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ELEC 412 RF & Microwave Engineering

Explore Richardson's transforms, matching networks, quality factor design, and stub tuners in microwave engineering.

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ELEC 412 RF & Microwave Engineering

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  1. ELEC 412 RF & Microwave Engineering Fall 2004 Lecture 17

  2. Stepped Low-Pass Filter Order of the filter N = 7

  3. Stepped Low-Pass Filter

  4. Stepped Low-Pass Filter

  5. 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

  6. High-Pass Filter Richardson Equivalent Shorted Stub Inductors

  7. General 2 Element Approach

  8. Load Impedance To Complex Conjugate Source Zs = Zs* = 50 

  9. Art of Designing Matching Networks

  10. 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)

  11. 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|/Rsor Qn = |BP|/GP and • QL = Qn/2 true for any L-type Matching Network

  12. Nodal Quality Factors Qn= |x|/r =2|i| / [(1- r)2 + i2

  13. Matching Network Design Using Quality Factor

  14. T-Type Matching Networks

  15. Pi-Type Matching Network

  16. Microstripline Matching Network • Distributed microstip lines and lumped capacitors • less susceptible to parasitics • easy to tune • efficient PCB implementation • small size for high frequency

  17. Microstripline Matching Design

  18. Two Topologies for Single-Stub Tuners

  19. Balanced Stubs • Unbalanced stubs often replaced by balanced stubs Open-Circuit StubShort-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

  20. Balanced Stub Example Balanced Stub Circuit Single Stub Smith Chart

  21. Double Stub Tuners • Forbidden region where yD is inside g = 2 circle

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