This thesis presents an examination of the jitter performance of different oscillator types in the presence of flicker noise, white noise and power supply noise. Key results are achieved using time domain simulations to determine cycle jitter of several different oscillator architectures, semiconductor processes and component features. In the end, a design procedure is developed for creating a low-jitter oscillator in a TSMC .25mm CMOS semiconductor process.

<p> This thesis is principally concerned with the performance of the phase-locked FM demodulator under conditions of interference in comparison to the conventional FM demodulator. The linear no interference performance of the phase-locked oscillator is well known, however this aspect is included in the interests of completeness and reference.</p> <p> Mechanisms tor threshold effects in the phase-locked and conventional FM demodulator are discussed and compared. It is shown theoretically and experimentally that the noise threshold is reduced in the phase-locked FM demodulator by virtue of the limits of Ψi (t) being restricted by the noise bandwidth of' the feedback loop. Fall off in baseband signal level in the presence of noise was seen to be a function of θ(t) and (S/N)IF.</p> / Thesis / Master of Engineering (MEngr)

<p> This thesis presents a derivation of a method to obtain two-body, diagonal and non-diagonal, reaction matrix elements for central and tensor forces respectively directly from nucleon-nucleon scattering phase shifts. This procedure eliminates the necessity for constructing a nuclear potential.</p> / Thesis / Master of Science (MSc)

In many Resistance-Capacitance Oscillators the oscillation amplitude is controlled by the use of a temperature-dependent resistor incorporated in the negative feedback loop. The use of thermistors and tungsten lamps is discussed and an approximate analysis is presented for the behaviour of the tungsten lamp. The result is applied in an analysis of the familiar Wien Bridge Oscillator both for the presence of a linear circuit and a cubic nonlinearity. The linear analysis leads to a highly unstable transient response which is uncommon to most oscillators. The inclusion of the slight cubic nonlinearity, however, leads to a result which is in close agreement to the observed response. / Thesis / Master of Engineering (MEngr)

A bulk of the research on piezoelectric systems in recent years can be classified into two categories, 1) studies of linear piezoelectric oscillator arrays, 2) studies of nonlinear piezoelectric oscillators. This dissertation derives novel linear and nonlinear modeling and estimation methods for such piezoelectric systems. In the first part, this work develops modeling and design methods for Piezoelectric Subordinate Oscillator Arrays (PSOAs) for the wideband vibration attenuation problem. PSOAs offer a straightforward and low mass ratio solution to cancel out the resonant peaks in a host structure's frequency domain. Further, they provide adaptability through shunt tuning, which gives them the ability to recover performance losses because of structural parameter errors. This dissertation studies the derivation of governing equations that result in a closed-form expression for the frequency response function. It also analyzes systematic approaches to assign distributions to the nondimensional parameters in the frequency response function to achieve the desired flat-band frequency response. Finally, the effectiveness of PSOAs under ideal and nonideal conditions are demonstrated in this dissertation through extensive numerical and experimental studies. The concept of performance recovery, introduced in empirical studies, gives a measure of the PSOA's effectiveness in the presence of disorder before and after capacitive tuning. The second part of this dissertation introduces novel modeling and estimation methods for nonlinear piezoelectric oscillators. Traditional modeling techniques require knowledge of the structure as well as the source of nonlinearity. Data-driven modeling techniques used extensively in recent times build approximations. An adaptive estimation method, that uses reproducing kernel Hilbert space (RKHS) embedding methods, can estimate the underlying nonlinear function that governs the system's dynamics. A model built by such a method can overcome some of the limitations of the modeling approaches mentioned above. This dissertation discusses (i) how to construct the RKHS based estimator for the piezoelectric oscillator problem, (ii) how to choose kernel centers for approximating the RKHS, and (iii) derives sufficient conditions for convergence of the function estimate to the actual function. In each of these discussions, numerical studies are used to show the RKHS based adaptive estimator's effectiveness for identifying linearities in piezoelectric oscillators. / Doctor of Philosophy / Piezoelectric materials are materials that generate an electric charge when mechanical stress is applied, and vice versa, in a lossless transformation. Engineers have used piezoelectric materials for a variety of applications, including vibration control and energy harvesting. This dissertation introduces (1) novel methods for vibration attenuation using an array of piezoelectric oscillators, and (2) methods to model and estimate the nonlinear behavior exhibited by piezoelectric materials at very high mechanical forces or electric charges. Arrays of piezoelectric oscillators attached to a host structure are termed piezoelectric subordinate oscillator arrays (PSOAs). With the careful design of PSOAs, we show that we can reduce the vibration of the host structure. This dissertation analyzes methodologies for designing PSOAs and illustrates their vibration attenuation capabilities numerically and experimentally. The numerical and experimental studies also illustrate the robustness of PSOAs. In the second part of this dissertation, we analyze reproducing kernel Hilbert space embedding methods for adaptive estimation of nonlinearities in piezoelectric systems. Kernel methods are extensively used in machine learning, and control theorists have studied adaptive estimation of functions in finite-dimensional spaces. In this work, we adapt kernel methods for adaptive estimation of functions in infinite-dimensional spaces that appear while modeling piezoelectric systems. We derive theorems that ensure convergence of function estimates to the actual function and develop algorithms for careful selection of the kernel basis functions.

