High Performance Direct Digital Frequency Synthesizers Using Piecewise Polynomial Approximation

This paper presents new techniques to implement direct digital frequency synthesizers (DDFSs) with optimized piecewise-polynomial approximation. DDFS performances with piecewise-polynomial approximation are first analyzed, providing theoretical upperbounds for the spurious-free dynamic range (SFDR), the maximum absolute error, and the signal-to-noise ratio. A novel approach to evaluate, with reduced computational effort, the near optimal fixed-point coefficients which maximize the SFDR is described. Several piecewise-linear and quadratic DDFS are implemented in the paper by using novel, single-summation-tree architectures. The tradeoff between ROM and arithmetic circuits complexity is discussed, pointing out that a sensible silicon area reduction can be achieved by increasing ROM size and reducing arithmetic circuitry. The use of fixed-width arithmetic can be combined with the single-summation-tree approach to further increase performances. It is shown that piecewise-quadratic DDFSs become effective against piecewise-linear designs for an SFDR higher than 100 dBc. Third-order DDFSs are expected to give advantages for an SFDR higher than 180 dBc. The DDFS circuits proposed in this paper compare favorably with previously proposed approaches

Hybrid DDS-PLL based reconfigurable oscillators with high spectral purity for cognitive radio

Analytical, design and simulation studies on the performance optimization of reconfigurable architecture of a Hybrid DDS – PLL are presented in this thesis. The original contributions of this thesis are aimed towards the DDS, the dithering (spur suppression) scheme and the PLL. A new design of Taylor series-based DDS that reduces the dynamic power and number of multipliers is a significant contribution of this thesis. This thesis compares dynamic power and SFDR achieved in the design of varieties of DDS such as Quartic, Cubic, Linear and LHSC. This thesis proposes two novel schemes namely “Hartley Image Suppression” and “Adaptive Sinusoidal Interference Cancellation” overcoming the low noise floor of traditional dithering schemes. The simulation studies on a Taylor series-based DDS reveal an improvement in SFDR from 74 dB to 114 dB by using Least Mean Squares -Sinusoidal Interference Canceller (LM-SIC) with the noise floor maintained at -200 dB. Analytical formulations have been developed for a second order PLL to relate the phase noise to settling time and Phase Margin (PM) as well as to relate jitter variance and PM. New expressions relating phase noise to PM and lock time to PM are derived. This thesis derives the analytical relationship between the roots of the characteristic equation of a third order PLL and its performance metrics like PM, Gardner’s stability factor, jitter variance, spur gain and ratio of noise power to carrier power. This thesis presents an analysis to relate spur gain and capacitance ratio of a third order PLL. This thesis presents an analytical relationship between the lock time and the roots of its characteristic equation of a third order PLL. Through Vieta’s circle and Vieta’s angle, the performance metrics of a third order PLL are related to the real roots of its characteristic equation