Butterworth filter

About: Butterworth filter is a research topic. Over the lifetime, 6187 publications have been published within this topic receiving 69070 citations.

Low-pass filters realizable as all-pass sums: design via a new flat delay filter

Abstract: This paper describes a new class of maximally flat low-pass recursive digital filters. The filters are realizable as a parallel sum of two all-pass filters, a structure for which low-complexity low-noise implementations exist. Note that, with the classical Butterworth filter of degree N which is retrieved as a special case, it is not possible to adjust the delay (or phase linearity). However, with the more general class of filters described in this paper, the adjustment of the delay becomes possible, and the tradeoff between the delay and the phase linearity can be chosen. The construction of these low-pass filters depends upon a new maximally flat delay all-pole filter, for which the degrees of flatness at /spl omega/=0 and /spl omega/=/spl pi/ are not necessarily equal. For the coefficients of this flat delay filter, an explicit solution is introduced, which also specializes to a previously known result.

Integrated filter construction

Abstract: A harmonic filter is added to a radio frequency filter comprising at least one transmission line resonator (R1; R2; R3) to filter harmonic multiples of the filter's operating frequency. Coupling to the harmonic filter occurs through matching couplings and transmission lines (7; L1 to L9; L20; L28) in the filter or via the electromagnetic field of said transmission line resonator (R1; R2; R3). The harmonic filter advantageously comprises striplines (L13 to L19; L21 to L27; L29 to L49) manufactured in conjunction with the other stripline structures in the filter.

Impedance-Transforming Symmetric and Asymmetric DC Blocks

Abstract: Design formulas of symmetric and asymmetric dc blocks are presented for achieving Chebyshev and Butterworth frequency responses. They can also be used for impedance transformers. Design formulas of symmetric dc blocks are first derived and those of asymmetric dc blocks are also computed based on the symmetric ones. For easy derivation of design formulas of the symmetric dc blocks, coupling coefficient, being proportional to bandwidth, is defined. It is then clarified that symmetric Chebyshev dc blocks are not possible for the impedance transforming. For the symmetric Butterworth dc blocks, three design methods are exploited. To verify the symmetric Butterworth dc blocks, a microstrip dc block with 50- and 25-Ω termination impedances designed at a center frequency of 2 GHz was fabricated. The measured S12 = S21 and S11 = S22 are - 0.19 and - 57 dB around 2 GHz, showing quite good agreement with simulation results. Based on synthesized symmetric dc blocks, the coefficients of transfer function |S12|2 are calculated and design formulas of the asymmetric dc blocks are derived based on the symmetric ones. Asymmetric Chebyshev dc blocks are verified by the measurements provided in a previously published paper and asymmetric Butterworth dc blocks by the symmetric Butterworth dc block measured in this paper.

Secondary LC filter analysis and design techniques for current-mode-controlled converters

Abstract: Small-signal characteristics of current-mode-controlled PWM converters with a second-stage LC filter are analyzed It is shown that a secondary filter can be designed to provide good attenuation of the switching ripple while maintaining adequate stability margins with capacitive loading The resonant frequencies and damping coefficients of the second filter are derived, and design guidelines are given It is shown that the current-loop gain of the buck converter is not affected by the addition of the second-stage filters when a small filter inductance is used Three design examples are presented to demonstrate the use of analysis results Two filter examples are designed for a buck converter One of the second filters shows the problems that arise with a poor design A third example is the design of a second-stage filter for a buck-boost converter In each of the design examples, the small-signal analysis was performed using EASY5 software and the circuits were simulated using the state-space simulation program COSMIR >

Filter with strip lines

Abstract: A filter (1) for filtering certain frequencies of an electric signal. The filter (1) comprises components (HX1-HX4) for forming the frequency response of the filter, and components (A,C) for accomplishing coupling and impedance matching. The filter is provided with a directional coupler (10) composed of two transmission lines (A,B), one of them being a coupling line (A) or an impedance matching line.