The dramatic increase in market demand for wireless products has inspired a trend for new designs. These designs are smaller, less expensive, and consume less power. A natural result of this trend has been the push for components that are more highly integrated and take up less real estate on the printed circuit board (PCB). Major efforts are underway to reduce the number of integrated circuits (ICs) in newer designs by incorporating several functions into a single chip. Availability of newer technologies such as silicon bipolar with complementary metal oxide semiconductor (BiCMOS) has helped facilitate this move toward more complex circuit topologies onto one die. BiCMOS achieves efficient chip area utilization by combining bipolar transistors, suited for higher frequency analog circuits with CMOS transistors that are useful for digital functions and lower frequency analog circuits. A voltage controlled oscillator (VCO) is just one radio frequency (RF) circuit block that can benefit from a more complex semiconductor process like BiCMOS. This thesis presents the design and evaluation of an integrated VCO in the IBM 5S BiCMOS process. IBM 5S is a 0.5 um, single poly, five-metal process with surface channel PFETs and NFETs. The process also features self-aligned extrinsic base NPN bipolar devices exhibiting ft of up to 24 GHz. The objective of this work is to obtain a VCO design that provides a high degree of functionality while maximizing performance over environmental conditions. It is shown that an external feedback and resonator network as well as a bandgap voltage referenced bias circuit help to achieve these goals. An additional objective for this work is to highlight several pragmatic issues associated with designing an integrated VCO capable of high volume production. The Clapp variant of the Colpitts topology is selected for this application for reasons of robust operation, frequency stability, and ease of implementing in integrated form. Design is performed at 560 MHz using the negative resistance concept. Simulation results from Pspice and the Agilent ADS are presented. Implementation related issues such as bondwire inductances and layout details are covered. The VCO characterization is shown over several environmental conditions. The final nominal design is capable of: tuning over 150 MHz (22%) and delivering â 4.2 dBm into a 50 Ohm load while consuming only 9mA from a 3.0V supply. The phase noise at these conditions is -92.5 dBc/Hz at a frequency offset of 10 kHz from the carrier. Finally, the conclusion of this work lists some suggestions for potential future research. / Master of Science

