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Impedance Matching with Lumped Elements

jX 1. jB 2. Y L. Impedance Matching with Lumped Elements. jX 1. Z L. jB 2. Single-Stub Matching. Load impedance . Input admittance=S. Series Stub. Voltage minimum. Input impedance=1/S. Double Stub Matching Network. a. b. Y L. jB 2. jB 1. b. a. x=1. Y L. P open circuit .

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Impedance Matching with Lumped Elements

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  1. jX1 jB2 YL Impedance Matching with Lumped Elements

  2. jX1 ZL jB2

  3. Single-Stub Matching Load impedance Input admittance=S

  4. Series Stub Voltage minimum Input impedance=1/S

  5. Double Stub Matching Network a b YL jB2 jB1 b a

  6. x=1 YL Popen circuit Pshort circuit r=1 0 r=0.5 Real part of Refl. Coeff. Smith Chart x=-1

  7. x=1 P2 YL G1=1 Popen circuit Pshort circuit r=1 0 r=0.5 Real part of Refl. Coeff. P3 Smith Chart x=-1 Rotate the the G=1 circle through an angle -f The intersection of G=1 and the GL circle determine The point P2

  8. x=1 YL Popen circuit Pshort circuit r=1 0 r=0.5 Real part of Refl. Coeff. x=-1 Smith Chart The shaded range is for the load impedance which cannot be matched when d=1/8 wavelength

  9. Quarter-Wave Transformers ZC=Z0 ZL ZC=Z1 l /4

  10. r Dq rm 3p/2 p/2 qm p q Bandwidth characteristic for a single Section quarter wave transformer

  11. 1 Z2 G3 G1 ZL Z1 G2 G T12 T21 Theory of Small Reflection q

  12. T21 1 G1 Multiple reflection of waves for a circuit with two reflection junctions

  13. Approximate Theory for Multi-Section Quarter Wave Transformers q q q G3 ZL Z2 Z1 Z0 ZN A multi-section quarter-wave transformer

  14. Binomial Transformer

  15. Example Z3 ZL Z2 Z1 Z0 Design a three section binomial transformer to match a 50 Ohms load to a 100 Ohms line. Calculate the bandwidth For max reflection =.05 over the passband.

  16. rm qm p/2 q p- qm Chebyshev Transformer

  17. Example Design a two section Chebyshev transformer (two sections) to Match a line of load impedance =2. The maximum tolerance Value of r is 0.05.

  18. Design of Complex Impedance Termination Amplifier Zc Zc Input Matching network ZL Output Matching network Zs Microwave amplifier circuit

  19. l l jB1 = ZL ZL G=1 Zc Stub Transmission Line Matching Network jX1 jX2 jB2 jB1 ZL ZL G=1 G=1 Alternative Matching Networks

  20. l/l = 0.0626 l/l = 0.4375 j1 Generator 1 Y’in YL G=2 ZL= 0.4-j0.2 2 Load Y”in G=1 -j1 Design Procedure for the Matching Network with Shunt Stub

  21. Impedance Mismatch Factor

  22. Z22-Z12 Z11-Z12 ZT ZS ZL ZL Z12 VS Voc ML Zin A T matching network Thevenin equivalent network

  23. Zg Z0 Vg ZL Impedance Transformation and Matching Review of Transmission Lines and Smith Chart Z=L Z=0 Finite Transmission Line terminated with load impedance L

  24. Standing wave ration (SWR) S: Smith Chart:

  25. Imaginary part of Refl. Coeff. x=1 Popen circuit Pshort circuit r=1 0 r=0.5 Real part of Refl. Coeff. x=-1 Smith Chart

  26. Review of Transmission Lines and Smith Chart Zg Z0 Z=L Vg Z=0 ZL L Finite Transmission Line terminated with load impedance

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