Student Number : 9713144D - MSc Dissertation - School of Electrical Engineering - Faculty of Engineering and the Built Environment / The performance of the Log Periodic dipole array antenna has been characterized, in the form of parametric curves available in most antenna design handbooks and other relevant literature. These characteristic curves are often limiting in scope, as for instance they do not contain parametric curves giving the relationship between the boom-length 'L' and the number of dipole element 'N' for any given bandwidth, even when it is known that these two parameters are the main cost determinants of a LPDA Antenna. The concept of convergence is introduced to aid cost optimization of the LPDA Antenna in terms of number of dipole element 'N'. Although 'N' is used as the minimization criterion, the criteria for establishing convergence encompass all the main electrical characteristics of the LPDA Antenna, such as VSWR, gain and radiation patterns. Lastly, the effects of boomimpedance 'Zo' and length to diameter ration 'Ln/Dn', on the performance characteristics of the LPDA Antenna was investigated with the view to determining if neglecting the effects of these two parameters were responsible for the disparity in the directive gain values obtained by R. L Carrel compared to those obtained by later researchers. The investigation indicates that if an LPDA Antenna is converged, then the effects of Zo and Ln/Dn ratio though significant can not alone account for the fairly large disparity in the gain values. In other to perform these investigations, a modern scientific tool in the form of numerical modeling by method of moments based, Super Numerical electromagnetic code version2 was utilized. The numerical modeling tool was first validated by agreement between measured values and the values as predicted by the modeling tool. Next, simulation of the performance of LPDA antennas under variations of their number of elements was done. Thereafter, the means and standard deviations of the gain were extracted from the simulated numerical models. Trends in the pattern of variation of the means and standard deviations of the gain are used as the basis for deciding the value of number of element at which the antenna can yield acceptable performance (convergence criteria). These are presented as convergence curves, which gives for any given boom-length and operating bandwidth, the minimum number of elements required for the antenna to yield acceptable performance. Finally, the effect of length to diameter ratio and boom-impedance on the gain of optimized LPDA antennas are presented as parametric curves.

In this thesis we examine the ability of the log-periodic power law model to accurately predict the end of speculative bubbles on financial markets through modeling of asset price dynamics on a selection of historical bubbles. The methods we use are based on a nonlinear least squares estimation which yields predictions of when the bubble will change regime.We find evidence which support the occurrence of LPPL-patterns leading up to the change in regime; asset prices during bubble periods seem to oscillate around a faster-than-exponential growth. In most cases the estimation yields accurate predictions, although we conclude that the predictions are quite dependent on at which point in time the prediction is conducted. We also find that the end of a speculative bubble seems to be influenced by both endogenous speculative growth and exogenous factors. For this reason we propose a new way of interpreting the predictions of the model, where the end dates should be interpreted as the start of a time period where the asset prices are especially sensitive to exogenous events. We propose that negative news during this time period results in a regime shift of the bubble. This study is the first to address both the possibilities and the limitations of the LPPL-model, and should therefore be considered as a contribution to the academia.

The Square Kilometer Array radio astronomy telescope will achieve the majority of its extremely large aperture area with thousands of parabolic dishes, each illuminated by a wideband antenna feed, and this thesis introduces a new such antenna. The wide bandwidth of this new antenna is achieved with the development of a directional log periodic antenna. Scaling the log periodic elements into three-dimensional space is the present method used for directional log periodic antennas. We propose confining these often complex log periodic elements into a single plane, while the ground "plane" takes on a three dimensional form, permitting low-cost implementations without requiring the introduction of a complicated scaffolding to support the log periodic elements in 3-D. This low-cost solution would scale well in the implementation of the thousands of antenna feeds that the Square Kilometer Array demands. We also introduce a previously unreported LP design: the log periodic log spiral antenna.

Thesis (MScEng)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: This thesis is about the design, simulation and measuring of ultra wide band antennas for use in the Square Kilometre Array (SKA). The SKA is a radio astronomy project with one of the aims of detecting hydrogen particles in deep space. Several thousand antennas over a wide band of frequencies are needed to receive the radiation from these particles. This motivates the need for a low-cost ultra wide band antenna with the focus on the low frequency part of the SKA. In this thesis we present two design strategies: The first design strategy is for a printed LPDA on a substrate and design curves are generated. A scale model was built and measurements did not correlate with simulation results. This is due to manufacturing tolerances and assembly of the pyramidal structure. The second design strategy is for a full scale zig-zag antenna and design curves were also generated. The aim here is to produce a low-cost prototype by using brazing rods for the wire structure and mount it on a wooden frame. A full scale model was built and measurements on the roof produced much interference for the radiation pattern, but the reflection coefficient was good. We suggest doing measurements in an interference free environment in order to achieve the needed results. To conclude we suggest using the zig-zag antenna for the SKA. Some issues do however need more attention as the transformer has some losses, the cross polarisation is probably not good enough and the beamwidth does not reach the specification. We demonstrated a low cost prototype and there is the possibility of low-cost large scale manufacturing but this needs to be addressed. This has however not been analysed as many factors for large scale manufacturing are very difficult to predict beforehand and lies outside the scope of this thesis. / AFRIKAANSE OPSOMMING: Hierdie tesis gaan oor die ontwerp, simulasie en opmeting van ultrawyebandantennas vir gebruik in die SKA ("Square Kilometre Array"). Die SKA is ’n radioastronomie projek met die doel om waterstof partikels op te spoor in die ruimte. Duisende antennas wat oor ’n wye band van frekwensies strek is nodig om die energie van die partikels op te vang. Hieruit is daar ’n aanvraag vir lae-koste ultrawyebandantennas met die fokus op die lae frekwensie deel van die SKA. In hierdie tesis word twee ontwerpstrategieë voorgestel: Die eerste ontwerpstrategie is vir ’n gedrukte logaritmies periodiese dipool reeks (LPDR) op ’n substraat tesame met ontwerpskurwes wat gegenereer word. ’n Skaal model is gebou en die gemete resultate stem nie ooreen met die simulasie nie. Dit kan toegeskryf word aan vervaardigingstoleransies en die aanmekaar sit van die piramide struktuur. Die tweede ontwerpstrategie is vir ’n vol skaal sigsag ("zig-zag") antenna met ontwerpskurwes wat ook gegenereer word. Die doel is om ’n lae-koste prototipe te bou deur sweissoldeerdraad te gebruik vir die draadstruktuur en dan op ’n hout raam te plaas. ’n Vol skaal model is gebou en metings op die dak het baie interferensie veroorsaak vir die stralingsveld, maar tog was die weerkaatskoëffisient goed. Ons stel voor om die metings te herhaal in ’n steuringvrye omgewing om sodoende die korrekte resultate te verkry. Om af te sluit stel ons voor om die sigsag antenna vir die SKA te gebruik. Sekere kwessies soos die transformator wat verlieserig is, die kruispolarisasie wat moontlik nie goed genoeg is nie en die bundelwydte wat nie die spesifikasie haal nie moet nog aandag geniet. Ons het ’n lae-koste prototipe gedemonstreer en daar is die moontlikheid om dit op grootskaalse vervaardiging ook goedkoop te doen, maar dit moet nog uigesorteer word. Dit was wel nie geanaliseer nie, siende dat vele faktore ’n rol speel by grootskaalse vervaardiging wat uiters moeilik is om voor die tyd te voorspel en buite die omvang van die tesis lê.

