Application of direct synthesis techniques to customize filters with complex frequency response

Recently, direct synthesis techniques (DSTs) have been presented for filter synthesis. Unlike conventional synthesis techniques, DSTs derive the filtering polynomials of the filters to be synthesized directly in their own frequency domain. These filtering polynomials are real coefficient so that they might find applications in various fields. Furthermore, DSTs might be used to customize filters with a more complex frequency response, such as asymmetric frequency response or multi‐band frequency response. In this paper, DSTs are compared with some well‐known filter synthesis techniques. Then, the application of DSTs in the design of lumped‐element LC filters, distributed‐element filters, active RC filters, and infinite impulse response digital filters with complex frequency response is discussed. Some examples are presented for demonstration. Copyright © 2015 John Wiley & Sons, Ltd.     

Inverse general Chebyshev bandpass filters

In this paper, the synthesis of inverse general Chebyshev bandpass filters is discussed. Unlike general Chebyshev filters that flexibly place transmission zeros to mainly control the performance of the filters in the stopband and keep constant ripple in the passband, inverse general Chebyshev filters are featured by flexible placement of reflection zeros in the passband and keep constant ripple in the stopband. Two approaches to directly derive filtering polynomials of inverse general Chebyshev bandpass filters in the bandpass domain are discussed in detail. By applying the zero‐extraction method, these filtering polynomials could be realized through appropriate networks. Finally, two examples are presented for demonstration.     

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.     

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.     

Experimental studies on realization of fractional inductors and fractional‐order bandpass filters

This paper presents the hardware realization and performance study of fractional inductors of order 0 < α < 2. The fractional inductors used in this work have been realized with the help of general impedance converter circuit and fractional capacitors. Impedance characterization of fractional inductors with different exponents has been carried out experimentally. Also a generalized approach to design a fractional‐order bandpass filter is discussed in this work. The fractional‐order bandpass filter consists of a series combination of a resistor, a fractional inductor of order 1 < α < 2, and a fractional capacitor of order 0 < β < 1. The performance of fractional‐order bandpass filters has been studied and compared with corresponding integer‐order filters through both experimentation and simulation. Copyright © 2014 John Wiley & Sons, Ltd.     

Microstrip band‐pass filters without source/load inverters

In radio frequency/microwave or even higher frequency range, various transmission‐line filters have been proposed for frequency selection. Specifically, there is a kind of transmission‐line filters not having source/load inverters. To design them is somewhat difficult, if their physical mechanism is not fully understood. In this paper, the concept of the distributed‐ to lumped‐element equivalence is applied in the synthesis of several microstrip band‐pass filters without source/load inverters. As demonstrated, it can help to reveal the physical mechanism of the filters such as how the resonances are created and coupled. In addition, the distributed‐ to lumped‐element equivalence relations between filter specifications and structural parameters are presented and good initial dimensions are calculated, which will facilitate filter design. Several examples are presented for demonstration.     

Generalized bessel polynomials with application to the design of bandpass filters with approximately flat group delay response

The continued fraction expansion of the ordinary Bessel polynomials is modified by replacing the complex frequency variable p by p/(1+γp), where γ=?0. The resulting polynomials, when a reactance transformation is applied, are capable of providing bandpass filters with an approximately flat group delay response.     

Nearly monotonic passband low‐pass filter design by using sum‐of‐squared Legendre polynomials

A new type of filter approximation, which utilizes orthonormal Legendre polynomials, referred to as sum‐of‐squared Legendre polynomials, is presented in this paper. Power transmission coefficient and the group delay of the proposed filter are compared with those of the Butterworth, Legendre–Papoulis, and Halpern filters. In order to illustrate the design of the proposed filter function, sum‐of‐squared Legendre polynomials coefficients and normalized element values of the low‐pass LC (inductor‐capacitor) ladder network prototype are given, up to the 10th degree. For continuous‐time domain filtering, doubly terminated LC ladder network topologies have very low sensitivities to changes of component values. In order to determine the effect of variation of all reactive components on the filter attenuation characteristic, the new sensitivity function has been proposed. Copyright © 2015 John Wiley & Sons, Ltd.     

