domingo, 27 de junio de 2010

Typical Matching Situations

It's relatively easy to design resistive terminations for waveguide and TEM structures that provide extremely wideband loads with Z=Zo of the transmission line. For situations where the loads must dissipate substantial power, thermal considerations come into play, and some form of conductive or convective cooling is necessary to prevent destruction of the load. In the extreme case, a long enough length of terminated lossy transmission line will present a high-power matched load to a transmission line of the same dimensions.
The going gets tough in cases where impedance matching is required to narrow-band elements such as antennas or to devices with substantial reactance and resistance levels that are much lower (or higher) than typical transmission lines.
An arbitrary impedance can, in principle, be matched at a single frequency by adding sufficient transmission line to move the impedance around the Smith chart until it lies on an admittance circle that passes through the center of the chart (g=20 millimhos or milliSiemens), then adding susceptance of the proper sign to move the combined admittance to the =0 point. The simplified Smith charts here show one of the two possible solutions for an arbitrary normalized impedance.

The other solution is

Although inconvenient to realize in transmission line format, there are two other solutions that are obtained by rotating the arbitrary impedance until it is on the 50 circle, then adding the proper series reactance to bring the resulting impedance to the 50 point.
Recall that a useful expression for the impedance of a lossless transmission line of characteristic impedance Zo with an arbitrary load ZL and electrical length tita is

This can be used in connection with a spreadsheet or other calculation aid to keep track of the real and imaginary parts with varying frequency.
But these are single-frequency solutions to the impedance matching problem. Because one of the major advantages of microwave usage is the opportunity to transmit substantial bandwidth, and because in practice one would hope to avoid a requirement for a unique circuit for each of the many frequencies in a typical 40% waveguide band, broadband solutions to the matching problem are valuable and sought-after.

Publicado por: Jahir Alonzo Linares Mora C.I: 19769430 CRF

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