The modified Pascal polynomial approximation and filter design method

Polynomial approximations are extensively used in analog and IIR digital filter design. In this paper, a comprehensive filter design and an optimization procedure are presented explicitly using a filter‐appropriate modified Pascal polynomial. The so‐designed all‐pole Pascal filters exhibit non‐equiripple passband and monotonic transition and stopband responses. The order of the new Pascal filters is calculated from the order inequality which, although it cannot be analytically solved, leads to a nomograph that has been created and is presented here. Inevitably, the mathematical complexity introduced by the nature of the Pascal polynomials makes the analytical expression of the poles of the transfer function unfeasible and for that reason poles are given by means of appropriate tables. The design method is demonstrated in several detailed examples and Pascal filters are compared with their all‐pole counterparts, Butterworth and Chebyshev, over which they reveal certain advantages and disadvantages. Copyright © 2010 John Wiley & Sons, Ltd.     

Minimal two‐transistor multifunction filter design

This paper presents a comprehensive method and analysis on the design of two‐transistor multi‐output filters where three possible functions are simultaneously available. Although two transistors are employed at its core, proper biasing does not require additional passive components. A total of thirteen valid second‐order filters are reported, and several of them are experimentally tested using discrete transistors as well as simulated using Spectre in a BiCMOS process. A fully differential realization of a MOS‐C band‐pass filter, based on one of the structures found, is designed and then used to realize a fourth‐order Chebyshev band‐pass filter. Copyright © 2017 John Wiley & Sons, Ltd.     

Ladder tuning‐block partitioned filters for simplified tuning

In this paper, we present a procedure for the design of low‐sensitivity, active‐RC filters that permits efficient functional tuning during the manufacturing process. Filters with finite zeros, such as elliptic (Chebyshev–Cauer) low‐pass filters are primarily considered, although the method can be applied to the design of other filters, e.g. allpole filters, as well. We show how to partition a given ladder filter into two parts. The first is a ladder filter of reduced order compared to the original; the second is a second‐ or third‐order active‐RC filter section, the ‘tuning block’, which, alone is used to tune the overall filter. The ladder, the components of which are fixed, provides most of the selectivity, while the cascaded tuning block determines the band‐edge characteristics and can be tuned relatively easily. A detailed design procedure for the filter partitioning is given. By obtaining a doubly terminated ladder filter, which is cascaded with a tuning block, both the inherent low sensitivity of the ladder and the tunability of the tuning block, are maintained. A Monte Carlo analysis of the partitioned filter demonstrates that the low sensitivity with respect to component tolerances, achievable by maintaining a doubly terminated ladder structure for the larger partitioned part of the filter, is preserved. Copyright © 2012 John Wiley & Sons, Ltd.     

Monotonic,critical monotonic,and nearly monotonic low‐pass filters designed by using the parity relation for Jacobi polynomials

A new class of continuous‐time low‐pass filter using a set of Jacobi polynomials, with all transmission zeros at infinity, is described. The Jacobi polynomial has been adapted by using the parity relation for Jacobi polynomials in order to be used as a filter approximating function. The resulting class of polynomials is referred to as a pseudo Jacobi polynomials, because they are not orthogonal. The obtained magnitude response of these filters is more general than the magnitude response of the classical ultraspherical filter, because of one additional degree of freedom available in pseudo Jacobi polynomials. This additional parameter may be used to obtain a magnitude response having either smaller passband ripples or sharper cutoff slope. Monotonic, critical monotonic, or nearly monotonic passband filter approximating functions can be also generated. It is shown that proposed pseudo Jacobi polynomial filter approximation also includes the Chebyshev filter of the first kind, the Chebyshev filter of the second kind, the Legendre filter, and many transitional filter approximations, as its special cases. Several examples are presented, and detailed formulas including the practical suggestions for their efficient implementation are also provided. The proposed nearly monotonic filter is compared with the least‐square‐monotonic filters, designed as critical monotonic, in details. The advantages of the new filters are discussed. Copyright © 2017 John Wiley & Sons, Ltd.     

