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Register a new userS-Parameter Uncertainties in Network Analyzer Measurements with Application to Antenna Patterns
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Added by
Petros Zimourtopoulos E.
Publication date
2007
fields
Physics
and research's language is
English
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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 users 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.
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The objective was to study uncertainty in antenna input impedance resulting from full one-port Vector Network Analyzer (VNA) measurements. The VNA process equation in the reflection coefficient p of a load, its measurement m and three errors Es -determinable from three standard loads and their measurements- was considered. Differentials were selected to represent measurement inaccuracies and load uncertainties (Differential Errors). The differential operator was applied on the process equation and the total differential error dp for any unknown load (Device Under Test DUT) was expressed in terms of dEs and dm, without any simplification. Consequently, the differential error of input impedance Z -or any other physical quantity differentiably dependent on p- is expressible. Furthermore, to express precisely a comparison relation between complex differential errors, the geometric Differential Error Region and its Differential Error Intervals were defined. Practical results are presented for an indoor UHF ground-plane antenna in contrast with a common 50 Ohm DC resistor inside an aluminum box. These two built, unshielded and shielded, DUTs were tested against frequency under different system configurations and measurement considerations. Intermediate results for Es and dEs characterize the measurement system itself. A number of calculations and illustrations demonstrate the application of the method.
Since S-parameter measurements without uncertainty cannot claim any credibility, the uncertainties in full two-port Vector Network Analyser (VNA) measurements were estimated using total complex differentials (Total Differential Errors). To express precisely a comparison relation between complex differential errors, their differential error regions (DERs) were used. To demonstrate the method in the most accurate case of a direct zero-length thru, practical results are presented for commonly used Z-parameters of a simple, two-port, DC resistive T-network, which was built and tested against frequency with a VNA measurement system extended by two lengthy transmission lines.
The wide band of frequencies that includes all those allocated to 2G/3G applications was defined as 2G/3G band and the discone antenna with a structure of radial wires was defined as radial discone. This antenna was theoretically analysed and software simulated with the purpose of computationally design a broadband model of it. As an application, a radial discone for operation from 800 to 3000 MHz, which include the 2G/3G band, was designed and an experimental model was built and tested. Mathematically expressed measurement error bounds were computed in order to evaluate the agreement between theory and practice.
An extensive comparison of the path uncertainty in single particle tracking systems for ion imaging was carried out based on Monte Carlo simulations. The spatial resolution as function of system parameters such as geometry, detector properties and the energy of proton and helium beams was investigated to serve as a guideline for hardware developments. Primary particle paths were sampled within a water volume and compared to the most likely path estimate obtained from detector measurements, yielding a depth-dependent uncertainty envelope. The maximum uncertainty along this curve was converted to a conservative estimate of the minimal radiographic pixel spacing for a single set of parameter values. Simulations with various parameter settings were analysed to obtain an overview of the reachable pixel spacing as function of system parameters. The results were used to determine intervals of detector material budget and position resolution that yield a pixel spacing small enough for clinical dose calculation. To ensure a pixel spacing below 2 mm, the material budget of a detector should remain below 0.25 % for a position resolution of 200 $mathrm{mu m}$ or below 0.75 % for a resolution of 10 $mathrm{mu m}$. Using protons, a sub-millimetre pixel size could not be achieved for a phantom size of 300 mm or at a large clearance. With helium ions, a sub-millimetre pixel spacing could be achieved even for a large phantom size and clearance, provided the position resolution was less than 100 $mathrm{mu m}$ and material budget was below 0.75 %.
An analytical method was developed to estimate errors in quantities depended on full one-port vector network analyser (VNA) measurements using differentials and a complex differential error region (DER) was defined. To evaluate the method, differences instead of differentials were placed over a DER which was then analysed and compared with another commonly used estimated error. Two real differential error intervals (DEIs) were defined by the greatest lower and least upper bounds of DER projections. To demonstrate the method, a typical device under test (DUT) was built and tested against frequency. Practically, a DER and its DEIs are solely based on manufacturers data for standard loads and their uncertainties, measured values and their inaccuracies.
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