X-parameter modeling paradigm constitutes a major advancement in circuit and system simulation and design. However being a frequency domain defined nonlinear model, its implementation in harmonic-balance simulators is not trivial. The implementation available in commercial simulators does not fully respond to the needs. In particular, the multi-tone simulations and the prediction of the dynamic effects remain challenges. This paper presents a method to implement such behavioral models into the RF engines. Despite the fact that this paper covers the implementation of X-parameter model, it's perfectly applicable to any behavioral models describing the relations between complex envelope signals. View full abstract»

This paper studies the envelope-domain dynamic X-parameter model of RF power-amplifier nonlinear behavior. Based on the analysis of its fundamental assumptions and the main applications for inter-modulation predictions, the consideration of model sensibility to variable carrier-frequency is proposed as one criterion to evaluate the reasonableness of the mathematical modeling. The experimental results in this paper show that the dynamic X-parameters are compatible with each other only within a small neighborhood around the desired carrier frequency, which on one hand may to some extent reflect the reasonableness of the theory, and on the other hand serve to investigate the validity and limits of dynamic X-parameters from a new perspective. View full abstract»

X-parameter technology provides simulation-based design of non-linear circuits with inherent accuracy that is attributed to measurement-based model extraction. Recent advancements have combined Non-linear Vector Network Analyzer measurements with impedance tuners to compliment the equivalent accuracy of load-pull measurements with the analytic convenience of equation-based large-signal models. This paper investigates the challenges incurred when modeling high-power transistors under variable complex impedance matching conditions. It also compares the predicted performance of the X-parameter model against an independent large-signal model provided by the manufacturer for a 10W transistor. The results show a good correlation between the two models when compared under load-pull impedance modulation. View full abstract»

Since the last decade, the behavioral modeling of RF functional blocks (amplifiers, mixers, (de)modulators, etc.) has been a flourishing research domain that has led to a better overall understanding of the nonlinear dynamics impact to the circuit performances. Recently the X-parameter paradigm has been introduced. The formalism provides a comprehensive description of the relationships between all the harmonics of the scattered and incident power waves at the ports of a device, and represents a major advancement in RF circuit characterization. The formalism however still needs effective handling of the long term memory effects. In this paper, a simple and efficient approach is proposed to model long-term memory effects within X-parameter. It ensures both a simple extraction procedure and an efficient numerical implementation. View full abstract»

X-parameters have been introduced as the natural extension of S-parameters capable of characterizing a nonlinear device excited by a large-signal input. This paper describes validation of the X-parameter model of a switching cascode power amplifier (PA), which has strong nonlinearity. The X-parameter model of the PA was measured and extracted by an Agilent N5245A PNA-X. Measurements were done on wafer and deem-bedded to the input and output pads of the device. An Enhanced Data rates for GSM Evolution (EDGE) signal was applied to the model for simulations. The simulated relative levels of output spectrum and RMS value of error vector magnitude (EVM) were compared with the measured data in order to validate the X-parameter model. A good match was achieved between the simulation and measurement. The maximum difference between the simulated and measured relative levels of output spectrum is 4 dB. The maximum error between the simulated and measured EVM is less than 3 %-point. View full abstract»

As a kind of superset of S-parameters, X-parameters are becoming increasingly popular in non-linear device simulation and measurement. Due to their good accuracy and convenient extraction procedures, X-parameter-based transistor device models have so far been mainly used in power amplifiers design. They have been limited to this kind of design up to now because the X-parameter models extracted are only suitable for fundamental frequency circuit design. In this paper, a new extraction method is described to allow the extracted model to be used to designing a frequency doubler, and verification through simulation results is presented. View full abstract»

X- parameters, referred to as the parameters of the Poly-Harmonic Distortion (PHD) nonlinear behavioral model as well, have been introduced as the natural extension of S-parameters to nonlinear devices under large-signal drive. This paper describes the approach and procedure of X-parameter characterization and nonlinear simulation of an RF amplifier designed to drive a comb-generator, including measurement experiment, modeling, and model validation. Firstly, a specially configured Nonlinear Vector Network Analyzer (NVNA) is used to the measurements. Secondly, the X-parameters are extracted. Then the parameters are used with the X-parameter framework in ADS to enable accurate nonlinear simulation of device behavior. Independent NVNA measurements validate the model predictions, and show the inadequacy of `Hot S22' in predicting such performance. View full abstract»

As a kind of superset of S-parameters, X-parameters are becoming increasingly popular in non-linear device simulation and measurement. Due to their good accuracy and convenient extraction procedures, X-parameter-based transistor device models have so far been mainly used in power amplifiers design. They have been limited to this kind of design up to now because the X-parameter models extracted are only suitable for fundamental frequency circuit design. In this paper, a new extraction method is described to allow the extracted model to be used to designing a frequency doubler, and verification through simulation results is presented. View full abstract»