Design nearly equiripple FIR filter by gradient scheme with dynamic step size

This paper proposes a gradient‐based algorithm with dynamic step size to design the nearly equiripple finite impulse response (FIR) filter, which iteratively updates the filter coefficient vector along the negative gradient direction of the peak approximation error. Moreover, besides the direction, the step size for updating is also an important parameter to be determined, and this paper proposes a dynamic method to find an appropriate step size at each round of iteration. Our results show that this dynamic step‐size scheme achieves a fast convergence rate, i.e. it can, i.e. it can design the nearly equiripple filters within a number of iterations. Specifically, by using the proposed method, the updating step size is relatively large at the early stage of iterations, which reduces the peak approximation error significantly. While, at the later stage of iterations, the updating step size becomes relatively small to approach to the equiripple solution as soon as possible. The extensive computer simulation demonstrates that the proposed algorithm outperforms the conventional algorithm in terms of the iteration number, the convergency and the performance. Copyright © 2013 John Wiley & Sons, Ltd.     

低互感高品质因素无源滤波器的优化设计分析

为降低无源滤波器中三相电抗器互感对单调谐滤波器滤波效果的影响,通过理论分析表明,将其严格按照水平三角方式排列摆放,可有效抑制相间电抗器互感;采用考虑无源滤波器性能和系统总成本的多目标模糊优化方法设计无源滤波器参数,能将多个优化目标转换为单目标的优化求解问题,设计出具有低互感高品质因素的无源滤波器,混合型滤波器系统。新方案投入运行后,取得了较好的现场效果。     

Direct synthesis technique (DST) for complex general Chebyshev filters

Recently, we discussed the concept of direct synthesis technique (DST), in which real‐coefficient filtering polynomials containing all information of the filters to be synthesized are derived directly for realization, and they could find applications in the design of lumped‐element LC filters, active RC filters, and infinite impulse response digital filters. In this paper, another DST for complex general Chebyshev bandpass filters is discussed, which is based on a complex mapping relation and featured by complex‐coefficient filtering polynomials. It is called as complex DST in this paper. Compared with real‐coefficient filtering polynomials whose polarities are determined by the number of their zeros at zero frequency, the polarities of complex‐coefficient filtering polynomials can be easily changed by multiplying imaginary unit j . Such advantage might make their realization more flexible. The analysis shows that conventional coupling matrix could be considered as narrow‐band approximation of network matrix derived by complex DST in the normalized frequency domain. In order to demonstrate the validity of complex DST in this paper, it is applied in the design of classic parallel‐coupled microstrip bandpass filters. Compared with conventional synthesis techniques, complex DST could find out better dimensions and provide more choices for realization and synthesize both even‐order and odd‐order parallel‐coupled microstrip bandpass filters. Copyright © 2017 John Wiley & Sons, Ltd.     

Approximate Synthesis of a Higher‐Order Passive Complex Coefficient Filter Using Autotransformers

In this paper, a new method for synthesizing a higher‐order passive complex filter using autotransformers is proposed. The proposed filter can be synthesized approximately by transforming the conventional one. Since the proposed transformation replaces all transformers with autotransformers, the proposed filter has no floating windings. As examples, both first‐order and third‐order complex filters are synthesized. The validity of the proposed method was confirmed through computer simulation and experiment. Due to approximate synthesis, the transfer function of the real output is different from that of the imaginary output. However, both of them have roughly the same response near the passband. Experimental results show good agreement with the theoretical value. It means that the proposed method is valid for the practical application.     

基于改进型Butterworth传递函数的高阶低通滤波器的有源设计

基于改进型Butterworth传递函数,提出了一种设计高阶低通滤波电路的方法.推导出奇数高阶低通滤波电路是1个一阶Butterworth低通滤波电路和若干个二阶滤波网络的级联,偶数高阶低通滤波电路是若干个二阶滤波网络的级联,给出设计高阶低通滤波电路元件参数的计算公式,利用这些公式可简单快速地设计出满足技术要求的任意高阶低通滤波电路.     

Direct synthesis techniques for general Chebyshev filters: lowpass,highpass, and bandstop cases

Conventional synthesis techniques for general Chebyshev lowpass, highpass, and bandstop filters are usually based on general Chebyshev filtering function, from which lowpass prototype is set up. By applying the lowpass to lowpass, highpass, or bandstop frequency transformation on realization networks of lowpass prototypes, final realization networks of general Chebyshev lowpass, highpass, and bandstop filters are obtained. In this paper, direct synthesis techniques for general Chebyshev lowpass, highpass, and bandstop filters are discussed. Transmission zeros can be placed wherever they are desired to control the performance of the filters. Unlike conventional synthesis techniques, they derive filtering polynomials constituting network parameters directly in the lowpass, highpass, or bandstop domain, which might find applications in analogue and digital filter design. Several examples are presented for demonstration. Copyright © 2015 John Wiley & Sons, Ltd.     

