Behavioral modeling for concurrent dual‐band power amplifiers using 2D hammerstein/wiener models

Behavioral modeling for the concurrent dual‐band power amplifier (PA) is a critical problem in practical applications. The nonlinear distortion in the concurrent dual‐band PA is quite different from that in the conventional single‐band PA. This article analyzes the nonlinearities in the concurrent dual‐band PA and reveals that both input signals in the dual bands are important for the behavioral modeling. The 2D Hammerstein model and 2D Wiener model are proposed for the first time for the concurrent dual‐band PA. They are extended versions of conventional Hammerstein and Wiener structures used in the single‐band PA by including the cross‐band intermodulation in the static nonlinearity block. The proposed 2D models require much less coefficients than the original work of the 2D‐DPD model. Experiments were carried out for an 880 MHz/1960 MHz concurrent dual‐band Doherty PA to demonstrate the effectiveness of the proposed models. The results clearly show that less than ?40 dB normalized mean square errors (NMSEs) are obtained in the dual bands in the behavioral modeling. © 2012 Wiley Periodicals, Inc. Int J RF and Microwave CAE 23: 646–654, 2013.     

Passive intermodulation of printed dipole antennas: Modeling,evaluation, and experiment

A theoretical treatment of electro‐thermally induced passive intermodulation (PIM) is developed for printed dipole antennas, yielding an expression of third‐order intermodulation distortion based on the surface current distribution. The simulation procedure of third‐order PIM products with the full‐wave frequency‐domain method was given to evaluate the PIM level. In particular, the PIM dependencies on input power, two‐tone frequency separation, and substrate parameters are analyzed leading to design guidelines for low distortion antennas. It is shown in this paper that the thermal factors have a noticeable impact on the PIM power generated by printed dipole antennas. Finally, two antenna samples are fabricated on different substrates, Rogers 5880 and FR4, and a two‐tone test at 2‐GHz band using a reflective PIM test system is reported. The PIM evaluation method and the design guidelines to reduce the PIM on printed antennas proposed in this paper are of great significance for telecommunication systems.     

New behavioral‐level simulation technique for RF/microwave applications. Part III: Advanced concepts

The quadrature modeling structure is widely accepted as an efficient tool for the nonlinear simulation of RF/microwave bandpass stages (power amplifiers, etc.) for wireless applications. The common belief is that this structure can be applied to model only bandpass memoryless nonlinearities (which, however, may exhibit amplitude‐to‐phase conversion). In two recent articles 1 , 2 ; the authors have extended the application of the quadrature modeling structure to modeling broadband nonlinearities, which makes possible to predict harmonics and even‐order nonlinearities, to take into account the frequency response, etc. This article completes the overview of the instantaneous quadrature technique. The authors discuss its application to modeling AM, FM and PM detectors, which are strongly nonlinear elements with large memory (both the strong nonlinearity and large memory effects are essential for the detector proper operation), thus removing the limitation of nonlinearity to be memoryless or quasimemoryless. The identification of nonlinear interference/distortion sources is of great relevance for a practical EMC/EMI design. In the second part of this article, we discuss the dichotomous identification method, which is much more computationally efficient than a simple single‐signal method, especially for a large number of input signals. Individual spectral components of a complex‐spectrum signal can also be considered as input signals and, hence, it is possible to identify the spectral components responsible for a particular nonlinear interference/distortion (say, for a particular intermodulation product). © 2002 Wiley Periodicals, Inc. Int J RF and Microwave CAE 12: 206–216, 2002.     

Recurrent neural network technique for behavioral modeling of power amplifier with memory effects

A new technique for behavioral modeling of power amplifier (PA) with short‐ and long‐term memory effects is presented here using recurrent neural networks (RNNs). RNN can be trained directly with only the input–output data without having to know the internal details of the circuit. The trained models can reflect the behavior of nonlinear circuits. In our proposed technique, we extract slow‐changing signals from the inputs and outputs of the PA and use these signals as extra inputs of RNN model to effectively represent long‐term memory effects. The methodology using the proposed RNN for modeling short‐term and long‐term memory effects is discussed. Examples of behavioral modeling of PAs with short‐ and long‐term memory using both the existing dynamic neural networks and the proposed RNNs techniques are shown. © 2014 Wiley Periodicals, Inc. Int J RF and Microwave CAE 25:289–298, 2015.     

