Dielectric and magnetic structures which inhibit the propagation of light for a given frequency range at any angle of incidence are said to have a photonic band gap (PBG). By placing defects inside of these PBG structures, useful devices can be constructed including micro-cavity lasers and nanometer scale waveguides. This thesis is concerned with the evaluation of these PBGs in order to obtain an understanding of how they work, as well as developing new methods to evaluate them. The photonic band gap configurations are modeled with the Finite Difference Time Domain (FDTD) method in one and two dimensions. By modeling these structures in the time domain, the finite amount of time that it takes to establish the photonic band gaps may be observed. Also, methods using the Fast Fourier Transform in combination with the FDTD algorithm are capable of determining the frequency spectrum of a structure with little computation time.

This thesis presents a novel spatial spectrum estimation technique, ∂-MUSIC, for discriminating between two closely spaced sources which are highly correlated. The ∂-MUSIC algorithm is tested, modified, and compared to the MUSIC algorithm using a point source simulation. Various power levels, samples sizes and angle separations are used on a linear and a planar array for correlated and uncorrelated sources. The algorithm is found to be relatively insensitive to correlation and can separate targets to one-half of the angular separation threshold of ∂-MUSIC. The ∂-MUSIC algorithm is tested using a simulation that generated terrain scattered interference representative of a propagation scenario involving multiple paths. The simulation shows that ∂-MUSIC is able to resolve the direct path and image at less than one-fourth of a beam width, with a ten degree angle to the surface, whereas MUSIC finds a single angle which is biased toward the image.

This work contains a discussion of symbolic analysis techniques, symbolic and numerical analysis results, and loosely structured analog design methodologies that one can use in the development of high frequency, low distortion bipolar amplifiers. Central to this purpose is the development of simplified, yet informative symbolic expressions for harmonic distortion by applying power and Volterra series expansions. Instead of analyzing complete and complex amplifiers, critical bipolar amplifier subcircuits are examined to provide design-oriented insight into the root causes of distortion. In each case we determine low frequency distortion, and where it is most appropriate, frequency dependent distortion. We also address common and uncommon distortion reduction schemes like global feedback, bootstrapping, and feedforward error correction.

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