double stub smith chart examples with solutions

Now, since the input admittance y sB of a short-circuited stub is purely imaginary, the above equation can be satisfied only if, In terms of normalized admittances, the above equation becomes, For impedance matching with a main line that has a characteristic resistance R 0, we demand the total input admittance at terminals B-B', looking toward the load, to equal the caracteristic conductance of the lne that is, In the above figure a stub of length l A is connected directly in parallel with the load impedance Z L at terminals A-A', and a second stub of length l B is attached at terminals B-B', at a fixed distance d 0 away. Here, distance d 0 is fixed and arbitrarily chosed and the lengths of the two stub tuners are adjusted to match a given load impedance Z L to the main line. In such cases an alternative method for impedance-matching is to use two short-circuited stubs attached to the main line at fixed positions, as shown in the figure, Furthermore, it is very difficult to build a variable-length coaxial line with a constant caracteristic impedance. This requirement often presents practical difficulties because the specified junction point may occur at an undesirable location from a mechanical viewpoint. However, the single-stub method requires that the stub be attached to the main line at a specific point, which varies as the load imedance or the operating frequency is changed. The method of impedance matching by means of a single stub described in the previous section can be used to match any arbitrary, nonzero, finite load impedance to the characteristic resistance of a line.

Double stub smith chart examples with solutions