A modified Chebyshev bandpass filter with attenuation poles in thestopband

This paper describes a design method of a modified Chebyshev bandpass filter with attenuation poles in the stopband. The insertion of attenuation poles into resonators in the authors' bandpass-filter design is accomplished by connecting a lumped inductor or capacitor in series with a shunt-type coaxial transmission-line resonator. The inserted poles which are distributed over the stopband can be chosen such that the insertion loss of the filter has equiripple characteristic and maximum attenuation in the stopband with the given number of attenuation poles. The modified Chebyshev bandpass filter designed by this method can be effectively used in diplexer design     

Designing IIR filters with a given 3-dB point

Often in infinite impulse response (IIR) filter design, our critical design parameter is the cutoff frequency at which the filter's power decays to half (-3 dB) the nominal passband value. This article presents techniques that aid in the design of discrete-time Chebyshev and elliptic filters given a 3-dB attenuation frequency point. These techniques place Chebyshev and elliptic filters on the same footing as Butterworth filters, which traditionally have been designed for a given 3-dB point. The result is that it is easy to replace a Butterworth design with either a Chebyshev or an elliptic filter of the same order and obtain a steeper rolloff at the expense of some ripple in the passband and/or stopband of the filter.     

Compact Structure With Three Attenuation Poles for Improving Stopband Characteristics

A novel compact structure with three controllable finite attenuation poles at stopband is presented. The new structure is composed of a pair of symmetrical parallel coupled-lines and a capacitive load. With this configuration, three finite attenuation poles are available, which can improve the stopband characteristics of low-pass filters (LPFs) or the upper stopband performances of band-pass filters. The research method is based on a transmission-line model for tuning the finite attenuation poles. In order to examine the feasibility of the proposed structure, a new type of LPF with broad stopband and sharp cutoff frequency response is designed, fabricated, and measured. The experimental results of the fabricated circuit agree well with the simulation and analytical ones     

Filters with Single Transmission Zeros at Real or Imaginary Frequencies

A new unified theory is presented for the synthesis of exactly equiripple low-pass prototypes having: a) one simple pole of attenuation at a real frequency; or b) a single pair of real-axis transmission zeros (giving linear-phase performance). These types of filters may be regarded as representing the least possible degree of complication over the conventional Chebyshev filter, and are usually realized with one extra cross coupling in the structure. It is demonstrated that this gives much improved skirt selectivity in the case of a finite frequency pole, making it a viable intermediate case between the Chebyshev and elliptic function filters, while in the case of real-frequency zeros, very flat group delay over 50 percent of the passband is achieved with minimal cost in insertion loss and skirt rejection. Approximate and exact synthesis techniques are described, including results for the previously neglected odd-degree case. Experimental results demonstrate agreement with theory.     

A new method for the design of IIR filters with flat magnitude response

This paper presents a new direct design of infinite-impulse response (IIR) filters with a flat magnitude response in both passband and stopband (Butterworth filters). The design specifications are passband and stopband frequencies and passband droop and stopband attenuation. The approach is based on an allpass filter with flatness at frequency points /spl omega/=0 and /spl omega/=/spl pi/. Depending on the parity of the IIR filter order, the allpass filter is either real or complex. However, in both cases, the resulting IIR filter is real.     

Photonic bandpass filters with high skirt selectivity and stopband attenuation

A new photonic signal processor topology that simultaneously achieves both a high-Q and a high skirt selectivity and stopband attenuation filter response is presented. It is based on a novel dual-cavity bandpass optical structure in which two pairs of active fiber Bragg grating cavities are used with an optical gain offset to control the poles and stopband attenuation characteristics of the filter. This concept enables a large improvement in the filter stopband attenuation, rejection bandwidth, and skirt selectivity to be realized. Measured results demonstrate both a narrow bandpass bandwidth of 0.4% of center frequency and a skirt selectivity factor of 16.6 for 40 dB rejection, which corresponds to a 6.5-fold improvement in comparison to conventional single cavity high-Q structures. To our knowledge, this is the best skirt selectivity reported for a photonic bandpass filter to date. The new photonic filter structure has been experimentally verified and excellent agreement between measured and predicted responses is shown.     

Design of maximally flat sharp cutoff low-pass filters

A method is given for obtaining the parameters of a maximally flat sharp cutoff low-pass filter with coincident multiple transmission zeros, which satisfies arbitrary passband and stopband specifications.     

