Lec.10 ABCD Parameters

RF & Microwave EngineeringBETE-Spring 2009

Department of Electrical EngineeringAir University

Transmission Matrix

[ABCD] Parameters

Lecture No. 10

RF & Microwave EngineeringBETE-Fall 2009

Basit Ali ZebDepartment of Electrical Engineering, AU

Equivalent Port Representations

• Z-parameters are useful for series connected networks.

• Y-parameters are useful for parallel connected networks.

• S-parameters are useful for describing interactions of voltage and current waves with a network.

• ABCD or Transmission parameters - useful when cascading two-port networks

RF & Microwave EngineeringBETE-Fall 2009

Basit Ali ZebDepartment of Electrical Engineering, AU

Introduction

• ABCD parameters of each network can be found by simple cascade connection, and matrix multiplication of the ABCD parameters to asses the overall behavior.

• In this case, it is useful to determine a transmission matrix or ABCD matrix for two port network of each microwave element.

• In practice, however microwave networks consists of a chain of devices connected together in cascade e.g., front end of a microwave receiver may contain a TL section, followed by an impedance or a 3-dB attenuator.

RF & Microwave EngineeringBETE-Fall 2009

Basit Ali ZebDepartment of Electrical Engineering, AU

ABCD Parameters

where V1,I1 is the input voltage & current. The current direction is positive with I2 flowing out of the port 2. In matrix form:

The determinant of this transmission matrix is AD-BC=1 and holds for all Passive electrical networks.

RF & Microwave EngineeringBETE-Fall 2009

Basit Ali ZebDepartment of Electrical Engineering, AU

Calculation of ABCD Parameters

This indicates only three of the parameters are independent and therefore only three independent equations are solved

for these parameters.

By making an open and a short circuit at port 2 and using the matrix equations, we can find:

An equivalent lumped network can be derived using ABCD parameters. For example, a pi, T or TL network.

RF & Microwave EngineeringBETE-Fall 2009

Basit Ali ZebDepartment of Electrical Engineering, AU

Cascaded ABCD Matrix

In matrix form:

RF & Microwave EngineeringBETE-Fall 2009

Basit Ali ZebDepartment of Electrical Engineering, AU

Cascaded ABCD Matrix

We cascade both networks as shown below:

Note why the direction of current I2 is assumed outwards.

RF & Microwave EngineeringBETE-Fall 2009

Basit Ali ZebDepartment of Electrical Engineering, AU

Example-1

Compute the parameters by

calculating the ratios of voltage drop to currents by

making open and short

circuit at port 2 .

The accurate prediction of parameters depends on the ability to

enforce the open and short circuit terminal conditions.

RF & Microwave EngineeringBETE-Fall 2009

Basit Ali ZebDepartment of Electrical Engineering, AU

Example-2: T Network

Compute the ABCD parameters of the above T network ?

RF & Microwave EngineeringBETE-Fall 2009

Basit Ali ZebDepartment of Electrical Engineering, AU

Important Points

• A cascade connection of 2-port networks is equivalent to a 2-port network containing a product of the two ABCD matrices.

• Order of matrix multiplication must be the same as the cascade arrangement of the individual elements.

• Matrix multiplication is not cumulative in general.

RF & Microwave EngineeringBETE-Fall 2009

Basit Ali ZebDepartment of Electrical Engineering, AU

A Lossless Transmission Line!

Compute the ABCD parameters of the Transmission

line network with parameters shown above?

RF & Microwave EngineeringBETE-Fall 2009

Basit Ali ZebDepartment of Electrical Engineering, AU

Study

• Article 4.4 from the text book