Читать книгу Handbook of Microwave Component Measurements - Joel P. Dunsmore - Страница 125

The Smith chart is a visualization tool that every RF engineer should strive to master. It provides a compact form for describing the match characteristics of a DUT, as well as being a useful tool for moving the match point of a device to a more desired value. Invented by Philip Smith (1944), it maps the normalized complex value of a termination impedance onto a circular‐based chart, from which the impedance effects of adding lengths of transmission line onto the termination impedance are easily computed. The original intention for the use of a Smith chart was for the computing of impedances presented to a generator as lengths of transmission line were added to a load and was intended particularly for the use of telephone line impedance matching. Adding a length of transmission lines changes the apparent termination impedance, Z_T, according to

(2.14)

where α and β are the real and imaginary propagation constants, and z is the distance from the load. This computation was tedious, in part because the argument of the hyperbolic tangent is complex, so a nomographic approach was desirable. A Smith chart solves by this mapping impedance to reflection coefficient (Γ), and plotting the return loss on a polar plot, as

(2.15)

The genius of the Smith chart is recognizing that rotating an impedance value through a length of transmission line is the same as rotating the phase of the reflection coefficient value on the chart. The Smith chart maps the impedance onto the polar reflection coefficient plot, but with the graticule lines marked with circles of constant resistance and circles of constant reactance. As such, any return loss value can be plotted, and the equivalent resistance and reactance can be determined immediately. To see the effect of adding some Z₀ transmission line, the impedance is simply rotated on the polar plot by the phase shift of the transmission line. If the line is lossy, the return loss is modified by the line loss (two times the one‐way loss of the line), and from this new position, the resistance and the reactance are directly read.