Investigating the adequacy of a low-cost vector network analyser for microwave measurements in quasispherical resonators

Abstract

Microwave measurements in quasispherical resonators (QSRs) have enabled remarkable improvements in primary gas thermometry, but the expense of vector network analysers (VNAs) restricts wider use of the technique. In this work we compare the performance of a commercially available, low-cost VNA with a fully-featured VNA in microwave resonance measurements in a QSR. For acoustic gas thermometry (AGT) where a relative uncertainty in frequency measurement in an order of 10−7 is required, we have found that the accuracy of the low-cost VNA is easily sufficient. The use of a +20 dB amplifier was also tested for both VNAs and allowed statistical uncertainties to be reduced by a factor of 5 to 12. The two VNAs showed agreement within 20 × 10−9 of the absolute frequency of microwave resonances. However, when the low-cost VNA was used with the amplifier, some spurious systematic effects were found which biased the measured resonance frequency at levels below 20 × 10−9. These effects were apparent only when the amplifier was used with the low-cost VNA, because, when the amplifier was not used, the statistical uncertainty was much larger than the magnitude of these effects. While the physical cause of these systematic effects is not investigated in the present work, we made observations that could help to estimate their magnitudes. The comparison showed that the low-cost VNA, although being perfectly suitable for the AGT, may not be sufficiently accurate for applications where the required relative uncertainty in the frequency determination is of an order of 10−9.