X-parameters are the mathematically correct supersets of S-parameters valid for nonlinear (and linear) components under large-signal (and small-signal) conditions. This paper compares a PHD model generated from arbitrary load-dependent measured X-parameters and a measurement-based non-quasi-static device model and validates them against tuned-load measurements. CW, IMD, and ACPR swept-power measurements are compared. The models agree on the simulated device behavior and compare well to validation measurements. View full abstract»

A new nonlinear FET model formulation is proposed which comprises an X-parameter (S-function or Poly Harmonic Distortion) intrinsic model combined with lumped extrinsic circuit model shells This enables the correct gate width scaling of the intrinsic and extrinsic model by finger number and unit gate width. An extraction technique is described based on de-embedding the X-parameters to the intrinsic plane. A verification example of scaling of a 10×90um 0.15um pHEMT X-parameter model (generated from a scalable compact model) down to a 4×50um device (a factor of 4.5), is shown without loss of accuracy in power sweep and loadpull contour results compared to the reference compact model simulation. View full abstract»

X-parameters, also referred to as the parameters of the Poly-Harmonic Distortion (PHD) nonlinear behavioral model, have been introduced as the natural extension of S-parameters to nonlinear devices under large-signal drive [1]-[3]. This paper describes a new approach to X-parameter characterization and nonlinear simulation - including large-signal experimental model validation - of a commercially available GSM amplifier. A specially configured Nonlinear Vector Network Analyzer (NVNA) and procedure for measuring, for the first time, X-parameters under pulsed bias conditions is presented. The measured pulsed bias X-parameters are then used with the PHD framework to enable accurate nonlinear simulation of device behavior, including harmonics (magnitude and phase) under pulsed bias large-signal conditions with mismatch. Independent NVNA measurements validate the predictions of the X-parameter simulations of output match under drive, and show the inadequacy of "Hot S22" techniques to predict such device performance. View full abstract»

This paper presents a measurement system that is capable of characterizing and modeling high-power (>;250W) RF devices outside the standard 50Q environment. The system is based on the Agilent PNA-X and Nonlinear Vector Network Analyzer (NVNA) measurement platforms. It is configured for measurements on a commercially available 250W average output power Lateral Diffused Metal Oxide Semiconductor (LDMOS) technology power transistor from NXP. A number of practical considerations are described in the paper such as setup of the PNA-X pulse generators and RF modulators to provide adequate pulsed measurement conditions, NVNA power budget calculations to sustain PNA-X measurement receiver linearity requirements, and configuration of accurate in-pulse drain current measurements to ensure proper transistor drain efficiency calculations. Procedures for performing accurate high-power vector and NVNA phase and amplitude calibrations are also described as well as source-and load-pull measurement results and X-parameter modeling results on the 250W LDMOS power transistor. View full abstract»

In this paper, a PA (Power Amplifier) used for TD-SCDMA terminal is simulate and measured, and the simulation results are verified by measurement results. Firstly, PHD (Poly-Harmonic Distortion) nonlinear behavioral model, which is referred to as X-parameters, of the PA extracted from Agilent NVNA (Nonlinear Vector Network Analyzer) measurement is imported to Agilent ADS (Agilent Advance Design System) to simulate its performance and distortion under TD-SCDMA signal stimulation, which is referred to as PHD model simulation. Secondly, the TD-SCDMA signal used for PHD model simulation is downloaded into the Agilent E4438C signal generator to be as the input for PA during measurement. Thirdly, the signal output from PA is caught and recorded by Vector Signal Analyzer under control of 89600 vector Signal analyzer software, and the signal recorded is imported to ADS to be analyzed by the same method used in PHD model simulation. At last, results such as output power, available gain, spectrum, ACPR (Adjacent Channel Power Ratio), RMS (Root Mean Square) EVM (Error Vector Magnitude) and signal constellation from PHD model simulation and measurement are compared, and it can be found that the PHD model simulation results agree very well with measurement results. As a result, the simulation method designed in this paper can be used to evaluate PA performance and PA distortion correctly. View full abstract»

This paper addresses two areas of improvement to microwave linear and non-linear modeling. The first area concerns best-practice application examples of electromagnetic (EM) analysis combined with accurate broad-band parasitic models for improved board-based designs using surface mount components. The focus is on co-simulation - which combines circuit and EM simulation - of surface mount capacitors in shunt configurations. The second area that is covered in this paper is to study the X-parameter modeling technique used in characterizing nonlinear devices compared to traditional compact modeling technique. The results show that X-parameter models can be helpful for compact model validation and can also provide a good alternative to compact models for specific devices and operating conditions. View full abstract»

