Relationship between Volterra series and generalized power series

The relationship between the Volterra nonlinear transfer functions of a system and the elements of its generalized power series is established. A formula is derived which enables the Volterra nonlinear transfer functions to be obtained from the power series expansion of the nonlinear system.     

Complexity-reduced Volterra series model for power amplifier digital predistortion

This paper expounds a complexity-reduced Volterra series model for radio frequency power amplifier (PA) behavioral modeling and digital predistortion (DPD). An analysis was conducted, which took into account the memory effect mechanisms of the PA. This led to a closed-form expression that relates the memoryless behavior of the PA to the finite impulse response feedback filter, which approximates the memory effects’ behavior. The analysis resulted in a complexity-reduced Volterra series model which allows for a substantial reduction in the requirements for digital signal processors and the time needed to construct and implement the DPD in a real-time environment. The proposed model was validated as a behavioral model and a DPD using two different PA architectures, employing two different transistor technologies, driven by both 20 MHz 1001 wideband code division multiple access and long term evolution signals. The results obtained demonstrate the excellent modeling and linearization capability of the complexity-reduced Volterra series model.     

Hybrid systems modeling for power systems

In this work a framework for modeling power systems using hybrid input/output automata (HIOA) is proposed. The system is assumed to consist of several distinct components. Some of them drive the continuous dynamics while others exhibit event-driven discrete dynamics. Such behavior is characterized by interactions between continuous dynamics and discrete events. Therefore the power systems are an important example of hybrid systems. This hybrid modeling process is applied to a simple power system.     

基于简化Volterra级数的射频功率放大器建模与辨识

目前的射频功率放大器模型通常将其看作无记忆器件,但在宽带通信系统中,功率放大器的记忆效应明显,无记忆模型无法准确描述其输入输出特性.本文对功率放大器的Volterra级数模型进行了简化,在考虑记忆效应的同时,也有效克服了一般Volterra级数模型参数数量过于庞大的缺点.采用观测矩阵维数固定的递推最小二乘算法对模型参数进行辨识,不仅能实时跟踪射频功率放大器非线性特性的变化,而且减小了参数辨识所需的运算量和数据存储空间.     

Harmonic analysis of GaN-HEMTs at different temperatures and frequencies using Volterra power series

In this study, the detailed harmonic analysis of GaN high electron mobility transistor (HEMT) at different temperatures and frequencies is presented. Volterra power series and multi-dimensional Laplace transform are used as a method. The Volterra power series is also solved up to third degree, and the small signal transfer functions of kernels (H₁, H₂ and H₃) are obtained. The relationship between drain inductance (L_d), gate–source voltage (V_gs), impedance (Z_L) and the effect of frequency (F_r) to the output gain is identified. Besides, the nonlinear gains of H₁, H₂ and H₃ kernels of the GaN-HEMT are obtained. The inverse relationship between the output gains of H₁, H₂ and H₃ kernels are derived. An unsuitable situation has also been identified for sub-carrier inter-modulation systems. In addition, an asymmetric structure is also obtained between the output gain of H₂ and side-band frequencies. The effects of other parameters are carried out for the output gain.     

Volterra series representation of time-frequency distributions

This paper addresses a Volterra series representation of bilinear (or quadratic) time-frequency distributions that belong to Cohen's class, whereby the analogy of the bilinear class with a second-order double Volterra series is utilized. In addition, a different viewpoint for the bilinear kernel and a complementary interpretation concerning the quadratic time-frequency distributions are provided.     

Modified Volterra series transfer function method

In this letter, we offer a modified version of the Volterra series transfer function (VSTF) method that has been previously proposed as an analytical solution to the nonlinear Schrodinger equation for single-mode fibers. The modified VSTF provides a simple closed-form expression of the output of a mildly nonlinear fiber. It gives orders more accurate result than the original VSTF method and can successfully solve the energy divergence problem experienced by the original method. The result is a stronger analytical tool for modeling signal propagation in optical communication systems     

