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

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This work is concerned with the derivation of general analytical formulae for the matrix elements, in an M representation, of effective two-nucleon interaction. The anisotropic harmonic oscillator wave equation is solved in cylindrical coordinates and the subsequent wave functions used to find the desired matrix element expressions. Since these expressions are in a form conducive to rapid machine computation this representation is well suited for spectroscopic calculations for deformed nuclei. This is illustrated by the calculation of the relative Mng energies, by means of a limited Hartree—Fock method, of several nucleonic configurations in the 2s-ld shell. / Thesis / Master of Science (MS)

The competitive market of wireless communication devices demands low power and low cost RF solutions. A quadrature local oscillator (LO) is an essential building block for most transceivers. As the CMOS technology scales deeper into the nanometer regime, design of a low-power low-voltage quadrature LO still poses a challenge for RF designers. This dissertation investigates a new quadrature LO topology featuring a transformer-based voltage controlled oscillator (VCO) stacked with a divide-by-two for low-power low-voltage wireless applications. The transformer-based VCO core adopts the Armstrong VCO configuration to mitigate the small voltage headroom and the noise coupling. The LO operating conditions, including the start-up condition, the oscillation frequency, the voltage swing and the current consumption are derived based upon a linearized small-signal model. Both linear time-invariant (LTI) and linear time-variant (LTV) models are utilized to analyze the phase noise of the proposed LO. The results indicate that the quality factor of the primary coil and the mutual inductance between the primary and the secondary coils play an important role in the trade-off between power and noise. The guidelines for determining the parameters of a transformer are developed. The proposed LO was fabricated in 65 nm CMOS technology and its die size is about 0.28 mm2. The measurement results show that the LO can work at 1 V supply voltage, and its operation is robust to process and temperature variations. In high linearity mode, the LO consumes about 2.6 mW of power typically, and the measured phase noise is -140.3 dBc/Hz at 10 MHz offset frequency. The LO frequency is tunable from 1.35 GHz to 1.75 GHz through a combination of a varactor and an 8-bit switched capacitor bank. The proposed LO compares favorably to the existing reported LOs in terms of the figure of merit (FoM). More importantly, high start-up gain, low power consumption and low voltage operation are achieved simultaneously in the proposed topology. However, it also leads to higher design complexity. The contributions of this work can be summarized as 1) proposal of a new quadrature LO topology that is suitable for low-power low-voltage wireless applications, 2) an in-depth circuit analysis as well as design method development, 3) implementation of a fully integrated LO in 65 nm CMOS technology for GPS applications, 4) demonstration of high performance for the design through measurement results. The possible future improvements include the transformer optimization and the method of circuit analysis. / Ph. D.

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International Telemetering Conference Proceedings / October 28-31, 1996 / Town and Country Hotel and Convention Center, San Diego, California / In this paper design and development of a PC- Based S- Band Down Converter/ FM Telemetry Receiver are discussed. With the advent of Direct Digital Synthesis (DDS) & Phase Locked Loop (PLL) technology, availability of GaAs & Silicon MMICs, Coaxial Resonator Oscillator (CRO), SAW Oscillator, SAW Filters and Ceramic Filters, realisation of single card PC- Based Down Converter and Telemetry Receiver has become a reality. With the availability of Direct Digital Synthesis and Phase Locked Loop devices having microprocessor bus compatibility, opens up many application in Telemetry and Telecommunications. In this paper design of local oscillator based on hybrid DDS & PLL technique, Coaxial Resonator Oscillator and Front-end are discussed in detail.