The interest in tiny wireless applications raises the demand for an integrated reference oscillator with the same performance as the macroscopic quartz crystal reference oscillators. The main challenge of the thesis is to prove that it is possible to build a MEMS based oscillator that approaches the accuracy level of existing quartz crystal oscillators. The MEMS resonator samples which Philips provides are measured and an equivalent electrical model is designed for them. This model is used in the simulations of the Pierce oscillator and the transresistance amplifier oscillator that are evaluated in this thesis. Finally the Pierce oscillator is implemented in the A BCD2 process and manufactured at Philips Semiconductors in Nijmegen, The Netherlands. A test board, for measuring the Pierce oscillator together with a MEMS resonator or a quartz crystal resonator, is built. The Pierce oscillator is then measured with a quartz crystal resonator. In order to simulate the higher series resistance of the MEMS resonators a resistor is put in series with the quartz crystal. The Pierce oscillator is working with a series resistance of 1 kΩ. With higher series resistance the Pierce oscillator stops working. In circuit simulations the Pierce oscillator is working with a series resistance of about 5 kΩ in the MEMS resonator model. To be sure whether the Pierce oscillator has enough gain for the MEMS resonators, it needs to be measured with them. Temperature variations in the MEMS resonators need to be handled and the phase noise performance of the oscillator must be improved, in order for the MEMS based reference oscillator to be a successful replacement for the quartz crystal reference oscillator.

Because of IC technology evolution and the increase of market demand, the communication industry grows vigorously in recent years. The voltage-controlled oscillator plays a key role in the RF transceiver and provides oscillation signals needed for upconversin and downconvertion. Usually, we separate the signals into I/Q channels for modulation and demodulation in upconversin and downconvertion. Because the quality of the local oscillator influences the performance of communication system, designing a voltage-controlled oscillator that can provide two identical signals in accurate quadrature is necessary. In this thesis, a new quadrature voltage-controlled oscillator is presented. We use two identical relaxation oscillators with adjustable Schmitt triggers to construct the cross-coupled architecture. This oscillator has accurate ( <1¢X) and stable quadrature outputs which are independent of operating frequency and process variations. This oscillator circuit is fabricated in TSMC 0.35£gm CMOS Mixed-Signal process provided by National Chip Implementation Center (CIC). Our design is verified by simulation and measurement results.

abstract: Wearable robotics is a growing sector in the robotics industry, they can increase the productivity of workers and soldiers and can restore some of the lost function to people with disabilities. Wearable robots should be comfortable, easy to use, and intuitive. Robust control methods are needed for wearable robots that assist periodic motion. This dissertation studies a phase based oscillator constructed with a second order dynamic system and a forcing function based on the phase angle of the system. This produces a bounded control signal that can alter the damping and stiffens properties of the dynamic system. It is shown analytically and experimentally that it is stable and robust. It can handle perturbations remarkably well. The forcing function uses the states of the system to produces stable oscillations. Also, this work shows the use of the phase based oscillator in wearable robots to assist periodic human motion focusing on assisting the hip motion. One of the main problems to assist periodic motion properly is to determine the frequency of the signal. The phase oscillator eliminates this problem because the signal always has the correct frequency. The input requires the position and velocity of the system. Additionally, the simplicity of the controller allows for simple implementation. / Dissertation/Thesis / Doctoral Dissertation Mechanical Engineering 2016