Volterra series transfer function of single-mode fibers

A nonrecursive Volterra series transfer function (VSTF) approach for solving the nonlinear Schrodinger (NLS) wave equation for a single-mode optical fiber is presented. The derivation of the VSTF is based on expressing the NLS equation In the frequency domain and retaining the most significant terms (Volterra kernels) in the resulting transfer function. Due to its nonrecursive property and closed-form analytic solution, this method can excel as a tool for designing optimal optical communication systems and lumped optical equalizers to compensate for effects such as linear dispersion, fiber nonlinearities and amplified spontaneous emission (ASE) noise from optical amplifiers. We demonstrate that a third-order approximation to the VSTF model compares favorably with the split-step Fourier (recursive) method in accuracy for power levels used in current optical communication systems. For higher power levels, there is a potential for improving the accuracy by including higher-order Volterra kernels at the cost of increased computations. Single-pulse propagation and the interaction between two pulses propagating at two different frequencies are also analyzed with the Volterra method to verify the ability to accurately model nonlinear effects. The analysis can be easily extended to include inter-channel interference in multi-user systems like wavelength-division multiple-access (WDM), time-division multiplexed (TDM), or code-division multiplexed (CDM) systems     

Volterra series analysis of semiconductor laser diode

Theoretical models for laser nonlinearities are analyzed. Volterra transfer function G/sub n/ are calculated from the laser rate equations using an output-to-input approach. Nonlinear models for second-harmonic, third-harmonic, and two-tone third-order intermodulation distortions are calculated from G/sub n/. The transfer function-based models are simplified and a new equation for intermodulation distortion is developed. Comparisons with previous results are presented. It is suggested that this analytical technique offers a valuable tool for the performance analysis of future broadband optical communication systems.<>     

Behavioral modeling of RF power amplifiers based on pruned volterra series

Behavioral modeling techniques provide a convenient and efficient means to predict system-level performance without the computational complexity of full circuit simulation or physics-level analysis of nonlinear systems, thereby significantly speeding up the analysis process. General Volterra series based models have been successfully applied for radio frequency (RF) power amplifier (PA) behavioral modeling, but their high complexity tends to limit their applications to "weakly" nonlinear systems. To model a PA with strong nonlinearities and long memory effects, for example, the general Volterra model involves a great number of coefficients. In this letter, we propose a new simplified Volterra series based model for RF power amplifiers by employing a "near-diagonality" pruning algorithm to remove the coefficients which are very small, or else not sensitive to the output error, therefore dramatically reducing the complexity of the behavioral model.     

Continuum modeling of electromechanical dynamics in large-scale power systems

In this paper, we propose a continuum model for real power systems that tend to be highly irregular in terms of their geographical topology and the power injections, loads, and shunt elements at the bus locations. The continuum model presented here therefore relaxes the isotropy and homogeneity constraints assumed in our prior work. The network, with its transmission lines, generators, and loads, are treated as a continuum in spatial coordinates. We are consequently able to model the system as a pair of nonlinear partial differential equations (PDEs). The first PDE is the continuum equivalent of the load flow equations of the power system and is a boundary value problem. The second equation is the continuum equivalent of the swing equations of the power system. The parameters of these equations are functions of spatial coordinates and the network topology is embedded in them. The computational effort needed to solve the PDEs depends on the uniformity in the parameter distributions. A systematic approach of smoothening the parameter distributions is also proposed. While a continuum system with these smooth parameter distributions looses some of its ability to accurately model the detailed behavior of the power system, the global behavior of the system remains preserved. Furthermore, the electromechanical wave propagation behavior observed in actual power systems is readily recognized from the PDE model. A theoretical analysis of the continuum model as well as test simulations show that disturbances in the system's phase angles propagate through the continuum system with velocities much slower than the speed of light and exhibit dispersion phenomena.     

Uniform approximation with doubly finite Volterra series

The assumption that a system possesses a certain discrete-time Volterra series representation frequently forms the basis for studies in the areas of signal processing and communication theory. A further assumption often made, always without discussion, is that the representation can be suitably approximated by a corresponding `double finite' series. It is shown that, for a very large class of nonlinear discrete-time systems, such doubly finite approximations exist in the sense of uniform approximation on a ball of bounded inputs. Several additional results are also given. These concern, for example, asymptotic properties of the expansions. The results provide a more firm foundation for applications involving Volterra series     

Volterra kernels in nonlinear systems

A general expression for the functional expansion of an operator corresponding to a pth-order Volterra kernel is obtained. This expansion eliminates the use of special algorithms, such as those developed by Van Trees, for the optimum synthesis of nonlinear control systems.     

Volterra series representation of a forward-biased p-i-n diode

A nonlinear model is proposed for a forward-biased p-in diode controlled by an ac signal consisting of a group of sinusoidal signals. The model is applicable to these phases of diode operation where linearized basic physical equations are valid. Current-voltage relations have been obtained for junctions and the "i" region in the form of a Taylor series with frequency-dependent coefficients. The new model is valid for signal levels considerably exceeding those admissible for the known linear model [3], [4]. A new form of signal limiting condition, suitable for measurement verification and calculations, has been obtained. The Volterra series for the equations representing the diode has been found which correspond to the Taylor series obtained. The convergency condition for this series is identical to that for thel Taylor series. The conformability of measurement and calculation results fully testifies to the usefulness of the proposed model for nonlinear distortion analysis.     

