We develop a covariance matrix describing the uncertainty of mismatch-corrected measurements performed on the National Institute of Standards and Technology's 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

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.

We describe a method for calibrating the voltage that a step-like pulse generator produces at a load at every time point in the measured waveform. The calibration includes an equivalent-circuit model of the generator that can be used to determine how the generator behaves when it is connected to arbitrary loads. The generator is calibrated with an equivalent-time sampling oscilloscope and is traceable to fundamental physics via the electro-optic sampling system at the National Institute of Standards and Technology. The calibration includes a covariance-based uncertainty analysis that provides the uncertainty at each time in the waveform vector and the correlations between the uncertainties at the different times. From the calibrated waveform vector and its covariance matrix, we calculate pulse parameters and their uncertainties. We compare our method with a more traditional parameter-based uncertainty analysis.

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.