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ABCD Matrix
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Definition of ABCD matrix

ABCD matrix is an another set of network parameters particularly suited for cascading two-port network. This set is called the ABCD matrix, the transmission matrix or cascading matrix.

Consider this two-port network:

[ABCD matrix]

Unlike in the definition used for Z and Y parameters, notice that I2 is directed away from the port. This is and important point and a condition for cascading operation.

The ABCD matrix is defined as:

[ABCD matrix]

Where:

[ABCD matrix]

The usefulness of the ABCD matrix is that cascaded two-port networks can be characterized by simply multiplying their ABCD matrices.

To see this, consider the following two-port metworks are cascaded:

[ABCD matrix]

It is apparent that V'2=V2 and I'2=I2


[ABCD matrix]


S-Parameters from ABCD-Parameters ABCD-Parameters from S-Parameters
S-Parameters from ABCD-Parameters ABCD-Parameters from S-Parameters
S-Parameters from ABCD-Parameters ABCD-Parameters from S-Parameters
S-Parameters from ABCD-Parameters RF Cafe - ABCD-Parameters from S-Parameters
S-Parameters from ABCD-Parameters ABCD-Parameters from S-Parameters

Note:

Z01 and Z02 are the complex impedances of ports 1 and 2, respectively; similarly, Z*01 and Z*02 are the complex conjugates of the respective impedances.

The values R01 and R02 are the real parts of port impedances Z01 and Z02.



If Z01=Z02=real=Z0
S-Parameters from ABCD-Parameters ABCD-Parameters from S-Parameters
S-Parameters from ABCD-Parameters ABCD-Parameters from S-Parameters