The paper extends the analytical results obtained by Hwung et al. (1981) and further considers the non-linearity of waves to investigate variation horizontal velocity, temperature distribution induced by interaction of 2-D plane jet and waves. On the steady state, the nonlinear wave is considered as external force in motion equations, the property of momentum conservation of jet flow, and radiation stress are applied to analyze the interaction of waves- jet flow in arbitrary profile. The scale function 1 £` £\1(x) , 2 2£` £\ (x) between the variation function f (x,y) and velocity distribution can also be obtained. The non-dimensional theoretical solution is also useful to estimate the relative characteristics in the physical field. The momentum equation and velocity distribution of interaction without property of temperature diffusion are employed to find the temperature distribution for arbitrary sections. Based on the experiments and theory solution obtained by Hwung et al. (1981) it is found that time-averaged horizontal velocity and temperature are Gaussian distribution, the coefficient of horizontal velocity 1 c , and temperature distribution 2 c are 0.105, 0.148, respectively. In the present, two coefficients considered as non-linearity of waves 1 c = 0.124 and 2 c = 0.152 are determined. In other words, it is shown that exact solution and boundary effect included non-linearity of waves is related to velocity of jet flow, wave periods, relative depth and steepness of waves respectively. Comparing with experiments indicated that the analytical solution of the present for MSE is well confirm the experimental results and better than linear results obtained by Hwung et al. (1981) The influence due to interaction of 2-D turbulent jet flow and Stokes waves can be obtained by using dimension analysis. Moreover, the related properties inside the flow also can be estimated.

Analog circuits that operate with low voltage supply headroom generally suffer from poor linearity performance, poor noise performance, etc. However, with the aggressive scaling of the supply voltage in Complementary Metal Oxide Semiconductor (CMOS) technology and the advent of System-On-Chip (SOC) technologies, it is inevitable that these circuits are to be operated with low voltage supply headroom. In this thesis, three low-voltage Integrated Circuits (IC) for Radio Frequency (RF) communication systems are presented. They are all designed and fabricated with 0.13um CMOS technology. Their experimental verifications are performed on die with Coplanar Waveguide (CPW) probes. The first circuit is an ultra-low-voltage low-power single-balanced $\times$2 subharmonic down-conversion mixer. A linearity analysis for the inductive source degenerated transconductor of the mixer is provided using Volterra series. This analysis provides a guideline for designing the inductive source degenerated transconductor with high linearity at the RF frequency of 8.6 GHz. The circuit achieves a conversion gain of 6.0 dB and an $IIP_{3}$ of -8.0 dBm at the RF frequency of 8.6 GHz while consuming 0.6 mW of DC power with the supply voltage of 0.6 V. The second circuit is a low-voltage low-noise wideband down-conversion mixing frontend that consists of a Low-Noise Amplifier (LNA) and a passive mixer. The linearity analysis for the LNA, which is used as a transconductor, is analyzed using Volterra series. Through this analysis, the trade-off between noise cancellation and distortion cancellation is discussed. A simple distortion cancellation scheme that decouples the design guidelines from this trade-off is proposed. From 300 MHz to 1.2 GHz, the circuit achieves a conversion gain of 8.8 dB and a maximum $IIP_{3}$ of -0.8 dBm, while having less than 4.8 dB noise figure. The overall circuit consumes 24.0 mW of power with the supply voltage of 0.9 V. The third circuit is a low-voltage low-noise wideband active balun. The linearity analysis for the active balun circuit is also analyzed using Volterra series. The design consideration involving noise cancellation and distortion cancellation is discussed through this analysis. A simple distortion cancellation scheme that aims at improving the linearity performance of the circuit with low-voltage supply constraint is proposed. From 300 MHz to 2.4 GHz, the circuit achieves an average voltage gain of 15.5 dB and a maximum $IIP_{3}$ of -1.7 dBm, while having less than 4.0 dB noise figure from 500 MHz to 3.0 GHz. The overall circuit consumes 15.8 mW of power with the supply voltage of 0.9 V. / Thesis (Master, Electrical & Computer Engineering) -- Queen's University, 2011-09-22 02:48:14.824

