Abstract This paper studies the problem of construction of optimal quadrature formulas in the sense of Sard in the space ( ) 2 (0,1) m L . In this paper the quadrature sum consists of values of the integrand and its first derivative at nodes. The coefficients of optimal quadrature formulas are found and the norm of the optimal error functional is calculated for arbitrary natural number 1 N m ≥ ...

A low power and low-phase noise quadrature voltage controlled oscillator (QVCO) using the differential complementary Colpitts oscillator topology has been developed. A transformer inductor is used to form a differential output oscillator and the back-gate coupling technique is used to generate quadrature outputs. The advantage of proposed QVCO is analyzed in terms of power consumption, phase no...