I den här avhandlingen visas hur lasrar och optiska parametriska oscillatorer (OPO:er) kan styras spektralt med hjälp av volymbraggitter. Volymbraggitter utgörs av ett periodiskt varierande brytningsindex som skrivits i ett fototermorefraktivt glas. Gittret reflekterar därmed en specifik våglängd som bestäms av perioden hos modulationen, och kan tillverkas med smal bandbredd och hög reflektans beroende på modulationens längd och styrka. En teoretisk modell har utvecklats för reflektiva volymbraggitters egenskaper om den infallande strålen har en större vinkelspridning än gittrets vinkeltolerans. Detta kan bl.a. inträffa i en laserkavitet där gittret används vid snett infall, och en teoretisk beskrivning är därför ett viktigt redskap för att kunna designa sådana lasrar. Spektral kontroll av ett antal fasta tillståndslasrar med hjälp av volymbraggitter har i försök påvisats, och lasern har därvid både kunnat avstämmas spektralt samtidigt som en avsmalnad spektral bandbredd erhållits. Lasern kan göras väldigt enkel genom att byta ut en av kavitetsspeglarna mot gittret. Tack vare gittrets goda spektrala urvalsmekanism kan lasern låsas var som helst i förstärkningsspektrumet. De tekniker och lasrar som demonstrerats experimentellt är följande: Lasring i en enda longitudinell mod erhölls både för en diodpumpad ErYb:glas-laser vid 1553 nm med ca 10 mW:s effekt och 90 kHz linjebredd samt för en diodpumpad Nd:GdVO4-laser vid 1066 nm med 0.85 W:s effekt. Lasrarnas våglängd kunde avstämmas över större delen av gittrets bandbredd på ca. 30 GHz. Genom att bygga Nd:GdVO4-lasern med en monolitisk kavitet kunde även en spektralt synnerligen stabil laser erhållas med under 40 MHz bandbredd. Tillämpningar för dessa lasrar finns både inom spektroskopi samt som källor för intrakavitetsfördubbling till synliga våglängder. Genom att använda gittret som inkopplingsspegel går det även att framställa lasrar med en väldigt låg kvantdefekt, som därför får minskad värmeutveckling i lasermediet. Detta medger i sin tur att lasrar med höga medeleffekter kan konstrueras, som kan användas bl.a. för olika former av materialbearbetning. I detta arbete har lasrar med låg kvantdefekt byggts med Yb:KYW som laserkristall; både en laser vid 998 nm på 3.6 W som diodpumpades vid 982 nm och med en bandbredd på 10 GHz, samt en laser vid 990 nm på 70 mW som pumpades av en Ti:safir-laser vid 980 nm. Om volymbraggittret används vid snett infall kan den reflekterade våglängden avstämmas genom att gittret roteras. Denna princip användes i en diodpumpad Yb:KYW-laser till att erhålla en brett avstämbar laservåglängd mellan 996 nm och 1048 nm med en maximal effekt på 3 W och med 10 GHz bandbredd. Genom att placera gittret i en retroreflektor kunde avstämningen göras utan att kaviteten behövde linjeras om. En laser som denna kan exempelvis användas för olika typer av materialkarakterisering och spektroskopi. Med optiska parametriska oscillatorer (OPO:er) kan laserljus omvandlas till nya våglängder. Därmed kan OPO:er användas som koherenta ljuskällor där inga effektiva lasrar existerar. OPO-processen kan göras effektiv om en pulsad pump används, och den genererade våglängden kan enkelt styras med hjälp av periodiskt polade (PP) icke-linjära kristaller, såsom PP-KTiOPO4, som användes i detta arbete. En nackdel med OPO:er är att i allmänhet är den genererade signalen tämligen spektralt bredbandig. Signalens bandbredd kan dock avsmalnas betydligt om ett spektralt filter såsom ett volymbraggitter används. Genom att byta ut en av speglarna i OPO-kaviteten mot gittret kan utformningen av OPO:n göras väldigt enkel. I en OPO med en signalvåglängd på 975 nm kunde en avsmalning av bandbredden till 50 GHz påvisas med hjälp av ett braggitter. Detta motsvarar 20 gångers minskning jämfört med om en konventionell spegel används. Som mest erhölls en pulsenergi på 0.34 mJ i signalen. Genom att rotera gittret kunde våglängden avstämmas 21 THz. För att förenkla avstämningen konstruerades även en OPO med gittret i en retroreflektor, samtidigt som kaviteten var av ringtyp. I denna OPO vid en våglängd på 760 nm och med en pulsenergi i signalen på upp till 0.42 mJ erhölls en bandbredd på 130 GHz och ett avstämningsområde på 2.6 THz. Slutligen har en OPO vid 1 µm konstruerats med ett gitter med en transversellt varierande period, s.k. chirp. Därigenom kan våglängden avstämmas väldigt enkelt genom att bara flytta gittret transversellt. En tillämpning av dessa OPO:er är såsom ljuskällor i olika typer av laserbaserade sensorer, i vilka en specifik och stabil våglängd erfordras. Dessutom kan de smalbandiga OPO:erna användas som första steg i ickelinjära processer i flera steg. Smal bandbredd är då viktig för effektiviteten i den påföljande ickelinjära omvandlingen i nästa steg. / The object of this thesis is to explore the usage of reflective volume Bragg gratings in photo-thermo-refractive glass for spectral control of solid-state lasers and optical parametric oscillators, to build tunable and narrowband coherent light-sources. In order to provide a design tool for use of reflective volume Bragg gratings in laser cavities, a theory was developed that describes the performance of the gratings if the incident beam has finite width with an angular spectrum that is comparable to the grating's angular acceptance bandwidth. Spectral control was demonstrated in a number of cw solid-state lasers, in terms of narrow bandwidth and tunable wavelength, by use of a volume Bragg grating. The design could be made very simple by replacing one of the cavity mirrors with the grating. Thanks to the grating's strong spectral selectivity, the lasers could be locked anywhere in the gain spectrum, while the laser bandwidth was substantially narrowed. In particular, the following lasers were demonstrated: Single-longitudinal-mode lasing in ErYb:glass at 1553 nm with 90 kHz linewidth and in Nd:GdVO4 at 1066 nm with a linewidth below 40 MHz. Very low quantum defect in Yb:KYW lasers, diode-pumped at 982 nm and lasing at 998 nm with 10 GHz bandwidth, as well as Ti:sapphire-pumped at 980 nm and lasing at 990 nm. An Yb:KYW laser that was widely tunable from 996 nm to 1048 nm with 10 GHz bandwidth. In nanosecond pulsed optical parametric oscillators (OPOs) based on periodically poled KTiOPO4, narrowband operation and a tunable wavelength were demonstrated with a volume Bragg grating as a cavity mirror. At a signal wavelength of 975 nm, the bandwidth was 50 GHz, a reduction by 20 times compared to using a conventional mirror. A tuning range of 21 THz was also demonstrated. In another OPO at a signal wavelength of 760 nm, a ring-cavity design was demonstrated to provide convenient tuning. A tuning range of 2.6 THz and a bandwidth of 130 GHz was shown. Also, narrowband operation and tuning in an OPO around 1 µm was demonstrated by use of a transversely chirped Bragg grating. / QC 20100813