新型开环耦合谐振滤波器的设计与应用

为了满足日新月异的无线通信对小型化带通滤波器的要求,针对传统类型滤波器存在线性度、矩形系数、插入损耗、体积等方面的问题,笔者介绍了一种通过在微带开环谐振滤波器中引入交叉耦合,产生一对传输极点,从而提高滤波器选择性的滤波器设计方法,并讨论了这种滤波器的综合方法和实现流程。实际设计了一个六阶开环谐振滤波器,并给出了全波仿真结果。分析和仿真都表明这种滤波器具有体积紧凑、选择性高的优点。     

Advanced filter design technique based on equivalent circuits and coupling matrix segmentation

This paper presents a technique for the efficient design of bandpass waveguide microwave filters using a segmentation technique applied to an equivalent circuit. The technique is based on first developing an equivalent circuit that synthesizes the desired transfer function. Then, the different parts of the real physical structure are optimized by segmenting this equivalent circuit. The technique was originally developed for in‐line filters, and the main contribution of this paper is in the combination of this technique with the coupling matrix formalism. In this way, we adapt for the first time this design strategy to the design of complex coupling topologies, beyond the in‐line configuration. As an example, a complex sixth‐order dual‐mode filter, implemented in all‐inductive waveguide technology, is designed using the new coupling matrix segmentation technique, showing the effectiveness of the presented theory. A prototype of the filter has been manufactured, and the accuracy of the design technique is verified by measurements on the real prototype.     

耦合微带线参差谐振带通滤波电路

对于微波集成振荡器或放大器输出端的滤波器,要求具有较好的抑制谐波性能,本文提出耦合微带线参差谐振带通滤波电路,它由半波长谐振器式平行耦合微带线单元电路与传输线段联构成,其特点是有利于对谐波输出的抑制。     

Compact third-order microstrip bandpass filter designed by the distributed- to lumped-element equivalence

In reality, it is not easy to design microstrip filters for the sake of distributed-element effect. It is an effective approach to approximate distributed-element structures through appropriate lumped-element circuits. In this paper, some basic microstrip structures are discussed, whose equivalent lumped-element circuits are derived. Then, a novel microstrip filter is obtained by connecting these microstrip structures, according to the similar topology of the third-order lumped-element bandpass filter. The equivalent lumped-element counterpart of the proposed microstrip filter clearly reveals its physical mechanism, ie, how the resonances are created and coupled and how the transmission zeros are created. Furthermore, a set of the design formulas are presented, which can be used to calculate initial structure parameters and then facilitate design process. The proposed microstrip bandpass filter can realize a third-order elliptic bandpass response with one transmission zero at each side of the passband. In addition, two short-circuited stubs are added to input/output ports to create the third transmission zero. The filter is featured by good frequency selectivity and out-of-band suppression. For demonstration, an actual example was designed, fabricated, and measured.     

Stability of sinusoidal responses of marginally stable bandpass sigma delta modulators

In this paper, we analyse the stability of the sinusoidal responses of second‐order interpolative marginally stable bandpass sigma delta modulators (SDMs) with the sum of the numerator and denominator polynomials equal to one and explore new results on the more general second‐order interpolative marginally stable bandpass SDMs. These results can be further extended to the high‐order interpolative marginally stable bandpass SDMs. Copyright © 2006 John Wiley & Sons, Ltd.     

Performance Enhancement of Tunable Bandpass Filters Using Selective Etched Ferroelectric Thin Films

The inclusion of voltage-tunable barium strontium titanate (BSTO) thin films into planar band pass filters offers tremendous potential to increase their versatility. The ability to tune the passband so as to correct for minor deviations in manufacturing tolerances, or to completely reconfigure the operating frequencies of a microwave communication system, are highly sought-after goals. However, use of ferroelectric films in these devices results in higher dielectric losses, which in turn increase the insertion loss and decrease the quality factors of the filters. This study explores the use of patterned ferroelectric layers to minimize dielectric losses without degrading tunability. Patterning the ferroelectric layers enables us to constrict the width of the ferroelectric layers between the coupled microstrip lines, and minimize losses due to ferroelectric layers. Coupled one-pole microstrip bandpass filters with fundamental resonaces at ～7.2 GHz and well-defined harmonic resonances at ～14.4 and ～21.6 GHz, were designed, simulated and tested. For one of the filters, experimental results verified that its center frequency was tunable by 528 MHz at a center frequency of 21.957 GHz, with insertion losses varying from 4.3 to 2.5 dB, at 0 and 3.5 V/ w m, respectively. These data demonstrate that the tuning-to-loss figure of merit of tunable microstrip filters can be greatly improved using patterned ferroelectric thin films as the tuning element, and tuning can be controlled by engineering the ferroelectric constriction in the coupled sections.     

