Efficient Uncertainty Evaluation of Vector Network Analyser Measurements Using Two-Tier Bayesian Analysis and Monte Carlo Method

Antennas are a key element in any communication system and vector network analyser (VNA) is popular tool for charactering antenna impedance bandwidth. In this paper, an efficient uncertainty evaluation method is proposed for VNA measurement based on its uncertainty propagation mechanism using Bayesian analysis and Monte Carlo method. The proposed method is generic and can be applied to VNA with arbitrary number of ports. In order to obtain the complete information of measurement uncertainty distribution, a two-tier Bayesian analytic process is carried out. The proposed method contains three steps. In the first step, the posterior distribution of each uncertainty source of VNA calibrations is deduced by the use of prior and current sample information through the first-tier Bayesian analysis. In the second step, the obtained posterior distributions of uncertainty sources are taken into the Monte Carlo simulation of one-port VNA measurement uncertainties. In the last step, the results obtained in the second step are used as the prior distribution of the secondary Bayesian evaluation, then the evaluation results of the measurement uncertainty can be obtained with the means, variances and skewness of the probabilistic distribution. The numerical analysis using an antenna measurement results demonstrate the high-efficiency and reliability of this proposed method.