lec.8 s parameters

RF & Microwave EngineeringBETE-Spring 2009

Department of Electrical EngineeringAir University

Scattering Matrix

Introduction to S - Parameters

Lecture No. 8

RF & Microwave EngineeringBETE-Fall 2009

Basit Ali ZebDepartment of Electrical Engineering, AU

Why Scattering Parameters?

• When dealing with wave propagation phenomenon, it is not desirable to introduce a reflection coefficient of magnitude 1. Terminal discontinuity will cause unwanted voltage or current wave reflections, which will lead to oscillations and hence the destruction of device.

• Practical system characterization can no longer be accomplished using simple open or short-circuit measurements as is done in low frequency applications.

• With S-parameters, RF/Microwave engineer has a tool to characterize the 2-port network description of nearly all microwave devices without causing harm to the device under test.



Using S-Parameters

S parameters are usually measured with the device embedded between a 50 ohm load and source, and

there is very little chance for oscillations to occur.



What are S-Parameters?

S-parameters are basically the power wave descriptors that help us determine the input-output relationship of a network in terms of incident and reflected power waves.



S-parameters

Consider again the multi-port network from the last lecture, which is connected to N transmission lines:



S-Matrix

When the characteristic impedances of all transmission lines connected to the network are same, as is shown in the

previous figure, the scattering parameters are defined as:



S-parameters Definition

Each of the S-parameter in the scattering matrix can be determined as:

This means that the scattering parameters are the amplitude ratios of the port incident and reflected waves. Here the wave

amplitude ratio is defined from port “j ” to port “i ”:



Two Port S-parameters

Simple enough, but how do we ensure V2+ = 0 ?

Reflection coefficient at port 1 with

Also the Input Reflection Coefficient

Port 1 Port 2



S-parameters

Transmission coefficient from port

1 to 2 with

Transmission coefficient from port 2 to1

with

Reflection coefficient at port 2 with



Meaning of S-Parameters

• S11 is the input reflection coefficient when all other ports are matched terminated.

• Return Loss

• S11 is related to reflection or mismatch at input port

• S21 is related to forward voltage gain or transmission through the device

It is very important to realize that it is a mistake to say S11 is the reflection coefficient at port 1. Actually S11 is

the reflection coefficient only when port 2 has V2+ = 0.



Properties of S-Matrices

• Recall the two important properties of Z and Y matrices

• In case of Reciprocal Network, it can be shown that:

– S-matrix is symmetric about the main diagonal i.e.,

• If a network is lossless, then S is a unitary

matrix.



Example

S-parameters of a TL



S-parameters of T-Network

• Determine the S-parameters of the resistive T-Network shown below ?:



A simple 3-dB attenuator



Shifting Reference Planes

• Consider the N-port network where we have defined the terminal planes

• We have chosen arbitrarily phase = 00 reference planes when TL are connected to the ports.

• What happens if we shift these reference planes to some other position along the transmission line?

• Would there be any change in the [S] matrix?



Shifting Reference Planes



Phase Shifts along TL

• Any movement away from the ports will introduce phase changes in the voltage amplitudes.

Where

Electrical distance

For example, if reference plane of port 1 of a 2-port network

is moved outwards an electrical distance, then:

Simple transformation is required:



A Tip

Many times you will notice that your measured

S parameters differ from the simulation by a

phase angle, even though the magnitude is in

good agreement. This likely occurred because

your terminal planes were defined differently in

simulations as was set during measurements!

lec.8 s parameters

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