0.