Elliptic filter

About: Elliptic filter is a research topic. Over the lifetime, 2006 publications have been published within this topic receiving 28884 citations. The topic is also known as: Cauer filter & Zolotarev filter.

Chebyshev Approximation for Nonrecursive Digital Filters with Linear Phase

Abstract: An efficient procedure for the design of finite-length impulse response filters with linear phase is presented. The algorithm obtains the optimum Chebyshev approximation on separate intervals corresponding to passbands and/or stopbands, and is capable of designing very long filters. This approach allows the exact specification of arbitrary band-edge frequencies as opposed to previous algorithms which could not directly control pass- and stopband locations and could only obtain (N - 1)/2 different band-edge locations for a length N low-pass filter, for fixed \delta_{1} and \delta_{2} . As an aid in practical application of the algorithm, several graphs are included to show relations among the parameters of filter length, transition width, band-edge frequencies, passband ripple, and stopband attenuation.

A filter family designed for use in quadrature mirror filter banks

Abstract: This paper discusses a family of filters that have been designed for Quadrature Mirror Filter (QMF) Banks. These filters provide a significant improvement over conventional optimal equiripple and window designs when used in QMF banks. The performance criterion for these filters differ from those usually used for filter design in a way which makes the usual filter design techniques difficult to apply. Two filters are actually designed simultaneously, with constraints on the stop band rejection, transition band width, and pass and transition band performance of the QMF filter structure made from those filters. Unlike most filter design problems, the behavior of the transition band is constrained, which places unusual requirements on the design algorithm. The requirement that the overall passband behavior of the QMF bank be constrained (which is a function of the passband and stop band behavior of the filter) also places very unusual requirements on the filter design. The filters were designed using a Hooke and Jeaves optimization routine with a Hanning window prototype. Theoretical results suggest that exactly flat frequency designs cannot be created for filter lengths greater than 2, however, using the discussed procedure, one can obtain QMF banks with as little as ±.0015dB ripple in their frequency response. Due to the nature of QMF filter applications, a small set of filters can be derived which will fit most applications.

Design of Analog Filters

Abstract: PREFACE 1. Introduction 1.1 Fundamentals 1.2 Types of Filters and Descriptive Terminology 1.4 Why We Use Analog Filters Problems 2. Operational Amplifiers 2.1 Operational Amplifier Models 2.2 Op-Amp Slew Rate 2.3 The Operational Amplifier with Resistive Feedback-Non-Inverting and Inverting Amplifiers 2.4 Analysis Op-Amp Circuits 2.5 Block Diagrams and Feedback 2.6 The Voltage Follower 2.7 Addition and Subtraction 2.8 Applications of Op-Amp Resistor Circuits Problems 3. First-Order Filters: Bilinear Transfer Functions and Frequency Response 3.1 Bilinear Transfer Functions and Its Parts 3.2 Realization with Passive Elements 3.3 Bode Plots 3.4 Active Realizations 3.5 The Effect of A(s) 3.6 Cascade Design 3.8 And Now Design Problems 4. Second-Order Lowpass and Bandpass Filters 4.1 Design Parameters - Q and W 4.2 The Second-Order Circuits 4.3 Frequency Response of Lowpass and Bandpass Circuits 4.4 Integrators - The Effects of A(s) 4.5 Other Biquads Problems 5. Second-Order Filters with Arbitrary Transmission Zeroes 5.1 Using Summing 5.2 By Voltage FeedForward 5.3 Cascade Design Revisited Problems 6. Lowpass Filters with Maximally Flat Magnitude 6.1 The Ideal Lowpass Filter 6.2 Butterworth Response 6.3 Butterworth Pole Locations 6.4 Lowpass Filter Specifications 6.5 Arbitrary Transmission Zeroes Problems 7. Lowpass Filters with Maximally Flat Magnitude 7.1 Lissajou Figures 7.2 The Chebyshev Magnitude Response 7.3 Location of Chebyshev Poles 7.4 Comparison of Maximally Flat and Equal-Ripple Responses 7.5 Chebyshev Filter Design Problems 8. Inverse Chebyshev and Cauer Filters 8.1 The Inverse Chebyshev Response 8.2 From Specifications to Pole and Zero Locations 8.3 Cauer Magnitude Response 8.4 Chebyshev Rational Functions 8.5 Cauer Filter Design 8.6 Comparison of the Classical Filter Responses Problems 9. Frequency Transmission 9.1 Lowpass-to-Highpass Transformation 9.2 Lowpass-to-Highpass Transformation 9.3 Lowpass-to-Band-Elimination Transformation 9.4 Lowpass-to-Multiple Passband Transformation 9.5 The Foster Reactance Function Problems 10. Delay Filters 10.1 Time Delay and Transfer Functions 10.2 Bessel-Thomson Response 10.3 Bessel Polynomials 10.4 Further Comparisons of Responses 10.5 Design of Bessel-Thomson Filters 10.6 Equal-Ripple Delay Response 10.7 Approxmating an Ideal Delay Function 10.8 Improving High-Frequency Attenuation Generating Gain Boosts Problems 11. Delay Equalization 11.1 Equalization Procedures 11.2 Equalization with First-Order Modules 11.3 Equalization with Second-Order Modules 11.4 Estimating the Number of Sections Needed for Equalization Problems 12. Sensitivity 12.1 Definition of Bode Sensitivity 12.2 Second-Order Sections 12.3 High-Order Filters Problems 13. LC Ladder Filters 13.1 Some Properties of Lossless Ladders 13.2 A Synthesis Strategy 13.3 Tables for Other Responses 13.4 General Ladder Design Methods 13.5 Frequency Transformation 13.6 Design of Passive Equalizers Problems 14. Ladder Simulations by Element Replacement 14.1 The General Impedance Converter 14.2 Optimal Design of the GIC 14.3 Realizing Simple Ladders 14.4 Gorski-Popiel's Embedding Technique 14.5 Bruton's FDNR Technique 14.6 Creativing Negative Components Problems 15. Operational Simulations of Ladders 15.1 Simulation of Lowpass Ladder 15.2 Design of General Ladders 15.3 Bandpass Ladders Problems 16. Oscillators 16.1 Unintentional Oscillators 16.2 The Oscillator Feedback Loop 16.3 Automatic Gain Control 16.4 The Wein Bridge Oscillator 16.5 The RC Phase Shift Oscillator 16.6 The Active-Bandpass-Filter Oscillator Problems 17. Transconductance-C Filters 17.1 Transconducting Cells 17.2 Elementary Transconductor Building Blocks 17.3 First- and Second-Order Filters 17.4 High-Order Filters 17.5 Automatic Tuning Problems 18. Switched-Capacitor Filters 18.1 The Moss Switch 18.2 The Switched Capacitor 18.3 First-Order Building Blocks 18.4 Second-Order Building Blocks 18.5 Sampled-Data Operation 18.6 Switched-Capacitor First- and Second-Order Sections 18.7 The Bilinear Transformation 18.8 Design of Switched-Capacitor Cascade Filters 18.9 Design of Switched-Capacitor Ladder Filters Problems REFERENCES APPENDICES A1 Introduction to MATLAB A2 Introduction to Electronics Workbench

