Phase noise and spur reduction in an array of direct digital synthesizers

Many applications, including communications, test and measurement, and radar, require the generation of signals with a high degree of spectral purity. One method for producing tunable, low-noise source signals is to combine the outputs of multiple direct digital synthesizers (DDSs) arranged in a parallel configuration. In such an approach, if all noise is uncorrelated across channels, the noise will decrease relative to the combined signal power, resulting in a reduction of sideband noise and an increase in SNR. However, in any real array, the broadband noise and spurious components will be correlated to some degree, limiting the gains achieved by parallelization. This thesis examines the potential performance benefits that may arise from using an array of DDSs, with a focus on several types of common DDS errors, including phase noise, phase truncation spurs, quantization noise spurs, and quantizer nonlinearity spurs. Measurements to determine the level of correlation among DDS channels were made on a custom 14-channel DDS testbed. The investigation of the phase noise of a DDS array indicates that the contribution to the phase noise from the DACs can be decreased to a desired level by using a large enough number of channels. In such a system, the phase noise qualities of the source clock and the system cost and complexity will be the main limitations on the phase noise of the DDS array. The study of phase truncation spurs suggests that, at least in our system, the phase truncation spurs are uncorrelated, contrary to the theoretical prediction. We believe this decorrelation is due to the existence of an unidentified mechanism in our DDS array that is unaccounted for in our current operational DDS model. This mechanism, likely due to some timing element in the FPGA, causes some randomness in the relative phases of the truncation spurs from channel to channel each time the DDS array is powered up. This randomness decorrelates the phase truncation spurs, opening the potential for SFDR gain from using a DDS array. The analysis of the correlation of quantization noise spurs in an array of DDSs shows that the total quantization noise power of each DDS channel is uncorrelated for nearly all values of DAC output bits. This suggests that a near N gain in SQNR is possible for an N-channel array of DDSs. This gain will be most apparent for low-bit DACs in which quantization noise is notably higher than the thermal noise contribution. Lastly, the measurements of the correlation of quantizer nonlinearity spurs demonstrate that the second and third harmonics are highly correlated across channels for all frequencies tested. This means that there is no benefit to using an array of DDSs for the problems of in-band quantizer nonlinearities. As a result, alternate methods of harmonic spur management must be employed.

Shape and chemically anisotropic colloidal particles: A theoretical study of their structure, phase behavior, and slow dynamics

A detailed non-equilibrium state diagram of shape-anisotropic particle fluids is constructed. The effects of particle shape are explored using Naive Mode Coupling Theory (NMCT), and a single particle Non-linear Langevin Equation (NLE) theory. The dynamical behavior of non-ergodic fluids are discussed. We employ a rotationally frozen approach to NMCT in order to determine a transition to center of mass (translational) localization. Both ideal and kinetic glass transitions are found to be highly shape dependent, and uniformly increase with particle dimensionality. The glass transition volume fraction of quasi 1- and 2- dimensional particles fall monotonically with the number of sites (aspect ratio), while 3-dimensional particles display a non-monotonic dependence of glassy vitrification on the number of sites. Introducing interparticle attractions results in a far more complex state diagram. The ideal non-ergodic boundary shows a glass-fluid-gel re-entrance previously predicted for spherical particle fluids. The non-ergodic region of the state diagram presents qualitatively different dynamics in different regimes. They are qualified by the different behaviors of the NLE dynamic free energy. The caging dominated, repulsive glass regime is characterized by long localization lengths and barrier locations, dictated by repulsive hard core interactions, while the bonding dominated gel region has short localization lengths (commensurate with the attraction range), and barrier locations. There exists a small region of the state diagram which is qualified by both glassy and gel localization lengths in the dynamic free energy. A much larger (high volume fraction, and high attraction strength) region of phase space is characterized by short gel-like localization lengths, and long barrier locations. The region is called the attractive glass and represents a 2-step relaxation process whereby a particle first breaks attractive physical bonds, and then escapes its topological cage. The dynamic fragility of fluids are highly particle shape dependent. It increases with particle dimensionality and falls with aspect ratio for quasi 1- and 2- dimentional particles. An ultralocal limit analysis of the NLE theory predicts universalities in the behavior of relaxation times, and elastic moduli. The equlibrium phase diagram of chemically anisotropic Janus spheres and Janus rods are calculated employing a mean field Random Phase Approximation. The calculations for Janus rods are corroborated by the full liquid state Reference Interaction Site Model theory. The Janus particles consist of attractive and repulsive regions. Both rods and spheres display rich phase behavior. The phase diagrams of these systems display fluid, macrophase separated, attraction driven microphase separated, repulsion driven microphase separated and crystalline regimes. Macrophase separation is predicted in highly attractive low volume fraction systems. Attraction driven microphase separation is charaterized by long length scale divergences, where the ordering length scale determines the microphase ordered structures. The ordering length scale of repulsion driven microphase separation is determined by the repulsive range. At the high volume fractions, particles forgo the enthalpic considerations of attractions and repulsions to satisfy hard core constraints and maximize vibrational entropy. This results in site length scale ordering in rods, and the sphere length scale ordering in Janus spheres, i.e., crystallization. A change in the Janus balance of both rods and spheres results in quantitative changes in spinodal temperatures and the position of phase boundaries. However, a change in the block sequence of Janus rods causes qualitative changes in the type of microphase ordered state, and induces prominent features (such as the Lifshitz point) in the phase diagrams of these systems. A detailed study of the number of nearest neighbors in Janus rod systems reflect a deep connection between this local measure of structure, and the structure factor which represents the most global measure of order.