切比雪夫低通滤波器的仿真设计

设计了一个切比雪夫低通滤波器,切比雪夫滤波器的通带内有纹波,阻带内衰减快,它是以通带内的波纹换取截止频率处的最大衰减。波纹越大,截止频率处的衰减越大。该设计方案能达到较好的滤波效果,并用电路仿真软件对其进行了仿真,仿真结果非常接近于理想滤波器的频率响应曲线。     

All-pass-based design of nearly-linear phase IIR low-pass differentiators

ABSTRACT

A new approach to the design of the nearly linear phase infinite impulse response low-pass differentiators using a parallel all-pass structure is discussed in this paper. The magnitude and phase responses of the proposed low-pass differentiators are first formulated as functions of the phase responses of the corresponding all-pass filters, and a set of equations is derived such that the magnitude response approximates the ideal one in the weighted Chebyshev sense both in the passband and the stopband. The maximum passband phase response linearity error is shown to be related to the maximum passband magnitude error and the value of an additional design parameter. Comparison with the existing nearly-linear phase infinite impulse response low-pass differentiators shows that the low-pass differentiators designed using the proposed method usually require less multiplications, which comes at the cost of a somewhat higher filter order and consequently higher group delay. However, as the reduced number of multiplications lead to lower power consumption if hardware implementation is considered, the proposed low-pass differentiators are an attractive alternative in applications where low group delay is not of crucial importance.     

Optimal Design of 2D FIR Filters with Quadrantally Symmetric Properties Using Fractional Derivative Constraints

In this article, an optimal design of two-dimensional finite impulse response (2D FIR) filter with quadrantally even symmetric impulse response using fractional derivative constraints (FDCs) is presented. Firstly, design problem of 2D FIR filter is formulated as an optimization problem. Then, FDCs are imposed over the integral absolute error for designing of the quadrantally even symmetric impulse response filter. The optimized FDCs are applied over the prescribed frequency points. Next, the optimized filter impulse response coefficients are computed using a hybrid optimization technique, called hybrid particle swarm optimization and gravitational search algorithm (HPSO-GSA). Further, FDC values are also optimized such that flat passband and stopband frequency response is achieved and the absolute \(L_1\)-error is minimized. Finally, four design examples of 2D low-pass, high-pass, band-pass and band-stop filters are demonstrated to justify the design accuracy in terms of passband error, stopband error, maximum passband ripple, minimum stopband attenuation and execution time. Simulation results have been compared with the other optimization algorithms, such as real-coded genetic algorithm, particle swarm optimization and gravitational search algorithm. It is observed that HPSO-GSA gives improved results for 2D FIR-FDC filter design problem. In comparison with other existing techniques of 2D FIR filter design, the proposed method shows improved design accuracy and flexibility with varying values of FDCs.     

Classes of Sub-Miniature Microwave Printed Circuit Filters with Arbitrary Passband and Stopband Widths

Four new classes of microwave bandpass filters are defined herein. They are realized in triplate stripline and are exceedingly small devices as a result of using transmission line elements which are a quarter-wavelength well above the frequency of the passband. Each filter corresponds to a bandpass S-plane prototype which is derived using exact synthesis procedures from a specification of transmission zero locations. Passband and stopband widths may be independently specified and an extremely high degree of selectivity can be achieved when necessary. The slope of a filter skirt can he chosen to be such that 60 dB of attenuation is reached at a frequency < 3 percent from the comer of the passband.     

Optimal Use of Some Classical Approximations in Filter Design

The classical Butter worth, Chebyshev and Elliptic (Cauer) low-pass filter approximations can be used in the design of analog and IIR digital filters in such a way as to obtain passband, stopband and transition band optimized filters at no order cost. The exact analytical relationships for such an optimal deployment of these approximations are developed and presented in this paper and their use is demonstrated through design examples.     

All-pole transitional Bessel-Chebyshev filters

A new family of all-pole equiripple transitional Bessel-Chebyshev filters is derived. These filters have improved delay characteristics in comparison with Chebyshev phase characteristics and can provide more attenuation in the stopband than Butterworth filters. Design information in tabular form is given for filters up to 10th-order.<>     

Least-squares monotonic lowpass filters with sharp cutoff

A new class of lowpass-filter functions with no finite zeros and a monotonic magnitude response is first derived by using a least-squares norm to minimise the passband attenuation, and these filter functions are then augmented by adding one pair or multiple pairs of j?-axis zeros. The magnitude characteristics of these filters are compared with those of the generalised inverse Cheby?shev filters and are found to be superior, both in the passband and in the stopband.     