分裂增强型Hammerstein模型的研究

提出一种带有附加失真路径的分裂增强型Hammerstein模型,使用无记忆多项式和有限冲激响应(FIR)滤波器分别构建该模型中的无记忆子系统和记忆效应子系统。利用飞思卡尔(Freescale)半导体晶体管MRF7S21170进行功放电路设计,从ADS中导出输入输出数据进行模型验证。仿真结果表明,提出的模型性能优于增强型Hammerstein模型,具有较高的精度,能够精确模拟功率放大器的特性,对射频功放行为建模的研究与发展具有重要的参考价值。     

An improved empirical large‐signal model for the GaAs‐ and GaN‐based HEMTs

A complete empirical large‐signal model for the GaAs‐ and GaN‐based HEMTs is presented. Three generalized drain current I–V models characterized by the multi‐bias Pulsed I–V measurements are presented along with their dependence on temperature and quiescent bias state. The new I–V equations dedicated for different modeling cases are kept accurate enough to the higher‐order derivatives of drain‐current. Besides, an improved charge‐conservative gate charge Q–V formulation is proposed to extract and model the nonlinear gate capacitances. The composite nonlinear model is shown to accurately predict the S‐parameters, large‐signal power performances as well as the two‐tone intermodulation distortion products for various types of GaAs and GaN HEMTs. © 2011 Wiley Periodicals, Inc. Int J RF and Microwave CAE , 2011.     

Modeling power and intermodulation behavior of microwave transistors with unified small‐signal/large‐signal neural network models

This article presents a detailed procedure to learn a nonlinear model and its derivatives to as many orders as desired with multilayer perceptron (MLP) neural networks. A modular neural network modeling a nonlinear function and its derivatives is introduced. The method has been used for the extraction of the large‐signal model of a power MESFET device, modeling the nonlinear relationship of drain‐source current I_ds as well as gate and drain charge Q_g and Q_d with respect to intrinsic voltages V_gs and V_ds over the whole operational bias region. The neural models have been implemented into a user‐defined nonlinear model of a commercial microwave simulator to predict output power performance as well as intermodulation distortion. The accuracy of the device model is verified by harmonic load‐pull measurements. This neural network approach has demonstrated to predict nonlinear behavior with enough accuracy even if based only on first‐order derivative information. © 2003 Wiley Periodicals, Inc. Int J RF and Microwave CAE 13: 276–284, 2003.     

Complex radial basis function networks trained by QR‐decomposition recursive least square algorithms applied in behavioral modeling of nonlinear power amplifiers

In this article, we propose a novel complex radial basis function network approach for dynamic behavioral modeling of nonlinear power amplifier with memory in 3 G systems. The proposed approach utilizes the complex QR‐decomposition based recursive least squares (QRD‐RLS) algorithm, which is implemented using the complex Givens rotations, to update the weighting matrix of the complex radial basis function (RBF) network. Comparisons with standard least squares algorithms, in batch and recursive process, the QRD‐RLS algorithm has the characteristics of good numerical robustness and regular structure, and can significantly improve the complex RBF network modeling accuracy. In this approach, only the signal's complex envelope is used for the model training and validation. The model has been validated using ADS simulated and real measured data. Finally, parallel implementation of the resulting method is briefly discussed. © 2009 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2009.     

A simplified adaptive sparse digital pre‐distorter for joint mitigation of frequency‐dependent transmitter impairments

The interplay between the unavoidable various nonlinearities of the direct conversion transmitter, such as local oscillator leakage, power amplifier (PA) nonlinearities, and in‐phase and quadrature (I/Q) branch imbalance, and so forth will degrade the communication system performance seriously. To overcome these nonlinear interactive effects, an accurate adaptive sparse behavioral model is proposed for the joint compensation of the transmitter impairments in this article. First, a three‐input nonlinear joint compensation model, which is composed of the nonlinear frequency‐dependent cross terms between the I and Q branches as well as the magnitudes of the input signal, is developed. Second, to prune the redundant terms and reduce the computational complexity of the full three‐input model, an efficient robust quasi‐newton–based adaptive greedy algorithm is developed. To verify the performance of the proposed method, the different imperfect transmitters based on single‐device GaN Class‐F PA and GaN Doherty PA are used for experimental verification and analysis. Experiment results show that the proposed method can efficiently construct a sparse joint compensation model with improved modeling and distortion mitigation capability than the reported I/Q imbalance model, where nonlinear distortion and I/Q imbalance characteristics in the transmitter can be almost completely removed.     

