Electromagnetic Field Theory: A Problem Solving Approach Part 66. Electromagnetic field theory is often the least popular course in the electrical engineering curriculum. Heavy reliance on vector and integral calculus can obscure physical phenomena so that the student becomes bogged down in the mathematics and loses sight of the applications. This book instills problem solving confidence by teaching through the use of a large number of worked problems. To keep the subject exciting, many of these problems are based on physical processes, devices, and models. This text is an introductory treatment on the junior level for a two-semester electrical engineering. | Stub Tuning 625 c Figure 8-24 of A 2 . Thus the solutions can be summarized as I nA 2 12 A 8 mA 2 or 9 nA 2 l2 3X 8 mk 2 where n and m are any nonnegative integers including zero . When the load is matched by the stub to the line the VSWR to the left of the stub is unity while to the right of the stub over the length the reflection coefficient is n. 7 7 7 10 ZnL l 2 which has magnitude ITJ 1 5 11 so that the voltage standing wave ratio is VSWR 12 1 zj The disadvantage to single-stub tuning is that it is not easy to vary the length lt. Generally new elements can only be connected at the ends of the line and not inbetween. 8-5-3 Double-Stub Matching This difficulty of not having a variable length line can be overcome by using two short circuited stubs a fixed length apart as shown in Figure 8-25a. This fixed length is usually A. A match is made by adjusting the length of the stubs lt and Figure 8-25 a A double stub tuner of fixed spacing cannot match all loads but is useful because additional elements can only be placed at transmission line terminations and not at any general position along a line as required for a single-stub tuner. 6 Smith chart construction. If the stubs are apart normalized load admittances whose real part exceeds 2 cannot be matched. 626 Stub Tuning 627 l2. One problem with the double-stub tuner is that not all loads can be matched for a given stub spacing. The normalized admittances at each junction are related as Ya Y. YL Y Y2 Yb 13 where Ti and Y2 are the purely reactive admittances of the stubs reflected back to the junctions while Yb is the admittance of Ya reflected back towards the load by A. For a match we require that Yn be unity. Since Y2 iS purely imaginary the real part of Yb must lie on the circle with a real part of unity. Then Ya must lie somewhere on this circle when each point on the circle is reflected back by A. This generates another circle that is fir back in the counterclockwise direction as we are .
