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Prof. David R. Jackson

ECE 3317. Prof. David R. Jackson. Spring 2013. Notes 13 Transmission Lines ( Impedance Matching). Smith Chart. S. Z g. Z 0. Sinusoidal source. Z L. z = 0. z.

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Prof. David R. Jackson

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  1. ECE 3317 Prof. David R. Jackson Spring 2013 Notes 13 Transmission Lines(Impedance Matching)

  2. Smith Chart S Zg Z0 Sinusoidal source ZL z = 0 z Impedance matching is very important to avoid reflected power, which causes a loss of efficiency and interference. • We will discuss two methods: • Quarter-wave transformer • Single-stub matching

  3. Quarter-Wave Transformer Z0 Z0T ZL = RL Zin Quarter-Wave Transformer: First consider a real load. Hence

  4. Quarter-Wave Transformer (cont.) Z0 Z0T ZL = RL Zin Example: Set Hence This gives us

  5. Quarter-Wave Transformer (cont.) Z0 Z0T YL = 1 / ZL Next, consider a general (complex) load impedance ZL. Shunt (parallel) susceptance Bs = -BL New model: YLTOT= GL Z0 Z0T ZLTOT= 1 / GL (real)

  6. Quarter-Wave Transformer (cont.) Z0 Z0T YL = GL + j BL Ys = jBs Summary of quarter-wave transformer matching method

  7. Quarter-Wave Transformer (cont.) Z0 Z0T YL = GL + j BL Bs = -BL Z0s ls Realization using a shorted stub (An open-circuited stub could also be used.)

  8. Quarter-Wave Transformer with Extension Z0 Z0T Z0 ZL Zin(-d) • We choose the length d to make the input impedance Zin (-d) real. • We then use a quarter-wave transform to change the impedance to Z0.

  9. Quarter-Wave Transformer with Extension (cont.) Example Z0 Z0T Z0 ZL

  10. Quarter-Wave Transformer with Extension (cont.) Wavelengths towards generator

  11. Quarter-Wave Transformer with Extension (cont.) Z0T Z0

  12. Single-Stub Matching A susceptance is added at a distance d from the load. d ZL Y0 = 1 / Z0 1) We choose the distance d so that at this distance from the load (i.e., Gin = Y0) 2) We then choose the shunt susceptance so that

  13. Single-Stub Matching (cont.) d ZL Y0 The feeding transmission line on the left sees a perfect match.

  14. Single-Stub Matching (cont.) d Z0 ZL Z0s ls Realization using a shorted stub (An open-circuited stub could also be used.)

  15. Single-Stub Matching (cont.) d Z0 ZL Z0s ls We use the Smith chart as an admittance calculator to determine the distance d. • Convert the load impedance to a load admittance YL. • Determine the distance d to make the normalized input conductance equal to 1.0. • Determine the required value of Bs to cancel Bin. • If desired, we can also use the Smith chart to find the stub length ls.

  16. Single-Stub Matching (cont.) d Z0 ZL Z0s ls Example

  17. Single-Stub Matching (cont.) Use this one X X X X Smith chart scale: Wavelengths toward load Wavelengths toward generator

  18. Single-Stub Matching (cont.) Next, we find the length of the short-circuited stub: Rotate clockwise from S/C to desired Bs value. Assume Z0s = Z0 Otherwise, we have to be careful with the normalization (see the note below). 0+j1 0+j2 0+j0.5 0+j0 0-j0.5 0-j2 Note: In general, 0-j1 Admittance chart

  19. Single-Stub Matching (cont.) From the Smith chart: Admittance chart Analytically: X

  20. Single-Stub Matching (cont.) UNMATCHED ZL z 1.62 1.55 1.0 0.78 0.38 z X Crank diagram

  21. Single-Stub Matching (cont.) 1.62 UNMATCHED 1.55 1.0 ZL 0.78 0.38 SWR = 4.26 z z MATCHED 1.62 1.55 SWR = 1.0 ZL jBs 0.78 z z

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