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By Gary Simpson, Jason Horn, Dan Gunyan, and David E. Root, Maury Microwave Corporation

Abstract
X-parameters [1-4] are the mathematically correct supersets of S-parameters valid for nonlinear (and linear) components under large-signal (and small-signal) conditions. This work presents an automated application combining a Nonlinear Vector Network Analyzer (NVNA) instrument with automated load-pull measurements that extends the measurement and extraction of X-parameters over the entire Smith Chart. The augmented X-parameter data include magnitude and phase as nonlinear functions of power, bias, and load, at each harmonic generated by the device and measured by the NVNA. The X-parameters can be immediately used in a nonlinear simulator for complex microwave circuit analysis and design. This capability extends the applicability of measurement-based X-parameters to highly mismatched environments, such as high-power and multi-stage amplifiers, and power transistors designed to work far from 50 ohms. It provides a powerful and general technology-independent alternative, with improved accuracy and speed, to traditional large-signal device models which are typically slow to develop and typically extrapolate large-signal operation from small-signal and DC measurements.

Introduction

Device characterization is required for power amplifier design, and the ideal form of the device data is a large signal model. With a model, the performance can be analyzed for varying drive and impedance conditions, so complex or multi-stage circuits can be designed.

Much work has been devoted to large signal model development at microwave frequencies, and improvements have been made in recent years. But though these analytical models can be accurate over certain regions of the device operation, they may fail in other areas. Since they are typically extrapolated from DC and small signal measurements, verification under actual large-signal operation is generally required. In many cases of practical interest, the device is used over a wider range of voltage and current than can even be characterized under DC and linear S-parameter conditions. Load pull is a measurement of a device under actual large signal operation. It may include measuring device performance vs. impedance, drive power, bias, temperature, or other factors. Since it is a direct device measurement, the data can be used with confidence over the conditions of the measurement.

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•Application Note: Load Pull + NVNA = Enhanced X-Parameters For PA Designs With High Mismatch And Technology-Independent Large-Signal Device Models