Revisiting mismatch uncertainty with the rayleigh distribution
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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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Revisiting mismatch uncertainty with the rayleigh distribution

Revisiting Mismatch Uncertainty with the Rayleigh Distribution

Michael Dobbert

Joe Gorin


Overview

Overview

  • Mismatch Model.

  • The Rayleigh distribution.

  • Finding the Rayleigh parameter.

  • Is the Rayleigh assumption reasonable?


Mismatch error

Mismatch Error

~

Zl

generator

load

Power equation


Mismatch model

Mismatch Model

Mismatch error equation.

Im

?

Circular symmetry about the origin.

Re

Mismatch uncertainty equation.

(real components)


Reflection coefficient uncertainty fixed

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.


Reflection coefficient uncertainty fixed1

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.


Reflection coefficient uncertainty measured

Reflection Coefficient Uncertainty (measured)

Im

pdf

Re

0


Reflection coefficient uncertainty uniform

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.


Reflection coefficient uncertainty rayleigh

Reflection Coefficient Uncertainty (Rayleigh)

Im

pdf

Re

σis the Rayleigh distribution parameter.

0


Finding the rayleigh parameter

Finding the Rayleigh Parameter

Rayleigh cumulative distribution function


Is the rayleigh assumption reasonable

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.


Power sensor

Power Sensor


Signal generator

Signal Generator


Signal analyzer

Signal Analyzer


Signal generator reflection coefficient real component

Signal Generator Reflection Coefficient Real Component


Comparing models

Comparing Models

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


Rayleigh conclusion

Rayleigh Conclusion

  • Reasonable model,

  • Straight forward to calculate,

  • Significantly lower estimate of mismatch uncertainty.


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