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]](img/_abcdmatrix/abcdmatrix.png)
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]](img/_abcdmatrix/abcdmatrix_eq.png)
Where:
![[ABCD matrix]](img/_abcdmatrix/abcdmatrix_eq1.png)
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]](img/_abcdmatrix/abcdmatrix_cascade.png)
It is apparent that V'2=V2 and I'2=I2
![[ABCD matrix]](img/_abcdmatrix/abcdmatrix_cascade_eq.png)
| S-Parameters from ABCD-Parameters | ABCD-Parameters from S-Parameters |
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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 |
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