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Microwave Network Analysis Lecture 2: Passive Microwave Components (I)
ELC 305a – Fall 2011
Department of Electronics and Communications Engineering
Faculty of Engineering – Cairo University
Introduction and Examples
Basic Properties
Three-Port Devices
Four-Port Devices
Power Dividers
T-Junction
Wilkinson Power Divider
© Islam A. Eshrah, 2008
2
Outline
1
2
3
Introduction and Examples Basic Properties Power Dividers
Introduction and Examples
Basic Properties
Three-Port Devices
Four-Port Devices
Power Dividers
T-Junction
Wilkinson Power Divider
© Islam A. Eshrah, 2008
3
Outline
1
2
3
Introduction and Examples Basic Properties Power Dividers
Three-Port Devices
© Islam A. Eshrah, 2008
4
Circulators, T-Junctions, and Power Dividers
Power Divider
Circulator
T-Junction
Introduction and Examples Basic Properties Power Dividers
Four-Port Devices
© Islam A. Eshrah, 2008
5
Couplers
Quadrature Hybrid
Rat Race
Introduction and Examples Basic Properties Power Dividers
Actual Devices
© Islam A. Eshrah, 2008
6
Microstrip Implementation and Commercial Packages
Wilkinson Power Divider
Rat Race
Circulator
Hybrid Coupler
Introduction and Examples Basic Properties Power Dividers
Introduction and Examples
Basic Properties
Three-Port Devices
Four-Port Devices
Power Dividers
T-Junction
Wilkinson Power Divider
© Islam A. Eshrah, 2008
7
Outline
1
2
3
Introduction and Examples Basic Properties Power Dividers
Three-Port Devices
© Islam A. Eshrah, 2008
8
Circulators, T-Junctions, and Power Dividers
In three-port networks reciprocity, losslessness, and matching cannot be satisfied simultaneously. (What are the properties of the devices above?)
0 0 1
1 0 0
0 1 0
S
1 2 212 1 2
32 2 1
S
01
0 02
0 0
j j
S j
j
0Z
0Z
0Z
Power Divider
Circulator
T-Junction
Introduction and Examples Basic Properties Power Dividers
Four-Port Devices
© Islam A. Eshrah, 2008
9
Lossless, Reciprocal, and Matched Devices
In four-port networks reciprocity, losslessness, and matching can be satisfied simultaneously.
12 13 14
12 23 24
13 23 34
14 24 34
0
0
0
0
S S S
S S SS
S S S
S S S
*
SS U
Reciprocal and Matched Lossless
Introduction and Examples Basic Properties Power Dividers
Four-Port Devices
© Islam A. Eshrah, 2008
10
Unitary Condition – Mutual Products
12 13 14
12 23 24
13 23 34
14 24 34
0
0
0
0
S S S
S S SS
S S S
S S S
* *
13 23 14 24
* *
14 13 24 23
0
0
S S S S
S S S S
* *
12 23 14 34
* *
14 12 34 23
0
0
S S S S
S S S S
12
34
S
S
*
24
*
13
S
S
2 2*
14 13 24 0S S S 2 2
23 12 34 0S S S
14 23 0S S
The unitary condition yields 10 equations (6 mutual products and 4 self products).
One Possibility
Introduction and Examples Basic Properties Power Dividers
Four-Port Devices
© Islam A. Eshrah, 2008
11
Unitary Condition – Self Products
2 2
12 13
2 2
12 24
2 2
13 34
2 2
24 34
1
1
1
1
S S
S S
S S
S S
13 24
12 34
S S
S S
12 34
13
24
jθ
jφ
S S α
S βe
S βe
14 23 0S S
0 0
0 0
0 0
0 0
jθ
jφ
jθ
jφ
α βe
α βeS
βe α
βe α
Show that the other possibilities yield the same solution, i.e., any reciprocal, lossless, and matched four-port network is a directional coupler.
Introduction and Examples Basic Properties Power Dividers
Four-Port Devices
© Islam A. Eshrah, 2008
12
Types of Directional Couplers
Example: Quadrature Hybrid
Symmetrical Asymmetrical
0 0
0 0
0 0
0 0
α jβ
α jβS
jβ α
jβ α
0 0
0 0
0 0
0 0
α β
α βS
β α
β α
2θ φ π 0,θ φ π
Example: Rat Race, Magic T
2 2 1, 2α β θ φ π nπ
Introduction and Examples Basic Properties Power Dividers
Four-Port Devices
© Islam A. Eshrah, 2008
13
Parameters of Directional Couplers
1
3
Coupling 10logP
CP
3
4
1
4
Directivity 10log
Isolation 10log
PD
P
PI
P
Introduction and Examples Basic Properties Power Dividers
Introduction and Examples
Basic Properties
Three-Port Devices
Four-Port Devices
Power Dividers
T-Junction
Wilkinson Power Divider
© Islam A. Eshrah, 2008
14
Outline
1
2
3
Introduction and Examples Basic Properties Power Dividers
T-Junction
© Islam A. Eshrah, 2008
15
Properties and Scattering Matrix
0Z
1Z
2Z
• The T-junction is not matched. • Power division may be equal or unequal.
1 2 212 1 2
32 2 1
S
Introduction and Examples Basic Properties Power Dividers
Wilkinson Power Divider
© Islam A. Eshrah, 2008
16
Properties and Scattering Matrix
• Wilkinson divider is matched. • Power division may be equal or unequal.
01
0 02
0 0
j j
S j
j
Introduction and Examples Basic Properties Power Dividers
Wilkinson Power Divider
© Islam A. Eshrah, 2008
17
Even-Odd Mode Analysis – Output Ports
Even Mode Odd Mode
Normalized Circuit (Z0 = 1)
Introduction and Examples Basic Properties Power Dividers
Wilkinson Power Divider
© Islam A. Eshrah, 2008
18
Even-Odd Mode Analysis – Input Port
Introduction and Examples Basic Properties Power Dividers
Wilkinson Power Divider
© Islam A. Eshrah, 2008
19
Frequency Response
Three-port network cannot satisfy reciprocity, losslessness, and matching simultaneously, whereas four-port networks can.
Any four-port network satisfying the previous properties simultaneously is a directional coupler.
Directional couplers are characterized by coupling, directivity, and isolation.
Even and odd mode analysis technique can be used to analyze devices having geometrical symmetry.
© Islam A. Eshrah, 2008
20
Conclusion