Volterra series approach for optimizing fiber-optic communicationssystem designs

A new methodology for designing long-haul fiber-optic communication systems is presented. We derive the overall Volterra series transfer function of the system including linear dispersion, fiber nonlinearities, amplified spontaneous emission (ASE) noise from the fiber amplifiers, and the square-law nature of the direct detection (DD) system. Since analytical expressions for the probability of error are difficult to derive for the complex systems being used, we derive analytical expressions for an upper bound on probability of error for integrate-and-threshold detection at the receiver. Using this bound as a performance criterion, we determine the optimal dispersion parameters of each fiber segment required to minimize the effects of linear dispersion, fiber nonlinearities and ASE noise from the amplifiers. We study the dependence of optimal dispersion parameters on the average power levels in the fiber by varying the peak input power levels and the amplifier gains. Analytical expressions give us the freedom to choose system parameters in a practical manner, while providing optimum system performance. Using a simple system as an example, we demonstrate the power of the Volterra series approach to design optimal optical communication systems. The analysis and the design procedure presented in this work can be extended to the design of more complex wavelength division multiplexed (WDM) systems     

Volterra functional series expansions for semiconductor lasersunder modulation

An analytical model based on Volterra nonlinear functionals applied to semiconductor lasers has been developed. Analytical expressions are obtained for different laser diode responses, giving powerful tools for analysis. For harmonic input, the response is given including the gain compression factor ϵ. Second-harmonic distortion (2HD) shows two maxima at half relaxation oscillation frequency Ω_R/2 and at Ω_R, in agreement with experiments; the residual dc component due to nonlinearities is estimated and experimentally verified. Dynamic frequency deviation as function of bias current shows resonant characteristics. Relaxation frequency and damping rate Γ_R reveal their precise dependence on ϵ and differential gain A. For step input, the turn-on delay t_on and the overshoot P_P/P_on expressions of our model are only functions of Γ_R and Ω_R. P_P/P_on, and the ringing phenomena decrease with increasing bias current level     

Volterra functional series expansions for noise in semiconductorlasers

In this paper, we present a full analysis of noise in semiconductor lasers. Time-covariance and cross-covariance functions of all variables governing single-mode semiconductor laser behavior are given including all Langevin noise sources and considering all terms of the laser rate equations, RIN, carrier noise spectrum, frequency noise spectrum, coherence between the FM and AM noise, variance of the phase change and coupling between amplitude and phase are investigated analytically in their more general form. Spectral line shape has been derived showing dissymmetrical satellite lines centered at multiple integers of relaxation frequency around a central line. It is shown that neglecting the shot noise and considering only the carrier contribution in phase dynamics (common procedure) are too general approximations     

Application of Volterra series to the problem of self-oscillatingmixer

A new approach to the nonlinear problem of self-oscillating mixer has been investigated using Volterra series. The circuit under consideration is first converted into a one-port network. The input and coupling impedances of various ports are represented by Volterra kernels generated by nonlinear current method. Advantage of this approach is that the phase relationships among signals are not required for the analysis. Also, no stability criterion testing is needed to ensure convergence to the correct solution numerically. It is computationally efficient and mathematically simple, yet reasonably accurate. Measured results with respect to RF frequency and power show good agreement with that calculated     

Efficient resonant power conversion

The DC analysis of a series-resonant converter operating above resonant frequency is presented. The results are used to analyze the current form factor and its effect on the efficiency. The selection of the switching frequency to maximize the efficiency is considered. The derived expressions are generalized and can be applied to calculations in any of the switching modes for a series-resonant circuit. For switching frequencies higher than the resonant frequency, an area of more efficient operation is indicated which will aid in the design of this class of converters and power supplies. It is pointed out that (especially for power MOSFETs where ohmic losses dominate) it is more attractive to select switching frequencies that are higher than the resonant frequency because of the possibility of nondissipative snubbers. Slowing down the rise of the gate voltage and, hence, the slow decrease of ON resistance during turn-on is also not a drawback to high-frequency switching. Because of this safer operation, the standard intrinsic diode of the power MOSFET could be used at high frequencies instead of the more expensive FREDFET