Nowadays there has been a growing interest in anomalous diffusion: the super difusive and sub-difusive processes. The problem about normal diffusion already well established whereas many problems still exist in anomalous diffusion. Several mathematical models and computational techniques have been developed to model such processes. In this work we studied a non-Markovian Random Walk (RW), in one dimension in which the development of the process is governed by decisions taken in the distant past. We used as tool of analysis, analytical and numerical procedures (Monte Carlo method). In this problem, the walker takes its decisions (go right or left) at a given time t, based on the decisions taken in the past, namely in a fraction f of the total time. As far as the decision making process is considered only the distant past is taken into account. This loss of recent memory leads the probability density function of the position to change from Gaussian to non-Gaussian and leads to the emergence of log-periodic oscillations in position, besides producing a change in the behavior of non-persistent to persistent, causing anomalous diffusion. This change is characterized by the Hurst exponent, and is found, surprisingly, in a region where there is negative feedback. The diagram of phases depending on the parameters f and p (fraction of old memory and feedback), shows the following phases: classical non persistence, classical persistence, log-periodic non persistence, log-periodic persistence, Gaussian and non Gaussian with respect to the position of the walker. / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Atualmente tem crescido o interesse por processos de difusão anômala, i.e., os super difusivos e sub-difusivos. O problema voltado para difusão normal já é bem conhecido, enquanto para difusões anômalas ainda existem vários problemas em abertos. Várias técnicas computacionais e modelos matemáticos têm sido desenvolvidos para modelar tais processos. Estudamos neste trabalho uma caminhada aleatória, não Markoviana em uma dimensão, em que o desenvolvimento do processo é regido por decisões tomadas em relação ao passado distante. Utilizamos como ferramenta de análise uma abordagem analítica e numérica (via método de Monte Carlo). Nesse problema, o caminhante toma suas decisões (entre ir para a direita ou para a esquerda), num determinado tempo t, com base nas decisões tomadas no passado, numa fração f do tempo transcorrido. Quando f<1 o passado recente é esquecido e apenas o passado distante é considerado. Essa perda de memória recente induz a função densidade de probabilidade da posição a passar de um regime Gaussiano para não Gaussiano e leva ao surgimento de oscilações log-periódicas na posição, além de produzir uma mudança no comportamento, de não persistente para persistente, ocasionando difusão anômala. Essa mudança é caracterizada pelo expoente de Hurst e ocorre também, surpreendentemente, numa região de feedback negativo. O diagrama de fases em função dos parâmetros f e p (fração de memória antiga e feedback), mostra as seguintes regiões: não persistência clássica; persistência clássica; não persistência log-periódica e persistência log-periódica; região Gaussiana e não Gaussiana da posição.

The thesis is focused on the design of a measuring antenna for 1 – 6 GHz band. It deals with the types of log periodic antennas with the the detailed elaboration of log periodic dipole antennas (LPDA). One can find the description of their functions, maximum features and the possibilities to use the asymmetrical feeder. Also there is the procedure of LPDA design and the realization of the design itself including simulation in 4NEC2 programme. In the next part there is a planar LPDA realization with the microstrip-to-balanced stripline balun symmetrization. This design was simulated and tested within the frames of Zeland IE3D programme. The last part contains the measuring results of S parametres as well as beam characteristics of the planar version of LPDA.

This diploma thesis deal with the design of log-periodic antenna. The log-periodic antenna is self-complementary and broadband antenna. Antenna self-complementary structures are described only by angles. Input impedance of log-periodic antenna is equal to theoretical impedance ohms. The input impedance and radiation patterns of broadband antenna structures are independent of frequency over theoretically unlimited bandwidths. The log-periodic antennas provide linearly polarized radiation pattern. In this thesis is designed antenna for bandwidths 1 to 5GHz. In this diploma thesis is introduced design balanced unit, this is compound broadband balun and broadband impedance transformer. The broadband balun is based on conversion of microstrip line to balanced stripline. The Klopfenstein impedance taper is used for design. For simulation was used software from firma Zeland software IE3D.