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susceptance at the reference piane B because we do not know the susceptance provided

by stub SI. Given that the normalised conductance at reference piane D is g = 1, we can say that the noralised admittance at reference piane B lies on the g = 1 circle. The set of points which form the g = 1 circle have been shown as locus B on the diagram of Figurę 3.13.

6.    We are now in the position of having locus A representing some of the information about the solution and locus B representing different information about the solution. We might be tempted to simply look for an intersection between locus A and locus

B to find a point which is consistent with both pieces of information, but to do so would be incorrect, because locus A expresses information which is valid at the right hand end of the tuner, i.e at reference piane A, and locus B represents information which is valid at the left hand end of the tuner, i.e. at the different reference piane B.

7.    What we need to do is to take the information that we have contained in locus B and

re-express it as a different set of points which correspond to the same information but expressed at the position of the reference piane at the load end of the tuner, i.e. at the reference piane which has been labelled as both A and C, and which is distant 3A/8 from reference piane B in the direction of the load.

To do this we take locus B as a solid object, and rotate it by three quarters of a revolution in a counter-clockwise direction, the fixed point of the rotation being the centre of the Smith chart. This leads us to the locus shown at C in Figurę 3.13.

8.    We now have partial information about the solution in locus A and partial information

about the solution in locus C, and both locus A and locus C express their information at a common reference piane, namely that labelled as both A and C in Figurę 3.12. It is now true that the point of intersection of locus A and locus C defines a solution to the problem.

9.    Thus two Solutions, at points X and Xocan be found at the intersection of locus A and locus C. We select one of these Solutions, at the point X, for the further development below.

10.    We are now in a position to determine the normalisedsusceptance to be provided by stub S2, and hence the length S2 of stub S2.

11.    To do this we observe that the function of stub S2 is to modify the normalised susceptance at the reference piane denoted as A and C so that the total normalised susceptancebxat that point consists of the sum of the normalised load susceptance bLand the normalisedsusceptancebs2 of stub s2.

12.    Thus we calculate the normalisedsusceptance to be provided by stub S2 as bs2 = bx-bi, both of the quantities on the right hand side of this equation being readable from the Smith Chart.

13.    We then calculate from the desired normalisedsusceptance the length S2 of stub S2