Tight-Binding Approximations in 1D and 2D Coupled-Cavity Photonic Crystal Structures

Light confinement and controlling an optical field has numerous applications in the field of telecommunications for optical signals processing. When the wavelength of the electromagnetic field is on the order of the period of a photonic microstructure, the field undergoes reflection, refraction, and coherent scattering. This produces photonic bandgaps, forbidden frequency regions or spectral stop bands where light cannot exist. Dielectric perturbations that break the perfect periodicity of these structures produce what is analogous to an impurity state in the bandgap of a semiconductor. The defect modes that exist at discrete frequencies within the photonic bandgap are spatially localized about the cavity-defects in the photonic crystal. In this thesis the properties of two tight-binding approximations (TBAs) are investigated in one-dimensional and two-dimensional coupled-cavity photonic crystal structures We require an efficient and simple approach that ensures the continuity of the electromagnetic field across dielectric interfaces in complex structures. In this thesis we develop \textrm{E} -- and \textrm{D} --TBAs to calculate the modes in finite 1D and 2D two-defect coupled-cavity photonic crystal structures. In the \textrm{E} -- and \textrm{D} --TBAs we expand the coupled-cavity \overrightarrow{E} --modes in terms of the individual \overrightarrow{E} -- and \overrightarrow{D} --modes, respectively. We investigate the dependence of the defect modes, their frequencies and quality factors on the relative placement of the defects in the photonic crystal structures. We then elucidate the differences between the two TBA formulations, and describe the conditions under which these formulations may be more robust when encountering a dielectric perturbation. Our 1D analysis showed that the 1D modes were sensitive to the structure geometry. The antisymmetric \textrm{D} mode amplitudes show that the \textrm{D} --TBA did not capture the correct (tangential \overrightarrow{E} --field) boundary conditions. However, the \textrm{D} --TBA did not yield significantly poorer results compared to the \textrm{E} --TBA. Our 2D analysis reveals that the \textrm{E} -- and \textrm{D} --TBAs produced nearly identical mode profiles for every structure. Plots of the relative difference between the \textrm{E} and \textrm{D} mode amplitudes show that the \textrm{D} --TBA did capture the correct (normal \overrightarrow{E} --field) boundary conditions. We found that the 2D TBA CC mode calculations were 125-150 times faster than an FDTD calculation for the same two-defect PCS. Notwithstanding this efficiency, the appropriateness of either TBA was found to depend on the geometry of the structure and the mode(s), i.e. whether or not the mode has a large normal or tangential component.

Method to Improve the Conversion Gain Flatness of Transformer-Coupled Mixers

A 4-10 GHz, on-chip balun based current commutating mixer is proposed. Tunable resistive feedback is used at the transconductance stage for wideband response, and interlaced stacked transformer is adopted for good balance of the balun. Measurement results show that a conversion gain of 13.5 dB, an IIP3 of 4 dBm and a noise figure of 14 dB are achieved with 5.6 mW power consumption under 1.2 V supply. The simulated amplitude and phase imbalance is within 0.9 dB and ±2◦ over the band.

ADVANCED ISLANDING DETECTION METHODS FOR SINGLE PHASE GRID CONNECTED PV INVERTERS

Due to the growing concerns associated with fossil fuels, emphasis has been placed on clean and sustainable energy generation. This has resulted in the increase in Photovoltaics (PV) units being integrated into the utility system. The integration of PV units has raised some concerns for utility power systems, including the consequences of failing to detect islanding. Numerous methods for islanding detection have been introduced in literature. They can be categorized into local methods and remote methods. The local methods are categorically divided into passive and active methods. Active methods generally have smaller Non-Detection Zone (NDZ) but the injecting disturbances will slightly degrade the power quality and reliability of the power system. Slip Mode Frequency Shift Islanding Detection Method (SMS IDM) is an active method that uses positive feedback for islanding detection. In this method, the phase angle of the converter is controlled to have a sinusoidal function of the deviation of the Point of Common Coupling (PCC) voltage frequency from the nominal grid frequency. This method has a non-detection zone which means it fails to detect islanding for specific local load conditions. If the SMS IDM employs a different function other than the sinusoidal function for drifting the phase angle of the inverter, its non-detection zone could be smaller. In addition, Advanced Slip Mode Frequency Shift Islanding Detection Method (Advanced SMS IDM), which has been introduced in this thesis, eliminates the non-detection zone of the SMS IDM. In this method the parameters of SMS IDM change based on the local load impedance value. Moreover, the stability of the system is investigated by developing the dynamical equations of the system for two operation modes; grid connected and islanded mode. It is mathematically proven that for some loading conditions the nominal frequency is an unstable point and the operation frequency slides to another stable point, while for other loading conditions the nominal frequency is the only stable point of the system upon islanding occurring. Simulation and experimental results show the accuracy of the proposed methods in detection of islanding and verify the validity of the mathematical analysis.