This paper presents a behavioral model for RF power amplifiers including load-pull and self-heating effects for radar applications. The model topology combines nonlinear scattering functions with a thermal model. This work focuses on model identification from time domain load-pull measurements and thermal simulations of the power amplifier. Comparisons between model and pulsed measurements, demonstrate its ability to accurately reproduce the signals and temperature for arbitrary load impedances. View full abstract»

This paper introduces an analytical approach to obtain fundamental and harmonic load-pull contours using X-parameters. This method is proposed to obtain the optimum load impedance at different harmonics. This approach has been applied on a two port X-parameter model and its results are independently verified by ADS simulation. View full abstract»

Power amplifier (PA) behavior is inextricably linked to the characteristics of the transistors underlying the PA design. All transistors exhibit some degree of memory effects, which must therefore be taken into account in the modeling and design of these PAs. In this paper, we will present new trends for the characterization, device modeling, and behavioral modeling of power transistors and amplifiers with strong memory effects. First the impact of thermal and electrical memory effects upon the performance of a transistor will be revealed by comparing continuous wave and pulsed RF large-signal measurements. Pulsed-RF load-pull from the proper hot bias condition yields a more realistic representation of the peak power response of transistors excited with modulated signals with high peak-to-average power ratio. Next, an advanced device modeling method based on large-signal data from a modern nonlinear vector network analyzer instrument, coupled with modeling approaches based on advanced artificial neural network technology, will be presented. This approach enables the generation of accurate and robust time-domain nonlinear simulation models of modern transistors that exhibit significant memory effects. Finally an extension of the X-parameter (X-parameter is a trademark of Agilent Technologies Inc.) behavioral model to account for model memory effects of RF and microwave components will be presented. The approach can be used to model hard nonlinear behavior and long-term memory effects and is valid for all possible modulation formats for all possible peak-to-average ratios and for a wide range of modulation bandwidths. Both the device and behavioral models have been validated by measurements and are implemented in a commercial nonlinear circuit simulator. View full abstract»

In this work, the polyharmonic distortion (PHD) model is used to analyze the behavior of high-speed nonlinear links. The model assumes the validity of the harmonic superposition principle for high-speed I/O links. From the PHD formalism, a frequency-domain X-parameter matrix formulation is derived. The formulation accommodates both port and harmonic dependence of the signals. Relationships are derived that permit to combined various nonlinear sub-blocks described by their X parameters. Simulations are performed and compared with other methods. View full abstract»

X parameters have been shown to have a wide array of applications in the modeling of nonlinear devices and systems. In this work, the polyharmonic distortion (PHD) model and the latency insertion method (LIM) are combined to generate X parameters describing the nonlinear relationship between power waves. This technique leverages the speed and convergence advantages of the LIM simulation method to generate frequency-domain models. Results are compared with those of other methods. View full abstract»

This paper presents a complete power amplifier design using new Nonlinear Vector Network Analyzer (NVNA) and X-parameter technologies. A high-power, pulsed Continuous Wave (CW) NVNA setup is presented and harmonic tuning capabilities of the measured X-parameter model is demonstrated using the same setup. From fundamental and harmonic impedance tuning, input and output power amplifier matching networks are synthesized and first-pass design success is confirmed by measurements of the fabricated power amplifier. View full abstract»

In this paper we analyze the performance of ground moving target detection by means of single-baseline and dual-baseline along track interferometric synthetic aperture radar (SAR) systems, obtained using a generalized likelihood ratio test (GRLT). Detection performance are evaluated in terms of probability of detection and probability of false alarm using data simulated with TerraSAR-X parameters. View full abstract»

X-parameters 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. View full abstract»

An original way is presented to model memory effects of microwave amplifiers in the case of wideband modulated signals. The model is derived as a limiting case of the more general dynamic X-parameter theory. For a given component, the model is identified from pulsed envelope X-parameter measurements performed with an NVNA. The resulting nonlinear X-parameter model is quantitatively described by a 2-variate kernel function that enables the derivation of an optimal static AM-AM AM-PM characteristic for every possible input envelope probability density function. The model is validated by performing a set of 2-tone experiments. The model can be implemented in the ADS circuit envelope simulator. View full abstract»

Predictable measurement-based large-signal design has been demonstrated with a unique set of interoperable commercially available nonlinear technologies for measurement, simulation, and design of nonlinear components. The new NVNA instrument, automated X-parameter measurements and extraction, and auto-configurable compiled PHD component in ADS, together enable design of nonlinear circuits entirely from fully calibrated nonlinear component data. View full abstract»