ABCD Parameters of Transmission Lines
Key Takeaways

The ABCD parameters of a transmission line give the relationship of the input voltage and currents to the output voltage and currents.

ABCD parameters simplify complex calculations when transmission lines are cascaded.

ABCD parameters are dependent on the length of a transmission line.
Modeling a system as a twoport network is common in electronics circuit analysis. Transmission line characterization can be done using twoport network models such as hybrid parameters, scattering parameters, impedance parameters, admittance parameters, or ABCD parameters (also known as transmission parameters, chain parameters, or cascade parameters).
Twoport models make the analysis of transmission lines easier and the relationship between the port voltages and currents of interest can be deduced. Among the parameters, the ABCD parameters of a transmission line give the relationship of the input voltage and currents to the output voltage and currents. In this article, we will take a closer look at the twoport model of a transmission line and its ABCD parameters.
ABCD Parameters of a Transmission Line
To characterize transmission lines using ABCD parameters, the line is modeled as a general twoport network.
The twoport model of the transmission line takes input current I_{1} at port 1, with an input voltage equal to V_{1}. The output voltage and current are V_{2} and I_{2}, respectively. The current directions are taken so that I_{1} is entering and I_{2} is leaving the twoport network. Among the four electrical quantities, V_{1 }and I_{1} are the dependent variables. The voltage V_{1} and current I_{1} are represented mathematically in terms of independent variables V_{2} and I_{2 } as follows:
The same can be represented in matrix form as:
ABCD parameters simplify complex calculations when transmission lines are cascaded. The cascaded connection can be modeled as a single twoport network having ABCD parameters equal to the product of ABCD parameters of each individual transmission line in the cascade.
The table below gives more details on ABCD parameters:
ABCD parameters
To model a twoport network of transmission lines, we assume that the network is linear and bilateral. The type of network can be identified from ABCD parameters.
Conditions of ABCD parameters
ABCD Parameters of Lossless Transmission Lines
Consider a lossless transmission line of uniform length. In this line, the attenuation constant 𝛼ᶛ is equal to zero and the phase constant is given by 𝛽. The voltages and currents of the lossless transmission line can be given as follows:
Comparing the equations above with the first two equations in this article, the ABCD parameters of a lossless transmission line can be given in matrix form as:
From the matrix above, it is clear that the ABCD parameters are dependent on the length of a transmission line; therefore, the ABCD parameters of a short line vs. a long transmission line will differ from each other.
Understanding the ABCD parameters of transmission lines is useful for analyzing the characteristics and behaviors of single and multiple line structures. Cadence’s software can also help with transmission line modeling and analysis.
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