Passive Devices (3 port network)

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Passive Devices (3 port network)
S-matrix of 3 port networks
(1) All ports are matched and network is
reciprocal
(2) can be lossless?
3 Port Network can not be lossless, reciprocal,
and match at all port
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Matched, lossless, and nonreciprocal 3 port
network Circulator
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Reciprocal, lossless, and only 2 ports matched
Port 3 is isolated
Reciprocal, matched, and lossy 3 port network
Lossy power divider
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Passive Devices (4 port network)
S-matrix of reciprocal and matched network
For lossless, S-matrix must be unitary matrix
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Hybrid Coupler(3 dB Coupler)
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Even-Odd Mode Circuit Analysis

• If circuit can be decomposed into the
  superposition of an even-mode excitation and
  odd-mode excitation
• Adding two sets( even odd) of excitations
  produces the original excitation

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3-Port Network Power Divider
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Wilkinson Power Divider( equal power
division) Resistive divider -all ports are
matched -out-ports are
isolated
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Wilkinson Power Divider
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Wilkinson Power Divider even mode
Voltage on transmission line
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Wilkinson Power Divider odd mode
All power from Port 2 is delivered to r/2
resister, and all dissipated No power is
delivered to Port 1
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Wilkinson Power Divider input port
Wilkinson Power Divider S-matrix

• All ports are matched
• Reciprocal
• Lossy
• Output ports are isolated

• Symmetric
• Not Unitary

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Wilkinson Power Divider unequal power division
Wilkinson Power Divider N-way Divider
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4-Port Network Quadrature Hybrid
3 dB Directional Coupler with Quadrature Phase
Difference between two output ports Reciprocal,
Lossless, and all ports are matched.
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Odd-mode
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Coupled Line Theory
Propagating Modes on Symmetric Coupled Line
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Even Mode

• Line Characteristics for even mode propagation
• Capacitance per unit length w/o dielectrics
• Inductance per unit length
• Capacitance per unit length with dielectrics
• Characteristic Impedance
• Propagation Constant

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Odd Mode

• Line Characteristics for even mode propagation
• Capacitance per unit length w/o dielectrics
• Inductance per unit length
• Capacitance per unit length with dielectrics
• Characteristic Impedance
• Propagation Constant

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(1)Voltage and Current Waves of Even Mode
Excitation
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(1)Voltage and Current Waves of Odd Mode
Excitation
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Voltage and Current Waves on Coupled Lines
(1)Voltage and Current Waves on Line 1
(2)Voltage and Current Waves on Line 2
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Impedance Matrix Z11 Z22Z33 Z44
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Impedance Matrix Z12Z21Z34Z43
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Impedance Matrix Z13 Z31 Z24 Z42
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Impedance Matrix Z14 Z41 Z32 Z23
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4-Port Network Coupled Line Coupler
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Single Section Coupled Line Coupler
Boundary Condition at each Port
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