Analysis and design of a novel concurrent Class B/J continuum power amplifier

In this paper, a novel concurrent Class B/J continuum mode is presented based on waveform shaping of current and voltage. The behavior characteristics and performances of power amplifiers (PAs) in concurrent dual‐band mode are investigated in detail. According to the analysis of proposed concurrent mode, the optimal load impedances at fundamental, harmonic and intermodulation (IM) frequencies are related to the magnitude ratio of the two carriers. Comparing with concurrent Class‐B mode, two parameters α, β can be configured independently in the proposed concurrent mode, which provides more freedom and flexibility for design without output power and drain efficiency degradation. In order to verify the proposed theory, a 1.9/2.35 GHz dual‐band power amplifier based on proposed concurrent mode is designed, fabricated and measured. Experimental results show that when the PA is driven by two 10 MHz LTE signals concurrently with total 9.2 dB peak‐to‐average power ratio (PAPR), the total average power is 36.0 dBm with 40.6% drain efficiency, which indicates a good concurrent performance.     

Volterra series‐based model for concurrent dual‐band power amplifier using dynamic memory depth

In this article, a dynamic dual‐band baseband equivalent Volterra (DDBE) model is proposed to compensate the nonlinear distortions of the concurrent dual‐band power amplifier (PA). The DDBE model is obtained by improving the discretized dual‐band baseband equivalent Volterra model which can describe the output characteristics of concurrent dual‐band PA completely in theory but is lack of practicability. Three simplification rules are proposed in the article, and the relevance between in‐band intermodulation and in‐band cross modulation is employed to simplify the establishment complexity of the model. Then the dynamic kernels are categorized into three groups, and based on this, DDBE models with different level dynamical kernels are derived. In addition, draw on the experience of single‐band PA behavioral model, even‐order kernels are introduced into DDBE models. Digital predistortion performances of a wideband PA, which works in concurrent dual‐band mode, are evaluated to verify the feasibility and advantages of the proposed model.     

Parametric modeling of microwave passive components using combined neural networks and transfer functions in the time and frequency

A novel parametric modeling technique is proposed to develop combined neural network and transfer function models for both time and frequency (TF) domain applications of passive components, where the neural network is trained to map geometrical variables to the coefficients of transfer functions. Built on our previous work, a new order‐changing module is developed to enforce stability of transfer functions and simultaneously guarantee continuity of coefficients. A constrained optimization strategy is introduced to enforce passivity of transfer functions through a neural network training process. A general equivalent circuit for two‐port passive components is generated directly from coefficients of arbitrary‐order transfer functions. Once trained, the parametric model can provide accurate and fast prediction of the electromagnetic behavior of passive components with geometrical parameters as variables. Compared to our previous work, the proposed method enables models to work well in the time domain providing good accuracy in challenging modeling applications. Two parametric modeling examples of spiral inductors and interdigital capacitors, and their application in both time and frequency domain simulations of a power amplifier are examined to demonstrate the validity of the proposed technique. © 2012 Wiley Periodicals, Inc. Int J RF and Microwave CAE , 2013.     

Advanced system‐level simulation paradigm for ultra‐wideband systems using SCERNE platform

In this article, a progressive system‐level simulation framework is developed based on Simulation de Chaînes d'Emission/Réception Nouvelle gEnération (SCERNE) platform to simulate an ultra‐wideband (UWB) impulse radar transmitter and accurately predict its performance. With the purpose of demonstrating the usefulness of the SCERNE ability in system‐level modeling, we present and simulate a simplified structure of UWB impulse radar transmitter. First, after simulation each component in different circuit‐level tools such as ADS, CST, and HFSS, each part has been modeled by using different modeling methods to transfer their data into MATLAB environment. Then, we duplicate the transmitter structure in SCERNE toolbox to validate the results. The advantage conferred by the proposed SCERNE toolbox is that fast and accurate bilateral modeling method is available at multi‐medium structures in contrast with conventional unilateral modeling, and so a lower memory and higher accuracy of the behavioral model is achieved. It can also be beneficial when the user is looking for system‐level, as the increased components amounts can help as a surrogate model. The system model can be easily extended to other UWB radar systems by simply changing the input pulse shape, UWB channel environment, transceiver topology, etc. Various effects such as signal quality, and pulse shape that can easily investigate and re‐optimize for high performance are using the developed model. To validate the practicality of the proposed paradigm, the simulations and predictions through model results are being outlined.     

Neural network modeling of microwave FETs based on third‐order distortion characterization

A new method for characterization of HEMT distortion parameters, which extracts the coefficents of a Taylor series expansion of I_ds(V_gs, V_ds), including all cross‐terms, is developed from low‐frequency harmonic measurements. The extracted parameters will be used either in a Volterra series model around a fixed bias point for 3^rd‐order characterization of small‐signal I_ds nonlinearity, or in a large‐signal model of I_ds characteristic, where its partial derivatives are locally characterized up to the 3^rd order in the whole bias region, using a novel neural‐network representation. The two models are verified by one‐tone and two‐tone intermodulation distortion (IMD) tests on a PHEMT device. © 2006 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2006.     