In this thesis, we present a new continuously variable high frequency standing wave oscillator and demonstrate its use in generating the phase locked clock signal of a digital IC. The ring based standing wave resonant oscillator is implemented with a plurality of wires connected in a mobius configuration, with a cross coupled inverter pair connected across the wires. The oscillation frequency can be modulated by coarse and fine tuning. Coarse modification is achieved by altering the number of wires in the ring that participate in the oscillation, by driving a digital word to a set of passgates which are connected to each wire in the ring. Fine tuning of the oscillation frequency is achieved by varying the body bias voltage of both the PMOS transistors in the cross coupled inverter pair which sustains the oscillations in the resonant ring. We validated our PLL design in a 90nm process technology. 3D parasitic RLCs for our oscillator ring were extracted with skin effect accounted for. Our PLL provides a frequency locking range from 6 GHz to 9 GHz, with a center frequency of 7.5 GHz. The oscillator alone consumes about 25 mW of power, and the complete PLL consumes a power of 28.5 mW. The observed jitter of the PLL is 2.56 percent. These numbers are significant improvements over the prior art in standing wave based PLLs.

TO achieve high level of integration in order to reduce cost, heterodyne architecture has made way for low-IF and zero-IF (direct conversion) receiver architectures. However, a very serious issue in implementing both zero and low-IF receiver is of local oscillator (LO) pulling. Another challenge is on-chip generation of high-precision quadrature LO signals for image-rejection. We have addressed both these issues in this thesis. Regarding the first problem, we have developed a lowpower frequency multiplication technique which uses a low frequency ring oscillator and multiplies its frequency in power e cient way to generate the desired frequency. We then use this differential LO signal to generate high-precision quadrature phases by using polyphase filter and an injection-locked quadrature oscillator. Design examples are presented for 2.4 GHz band of IEEE 802.15.4 standard which is a low-data rate WPAN standard. The standard o ers relaxed performance specifications in order to help achieve low power of operation. Contributions in the thesis • The problem of local oscillator (LO) pulling can be addressed by running LO at a much reduced frequency and use a frequency multiplier (FM) to generate the desired frequency. Also, use of low-frequency LO saves power in VCO and helps eliminate first few dividers leading to significant power savings. In addition, the entire frequency synthesizer can be run at a lower supply voltage saving additional power. The frequency multiplier involves combining edges from the lower frequency ring oscillator. It improves upon the prior work by proposing a new lower-power edge-combiner. The overall power is reduced by exploiting the relaxed phase noise specification of IEEE 802.15.4 standard. Simulations using SpectreRF show that the circuit consumes only 550 ｵW of power in 0.13 ｵm RF-CMOS technology with 1.2 V supply voltage, and provides 950 VP-P sinusoidal output with phase noise of -85.5 dBc/Hz at 1 MHz offset. • An injection-locking based quadrature desensitization circuit is designed for precision quadrature generation. The differential (two phase) output of the frequency multiplier is fed to a polyphase filter to generate nearly quadrature signals. Output of polyphase filter is in turn fed to the desensitizer circuit to obtain high-precision quadrature signals. Designed for 2.4 GHz band in 0.13 µm RF-CMOS technology, it achieves a phase error of 0.5 for 1% mismatch in LC tanks. It achieves a phase noise of -84.3 dBc/Hz at 1 MHz o set and provides quadrature sinusoids of 475 mV amplitude while consuming 1.56 mW of power. • We have analyzed the popular cross-coupled LC-VCOs to generate quadrature sinusoids. In practical LC-oscillators built using low/moderate quality factor on-chip inductors, the actual frequency of oscillation is a little less than 1/2pvLC . This is known as Groszkowski effect. On the other hand, in quadrature oscillator topologies, consisting of two, cross-coupled, negative resistance LC-VCOs using parallel coupling transistors, an upward shift in frequency of oscillation from the free-running frequency of each LC-VCO is observed. This is because in order to satisfy the Barkhausen’s criteria, the LC-tanks have to operate at a frequency away from the frequency of resonance. This e ect called as quadrature detuning effect results in higher phase noise and reduced amplitude. We have shown that the old treatment given in literature is quite inaccurate for practical LC oscillators that are built using low/mo derate Q on-chip inductors. Also the prior work ignores Groszkowski effect which could be significant for low Q LC tanks. We have provided simple, accurate and closed-form expressions of associated frequency-shifts and amplitude of oscillation including both the effects. Our results show excellent match with results obtained from SpectreRF and Matlab simulations.