<p> A two-part scheme for the design of wideband linear phase SAW filters is proposed. The design uses curved finger interdigital transducers, and extension of slanted finger design, to compensate for circuit effects and eliminate the need for matching. Theory is combined with distortion minimizing techniques to realize devices which satisfy INTELSAT filter specifications. </p> <p> Basic SAW theory is reviewed. and curved finger theory presented, while methods of distortion minimization are both reviewed and proposed. Experimental results which illustrate and support the theory given are included. </p> / Thesis / Master of Engineering (MEngr)

The aim of this thesis is to implement flexible interpolators and decimators onField Programmable Gate Array (FPGA). Interpolators and decimators of differentwordlengths (WL) are implemented in VHDL. The Farrow structure is usedfor the realization of the polyphase components of the interpolation/decimationfilters. A fixed set of subfilters and adjustable fractional-delay multiplier valuesof the Farrow structure give different linear-phase finite-length impulse response(FIR) lowpass filters. An FIR filter is designed in such a way that it can be implementedfor different wordlengths (8-bit, 12-bit, 16-bit). Fixed-point representationis used for representing the fractional-delay multiplier values in the Farrow structure. To perform the fixed-point operations in VHDL, a package called fixed pointpackage [1] is used. A 8-bit, 12-bit, and 16-bit interpolator are implemented and their performancesare verified. The designs are compiled in Quartus-II CAD tool for timing analysisand for logical registers usage. The designs are synthesised by selecting Cyclone IVGX family and EP4X30CF23C6 device. The wordlength issues while implementingthe interpolators and decimators are discussed. Truncation of bits is required inorder to reduce the output wordlength of the interpolator and decimator.

The master thesis is based upon a new type of linear-phase Nyquist finitie impulse responseinterpolator and decimator implemented using a tree-structure. The tree-structure decreasesthe complexity, considerably, compared to the ordinary single-stage interpolator structure.The computational complexity is comparable to a multi-stage Nyquist interpolator structure,but the proposed tree-structure has slightly higher delay. The tree-structure should still beconsidered since it can interpolate with an arbitrary number and all subfilters operate at thebase rate which is not the case for multi-stage Nyquist interpolators.

The inhomogeneous B1 field at higher main fields (B0) becomes more serious, leading to unsatisfactory MR image quality. To improve the signal homogeneity of routinely used T1-weighted image, usually acquired by a well-known sequence, Magnetization Prepared Rapid Acquisition Gradient Echo (MPRAGE), a new pulse sequence, Magnetization Prepared 2 Rapid Acquisition Gradient Echoes (MP2RAGE), was proposed in 2009. This technique acquires two sets of high-resolution three- dimentional images at different inversion times after a series of inversion pulses. After any of two simple calculations of the raw images (Ratio or MP2RAGE reconstruction), the output volume was obtained with dramatically reduced spatial inhomogenuity of MR signal. In this study, the contrast-to-noise ratio (CNR) optimation at 3 T was implemented independently to reproduce the previous results of other group. After that, the simulation of scanning parameters was done to optimize CNR of brain tissue at 1.5 T according to different encoding methods, different pulse sequences, and different reconstruction algorithms. Phantom and human experiments were carried on a 1.5 T scanner for further validation. The results of phantom experiment showed that both MP2RAGE and Ratio reconstructions can achiever better B1 homogeneity than MPRAGE, even with the vendor-equipped correction packages, SCIC and PURE. In addition, the agreement was made between simulation and in-vivo imaging that MP2RAGE provides higher CNR than Ratio when centric encoding also outduels linear encoding.

