Arkadiusz Lewandowski

Covariance-Based Vector-Network-Analyzer Uncertainty Analysis for Time- and Frequency-Domain Measurements

We develop a covariance-matrix-based uncertainty analysis for vector-network-analyzer (VNA) scattering-parameter measurements. The covariance matrix not only captures all of the measurement uncertainties of the scattering-parameter measurements, but also the statistical correlations between them. This allows the uncertainties of VNA scattering-parameter measurements to be propagated into the uncertainties of other quantities derived from scattering parameters, including temporal waveforms and circuit model parameters.

Covariance-based uncertainty analysis of the NIST electrooptic sampling system

We develop a covariance matrix describing the uncertainty of mismatch-corrected measurements performed on the National Institute of Standards and Technologys electrooptic sampling system. This formulation offers a general way of describing the uncertainties of the measurement system in both the temporal and frequency domains. We illustrate the utility of the approach with several examples, including determining the uncertainty in the temporal voltage generated by the photodiode

Wideband measurement of extreme impedances with a multistate reflectometer

We present a technique for accurate wideband measurements of one-port devices with extreme impedances. Our technique uses a reflectometer with variable parameters (states) to obtain redundant measurements of the extreme impedance device. We process these measurements using statistical techniques that allow us to exploit the redundancy in order to increase the measurement bandwidth and reduce the measurement uncertainty. We demonstrate our technique for a simple setup containing a power splitter and an unknown variable reference impedance connected to one of its arms and an unknown extreme-impedance device connected to its other arm. The variable reference impedance is realized as either a set of mechanical standards or an electronically tunable impedance. Measurement results show that the repeatability of the reference impedance values is essential for achieving increased accuracy.

Compact Behavioral Models of Nonlinear Active Devices Using Response Surface Methodology

This paper presents the response surface methodology in modeling of nonlinear microwave devices. First, different combinations of sampling techniques and types of radial basis functions are evaluated in simulations of the drain current of a 0.15- μm GaAs HEMT transistor described by the Chalmers model. It allows to determine the best settings of the response surface methodology for the modeling of active microwave devices. It is shown that the best sampling strategy is a combination of space-exploration (Voronoi), problem-exploitation (LOLA), and model-error-driven sample rankers. From the various radial basis function models, the fastest convergence is achieved with exponential functions. This knowledge is then used in behavioral modeling of a low-power amplifier AG303 measured in the load-pull setup. It is shown that the response surface methodology outperforms commonly used factorial design of experiments. Moreover, it gives accurate models within just a few tens of samples. However, attention has to be paid at the noisy regions, which might be oversampled by the sampling techniques.

Multiple Reflect Technique for Wideband One-Port VNA Calibration

We present a statistical technique for one-port vector network analyzer (VNA) calibration based on multiple reflect and a single reference standards. The multiple reflect standards are assumed to be partly unknown and of the same type, e.g. offset terminations. Their reflection coefficients are modeled over frequency and identified during the calibration along with the VNA error terms. This novel technique is particularly useful for millimeter-wave VNA calibrations in which conventional transmission line standards and the TRL method become impractical. Experimental verification shows that the accuracy of our technique is very high and comparable with the one-port measurement accuracy of the multiline TRL method.

A Compact Variable-Temperature Broadband Series-Resistor Calibration

We present a broadband on-wafer calibration from 45 MHz to 40 GHz for variable temperature measurements, which requires three standards: a thru, reflect, and series resistor. At room temperature, the maximum error of this technique, compared to a benchmark nine-standard multiline thru-reflect-line (TRL) method, is comparable to the repeatability of the benchmark calibration. The series-resistor standard is modeled as a lumped-element -network, which is described by four frequency-independent parameters. We show that the model is stable over three weeks, and compare the calibration to the multiline TRL method as a function of time. The approach is then demonstrated at variable temperature, where the model parameters are extracted at 300 K and at variable temperatures down to 20 K, in order to determine their temperature dependence. The resulting technique, valid over the temperature range from 300 to 20 K, reduced the total footprint of the calibration standards by a factor of 17 and the measurement time by a factor of 3.

Accuracy and Bandwidth Optimization of the Over-Determined Offset-Short Reflectometer Calibration

We present a new method for calculating line lengths of offset-short standards so as to provide a broadband and accurate one-port vector-network-analyzer (VNA) calibration. Our method is based on an approximate uncertainty analysis of corrected VNA measurements. We estimate the maximum value of the total variance (i.e., the trace of the covariance matrix) of errors in those measurements at a single frequency, and then quantify the quality of the offset-short calibration in a given frequency range with two metrics: the upper bound for the total variance and the lower calibration frequency. We then apply a global bi-objective optimization to these metrics in order to determine the optimal lengths. In order to verify our approach we first validate assumptions made in the approximate uncertainty analysis through a Monte Carlo simulation. We further perform an experiment in which we compare measurements of verification devices after calibrating the VNA with different offset-short sets designed with our method and with a set of reference airlines. Finally, we perform an uncertainty analysis for these measurements, which demonstrates the tradeoff between the offset-short calibration bandwidth and accuracy, and shows that our approach for selecting the offset-short line lengths provides the broadest bandwidth for a given calibration accuracy.

Electronic vector-network-analyzer verification [Application Notes]

The National Institute of Standards and Technology (NIST) recently introduced a new electronic approach for verifying microwave vector- network-analyzer (VNA) calibrations with a single computer-controlled electronic verification artifact. The verification results are captured in easy-to-understand performance metrics that, unlike those derived from measurements of mechanical verification artifacts, are independent of the actual artifacts employed. The approach also verifies VNA calibrations more completely than was previously possible. Finally NISTs VeridiCal software automates the entire process and allows you to log results directly to NIST servers over the Internet or generate verification reports on site, greatly simplifying record keeping.

Statistical Measurement Techniques for Equivalent Source Mismatch of 1.85 mm Power Splitter

The equivalent source mismatch (GammaG) of a 1.85 mm coaxial power splitter was characterized by use of two statistical measurement techniques. The first technique, originally described by Juroshek uses a modified one-port calibration method to determine GammaG. The second method uses two-port measurements of the splitter with one of the ports loaded with a series of calibration standards. This second, ldquoindirectrdquo method provides measurements of S-parameters for the three-port device that can subsequently be used to calculate GammaG. Measurements of GammaG made with the two techniques are in good agreement. This demonstrates that the value of GammaG of a splitter can be determined by statistical measurement techniques, thus providing the possibility of exploiting redundant measurements to reduce the effect of random measurement errors. Analysis of repeated measurements of GammaG shows that the effect of random measurement errors is lower for the indirect method than for the Juroshek method.

Hybrid Nonlinear Modeling Using Adaptive Sampling

This paper proposes a direct method for the extraction of empirical-behavioral hybrid models using adaptive sampling. The empirical base is responsible for the functionality over a wide range of variables, especially in the extrapolation range. The behavioral part corrects the errors of the empirical part in the region of particular interest, thus, it improves the accuracy in the desired region. Employment of response surface methodology and adaptive sampling allows full automation of the hybrid model extraction and assures its compactness. We used this approach to build a hybrid model composed of a robust empirical model available in CAD tools and a Radial Basis Functions interpolation model with Gaussian basis function. We extracted the hybrid model from measurements of a 0.15 μm GaAs HEMT and compared it with the pure behavioral and pure empirical models. The hybrid model yields higher accuracy while maintaining extrapolation capabilities. Additionally, the extraction time of the hybrid model is relatively low. We also show that a good accuracy level can be achieved with a small number of measurements.