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Detail of the procedure The details of the procedure are illustrated in Figure 3.13 and the discussion below.
As indicated in Figure 3.12, the length 3λ/8 length of line, the two stubs and the
main line to be matched all have a characteristic admittance Y0. This is the normal case
but the procedure can be varied to allow for cases where the characteristic admittances
of those four line lengths do not have a common value. Such variation will be discussed
The steps of the procedure, all of which are in terms of normalized admittance, are as
follows.
1. Locate the normalised load admittance yL on the chart. In the example shown in
Figure 3.13 this point is shown towards the top of the chart.
2. Now we take note of the fact that the action of connecting stub S2 in parallel with
the load admittance YL will be to produce a resultant admittance at the reference
plane A, just to the left of the junction between stub S2 and the load, which has
the same normalised conductance as the load but has a normalised susceptance
which is at present unknown because we do not know the length of the stub S2, and
therefore do not know the value of the susceptance provided by it. Thus we can
say that the admittance looking to the right at the reference plane A has the same
normalised conductance as the load and an unknown normalised susceptance. Thus
that normalised admittance lies on the constant g circle which passes through the
point yL. We call this locus A, and draw it on the Smith Chart.
Locus A represents a partial solution to the problem in that when we do find a
solution, it must lie on that locus.
3. We for the moment put aside the information that we have obtained by working
from the load end of the tuner and is expressed in locus A, and transfer our attention
to the input end of the tuner, and examine what conclusions we can draw about the
normalsied admittance at the reference plane shown as D in Figure 3.12.
4. Firstly we note at the reference plane D our desire is that the transmission line lying
to the left of that point be matched. Thus we know that the normalised admittance
corresponding to the reference plane D has the values g = 1 and b = 0. This
corresponds to the single point which is shown as the origin of the Smith chart, i.e.
at its centre.
5. Next we consider what conclusions we can draw about admittances at the reference
plane B which is just to the right of the junction between the main line, the tuner
line, and stub S1. At this reference plane B, we can say that, because the parallel
connection of the stub can only change the susceptance, the normalised conductance
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