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Register a new userComparison of Error Estimations by DERs in One-Port S and SLO Calibrated VNA Measurements and Application
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Added by
Petros Zimourtopoulos E
Publication date
2011
fields
Physics
and research's language is
English
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In order to demonstrate the usefulness of the only one existing method for systematic error estimations in VNA (Vector Network Analyzer) measurements by using complex DERs (Differential Error Regions), we compare one-port VNA measurements after the two well-known calibration techniques: the quick reflection response, that uses only a single S (Short circuit) standard, and the time-consuming full one-port, that uses a triple of SLO standards (Short circuit, matching Load, Open circuit). For both calibration techniques, the comparison concerns: (a) a 3D geometric representation of the difference between VNA readings and measurements, and (b) a number of presentation figures for the DERs and their polar DEIs (Differential Error Intervals) of the reflection coefficient, as well as, the DERs and their rectangular DEIs of the corresponding input impedance. In this paper, we present the application of this method to an AUT (Antenna Under Test) selected to highlight the existence of practical cases in which the time consuming calibration technique results a systematic error estimation stripe including almost all of that of quick calibration.
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This paper introduces a one-port method for estimating model parameters of VNA calibration standards. The method involves measuring the standards through an asymmetrical passive network connected in direct mode and then in reverse mode, and using these measurements to compute the S-parameters of the network. The free parameters of the calibration standards are estimated by minimizing a figure of merit based on the expected equality of the S-parameters of the network when used in direct and reverse modes. The capabilities of the method are demonstrated through simulations, and real measurements are used to estimate the actual offset delay of a 50-$mathbf{Omega}$ calibration load that is assigned zero delay by the manufacturer. The estimated delay is $38.8$ ps with a $1sigma$ uncertainty of $2.1$ ps for this particular load. This result is verified through measurements of a terminated airline. The measurements agree better with theoretical models of the airline when the reference plane is calibrated using the new estimate for the load delay.
In the paper, a comparison is described of the microwave power standard based on thermoelectric sensors against an analogous standard based on bolometric sensors. Measurements have been carried out with the classical twin-type microcalorimeter, fitted with N-connector test ports suitable for the frequency band 0.05 - 18 GHz. An appropriate measurand definition is given for being suitable to both standard types. A system accuracy assessment is performed applying the Gaussian error propagation through the mathematical models that interpret the microcalorimeter response in each case. The results highlight advantages and weaknesses of each power standard type.
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.
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.
As noble liquid time projection chambers grow in size their high voltage requirements increase, and detailed, reproducible studies of dielectric breakdown and the onset of electroluminescence are needed to inform their design. The Xenon Breakdown Apparatus (XeBrA) is a 5-liter cryogenic chamber built to characterize the DC high voltage breakdown behavior of liquid xenon and liquid argon. Electrodes with areas up to 33~cm$^2$ were tested while varying the cathode-anode separation from 1 to 6~mm with a voltage difference up to 75~kV. A power-law relationship between breakdown field and electrode area was observed. The breakdown behavior of liquid argon and liquid xenon within the same experimental apparatus was comparable.
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