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.

**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 β_{i} is the
wave number of the ith transmission line segment and l_{i} is the
length of this segment, and Z_{i} is the front-end impedance that loads
the i^{th} segment.

The impedance transformation
circle along a transmission line whose characteristic impedance Z_{0,i}
is smaller than that of the input cable Z_{0}.

Conversely, if Z_{0},_{i} >
Z_{0}, 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 Z_{0,i} is often different
from that of the input cable Z_{0}, the impedance transformation circle
is off centered along the x axis of the Smith Chart whose impedance
representation is usually normalized against Z_{0}.

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Transmission Lines and Waveguides : Transmission Line Theory : Input and Transfer Impedance |

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