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# write a program that will analyse very general electrical circuits connected in the very common cascade connection.

INSTRUCTIONS TO CANDIDATES

The complete description of the Coursework or Mini-Project is in a separate document and on the Moodle site for EE20084. The Coursework is 50% of the assessment for EE20084. In this you are to produce:

Design Document (20%):   Describe the deisgn and test plan for the program that is to be developed.

Code submission (40%):   The .c and .h code files and the .exe executable for your program.

Report submission (40%):   A report describing the final code that has been developed and its testing.

The Coursework is to write a program that will analyse very general electrical circuits connected in the very common cascade connection. This is most easily done using the ABCD or chain matrix analysis method.

ABCD or Chain Matrix

The ABCD matrix relates voltages and currents at the input and output connection ports of a circuit element. The ABCD matrix is also known as the chain matrix or voltage transmission matrix.

Consider a linear two-port circuit with voltages V1 and V2 and currents I1 and I2 at the two ports.

V1   =   AV2+ BI2

I1   =  CV2    +  DI2

The four parameters of the matrix can be determined by examination of the circuit with open and short circuit load conditions.

: Examples of ABCD Matrices

series resistance

The cascade connection is a very common way of connecting components. Consider the case where there are several two-port circuits in cascade.

The behaviour of the overall circuit is determined by the ABCD matrices of the elements of the cascade:

So the ABCD matrix of the cascade network is determined by multiplying together the ABCD matrices of the elements in the order they appear in the cascade circuit. This is why the matrix is sometimes referred to as the chain or voltage transmission matrix

Observation

For a general cascade circuit the overall ABCD matrix is sim- ply the multiple of the ABCD matrices of the individual com- ponents of the cascade, in the order that they occur in the cascade:

[Tn]    =  [T1] [T2] [T3] . . . [TM ]

From the ABCD matrix of the complete cascade network various features of the complete network are easily found, such as input impedance, voltage gain, current gain, power gain.

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