Thermoacoustic instabilities are a problem in modern pre-mixed combustors causing reduced performance and leading in the extreme to combustor failure from excessive pressure cycles. Much work has been done using linear controllers to eliminate these instabilities. Many experimenters in the field have used pulsed and subharmonic fuel controllers to eliminate these instabilities, but very little investigative work has been done on these controllers. The goal of this work is to explain the mechanism of control behind pulsed controllers. It is shown that the combustion system can be treated as a linear system, thus meaning that frequency components of the control signal at the desired instability frequency are the dominant means of control, with nonlinear effects only serving to slightly reduce the gain necessary for control. Fourier analysis is thus performed on pulsed signals and the components analyzed, showing that there will indeed be a component of a pulsed signal at the frequency of the instability, aside from a few select cases. It is then proven that this frequency component is largely responsible for control of the thermoacoustic system using proportional height pulse train signals, which will change pulse height based on the amplitude of the instability. This analysis is then used to predict the height of instabilities resulting from the use of fixed height pulse control signals. Finally, numerical simulations and experimental observations support the analytical constructs. Acoustic control is mainly used for these experiments, although some preliminary work with liquid fuel controllers is also presented. / Master of Science

Lean premixed fuel-air conditions in large gas turbines are used to improve efficiency and reduce emissions. These conditions give rise to large undamped pressure oscillations at the combustor's natural frequencies which reduce the turbine's longevity and reliability. Active control of the pressure oscillations, called thermoacoustic instabilities, has been sought as passive abatement of these instabilities does not provide adequate damping and is often impractical on a large scale. Phase shift control of the instabilities is perhaps the simplest and most popular technique employed but often does not provide good performance in that controller induced secondary instabilities are generated with increasing loop gain. This thesis investigates the general underlying cause of the secondary instabilities and shows that high average group delay through the frequency region of the instability is the root of the problem. This average group delay is then shown to be due not only the controller itself but can also be associated with other components and inherent characteristics of the control loop such as actuators and time delay, respectively. An "optimum" phase shift controller, consisting of an appropriate shift in phase and a low order, wide bandwidth bandpass filter, is developed for a Rijke tube combustor and shown to closely match the response of an LQG controller designed only for system stabilization. Both the optimal phase shifter and the LQG controller are developed based on a modified model of the thermoacoustic loop which takes into account the change in density of the combustion reactants at the flame location. Additionally, the system model is coupled with a model of the control loop and then validated by comparison of simulated results to experimental results using nearly identical controllers. / Master of Science

Thesis (MScEng)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: Radar Cross Section (RCS) is an important parameter in radar engineering. Often, electrically large structures are of interest in RCS analysis due to the high operating frequencies of radar systems. Simulation of these problems can be more e cient than measurement due to the cost associated with measurement. The Method of Moments/Physical Optics (MoM/PO) hybrid method combines the advantages of the MoM and PO, making it suited to solving electrically large problems that may contain some small complex detail. The requirement for high meshing resolution when analysing some electromagnetic problems, however, signi cantly increases memory requirements. As a result, the hybrid MoM/PO becomes computationally expensive for electrically large problems. In this work, a linear phase term is introduced into the RWG basis function formulation of the MoM/PO hybrid. The addition of the linear phase term allows the use of large triangular mesh elements in the PO region, resulting in the analysis of electrically large problems. The bene t of this formulation is that it allows a reduction in computational cost whilst maintaining the accuracy of the hybrid MoM/PO. This improved hybrid is tested on various planar test cases and results show that it attains the same level of accuracy as the original MoM/PO hybrid. / AFRIKAANSE OPSOMMING: Radardeursnit is 'n belangrike parameter in radaringenieurswese. As gevolg van die hoë frekwensies wat deur baie radarstelsels gebruik word, is elektriesgroot probleme dikwels van belang in die berekening van die radardeursnit van teikens. Die modellering en berekening van die radardeursnit van teikens kan meer kostedoeltre end as metings wees, as gevolg van die beduidende koste van radardeursnitmetings. Die hibriede Moment-Metode/Fisiese-Optika tegniek kombineer die voordele van die twee tegnieke, wat dit geskik maak vir elektries-groot probleme met klein, komplekse detail. Indien die gewone benadering egter gevolg word om 'n hoë resolusie faset-model te gebruik, bly dit berekeningsintensief met groot rekenaar geheuevereistes vir elektries-groot probleme. In hierdie studie word 'n lineêre fase term ingesluit in die formulering van die Rao-Wilton-Glisson (RWG) basisfunksies vorm van die hibriede Moment-Metode/Fisiese-Optika tegniek. Die toevoeging van die lineêre fase term maak dit moontlik om groot driehoekfasette in die Fisiese-Optika gebied te gebruik, wat beteken dat elektries-groot probleme makliker opgelos kan word. Die voordeel van hierdie nuwe formulering is dat die berekeningslas en -tyd verminder word terwyl die akkuraatheid van die oorspronklike hibriede Moment-Metode/Fisiese-Optika tegniek behou word. Hierdie verbeterde hibriede tegniek word getoets aan die hand van verskeie platvlak toetsgevalle en die resultate dui daarop dat die akkuraatheid vergelykbaar is met die van die oorspronklike hibriede Moment-Metode/Fisiese-Optika tegniek.