Selective digital filters with quadratic phase

A method for design of a new class of digital infinite impulse response filters realized as parallel connection of two all‐pass filters is presented in this paper. A new approach to approximation of quadratic phase of all‐pass filter at all frequencies is given. Chosen parallel structure offers opportunity for realization of filters with arbitrary shape phase. The presented algorithm is based on all‐pass filter phase approximation. Phases of both all‐pass filters approximate ideal quadratic phase in minimax sense at all frequencies. Such filters can be applied for chirp signal compression or expansion. Magnitude characteristic of described filters is very selective and elliptic‐like. Obtained filters are compared with elliptic filter and group delay corrector in cascade. For the same specifications, much better results are achieved by the proposed filters. Parallel connection of all‐pass filters introduces lower signal delay, and for a given maximal phase, approximation error demands less complex network. Examples to illustrate the proposed method are given. Copyright © 2016 John Wiley & Sons, Ltd.     

On a class of cross coupled fully differential filters

In this paper, a class of cross‐coupled differential filters is presented. The filters implemented are second order, using two transistors cross‐coupled surrounded by passive RLC components. The input of each filter is differential and so is its output. Biasing of each filter is straightforward, and the stability of the filters is examined. Several of the filters were built experimentally using discrete components and simulated using SPICE in a 0.18 µm Taiwan Semiconductor Manufacturing Company (TSMC) complementary metal‐oxide semiconductor (CMOS) process, confirming the validity of the filters. Copyright © 2015 John Wiley & Sons, Ltd.     

Optimal design of lattice wave digital fractional‐order Butterworth filter

This letter presents the design of digital fractional‐order Butterworth filter (DFOBF) of order (n+α) , where n is an integer, and α ∈ (0,1) , from the perspective of optimal realization. The magnitude–frequency characteristic of the DFOBF is optimally modeled using the computationally efficient lattice wave digital filters (LWDFs). Design examples for the third‐ and fifth‐order LWDF‐DFOBFs with various values of n, α_, and cut‐off frequencies are presented.     

Fractional‐order electronically controlled generalized filters

Novel topologies of fractional‐order generalized filters are introduced in this paper. These offer the following benefits: (1) realization of lowpass, highpass, bandpass, allpass, or bandstop filter functions by the same topology; (2) resistorless realizations; (3) electronic adjustment of their frequency characteristics as well as their order; and (4) employment of only grounded capacitors. All the above have been achieved using Operational Transconductance Amplifiers as active elements and appropriate multi‐feedback topologies. The behavior of the proposed designs is verified through simulation results using the Cadence IC design suite and the Design Kit provided by the Austrian Micro Systems 0.35‐µm complementary metal–oxide–semiconductor process. Copyright © 2016 John Wiley & Sons, Ltd.     

On orthogonal realizations for adaptive IIR filters

Convergence speed is one of the main concerns in adaptive IIR filters. Fast convergence can be closely related to adaptive filter realization. However, with the exception of the lattice realization that is based on the nice properties of Szëgo orthonormal polynomials, no other adaptive IIR filter realization using orthonormal characteristics seems to be extensively studied in the literature. Furthermore, many orthogonal realizations for adaptive FIR filters, that are particularly suitable for rational modelling, have been proposed in the past years. Since rational orthogonal basis functions are a powerful tool for efficient system representation they seem attractive for adaptive IIR filters. In this paper, we present some theoretical results related to the properties of a generalized orthonormal realization when used for mean‐square output error minimization in a system identification application. One result is related to the low computational complexity of the updating gradient algorithm when some properties of the orthonormal realization are used. An additional result establishes conditions for the stationary points of the proposed updating algorithm. In order to confirm the expected performance of the new realization, some simulations and comparisons with competing realizations in terms of computational complexity and convergence speed are presented. Copyright © 2000 John Wiley & Sons, Ltd.     

Microstrip bandpass filter design using split‐path method and optimized curvature corrections

Bandpass filters with wide pass‐band are an essential requirement in various equipments of satellite and defence communication sectors. Here a method of split‐path interactions is proposed to approximately predict the resonant frequency and topology of bandpass filters which otherwise fall under the category of heuristic designs. Curved transmission lines are often required to make filter structures physically compact; however, curvature effects create errors in the theoretical (design) prediction of resonant or central frequencies for bandpass filter design. Earlier propositions on curvature corrections had been considerably precise, but recent design standards demand even higher accuracies. The prime feature of this work is the use of a meta‐heuristic optimization (i.e. Particle Swarm Optimization) technique in curvature corrections for the first time which brings accuracies of over 99% in the corrected results. The split paths used in this design are suitably curved, with the proposed optimized curvature correction technique, so as to attain a compact size of the filter. The resulting filter has a low insertion loss of around −1.00 dB and a sharp stopband cut‐off. Fabrication was done on a FR4 microstrip substrate with a good agreement between measured and simulated results. Copyright © 2015 John Wiley & Sons, Ltd.