Oscillators are ubiquitous to radio frequency circuits, where frequency translations and channel selection play a central role in the analogue communications channel. Oscillators also form part of digital systems as a time reference. Typical heterodyne receivers require an intermediate frequency channel. The associated oscillators and variable filters can only be centred perfectly at a single frequency, and degrade performance at the boundaries of the channel. These circuits also require image-rejecting filters and phase-locked loops in order to enable down-conversion. The penalties for these components are increased circuit area and power consumption. A direct down-conversion circuit will reduce the number of components in the system. A requirement added by the structural change is a passive sub-harmonic mixer. Quadrature oscillators may be achieved by cross-coupling two nominally identical LC differential voltage-controlled oscillators. Because of the widespread use of voltage-controlled oscillators in wireless communication systems, the development of comprehensive nonlinear analysis is pertinent in theory and applications. A key characteristic that defines the performance of an oscillator is the phase noise measurement. The voltage-controlled oscillator is also a key component in phase-locked loops, as it contributes to most of the out-of-band phase noise, as well as a significant portion of in-band noise. Current state-of-the-art modulation techniques, implemented at 60 GHz, such as quadrature amplitude modulation, and orthogonal frequency domain multiplexing, require phase noise specifications superior to 90 dBc/Hz at a 1 MHz offset. It has been shown that owing to the timing of the current injection, the Colpitts oscillator tends to outperform other oscillator structures in terms of phase noise performance. The Colpitts oscillator has a major flaw in that the start-up gain must be relatively high in comparison to the cross-coupled oscillator. The oscillation amplitude cannot be extended as in the cross-coupled case. The oscillator’s bias current generally limits the oscillation amplitude. The phase noise is defined by a stochastic differential equation, which can be used to predict the system’s phase noise performance. The characteristics of the oscillator can then be defined using the trajectory. The model projects the noise components of the oscillator onto the trajectory, and then translates the noise into the resulting phase and amplitude shift. The phase noise performance of an oscillator may be improved by altering the shape of the trajectory. The trajectory of the oscillator is separated into slow and fast transients. Improving the shape of the oscillator’s slow manifold may improve its phase noise performance, and improving the loaded quality factor of the tank circuit may be shown to directly improve upon close-in phase noise. The approach followed describes oscillator behaviour from a circuit-level analysis. The derived equations do not have a closed form solution, but are reformulated using harmonic balance techniques to yield approximate solutions. The results from this closed form approximation are very close to both the numerical solutions of the differential equations, as well as the Simulation Program with Integrated Circuit Emphasis solutions for the same circuits. The derived equations are able to predict the amplitude and frequency in the single-phase example accurately, and are extended to provide a numerical platform for defining the amplitude and frequency of a multiphase oscillator. The analysis identifies various circuit components that influence the oscillator’s phase noise performance. A circuit-level modification is then identified, enabling the decoupling of some of the factors and their interactions. This study demonstrates that the phase noise performance of a Colpitts oscillator may be significantly improved by making the proposed changes to the oscillator. The oscillator’s figure of merit is improved even further. When a given oscillator is set at its optimum phase noise level, the collector current will account for approximately 85% of the phase noise; with the approach in this work, the average collector current is reduced and phase noise performance is improved. The key focus of the work was to identify circuit level changes to an oscillator’s structure that could be improved or changed to achieve better phase noise performance. The objective was not to improve passive components, but rather to identify how the noise-to-phase noise transfer function could be improved. The work successfully determines what can be altered in an oscillator that will yield improved phase noise performance by altering the phase noise transfer function. / The concept is introduced on a differential oscillator and then extended to the multiphase oscillator. The impulse sensitivity function of the modified multiphase oscillator is improved by altering the typical feedback structure of the oscillator. The multiphase oscillator in this work is improved from -106 dBc/Hz to -113 dBc/Hz when considering the phase noise contribution from the tank circuits’ bias current alone. This is achieved by uniquely altering the feedback method of the oscillator. This change alters the noise-to-phase noise properties of the oscillator, reducing phase noise. The improvement in the phase noise does not account for further improvements the modification would incorporate in the oscillator’s limit cycle. For a given tank circuit, supply current and voltage, compared to an optimised Colpitts oscillator, the modifications to the feedback structure proposed in this work would further improve the figure of merit by 9 dB. This is not considering the change in the power consumption, which would yield a further improvement in the figure of merit by 7 dB. This is achieved by relaxing the required start-up current of the oscillator and effecting an improvement in the impulse sensitivity function. Future research could include further modelling of the phase shift in the feedback network, including the transmission lines in the feedback networks using the harmonic balance technique in a numerical form. The feedback technique can also be modified to be applicable to single and differential oscillators. / Dissertation (MEng)--University of Pretoria, 2017. / National Research Foundation / The Department of Science and Technology, South Africa / GEW Technologies (Pty) Ltd / Electrical, Electronic and Computer Engineering / MEng / Unrestricted