# Solved Problems-7

Problem-7

A 50-ohm line feeds an inductive load

*Z**= 35 +*_{L}*j*35 ohms. Design a double-stub tuner to match this load to the line (make use of a Smith chart).Solution

The normalised load admittance is given as,

**Steps of Design**

*we assume that the first stub is located at the load*.We locate the point of load admittance on the chart, say the point A.

(b) Also, as the

*distance between the stubs*is not mentioned, we assume it to be . Therefore, the auxiliary circle is drawn as shown in Smith chart.

**Designing a double-stub tuner**

*B*. Hence, the

*first stub is located at the point B*where the normalised admittance as read from the chart is,

*j*0.7142 â€“

*j*0.49) =

*j*0.224. The +0.224 constant susceptance circle intersects the rim of the chart at 0.036Î».

*O*and radius equal to

*OA*. This circle cuts the unitary conductance circle at the point

*C*. The second stub is located at the point

*C*.

(f) The portion of the line between the stubs changes the admittance at the point

*A*to the point

*C*. The normalised admittance at the point

*C*without the second stub as measured from the chart is (1 +

*j*0.65). For perfect matching, the second stub must eliminate the imaginary component of this admittance, i.e. the second stub must provide a susceptance of â€“

*j*0.65. This [â€“

*j*0.65] circle cuts the rim of the chart at 0.408Î».

- Length of first stub located at load,
*L*_{stub1}= 0.286Î» - Length of second stub,
*L*_{stub2}= 0.158Î» - Distance between stubs =