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Revisiting Mismatch Uncertainty with the Rayleigh Distribution

Revisiting Mismatch Uncertainty with the Rayleigh Distribution. Michael Dobbert Joe Gorin. Overview. Mismatch Model. The Rayleigh distribution. Finding the Rayleigh parameter . Is the Rayleigh assumption reasonable?. Mismatch Error. ~. Z l. generator. load. Power equation.

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Revisiting Mismatch Uncertainty with the Rayleigh Distribution

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  1. Revisiting Mismatch Uncertainty with the Rayleigh Distribution Michael Dobbert Joe Gorin

  2. Overview • Mismatch Model. • The Rayleigh distribution. • Finding the Rayleigh parameter. • Is the Rayleigh assumption reasonable?

  3. Mismatch Error ~ Zl generator load Power equation

  4. Mismatch Model Mismatch error equation. Im ? Circular symmetry about the origin. Re Mismatch uncertainty equation. (real components)

  5. Reflection Coefficient Uncertainty (fixed) Im pdf Re 0 Harris, I. A. and Warner, F. L., Re-examination of mismatch uncertainty when measuring microwave power and attenuation, Microwaves, Optics and Antennas, IEE Proceedings ~ H, February 1981, Volume 128, Issue 1.

  6. Reflection Coefficient Uncertainty (fixed) Im pdf Re 0 Harris, I. A. and Warner, F. L., Re-examination of mismatch uncertainty when measuring microwave power and attenuation, Microwaves, Optics and Antennas, IEE Proceedings ~ H, February 1981, Volume 128, Issue 1.

  7. Reflection Coefficient Uncertainty (measured) Im pdf Re 0

  8. Reflection Coefficient Uncertainty (Uniform) Im pdf Re 0 Fundamentals of RF and Microwave Power Measurements (Part 3) Power Measurement Uncertainty per International Guides. Agilent Application Note AN 1449-3, April 5, 2011, literature number 5988-9215EN.

  9. Reflection Coefficient Uncertainty (Rayleigh) Im pdf Re σis the Rayleigh distribution parameter. 0

  10. Finding the Rayleigh Parameter Rayleigh cumulative distribution function

  11. Is the Rayleigh Assumption Reasonable? Mullen, J. A. and Pritchard, W. L., The Statistical Prediction of Voltage Standing-Wave Ratio, Microwave Theory and Techniques, IRE Transactions, April 1957, Volume 5, Issue 2.

  12. Power Sensor

  13. Signal Generator

  14. Signal Analyzer

  15. Signal Generator Reflection Coefficient Real Component

  16. Comparing Models Mismatch uncertainty is roughly proportional to the reflection coefficient median value.

  17. Rayleigh Conclusion • Reasonable model, • Straight forward to calculate, • Significantly lower estimate of mismatch uncertainty.

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