Optimal analog active filter design using craziness‐based particle swarm optimization algorithm

Because of the manufacturing constraints, the optimal selection of passive component values for the design of analog active filter is very critical. As the search on possible combinations in preferred values for capacitors and resistors is an exhaustive process, it has to be automated with high accuracy within short computation time. Evolutionary computation may be an attractive alternative for automatic selection of optimal discrete component values such as resistors and capacitors for analog active filter design. This paper presents an efficient evolutionary optimization approach for optimal analog filter design considering different topologies and manufacturing series by selecting their component values. The evolutionary optimization technique employed is craziness‐based particle swarm optimization (CRPSO). PSO is very simple in concept, easy to implement and computationally efficient algorithm with two main advantages: fast convergence and only a few control parameters. However, the performance of PSO depends on its control parameters and may be influenced by premature convergence and stagnation problem. To overcome these problems, the PSO algorithm has been modified to CRPSO and is used for the selection of optimal passive component values of fourth‐order Butterworth low‐pass analog active filter and second‐order state variable low‐pass filter, respectively. CRPSO performs the dual task of efficiently selecting the component values as well as minimizing the total design errors of low‐pass active filters. The component values of the filters are selected in such a way so that they become E12/E24/E96 series compatible. The simulation results prove that CRPSO efficiently minimizes the total design error with respect to previously used optimization techniques. Copyright © 2014 John Wiley & Sons, Ltd.     

Quasi-passive filter for harmonic filtering

To overcome the limitations of conventional shunt passive filters, a quasi-passive filter has been proposed in this paper. It comprises of a parallel and series tuned LC tank circuit. Unlike the conventional shunt passive filter, the quasi-passive filter utilizes a large value ac capacitor. Unipolar dc capacitors and power semiconductor devices are used to realize the large value ac capacitor. The operation of the quasi-passive filter is simple and it does not require the complex control methods of active power filters. The proposed quasi-passive filter is verified through analysis and simulation.     

谐波治理中无源滤波装置的设计与应用

结合实例,对无源滤波装置的设计进行了理论分析,采用滤波装置设计专用仿真软件对分析结果进行仿真验证。仿真结果及实际运行效果证明,无源滤波装置能够有效解决谐波污染问题,且具有结构简单、操作方便等优点。     

无源电力滤波器及其实用化设计软件包

对无源电力滤波器的各种设计方法进行了分析，提出了工程设计中宜采取的谐波滤波方案；开发了电力滤波器实用化设计软件包，为滤波器设计提供了有力的工具。最后还以某冶炼厂为例进行了应用校验，获得了理想的设计结果。     

Design of IIR linear‐phase nonuniform‐division filter banks with signed powers‐of‐two coefficients

This paper deals with the minimax design of two‐channel linear‐phase (LP) nonuniform‐division filter (NDF) banks using infinite impulse response (IIR) digital all‐pass filters (DAFs) with signed powers‐of‐two (SPT) coefficients. Based on the theory of two‐channel NDF banks using two IIR DAFs, the design problem is appropriately formulated to result in an appropriate Chebyshev approximation for the desired phase responses of the IIR DAFs. Through a frequency sampling and iterative approximation method, the optimization problem for finding the SPT coefficients for the IIR DAFs can be solved by utilizing a weighted least‐squares approach in conjunction with a coordinate rotational digital computer (CORDIC) algorithm. The resulting two‐channel SPT coefficient NDF banks can possess approximately LP response without magnitude distortion. Several simulation examples are presented for illustration and comparison. Copyright © 2008 John Wiley & Sons, Ltd.     