0.5-V analog circuit techniques and their application in OTA and filter design

Abstract: We present design techniques that make possible the operation of analog circuits with very low supply voltages, down to 0.5 V. We use operational transconductance amplifier (OTA) and filter design as a vehicle to introduce these techniques. Two OTAs, one with body inputs and the other with gate inputs, are designed. Biasing strategies to maintain common-mode voltages and attain maximum signal swing over process, voltage, and temperature are proposed. Prototype chips were fabricated in a 0.18-/spl mu/m CMOS process using standard 0.5-V V/sub T/ devices. The body-input OTA has a measured 52-dB DC gain, a 2.5-MHz gain-bandwidth, and consumes 110 /spl mu/W. The gate-input OTA has a measured 62-dB DC gain (with automatic gain-enhancement), a 10-MHz gain-bandwidth, and consumes 75 /spl mu/W. Design techniques for active-RC filters are also presented. Weak-inversion MOS varactors are proposed and modeled. These are used along with 0.5-V gate-input OTAs to design a fully integrated, 135-kHz fifth-order elliptic low-pass filter. The prototype chip in a 0.18-/spl mu/m CMOS process with V/sub T/ of 0.5-V also includes an on-chip phase-locked loop for tuning. The 1-mm/sup 2/ chip has a measured dynamic range of 57 dB and draws 2.2 mA from the 0.5-V supply.

New microstrip "Wiggly-Line" filters with spurious passband suppression

Abstract: In this paper, we present a new parallel-coupled-line microstrip bandpass filter with suppressed spurious passband. Using a continuous perturbation of the width of the coupled lines following a sinusoidal law, the wave impedance is modulated so that the harmonic passband of the filter is rejected while the desired passband response is maintained virtually unaltered. This strip-width perturbation does not require the filter parameters to be recalculated and, this way, the classical design methodology for coupled-line microstrip filters can still be used. At the same time, the fabrication of the resulting filter layout does not involve more difficulties than those for typical coupled-line microstrip filters. To test this novel technique, 3rd-order Butterworth bandpass filters have been designed at 2.5 GHz, with a 10% fractional bandwidth and different values of the perturbation amplitude. It is shown that for a 47.5 % sinusoidal variation of the nominal strip width, a harmonic rejection of more than 40 dB is achieved in measurement while the passband at 2.5 GHz is almost unaltered.