Load-Pull System Aids Nonlinear Device Modeling

By combining harmonic load-pull measurements with X-parameter model extraction, it is possible to create transistor models that accurately represent device behavior under nonlinear operating conditions.

Transistor amplifier linearity is essential to many wireless systems. Unfortunately, linearity often comes at the expense of efficiency. However, a load-pull system from Focus Microwaves when combined with nonlinear X-parameter* measurements can help achieve the best compromise between linearity and efficiency for a given bias class of power amplifier.

A traditional load-pull measurement system consists of a signal source, two power meters, and a spectrum analyzer combined with a wideband model iCCMT-808 impedance tuner for input impedance tuning of a device under test (DUT), and a wideband harmonic impedance tuner model iMPT-1818, from Focus Microwaves, at the output of the DUT. The iCCMT-808 operates from 0.8 to 8.0 GHz while the iMPT- 1818 tunes fundamental and two harmonic frequencies from 1.8 to 18.0 GHz. The MPTs feature three independent wideband probes that control the amplitude and phase of the reflection factor at fundamental and selected harmonic frequencies independently. The system can be equipped with the iMPT Quattro-1018 tuner with four independent probes for impedance tuning of a fundamental frequency and three harmonics independently, with total frequency coverage of 1.8 to 10.0 GHz, and fourth-harmonic impedance tuning from 7.2 to 10.0 GHz.

The traditional system does not allow nonlinear model generation or waveform engineering and load-lines. Such capabilities are possible, however, with a modified system (Fig. 1) with a Nonlinear VNA (Agilent NVNA) option running as a resident software application in a PNA-X Vector Network Analyzer (VNA) from Agilent Technologies, and the Load Pull Explorer (LPEx) software from Focus Microwaves. The software programs in the PNA-X and LPEx are used concurrently to control the tuners and collect nonlinear measurement data for model development in the Agilent Advanced Design System (ADS) simulation software.

The importance of such a system is that precise harmonic tuning can help determine the base amplifier bias conditions for a given application. Although transistor models are used in amplifier design, these are typically small-signal S-parameter-based models that are not representative of the device's behavior under large-signal, nonlinear conditions. To better understand the behavior of a transistor under those conditions, it is necessary to achieve specific current and voltage waveforms at the device through the use of harmonic tuning. To achieve proper waveform shaping, a designer must have access to time-domain waveforms during the design process. The use of harmonic tuning and an NVNA allows the collection of nonlinear behavioral data, which can be used to develop an accurate model of the transistor's nonlinear behavior under different operating conditions. An accurate model can lead to the highest efficiency for a given mode of operation and reduce design revisions and tuning during the design cycle.

Characterizing an active device for its nonlinear behavior involves mapping the transistor's operating conditions to its output responses according to relationships that plot such parameters as output power and efficiency as functions of bias voltage, frequency, input power, and source and load reflection coefficients. Since the reflection coefficients must be defined, load-pull tuners are essential for performing the device characterization. Load-pull measurements provide data that maps the impedances seen by the DUT to different values of drain current and output power. Given enough data collected over representative operating conditions, a model of the device can be developed. Unfortunately, that model will be limited to the specific operating conditions of those measurements, but will lack the flexibility to be applied for amplifier performance simulations under varying input power, frequency, and bias conditions that do not match those of the measurements.

Traditional device models are based on small-signal S-parameters. Under linear conditions, these models can provide good results, but tend to be less reliable under nonlinear operating conditions. Load-pull measurements provide more insight into the behavior of a device under different source and load impedance conditions, but traditional load-pull systems only provide information about the relationship between the magnitude of the fundamental-frequency output power and the input power under predefined operating conditions. They do not provide the phase and harmonicfrequency information needed to extract the DUT's time-domain waveforms under different operating conditions. By combining load-pull measurement data with nonlinear X-parameter model extraction techniques, more accurate device models can be developed for application under nonlinear conditions. X-parameters are a mixer-based extension of traditional S-parameters measured using the nonlinear PNA software built into the PNA-X VNA. The nonlinear test system (Fig. 1) is an extension of a conventional 50-Ohm load-pull setup that allows X-parameters to be measured while varying the input and output impedance conditions of the DUT. The results for each measurement are captured in an X-parameter file, along with the various operating conditions used during each test. The different operating conditions can be swept across a range of values in order to characterize the DUT for a large set of operating conditions. The resulting X-parameter database can be imported into the ADS simulation software for modeling purposes.

X-parameter measurements can be performed with a system based on the PNA-X, a wideband impedance tuner at the input of the DUT, and a wideband harmonic impedance tuner at the output of the DUT. This system employs a model iCCMT-808 input tuner with coverage from 0.8 to 8.0 GHz and a model iMPT-1818 output tuner with frequency range of 1.8 to 18.0 GHz. X-parameter extraction is designed to achieve the accuracy of a load-pull measurement under all defined operating conditions. That accuracy can be evaluated by comparing an X-parameter model to measured load-pull data. For that purpose, a loadpull sweep was performed over most of the Smith chart to create a contour plot of load-pull measurement results while generating an X-parameter model of the DUT. After extracting the model, an independent simulated load-pull of the Smith chart was completed using the X-parameter component imported into ADS; then, the contours of the X-parameter simulation-based loadpull were compared with the load-pull measurement-based contours. Figure 2 shows that the load-pull measurements and X-parameter measurements are largely congruent for this DUT for all load conditions tested. Accuracy was high except when the load reflection coefficient had a high value.

The nonlinear behavior of the DUT was examined with the help of the harmonic-balance simulator in ADS, generating time-domain current and voltage waveforms as well as load-line behavior to better understand the DUT's performance under nonlinear conditions. By using the harmonic tuners, for example, it is possible to analyze the harmonic content of the DUT's output waveforms as a function of, for example, nonlinear gate-source input capacitance. The load-line results (Fig. 3) provide some insight into the DUT's nonlinear behavior.

"*X-parameters is a trademark of Agilent Technologies.

Focus Microwaves, 1603 St. Regis, Dollard-des-Ormeaux, Quebec City, Canada H9B 3H7; Internet: www.focusmicrowaves.com.

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