![]() By plotting the Smith-chart locus of input impedance as a Z0 generator is moved closer and farther from a load, insight is gained into the bandwidth of the circuit. For the first time, this paper presents a visual approach to investigating non- Z0 transmission lines, with a particular emphasis on bandwidth considerations. Note the stub is attached in parallel at the source end of the primary line.In electrical engineering education, there is currently no way to graphically study the bandwidth of transmission lines with arbitrary characteristic impedance. We now seek the shortest stub having an input admittance of Mho for the input admittance after attaching the primary line. So the equation to be solved forīy trial and error (or using the Smith chart see “Additional Reading” at the end of this section) we find for the primary line, yielding Is the wavelength in the transmission line. Of the primary line (that is, the one that connects the two ports of the matching structure) is the solution to the equation (from Section 3.22): With respect to the characteristic impedance of the transmission line) is Is the characteristic impedance of the transmission lines to be used. Since parallel reactance matching is most easily done using admittances, it is useful to express Equations 3.16.6 and 3.16.8 (input impedance of an open- and short-circuited stub, respectively, from Section 3.16) in terms of susceptance:Īre the source and load impedances respectively. The single-stub matching procedure is essentially the same as the single parallel reactance method, except the parallel reactance is implemented using a short- or open-circuited stub as opposed a discrete inductor or capacitor. This issue is avoided in the parallel-attached stub because the parallel-attached stub and the transmission line to which it is attached both have one terminal at ground. This is contrast to a discrete reactance (such as a capacitor or inductor), which does not require that either of its terminals be tied to ground. This is because most transmission lines use one of their two conductors as a local datum e.g., the ground plane of a printed circuit board for microstrip line is tied to ground, and the outer conductor (“shield”) of a coaxial cable is usually tied to ground. Although a series reactance scheme is also possible in principle, it is usually not as convenient. This scheme is usually implemented using the parallel reactance approach, as depicted in the figure. ![]() Figure 3.23.2: Single-stub matching.įigure 3.23.2 shows the scheme. Figure 3.23.1: A practical implementation of a singlestub impedance match using microstrip transmission line. This section explains the theory, and we’ll return to this implementation at the end of the section. Figure 3.23.1 shows a practical implementation of this idea implemented in microstrip. Section 3.16 explains how a stub can replace a discrete reactance. Whatever the reason, a possible solution is to replace the discrete reactance with a transmission line “stub” – that is, a transmission line which has been open- or short-circuited. In many problems, the required discrete reactance is not practical because it is not a standard value, or because of non-ideal behavior at the desired frequency (see Section 3.21 for more about this), or because one might simply wish to avoid the cost and logistical issues associated with an additional component. In Section 3.22, we considered impedance matching schemes consisting of a transmission line combined with a reactance which is placed either in series or in parallel with the transmission line. ![]()
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