Читать книгу Handbook of Microwave Component Measurements - Joel P. Dunsmore - Страница 128

While it is most common to define S‐parameters in a 50 Ω impedance, or 75 Ω for cable‐television applications, situations arise where it is necessary to define an S‐parameter matrix in other than 50 Ω, or to have it defined with 50 Ω on one port and with a different impedance on another port. This requirement occurs for matching circuits, or impedance transformers, as well as the use of waveguide adapters where it is common practice to define the terminal impedance as 1 Ω. Unfortunately, while S‐parameter definitions don't prohibit different impedances on different ports, the most common data files for S‐parameters, the so‐called Touchstone™ or S2P files, provide for only a single impedance in their definition. (Recently a second revision of the S2P file format has been defined that allows different impedances on different ports, but it has not yet been widely implemented.) Thus, it is often necessary to transform S‐parameters from one reference impedance to another. If the complete S‐parameter matrix is available, then a matrix transformation (Tippet and Speciale 1982) can be used to convert the impedance of by applying

(2.17)

where

This is a generalized formula so that an impedance, [Z_n], may be defined for any port of the original [S] matrix and any other impedance may defined for any other port for the new [S^′] matrix. However, the two most common cases are where the transformation occurs for all impedances at the ports being equal, so that each element in the X matrix and Γ matrix are identical, and where in the 2‐port case only one impedance is transformed, as when the S‐parameters of a network are defined in two different impedances.

If the measurement system impedance is pure‐real, an alternative method for obtaining S‐parameters at a different real impedance than the measurement system is to de‐embed an ideal transformer at each port, with the turns ratio set to the square root of the impedance change. De‐embedding methods are discussed in Chapter 9.