Capturing asymmetrical spectral regrowth in RF systems using a multislice behavioral model and enhanced envelop transient analysis

Nonlinear distortion in RF and microwave systems results in spectral regrowth of digitally modulated signals. The distortion above and below the main channel can be at different levels and this is attributed to baseband effects. This article presents a new multislice behavioral‐model architecture that captures this asymmetry and can be implemented in a variety of circuit simulators, including SPICE, harmonic balance (HB), envelope transient (ET), and system simulators. The work is experimentally validated using an HBT power amplifier at 2.5 GHz driven by a WCDMA signal. The model is used with envelope transient circuit simulation which is enhanced to accommodate an arbitrary baseband transfer function. © 2006 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2006.     

Neural‐space mapping‐based large‐signal modeling for MOSFET

In this article, a large‐signal modeling approach based on the combination of equivalent circuit and neuro‐space mapping modeling techniques is proposed for MOSFET. In order to account for the dispersion effects, two neuro‐space (S) mapping based models are used to model the drain current at DC and RF conditions, respectively. Corresponding training process in our approach is also presented. Good agreement is obtained between the model and data of the DC, S parameter, and harmonic performance for a 0.13 μm channel length, 5 μm channel width per finger and 20 fingers MOSFET over a wide range of bias points, demonstrating the proposed model is valid for DC, small‐signal and nonlinear operation. Comparison of DC, S‐parameter, and harmonic performance between proposed model and empirical model further reveals the better accuracy of the proposed model. © 2011 Wiley Periodicals, Inc. Int J RF and Microwave CAE , 2011.     

Behavioral modeling of power amplifiers for wireless applications

In this paper, an improved empirical behavioral model for radio‐frequency power amplifiers (RF‐PAs) is presented. The model was implemented in a commercial nonlinear microwave simulator. It belongs to the category of bandpass PA models, which exhibits memory effects due to the low frequency dependence of bias and temperature. Additionally, it facilitates accurate and efficient system level simulations of RF‐PA large‐signal behaviors such as self‐bias, AM‐AM, AM‐PM, gain expansion effects, and intermodulation distortion (IMD) sweet‐spots. The model was validated using measurement data obtained from a commercial CDMA PA at 1.88 GHz. © 2007 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2007.     

一种狼群智能算法及收敛性分析

针对狼群算法求解复杂函数时容易陷入局部极值、计算耗费大、学习能力差等局限性, 提出一种狼群智能算法. 首先, 通过构建智能猎杀行为提高算法自适应学习能力, 降低算法的计算耗费, 构建双高斯函数更新法以增强算法全局搜索能力; 然后, 运用马尔科夫过程证明狼群智能算法的收敛性; 最后, 对多种典型测试函数进行仿真实验并与多种智能算法进行对比分析. 实验结果表明, 所提出算法具有全局收敛性强、计算耗费低、寻优精度高等优势.     

Theoretical basis for extraction of mildly nonlinear behavioral models

The analytical and laboratory requirements for the extraction of a mildly nonlinear behavioral model are derived. This shows that they greatly exceed current capabilities in general, and a simplified procedure based on dynamic linear element deembedding is proposed. This procedure is then illustrated for a case of practical significance by discussing various methods to extract an intermodulation model of a MES field effect transistor. © 2003 Wiley Periodicals, Inc. Int J RF and Microwave CAE 13: 40–53, 2003.     

Automated time domain modeling of linear and nonlinear microwave circuits using recurrent neural networks

In this article, a recurrent neural network (RNN) method is employed for dynamic time‐domain modeling of both linear and nonlinear microwave circuits. An automated RNN modeling technique is proposed to efficiently determine the training waveform distribution and internal RNN structure during the offline training process. This technique extends a recent automatic model generation (AMG) algorithm from frequency‐domain model generation to dynamic time‐domain model generation. Two types of applications of the algorithm are presented, transient electromagnetic (EM) behavior modeling of microwave structures, and time‐domain envelope modeling of power amplifiers (PA). For transient EM modeling, we consider EM structures with varying material and geometrical parameters. AMG automatically varies the EM structural parameters during training and drives time‐domain EM simulators to generate necessary amount of data for RNN to learn. AMG aims to model the transient behavior with minimum RNN order while satisfying accuracy requirements. In modeling PA behavior, an envelope formulation is used to specifically learn the AM/AM and AM/PM distortions due to third‐generation (3G) digital modulation input. The RNN PA model is able to model these time domain distortions after training and can accurately model the amplifier behavior in both time (AM/AM, AM/PM) and frequency (spectral re‐growth). © 2008 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2008.