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Register a new userDifferential Error Region of a Quantity Dependent on Full One-Port Network Analyser Measurements
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Added by
Petros Zimourtopoulos E
Publication date
2006
fields
Physics
and research's language is
English
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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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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 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.
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.
Utilizing the effect of losses, we show that symmetric 3-port devices exhibit coherent perfect absorption of waves and we provide the corresponding conditions on the reflection and transmission coefficients. Infinite combinations of asymmetric inputs with different amplitudes and phase at each port as well as a completely symmetric input, are found to be perfectly absorbed. To illustrate the above we study an acoustic 3-port network operating in a subwavelength frequency both theoretically and experimentally. In addition we show how the output from a 3-port network is altered, when conditions of perfect absorption are met but the input waves phase and amplitude vary. In that regard, we propose optimized structures which feature both perfect absorption and perfect transmission at the same frequency by tuning the amplitudes and phases of the input waves.
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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