An efficient procedure to design passive LCL-filters for active power filters

Variable high switching frequencies in grid-connected active power filters could lead to low harmonic performance and expose power systems to EMI issues too. A low-pass passive LCL-filter is usually used to interconnect a power electronic converter to a grid system. (This can also be done by using a passive L-filter.) Nevertheless, designing an LCL-filter is not simple because of high compensating bandwidth and variable frequency modulations involved in active filters. This paper examines various effective conditions on designing this kind of passive LCL-filters. Then it will propose a comprehensive design procedure in which both the outcomes of the active filter and the network obligations are taken into account. Principal advantages of this proposal are reduction of power losses of the passive filter, lowering the converter’s switching ratings and the simplicity of the suggested design algorithm. A typical grid-connected shunt active filter is considered, and the needed interconnecting LCL-filter is designed using the proposed method. Then, the whole system is simulated with SIMULINK to verify the discussed procedure. Simulations confirm substantial reduction in power losses and converter current ratings.     

Optimal design of third‐order microstrip bandpass filters by direct synthesis technique (DST)

To design microstrip filters is not easy for the sake of their distributed‐element effect. Undoubtedly, to understand their physical mechanism is very important to their design. In this paper, one effective approach to design some third‐order microstrip bandpass filters with each of 2 transmission zeros at each side of the passband is discussed. Lumped‐element equivalent circuits are used to represent these microstrip filters. Then, these lumped‐element equivalent circuits can be synthesized by direct synthesis technique we recently proposed, so that it is likely to calculate initial structural parameters of these microstrip filters and then facilitate their design. Verified by the measured results of the filter designed through the approach in this paper, the performance of the filters is close to ideal frequency responses. Furthermore, another third‐order microstrip bandpass filter is presented, in which open‐circuited stubs at input/output ports are introduced to suppress one specified harmonic to improve out‐of‐band attenuation.     

An explicit form of all‐pole filter function with decreasing envelope of the summed sensitivity function

In this paper, the all‐pole lowpass filter function with the decreasing envelope of the summed sensitivity in the pass‐band is considered. The filter transfer function with maximal number of the ripples of the summed sensitivity in the pass‐band is obtained in the explicit form, by the application of the Chebyshev polynomials of the first kind. The slope of the decrease of the summed sensitivity envelope can be controlled by a free‐parameter α. We derived a new approximation function in order to achieve small summed sensitivity in the filter pass‐band. Consequently, the sensitivity analysis was carried out and a comparison of the summed sensitivity and the group delay with respect to the classic all‐pole filters was given. The approach presented in this paper is based on that the minimization of the summed sensitivity is important for the reduction of the deviation of the magnitude response caused by temperature changes of the continuous‐time active filters implemented into the analog front end or as programmable chips. Copyright © 2010 John Wiley & Sons, Ltd.     

分次补偿方式的并联型混合电力滤波器研制

介绍了由有源电力滤波器和无源滤波器并联构成混合滤波系统的工作原理，分析了有源和无源滤波器并联补偿谐波时谐波电流分配的问题，提出采用分次补偿的控制策略，并对系统控制策略的软件方法和控制电路的硬件实现进行了阐述。在此基础上研制了一台250kVA／380V并联混合型电力滤波器装置。该装置已应用于治理中频炉负载的工业现场。仿真和现场应用结果表明，采用该控制方法，可以在保证良好的补偿特性的同时，有效减少有源滤波器部分的容量，从而降低了整个装置的成本，更加适用于治理中大容量谐波负载的场合。     

Efficient optimization‐oriented design methodology of high‐order 3‐D filters using 2‐D and 3‐D electromagnetic simulators

This paper proposes a computationally highly efficient interface between two‐dimensional (2‐D) and three‐dimensional (3‐D) electromagnetic (EM) simulators for the optimization‐oriented design of high‐order 3‐D filters. In a first step, the novel optimization‐oriented design methodology aligns the 3‐D EM simulator response with the 2‐D EM simulator response of a low‐order 3‐D filter by using an inverse linear space mapping optimization technique. Then, a second mapping performs a calibration with the optimal 2‐D and 3‐D design parameters obtained from the first mapping. The optimization of high‐order filters is carried out using only the efficient 2‐D EM simulator, and the calibration equations directly give the design parameters of the 3‐D filter. The potential and the effectiveness of the proposed optimization‐oriented design methodology are demonstrated through the design of C‐band 3‐D evanescent rectangular waveguide bandpass filters with increasing orders from three to eight. Copyright © 2014 John Wiley & Sons, Ltd.