Power Dividers and Directional Couplers (7)juiching/microwave2.pdf · 2017. 11. 15. · Coupled...
Transcript of Power Dividers and Directional Couplers (7)juiching/microwave2.pdf · 2017. 11. 15. · Coupled...
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Microwave Circuits 1
Power Dividers and Directional Couplers(7)
The T-Junction Power Divider(7.2)
Lossless Divider
1. Lossless2. Match at the input port.3. Mismatch at the output ports.4. No isolation at the output ports.
Resistive Divider
1. Lossy.2. Match at all ports.3. No isolation.
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Microwave Circuits 2
From the figure
The Wilkinson Power Divider(7.3)
1. Matched at all ports.
2. Isolation between output ports.
3. No power loss from input to output ports.
4. Half power loss from output to input ports.
Analysis
1. Excite port 1.
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Microwave Circuits 3
Symmetry Y equal voltages at port 2 and 3 Y no current flowsthrough the resistor Y open. The circuit becomes
From the figure
To compute , let and denote the voltages of the
forward and backward propagating modes in one of the two
lines. Assume the reference plane is located at port 1. Let thevoltage of the incident wave at port 1 be and port 3 . We
have at port 1
At port 3,
2. Even and odd mode excitation at port 2 and 3
Rearranging the circuit as follow
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Microwave Circuits 4
a. Even mode: Symmetry Y equal voltages at port 2and 3 Y no current flows through the resistor Y open.The circuit becomes
b. Odd mode: Anti-symmetry Y opposite voltages atport 2 and 3 Y short at the middle of the resistor. Thecircuit becomes
Since
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Microwave Circuits 5
From , we have
Unequal Power Division
If power ration between ports 2 and 3 is ,
N-way, equal-split, Wilkinson power divider
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Microwave Circuits 6
Basic Properties of a Three Port Device(7.1)
Impossible scenario: reciprocal, matching at all ports, lossless.
Reciprocal and matching at all ports give the following S matrix
If lossless, the matrix is unitary, that is,
Two of must be zero to satisfy the last 3 equations.
However, then, the first 3 equations will not be satisfied.
Possible scenario:1. Nonreciprocal, matching at all ports, lossless.
Lossless
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Microwave Circuits 7
Two possible solutions
and
Example: Circulators
2. Reciprocal, lossless, matching only two ports.
Lossless
Possible solution
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Microwave Circuits 8
3. Lossy, matching at all ports, reciprocal.
Basic Properties of a Four Port Device(7.1)
Reciprocal, matched at all ports.
If lossless and (directional coupler), the following
conditions are required.
where are real.
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Microwave Circuits 9
1. Symmetrical:
2. Anti-symmetrical: ,
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Microwave Circuits 10
Detailed Formulation1. Row 1* Row 2, Row 3 Row 4*
2. Multiply 1 with and , respectively and then subtract
3. Similarly, Row 1* Row 3, Row 2 Row 4*
4. Multiply 3 with and , respectively and then subtract
5. If ,
,
6. Without lose generality, choose and
, then Row 2* Row 3
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Microwave Circuits 11
The Quadrature (90E) Hybrid (7.5)
Even-Odd Mode Analysis
Even Mode
Using ABCD matrix, we have
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Microwave Circuits 12
Odd mode
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Microwave Circuits 13
Coupled Line Directional Coupler (7.6)
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Microwave Circuits 14
Assume and , we have
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Microwave Circuits 15
where .
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Microwave Circuits 16
If , and . Also
For , choose the mid-band frequency such that
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Microwave Circuits 17
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Microwave Circuits 18
Example 7.7: Design a 20 dB single-section coupled line
coupler in stripline with a ground plane spacing of 0.32 cm, a
dielectric sonstant of 2.2, a characteristic impedance of 50 ,
and a center frequency 3 GHz.
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Microwave Circuits 19
Design of Multi-section Coupled Line Coupler
If ,
If ,
where
Example 7.8: Design a three-section 20 dB coupled line couplerwith a binomial response, a system impedance of 50 , and acenter frequency of 3 GHz.
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Microwave Circuits 20
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Microwave Circuits 21
180 Hybrid (7.8)
(a) Ring hybrid, rat-race.(b) Tapered coupled line hybrid.(c) Waveguide hybrid junction, magic-T.
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Microwave Circuits 22
The Lange Coupler
4-wire even mode:
4-wire odd mode:
2-wire even mode:
2-wire odd mode:
Also approximate as follow
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Microwave Circuits 23
Then we have
By applying coupled line theory
and
or in terms of and ,
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Microwave Circuits 24
Analysis of the Tapered Coupled Line Hybrid
Consider the taper as an ideal lossless transformer, the evenmode ABCD matrix satisfy
Since
We have
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Microwave Circuits 25
Therefore, the ABCD matrix of the transformers is
, for even mode.
Similarly,
, for odd mode.
Cascading all the ABCD matrices of the even mode, we have
Similarly, for odd mode
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Microwave Circuits 26
Thus,
Let
The S matrix of the tapered coupled is
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Microwave Circuits 27
Magic-T Junction