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S-PARAMETERS

By:

 Namrata V. L.

Assistant Professor 

Government Engineering College, Rajkot

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INTRODUCTION

Power dividers and directional couplers

are passive microwave components used

for power division or power combining,

as illustrated in Figure.

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INTRODUCTION

 The coupler or divider may have  three ports,  four ports,

or  more, and may be (ideally) lossless.  Three-port networks take the form of T-junctions and

other power dividers.

 While four-port networks take the form of directionalcouplers and hybrids.

 A microwave junction is an interconnection of two or more microwave components as shown in figure.

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SCATTERING MATRIX

 The low frequency circuits can be

represented in two port networks and

characterized by their parameters i.e.

impedances, admittances, voltage gain,current gain, etc. All these parameters relate

total voltages and currents at the two ports.

 But as operational frequency increases, it is

very hard to find correct voltage and current

at any point, due to rapid fluctuation of 

voltage and current.

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SCATTERING MATRIX  So at microwave frequency the logical variables used,

are travelling waves with associated powers, rather thantotal voltages and total currents. These logical variablesare called as S- parameters.

 So in microwave analysis, the power relationship

 between the various ports of microwave junction isdefined in terms of parameters, called as   S-parametersor scattering parameters.

 As the microwave junction is a multiport junction, the power relationship between the various ports are definedin terms of matrix form, and called as  S-matrix, whicha   square matrix   giving all the power combinations between the input port and output ports.

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SCATTERING MATRIX  an   is the amplitude of voltage wave incident on

 port n  bn is the amplitude of the reflected voltage wave

from port n.

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SCATTERING MATRIX The scattering matrix or [S] matrix is

defined in relation to these incident andreflected voltage waves as

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SCATTERING MATRIX The specific element of S-matrix is

i.e. scattering coefficient due to input at ith

 port and output taken from jth port.

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SCATTERING MATRIX

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SCATTERING MATRIX

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 Properties of S-matrix for Reciprocal and

Lossless Network 

◦ For reciprocal network   The impedance and

admittance matrices are symmetric.

◦ For lossless network     The impedance and

admittance matrices are imaginary.

◦

 Scattering matrix for a reciprocal network issymmetric and unitary for lossless network.

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SCATTERING MATRIX

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 Properties of S-matrix for Reciprocal and

Lossless Network 

◦ For reciprocal network [S] matrix is defined as

Sij= S ji.

◦ Also it can be written as [S]=[S]t.

◦ For lossless network [S]t[S*]=[I]

◦ For unitary network  [S*]={[S]t}-1.

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SCATTERING MATRIX

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 Example

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SCATTERING MATRIX

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WAVEGUIDE TEES

 WAVEGUIDE TEES

◦ E-Plane Tees.

◦ H-Plane Tees

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E-PLANE TEE

1.   [S] Matrix of order 3 x 3.

2.   The scattering coefficients are

3.   If port 3 is perfectly matched to the junction

4.   For symmetric property

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E-PLANE TEE

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E-PLANE TEE

 From equation 1 and 2, …………..(5)

 From equation 3, ………………...(6)

 From equation 4,

 Using the values of 6 and 7 in equation 1, we get

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E-PLANE TEE

 Thus resultant S-parameter will be,

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E-plane Tee

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E-PLANE TEE

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H-PLANE TEE

1.   [S] Matrix of order 3 x 3.

2.   The scattering coefficients are

3.   If port 3 is perfectly matched to the junction

4.   For symmetric property

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H-PLANE TEE

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H-PLANE TEE

 From equation 1 and 2, …………..(5)

 From equation 3, ………………...(6)

 From equation 4,

 Using the values of 6 and 7 in equation 1, we get

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H-PLANE TEE

 Thus resultant S-parameter will be,

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H-plane Tee

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H-PLANE TEE

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H-PLANE TEE

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Thank you