In this paper we take a new approach to solving the Ray-leigh-Sommerfeld-Smythe equation for a telescope’s optical impulse re-sponse to a monochromatic point source spherical wave radiating outward from the origin in the object plane. Two cases are covered: 1) the point source at the origin in the telescope’s near-field object plane; 2) the point source at the origin in the far-field object plane as is the case with satellite infrared sensors when the distance between the telescope and the point source is very much greater than the telescope’s circular aperture diameter. With only the assumption of a thin circular aperture we 1) derive a general solution that erases the distinction among the three classically defined zones of the optical axis: Near, Fresnel, and Fraunhofer; 2) reduce the computational complexity down from two-dimensional to one-dimensional Fourier transform integrals and; 3) identify Filon quadrature as the numerical method of choice for accurately and efficiently approximating the values of these integrals and; 4) provide a computational example.

Abstract:
The purpose of the paper is to discuss methods for constructing weighted cubature formulas in Sobolev spaces with periodic members. These formulas are intended to approximate the calculation of Fourier coefficients of functions under consideration. The explicit formulas for the weights and the errors of optimal cubature formulas are obtained by techniques from functional analysis and partial differential equations.

Abstract:
In this paper, we propose a design of a current controlled Quadrature Sinusoidal Oscillator. The proposed circuit employs three optimized Multi-output translinear second generation current conveyer (MCCII). The oscillation condition and the oscillation frequency are independently controllable. The proposed Quadrature Oscillator frequency can be tuned in the range of [198 MHz –261 MHz] by a simple variation of a DC current. PSpice simulation results are performed using CMOS 0.35 µm process of AMS.

Abstract:
In this paper, three types of three-parameters families of quadrature formulas for the Riemann’s integral on an interval of the real line are carefully studied. This research is a continuation of the results in the [1]-[3]. All these quadrature formulas are not based on the integration of an interpolant as so as the Gregory rule, a well-known example in numerical quadrature of a trapezoidal rule with endpoint corrections of a given order (see [4]). In some natural restrictions on the parameters we construct the only one quadrature formula of the eight order which belongs to the first, second and third family. For functions whose 8th derivative is either always positive or always negative, we use these quadrature formulas to get good two-sided bound on . Additionally, we apply these quadratures to obtain the approximate sum of slowly convergent series , where .

An electronically controllable fully uncoupled explicit current-mode quadrature oscillator employing Voltage Differencing Transconductance Amplifiers (VDTAs) as active elements has been presented. The proposed configuration employs two VDTAs along with grounded capacitors and offers the following advantageous features 1) fully and electronically independent control of condition of oscillation (CO) and frequency of oscillation (FO);2) explicit current-mode quadrature oscillations; and 3) low active and passive sensitivities. The workability of proposed configuration has been demonstrated by PSPICE simulations with TSMC CMOS 0.18μm process parameters.

A new family of numerical integration formula is presented, which uses the function evaluation at the midpoint of the interval and odd derivatives at the endpoints. Because the weights for the odd derivatives sum to zero, the derivative calculations cancel out for the interior points in the composite form, so that these derivatives must only be calculated at the endpoints of the overall interval of integration. When using N subintervals, the basic rule which uses the midpoint function evaluation and the first derivative at the endpoints achieves fourth order accuracy for the cost of N/2 function evaluations and 2 derivative evaluations, whereas the three point open Newton-Cotes method uses 3N/4 function evaluations to achieve the same order of accuracy. These derivative-based midpoint quadrature methods are shown to be more computationally efficient than both the open and closed Newton-Cotes quadrature rules of the same order. This family of derivative-based midpoint quadrature rules are derived using the concept of precision, along with the error term. A theorem concerning the order of accuracy of quadrature rule using the concept of precision is provided to justify its use to determine the leading order error term.

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Abstract:
Pulsed bias is an attempt to improve the performance of oscillators in integrated circuits as a result of architectural innovation. Given the relatively low value of resonator quality factor achievable on-chip, for a specified bias voltage level, pulsed bias may result in a lower power consumption and in an improvement of the spectral purity of the oscillation. The main drawback of this approach is the need to introduce a certain time delay in order to properly position pulses with respect to oscillation waveform. Delay accumulation requires further energy dissipation and introduce additional jitter. In this paper we present a new architecture capable to avoid unnecessary delay, based on the idea to apply the pulsed bias approach to a quadrature oscillator. A ?rst circuit-level implementation of this concept is presented with simulation results.

Abstract:
In this paper, new complex band pass filter architecture for continuous time complex band pass sigma delta modulator is presented. In continuation of paper the modulator is designed for GPS and Galileo receiver. This modulator was simulated in standard 0.18 μm CMOS TSMC technology and has bandwidth of 2MHz and 4MHz for GPS and Galileo centered in 4.092 MHz. The dynamic range (DR) is 56.5/49 dB (GPS/Galileo) at sampling rate of 125 MHz. The modulator has power consumption of 4.1 mw with 3 V supply voltage.

Abstract:
This paper aims to introduce a quadrature VCO (voltage control oscillator) which applies superharmonic coupling. The presented quadrature VCO is suitable to be used, both with 2 × subharmonic mixers, as well as 4×subharmonic mixers. It would be impossible to avoid the presence of harmonics in CMOS VCO circuits. These harmonics are in general, undesirable signals which tend to accompany the desired fundamental signal. There are common-mode nodes (similar to those in the two source nodes in a cross-coupled VCO) in deferential VCO at which higher-order harmonics are present while the fundamental is absent in essence. We can make use of these second-order harmonics which are present at the common-mode nodes of two VCO in order to implement a quadrature connection between the fundamental outputs. The technique through which this is done is called superharmonic coupling. This CMOS quadrature VCO which applies active superharmonic coupling puts an excellent performance in show, with an output power –0.942 dBm for fundamental and –9.751 dBm for subharmonic, phase noise –107.2 dBc/Hz for fundamental and –114.8 dBc/Hz at a 1MHz offset. All of circuit applied are designed and simulated by ADS, 2008.