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Prof. D. R. Wilton

ECE 3317. Prof. D. R. Wilton. Notes 10 Transmission Lines (Impedance Matching). [Chapter 6]. Smith Chart. S. Z g. Z 0. sinusoidal source. Z L. z = 0. z.

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Prof. D. R. Wilton

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  1. ECE 3317 Prof. D. R. Wilton Notes 10 Transmission Lines(Impedance Matching) [Chapter 6]

  2. Smith Chart S Zg Z0 sinusoidal source ZL z = 0 z Impedance matching is very important to avoid reflected power (loss of efficiency), presence of standing waves (SWR), and strong frequency dependences. • 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 Set Hence This yields Thus the tranformer section characteristic impedance is the “geometric mean” of the line and load impedances.

  5. Quarter-Wave Transformer (cont.) Z0 Z0T YL = 1 / ZL Next, consider a general (complex) load impedance ZL. shunt (parallel) susceptance New model: Z0 Z0T

  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. 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

  9. Single-Stub Matching (cont.) d ZL Y0 = 1 / Z0 The feeding transmission line on the left sees a perfect match.

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

  11. 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. • If desired, we can also use the Smith chart to find the stub length.

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

  13. Single-Stub Matching (cont.) use this one X X X X Smith chart scale: wavelengths toward load wavelengths toward generator

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

  15. 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 ZL jBs SWR = 1.0 0.78 z z

  16. 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 first denormalize to the line impedance, then renormalize to stub characteristic impedance! 0+j1 0+j2 0+j0.5 0+j0 0-j0.5 0-j2 0-j1 admittance chart

  17. Single-Stub Matching (cont.) admittance chart From the Smith chart: Analytically: X

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