S-Parameter Uncertainties in Network Analyzer Measurements with Application to Antenna Patterns

TL;DR

This paper presents an analytical method to estimate uncertainties in two-port VNA measurements, including system errors and S-parameter uncertainties, with practical demonstrations on antennas and network components.

Contribution

The paper introduces a differential error region approach for quantifying uncertainties in VNA measurements, applicable to complex and real quantities, and demonstrates its practical utility.

Findings

System error differentials for standard calibration loads

Uncertainty estimates for extended transmission lines

High uncertainties in Z-parameters of a T-network

Abstract

An analytical method was developed, to estimate uncertainties in full two-port Vector Network Analyzer measurements, using total differentials of S-parameters. System error uncertainties were also estimated from total differentials involving two triples of standards, in the Direct Through connection case. Standard load uncertainties and measurement inaccuracies were represented by independent differentials. Complex uncertainty in any quantity, differentiably dependent on S-parameters, is estimated by the corresponding Differential Error Region. Real uncertainties, rectangular and polar, are estimated by the orthogonal parallelogram and annular sector circumscribed about the Differential Error Region, respectively. From the user's point of view, manufactures' data may be used to set the independent differentials and apply the method. Demonstration results include: (1) System error differentials for Short, matching Load and Open pairs of opposite sex standards; (2) System error uncertainties for VNA extended by two lengthy transmission lines of opposite sex end-connectors; (3) High uncertainties in Z-parameters against frequency of an appropriately designed, DC resistive, T-Network; (4) Moderate uncertainties in amplitude and phase patterns of a designed UHF radial discone antenna (azimuthally rotated by a built positioner, under developed software control of a built hardware controller) polarization coupled with a constructed gain standard antenna (stationary) into an anechoic chamber.