基于SIW技术的毫米波滤波器研究与设计

基于基片集成波导（substrate integrated waveguide,SIW）结构设计了两款四阶的耦合带通滤波器,使用三维全波电磁场仿真软件HFSS对设计的两款滤波器进行了仿真设计和优化.由仿真结果分析得出,两款滤波器的工作频率均位于毫米波频段.第一款SIW滤波器实现了切比雪夫型响应,中心频率为20 GHz,带宽为2 GHz,通带内的插入损耗低于1.5 dB,回波损耗低于-20 dB,在阻带中对信号的衰减程度可以达到50 dB.第二款SIW滤波器实现了准椭圆函数型的响应,中心频率为29.1 GHz,带宽为300 MHz,通带内的插入损耗低于1 dB,回波损耗低于-20 dB,在通带到阻带的过渡中实现了两个陷波点.仿真结果表明,在毫米波滤波器设计中引入SIW结构,有利于优化滤波器尺寸,得到较好的滤波器性能指标,是毫米波滤波器发展的一个重要方向.     

Compact U-shaped dual planar EBG microstrip low-pass filter

In this paper, a novel high-performance compact dual planar electromagnetic bandgap (DP-EBG) microstrip low-pass filter with a U-shaped geometry is proposed. By employing the unique DP-EBG configuration and the U-shaped geometry of the microstrip line (MLIN), the proposed structure achieves a wide stopband with high attenuation and a high selectivity within a small circuit area. Its passband ripple level is low due to the U-shaped geometry and the electromagnetic bandgap (EBG) structure with square patches inserted at the bends of the MLIN. The Chebyshev tapering technique is used to taper components of the proposed structure in order to eliminate ripples caused by the EBG periodicity. The structure was fabricated and the measured results are in good agreement with the simulated results. This novel design demonstrates superior low-pass filtering functionality and can easily be applied to monolithic circuits.     

Narrow-Band Stripline or Microstrip Filters with Transmission Zeros at Real and Imaginary Frequencies

Simple approximate design equations are derived in this paper for an even degree (n /spl ges/ 6) low-pass inverter capacitance prototype filter having single transmission zeros at both real and imaginary frecuencies. This is achieved by utilizing one or two additional couplings. The transmission zeros improve considerably the passband group delay and increase the skirt selectivity compared to those of the ordinary Chebyshev prototype. An exact and more complicated method based on the known generalized Chebyshev rational function approximation is also presented for the comparison. The prototype with one additional coupling is utilized to realize narrow-bandpass printed circuit filters consisting of half-wave resonators.     

An improved method for the design of quadrature mirror filter banks using the Levenberg–Marquardt optimization

This paper presents an improved and efficient method for the design of a two-channel quadrature mirror filter (QMF) bank. In the proposed method, the filter bank design problem is formulated as a low-pass prototype filter design problem, whose responses in the passband and stopband are ideal and their filter coefficients value at quadrature frequency is 0.707. A new method is developed for the design of a low-pass prototype filter which minimizes the objective function by optimizing the filter taps weights using the Levenberg–Marquardt method. When compared with other existing algorithms, it significantly reduces peak reconstruction error (PRE), error in passband, stopband and transition band. Several design examples are included to show the increased efficiency and the flexibility of the proposed method over existing methods. An application of this method is considered in the area of subband coding of the ultrasound images.     

基于Matlab的模拟滤波器设计与仿真

巴特沃思、切比雪夫模拟低通滤波器通常是设计模拟高通、带通和带阻滤波器的原型,先按给定频率响应巴特沃思、切比雪夫低通Ha（s）逼近,然后由选定Ha（s）实现二端口网络的电路结构和参数值。在此对达林顿T型和П型电路结构的滤波器元件参数进行了编程计算,并对其系统函数的幅频特性进行仿真。仿真结果符合设计要求,该方法便捷,程序具有可扩展性。     

Quasi-elliptic compact high-power notch filters using a mixedlumped and distributed circuit

A quasi-elliptic notch filter response is defined as one in which the ultimate stopband depth is sacrificed in favor of a faster transition from the passband to a specified minimum equiripple stopband attenuation level (i.e., steeper attenuation slope) with no increase in filter order (as compared to a Chebyshev or similar transfer function design). Such notch-filter responses can be achieved if the topology synthesized includes arbitrary frequency invariant impedances and line lengths in the main series line of filters. Using lumped approximations to the series coaxial sections but with the series sections not at 50 Ω (for a 50-Ω filter), it is possible to improve upon the Chebyshev-based results. The resulting network provides lower passband insertion loss, with no reduction in minimum notch depth or power handling, improved temperature performance and additional harmonic reduction. The improvements are due to the implementation of the quasi-elliptic response defined above, and are made possible by the larger range of main line impedances and line lengths available using inductors and capacitors rather than lengths of transmission line. In principle, the technique can be extended to achieve full-elliptic responses