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The design of nearly linear-phase recursive digital filters using constrained optimization is investigated. The design technique proposed is expected to be useful in applications where both magnitude and phase response specifications need to be satisfied. The overall constrained optimization method is formulated as a quadratic programming problem based on Newton’s method. The objective function, its gradient vector and Hessian matrix as well as a set of linear constraints are derived. In this analysis, the independent variables are assumed to be the transfer function coefficients. The filter stability issue and convergence efficiency, as well as a ‘real axis attraction’ problem are solved by integrating the corresponding bounds into the linear constraints of the optimization method. Also, two initialization techniques for providing efficient starting points for the optimization are investigated and the relation between the zero and pole positions and the group delay are examined. Based on these ideas, a new objective function is formulated in terms of the zeros and poles of the transfer function expressed in polar form and integrated into the optimization process. The coefficient-based and polar-based objective functions are tested and compared and it is shown that designs using the polar-based objective function produce improved results. Finally, several other modern methods for the design of nearly linear-phase recursive filters are compared with the proposed method. These include an elliptic design combined with an optimal equalization technique that uses a prescribed group delay, an optimal design method with robust stability using conic-quadratic-programming updates, and an unconstrained optimization technique that uses parameterization to guarantee filter stability. It was found that the proposed method generates similar or improved results in all comparative examples suggesting that the new method is an attractive alternative for linear-phase recursive filters of orders up to about 30.

The design of nearly linear-phase recursive digital filters using constrained optimization is investigated. The design technique proposed is expected to be useful in applications where both magnitude and phase response specifications need to be satisfied. The overall constrained optimization method is formulated as a quadratic programming problem based on Newton’s method. The objective function, its gradient vector and Hessian matrix as well as a set of linear constraints are derived. In this analysis, the independent variables are assumed to be the transfer function coefficients. The filter stability issue and convergence efficiency, as well as a ‘real axis attraction’ problem are solved by integrating the corresponding bounds into the linear constraints of the optimization method. Also, two initialization techniques for providing efficient starting points for the optimization are investigated and the relation between the zero and pole positions and the group delay are examined. Based on these ideas, a new objective function is formulated in terms of the zeros and poles of the transfer function expressed in polar form and integrated into the optimization process. The coefficient-based and polar-based objective functions are tested and compared and it is shown that designs using the polar-based objective function produce improved results. Finally, several other modern methods for the design of nearly linear-phase recursive filters are compared with the proposed method. These include an elliptic design combined with an optimal equalization technique that uses a prescribed group delay, an optimal design method with robust stability using conic-quadratic-programming updates, and an unconstrained optimization technique that uses parameterization to guarantee filter stability. It was found that the proposed method generates similar or improved results in all comparative examples suggesting that the new method is an attractive alternative for linear-phase recursive filters of orders up to about 30.