EEE 194RF_L20 1

Matching Networks

• MNs are critical for at least two critical reasons– maximize power transfer: – minimize

• Primary goal of a MN is to achieve

0=Γin

)||1( 2inirit PPPP Γ−=−=

||1||1

in

inSWRΓ−Γ+

=

EEE 194RF_L20 2

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

EEE 194RF_L20 3

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

EEE 194RF_L20 8

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)

EEE 194RF_L20 12

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 = |BP|/GP and

• QL = Qn/2 true for any L-type Matching Network

EEE 194RF_L20 13

Nodal Quality FactorsQn = |x|/r =2|Γi| / [(1- Γr)2 + Γi

2

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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

1 22

2S

SBl

l tan tanπλ

π λ− =

1 21

2 2S

SBl

l tan tanπλ

π λ− =

Open-Circuit Stub 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

EEE 194RF_L20 21

Balanced Stub Example

Single Stub Smith Chart

Balanced Stub Circuit

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Double Stub Tuners

• Forbidden region where yD is inside g = 2 circle