ELEC 412 -Lecture 17 1

ELEC 412

RF & Microwave Engineering

Fall 2004

Lecture 17

ELEC 412 -Lecture 17 2

Order of the filter N = 7

Stepped Low-Pass Filter

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Stepped Low-Pass Filter

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Stepped Low-Pass Filter

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High-Pass Filter• Use Prototype Low-Pass Filter Equations

• Transform L’s and C’s

• Use odd order filters where possible

• Convert L’s via Richardson’s Transforms

• Maintain lumped parameter C’s and use waveguide L’s

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High-Pass FilterC1 C3 C7

l/8 l/8l/8

C5

Gnd

Richardson Equivalent Shorted Stub Inductors

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General 2 Element Approach

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Load Impedance To Complex Conjugate Source Zs = Zs* = 50

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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 = |BP|/GP and

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

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Nodal Quality Factors

Qn = |x|/r =2|i| / [(1- r)2 + i2

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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 tanl

l

1 21

2 2S

SBl

l tan tanl

l

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

ELEC 412 -Lecture 17 20

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