Showing papers on "Bessel filter published in 1996"

A low-distortion BiCMOS seventh-order Bessel filter operating at 2.5 V supply

Abstract: This paper presents the design of a seventh-order continuous-time Bessel filter using a new low-voltage and highly linear BiCMOS transconductor. A high-gain and parasitic-insensitive integrator is obtained by using an active capacitor scheme. The filter has been designed to operate at a 2.5 V supply with a nominal -3 dB cutoff frequency of 600 kHz. It has been fabricated in 1 /spl mu/m, double-poly 6-GHz BiCMOS process. The inband group delay variation is less than 10 ns. The total harmonic distortion (THD) measured with a 100 kHz input signal is less than -49 dB for a 2 V/sub pp/ amplitude and the dynamic range is 77 dB. The filter can be frequency tuned over almost one decade with a gain variation less than 0.2 dB in the passband. A common-mode rejection ratio (CMRR) of 53 dB in the passband is observed, thanks to a careful common-mode control strategy.

Theory of third-harmonic generation using Bessel beams, and self-phase-matching

Abstract: Taking Bessel beams ({ital J}{sub 0} beam) as a representation of a conical beam, and a slowly varying envelope approximation (SVEA) we obtain the results for the theory of third-harmonic generation from an atomic medium. We demonstrate how the phenomenon of self-phase-matching is contained in the transverse-phase-matching integral of the theory. A method to calculate the transverse-phase-matching integral containing four Bessel functions is described which avoids the computer calculations of the Bessel functions. In order to consolidate the SVEA result an alternate method is used to obtain the exact result for the third-harmonic generation. The conditions are identified in which the exact result goes over to the result of the SVEA. The theory for multiple Bessel beams is also discussed which has been shown to be the source of the wide width of the efficiency curve of the third-harmonic generation observed in experiments. {copyright} {ital 1996 The American Physical Society.}

The second harmonic component in the Bessel beam

Abstract: The analysis is based on the Khokhlov–Zabolotskaya–Kuznetsov wave equation. Analytical and approximate solutions are derived for the second harmonic component in the Bessel nondiffracting beam. The theoretical results indicate that the second harmonic beam is nearly nondiffracting in the radial direction and the pressure amplitude is proportional to the square root of propagation distance in the quasilinear approximation, and that the beamwidth of the second harmonic is just 1/2 times that of the fundamental component in the Bessel field, not as 1/√2 times in the fields radiated by other sources.

Diffractive patterns of small cores generated by interference of Bessel beams.

Abstract: The characteristic dimensions of Bessel beams are fully determined by the corresponding Bessel functions. We consider a way of obtaining a narrower diameter of the central core of a diffractive pattern generated by the Bessel beams. The method relies on superposition of two or more Bessel beams with appropriately chosen amplitudes and widths. The disturbing influence of the aperture's edges can be eliminated by addition of the proper amplitude filter.

Analytical results for a class of sums involving Bessel functions and square arrays

Abstract: We consider a class of sums involving Bessel functions summed over the square array. The sums involve the length (ξ) of an arbitrary vector lying within the central unit cell. We establish conditions under which the sums reduce to polynomial forms in ξ (possibly with a single logarithmic term in addition), and show how these polynomials may be conveniently evaluated.

A MOS switched-capacitor ladder filter in SIMOX technology for high temperature applications up to 300/spl deg/C

Abstract: This paper describes techniques and methods used to realize a seventh order switched-capacitor low pass filter in SIMOX technology. The filter has Bessel characteristic and a 3 dB-bandwidth of 20 Hz at a clock frequency of 100 kHz. Special design of transistors and transmission gates results in drastically reduced leakage currents at high temperatures. The power supply voltage of the switched-capacitor filter is 10 V. The temperature range is extended up to 300/spl deg/C. Experimental results of the transistors, the transmission gates, the operational amplifier, and the complete filter are presented.

Approximation of Bessel beams with annular arrays

Abstract: It is shown that the limited-diffraction Bessel beam of order zero can be generated by a transducer with equal-area division of elements and with a fixed prefocus, i.e. conventional transducers used in medical imaging equipment. The element division implies that the scaling parameter must be chosen to contain the first lobe of the Bessel function in the first element. In addition the prefocus must be such that the array is steerable to infinite depth. Examples of low- (3.5 MHz) and high-frequency (20 MHz) arrays are shown where the approximate Bessel beam compares favorably with a spherically focused beam with a fixed focus. The main advantages are a sharper nearfield and a more uniform beamwidth.

Design of linear phase Bessel IIR digital filters

Abstract: There are several methods in the literature for mapping from the s plane to the z plane. The two most common methods are the impulse-invariance method and the bilinear transform. In this paper, an algorithmic method is presented such that phase characteristics on the j/spl omega/ axis in the s plane are preserved on the unit circle in the z plane. This preservation of the phase is not accomplished with other methods. In this paper, the algorithm is applied to the design of linear phase Bessel IIR digital filters.

The simultaneous computation of Bessel functions of first and second kind

Abstract: Based on the qualitative properties of Bessel's differential equation and its solutions, a method is proposed for the simultaneous evaluation of Bessel functions of first and second kind. Special attention is paid to the numerical properties of the method and to the errors of approximation.

A 5.5MHz CMOS Low-Pass Filter using a `Soft-Switched' Transconductor

Abstract: A new transconductor has been used to implement a third-order 5.5MHz low-pass Bessel filter with extra notch. The filter was realised in 0.5 ?m double poly N-well CMOS process. At a 3.3V supply voltage the filter dissipates 12mW and the dynamic range equals 62dB where the THD is-50dB for an input voltage of IVpp. The continuously tuneable transconductor is based on `soft-switching' of resistors. The converter performance is only determined by the first order characteristics of the transistor. Due to reduced sensitivity for the second order effects of the transistors the converter is well suitable in modern and future sub-micron CMOS processes.

Jackson Integral Representations of Modified $q$-Bessel Functions and $q$-Bessel-Macdonald Functions

Abstract: The $q$ analog of Modified Bessel functions and Bessel-Macdonald functions, were defined in our previous work (q-alg/950913) as general solutions of a second order difference equations. Here we present a collection of their representations by the Jackson q-integral.