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Design of stubs

Practical reasons, will be discussed in lectures, make it morę convenient in many transmission

linę problems to work in admittance terms. Thus when we design a stub, we are seeking to find the stub length which will provide a particular susceptance.

We recall from Section 2.8.2 and Section 2.9.2 that we can obtain any desired susceptance

by using either a short-circuit or open-circuit stub of suitable length. Again, practical reasons suggest variable stubs should be short circuited.

The length of a short circuited stub to produce a desired susceptanceB may be obtained from the formulae in Table 2.3, or by using the Smith Chart as in Figurę 3.8. In this figurę, to produce a desired input susceptanceB we first of all find the normalised

input admittance ystubof the stub corresponding to the susceptanceB by dividing the admittance 0 + jBby the characteristic admittance of the transmission linę forming the

stub. If we are using a short circuited stub, the load end on the admittance chart is the right-most extremity of the unit circle, as illustrated in Figurę 3.8. The correct stub

length is found by moving clockwise from that point away from the load (considered to

be the short Circuit) towards the input end of the stub until the desired normalised input

admittance ystubis found.

To obtain the stub length from the angular rotation we can make use of the fact that a complete revolution around the Smith chart corresponds to movement along the linę by

a length of one half of a wave length, or we can use a peripheral scalę on the Smith Chart

which is specifically provided to assist in this calculation.

The rotation from the start point shown in Figurę 3.8 is always in the direction shown. In the example illustrated in that figurę the susceptance of the stub is negative, and the

rotation is less that half a revolution, and thus the stub length will be less than a quarter

of a wave length.

When the susceptance required for the stub is positive, a point on the upper half of the unit circle must be reached, and a rotation of morę than half a revolution is required,

and the length of the stub is morę than a quarer of a wave length.