Matching Networks
• MNs are critical for at least two critical
reasons
– maximize power transfer: Pt = Pi − Pr = Pi (1− | Γin |2 )
– minimize SWR = 1+ | Γin |
1− | Γin |
• Primary goal of a MN is to achieve
Γin = 0
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Matching Strategy
• Pick an appropriate two-element MN for
which matching is possible (based on a
given load impedance or S-parameter)
• Find the L, C values from the ZY Smith
Chart
• Convert discrete values into equivalent
microstriplines
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Region of matching for shunt L, series C matching network
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Region of matching for series C shunt L matching network
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Region of matching for series L shunt C matching network
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Region of matching for shunt C and series L matching network
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There are two strategies
A) Source impedance -> conjugate complex load impedance
B) Load impedance -> conjugate complex source impedance
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General 2 Element Approach
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Load Impedance To Complex Conjugate
Source Zs = Zs* = 50 Ω
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Art of Designing Matching Networks
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More Complicated Networks
• Three-element Pi and T networks permit the
matching of almost any load conditions
• Added element has the advantage of more
flexibility in the design process (fine
tuning)
• Provides quality factor design (see Ex. 8.4)
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Quality Factor
• Resonance effect has implications on design of
matching network.
• Loaded Quality Factor: QL = fO/BW
• If we know the Quality Factor Q, then we can find
BW
• Estimate Q of matching network using Nodal
Quality Factor Qn
• At each circuit node can find Qn = |Xs|/Rs or Qn =
|B P|/G P and
• QL = Qn/2 true for any L-type Matching Network
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Nodal Quality Factors
Qn = |x|/r =2|Γi | / [(1- Γr)2 + Γi2
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Matching Network Design Using Quality
Factor
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T-Type Matching Networks
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Pi-Type Matching Network
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Microstripline Matching Network
• Distributed microstip lines and lumped
capacitors
• less susceptible to parasitics
• easy to tune
• efficient PCB implementation
• small size for high frequency
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Microstripline Matching Design
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Two Topologies for Single-Stub Tuners
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Balanced Stubs
• Unbalanced stubs often replaced by
balanced stubs
2π lS 
λ
−1 
lSB =
tan  2 tan

2π
λ


Open-Circuit Stub
2π lS 
λ
−1  1
lSB =
tan  tan

λ
2π
2


Short-Circuit Stub
lS is the unbalance stub length and lSB is the balanced stub
length.
Balanced lengths can also be found graphically using the
Smith Chart
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Balanced Stub Example
Balanced Stub Circuit
Single Stub Smith Chart
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Double Stub Tuners
• Forbidden region
where yD is inside
g = 2 circle
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