May 2008 Issue: Technical Note

Calculating Mismatch Uncertainty

From: Vol. 51 | No. 5 | May 2008 | Page 252

by Tony Lymer, Satori-Technology Ltd.

Mismatch uncertainty is a very common and often underestimated source of error in microwave power measurements. It arises from an incomplete knowledge of the phase of the reflection coefficients of the source and load impedances, plus their interconnection, and is usually a large component of the overall measurement uncertainty budget in a microwave power transfer. It is easy to estimate and should not be ignored.

Theory

From Figure 1

Fig. 1 Signal flow diagram for source and load.

The power absorbed in the load is

The numerator of the fraction, 1–|Γ₁|², is known as the mismatch loss. If only the voltage reflection coefficient magnitudes of the source and load are given, and not their phases, the denominator term cannot be evaluated precisely. However, the maximum and minimum values can be determined.

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