Band-Pass Filter Design Example

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ELEC 412 RF Microwave Engineering
Fall 2004 Lecture 17
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Stepped Low-Pass Filter
Order of the filter N 7
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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 Ls and Cs
• Use odd order filters where possible
• Convert Ls via Richardsons Transforms
• Maintain lumped parameter Cs and use waveguide
  Ls

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High-Pass Filter
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

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
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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