TwoPort Network Modeling and Transmission Line SParameters
Key Takeaways

Measuring Sparameters is common in RF and microwave systems. These parameters can be measured with the help of network analyzers.

A transmission line is an example of a symmetrical twoport network, so interchanging port one and port two will not change the transmission properties.

Transmission line Sparameters are influenced by the characteristic impedance Z_{c} and propagation constant 𝛾.
In RF circuits, transmission lines act as connectors
In RF circuits, transmission lines are laid with precise dimensions, thickness, spacing, and impedance matching so that electromagnetic signals are transmitted with minimum reflections and power loss. Twoport network modeling is used in transmission line analysis, where numerous parameters—such as Zparameters, Yparameters, ABCD parameters, Hparameters, and Tparameters—define the relationship between dependent and independent quantities.
Transmission line scattering parameters (Sparameters) are similar to the family of parameters described above. Sparameters are elements of the scattering matrix that are used to model the behavior of linear RF and microwave networks. In this article, we will take a closer look at transmission line Sparameters.
A Generalized TwoPort Network Model of a Transmission Line and SParameters
Measuring Sparameters is common in RF and microwave systems. Sparameters can be directly measured with the help of network analyzers. In an Sparameter formulation, system inputs and outputs are replaced by incident waves and reflected waves. This approach is best suited for highfrequency RF and microwave applications. Sparameter transformations are based on the incidencereflection concept.
The transmission lines in RF circuits that interconnect various components can be modeled as twoport networks with two incident waves, which are a_{1} and a_{2} in ports one and two (shown in the figure below). The reflected waves in ports one and two are given by b_{1} and b_{2}, respectively. Usually, the incident and reflected waves are normalized with the characteristic impedance value. The general Sparameters of a twoport model of a transmission line can be written as:
When the incident wave at port one and the output are matched, there are no reflections in the transmission line, so a2 becomes zero. Additionally:
 The parameter S11 gives the input reflection coefficient.
 S12 is the reverse transmission coefficient (from port two to port one).
 S21 is the forward transmission coefficient (from port one to port two).
 S22 is the output reflection coefficient.
Lossy and Lossless Transmission Line SParameters
A transmission line is an example of a symmetrical twoport network. The Sparameters of a symmetrical network share a unique relationship:
Interchanging port one and port two does not change any transmission line Sparameter properties. The factors that can change transmission line Sparameters are:
 Line geometry
 Characteristic impedance
 Frequency
When any of these factors change, the Sparameters and transmission line properties also change.
Transmission line Sparameters are influenced by the characteristic impedance Z_{c} and propagation constant 𝛾. The propagation constant 𝛾 and characteristic impedance Z_{c} are given by the following equation, where R, L, G, and C are the distributed elements of the transmission line of length, l:
As the transmission line is symmetrical and reciprocal, S_{11}=S_{22} and S_{12}=S_{21}. The table below gives the Sparameters of the lossy and lossless transmission lines terminated by Z_{L}.
This table shows the Sparameters of lossy and lossless transmission lines
Transmission Line SParameter Frequencies
Voltage and current are more like traveling waves at high frequencies, and approaching transmission line analysis and synthesis using transmission line Sparameters is more suitable at RF and microwave frequencies. Cadence’s software supports the analysis of RF circuits and transmission lines by supporting the calculation of Sparameters.
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