The 21st century is emerging into an era of wireless ubiquity. To support this trend, the RF (Radio Frequency) front end must be capable of processing a range of wireless signals (cellular phone, data connectivity, broadcast TV, GPS positioning, etc.) spanning a total bandwidth of nearly 6 GHz. This warrants the need for multi-band/multi-mode radio architectures. For such architectures to satisfy the constraints on size, battery life, functionality and cost, the radio front-end must be made reconfigurable. RF-MEMS (RF Micro-Electro-Mechanical Systems) are seen as an enabling technology for such reconfigurable radios. RF-MEMS mainly include micromechanical switches (used in phase shifters, switched capacitor banks, impedance tuners etc.) and micromechanical resonators (used in tunable filters, oscillators, reference clocks etc.). MEMS technology also has the potential to be directly integrated into CMOS (Complementary metal-oxide semiconductor) ICs (Integrated Circuits) leading to further potential reductions of cost and size. However, RF-MEMS face challenges that must be addressed before they can gain widespread commercial acceptance. Relatively low switching speed, power handling, and high-voltage drive are some of the key issues in MEMS switches. Phase noise influenced by non-linearities, need for temperature compensation (especially Si based resonators), large start-up times, and aging are the key issues in Si MEMS Resonators. In this work potential solutions are proposed to address some of these key issues, specifically the reduction of high voltage drives in switches and the reduction of phase noise in MEMS resonators for timing applications. MEMS devices that are electrostatically actuated exhibit significant non-linearities. The origins of the non-linearities are both electrical (electrostatic actuation) and mechanical (dimensions and material properties). The influence of spring non-linearities (cubic and quadratic) on the performance of switches and resonators are studied. Gold electroplated fixed-fixed beams were fabricated to test the phenomenon of dynamic (or resonant) pull-in in shunt switches. The dynamic pull-in phenomenon was also tested on commercially fabricated lateral switches. It is shown that the resonant pull-in technique reduces the overall voltage required to actuate the switch. There is an additional reduction of total actuation voltage possible via applying an AC actuation signal at the correct non-linear resonant frequency. The demonstrated best case savings from operating at the non-linear resonanceis 50 % (for the lateral switch) and 60 % (for the vertical switch) as compared to 25 % and 40 % respectively using a fixed frequency approach. However, the timing response for resonant pull-in has been experimentally shown to be slower than the static actuation. To reduce the switching time, a shifted-frequency method is proposed where the excitation frequency is shifted up or down by a discrete amount 'Ω after a brief hold time. It was theoretically shown that the shifted-frequency method enables a minimum realizable switching time comparable to the static switching time for a given set of actuation frequencies. The influence of VDC on the effective non-linearities of a fixed-fixed beam is also studied. Based on the dimensions of the resonator and the type of resonance there is a certain VDC,Lin where the response is near linear (S ' 0). In the near-linear domain, the dynamic pull-in is the only upper bound to the amplitude of vibrations, and hence the amplitude of output current, thereby maximizing the power handling capacity of the resonator. Apart from maximizing the output current, it is essential to reduce the amplitude and phase variations of the displacement response which are due to noise mixing into frequency of interest, and are eventually manifested as output phase noise due to capacitive current nonlinearity. Two major aliasing schemes were analyzed and it was shown that the capacitive force non-linearity is the major source of mixing that causes the up-conversion of 1/f frequency into signal sidebands. The resonator's periodic response (displacement) is defined by a set of two first- order nonlinear ordinary differential equations that describe the modulation of amplitude and phase of the response. Frequency response curves of amplitude and frequency are determined from these modulation equations. The zero slope point on the amplitude resonance curve is the peak of the resonance curve where the phase ('dc) of the response is ±π/2. For a strongly non-linear system, the resonance curves are skewed based on the amount of total non-linearity S. For systems that are strongly non-linear, the best region to operate the resonator is the fixed point that correspond to infinite slope ('dc = ±2π/3) in the frequency response of the system. The best case phase noise response was analytically developed for such a fixed point. Theoretically at this fixed point, phase noise will have contributions only from 1/f noise and not from 1/f2 and 1/f3. The resonators phase can be set by controlling the rest of the phase in the loop such that the total phase around the loop is zero or 2π. In addition, this work has also developed an analytical model for a lateral MEMS switch fabricated in a commercial foundry that has the potential to be processed as MEMS on CMOS. This model accounts for trapezoidal cross sections of the electrodes and springs and also models electrostatic fringing as a function of the moving gap. The analytical model matches closely with the Finite Element (FEA) model. / Ph. D.

No description available.

Three components, gain analysis, tolerance analysis in-depth, and a brief non- linearity analysis, are presented. In the first component, the effects of an Erbium doped waveguide amplifier in a microring are investigated using a time domain simulation. Methods to simulate the gain versus average input signal power in the microring are studied, given that it has a long lifetime compared to the short delay time of the microring. The methods are based on the dependence of the gain on the power of the signal being fed to the ring. An algorithm is proposed to perform a thorough tolerance analysis on any optical circuit with respect to any optical parameter. The algorithm, based on Monte Carlo Simulation, is implemented on a complex optical circuit that is designed to obtain a bandpass filter response of given specifications. It is also tested on similar designs for a comparative study between them. The parameters and the structure of the designs used for the analysis are presented in detail. The results are presented in terms of the yield with respect to the parameter being varied, against their tolerance value. Algorithms for studying the effects of two types of non-linearities are presented. The Kerr nonlinearity and the two-photon absorption are included in the bandpass filter designs used for the tolerance analysis. The algorithms are based on the power circulating in different regions of the circuit under consideration. The variation in the original response because of the loss due to nonlinearity is observed and analyzed for different power levels of the input signal.

The CDMA standard operating over the wireless environment along with various other wireless standards places stringent specifications on the RF Front end. Due to possible large interference signal tones at the receiver end along with the carrier, the Low Noise Amplifier (LNA) is expected to provide high linearity, thus preventing the intermodulation tones created by the interference signal from corrupting the carrier signal. The research focuses on designing a novel LNA which achieves high linearity without sacrificing any of its specifications of gain and Noise Figure (NF). The novel LNA proposed achieves high linearity by canceling the IM3 tones in the main transistor in both magnitude and phase using the IM3 tones generated by an auxiliary transistor. Extensive Volterra series analysis using the harmonic input method has been performed to prove the concept of third harmonic cancellation and a design methodology has been proposed. The LNA has been designed to operate at 900MHz in TSMC 0.35um CMOS technology. The LNA has been experimentally verified for its functionality. Linearity is usually measured in terms of IIP3 and the LNA has an IIP3 of +21dBm, with a gain of 11 dB, NF of 3.1 dB and power consumption of 22.5 mW.

No description available.

The use of optical feedback for improving response linearity of electrooptic light modulators has been investigated. The modulator is configured as a straight channel waveguide flanked by electrodes in a lithium niobate (LiNbO3) substrate. Light is coupled into the waveguide in both TE and TM polarizations, and a voltage applied across electrodes causes a relative phase shift between two polarization components. An output analyzer converts the phase modulation to intensity modulation. Optical feedback of light in both polarization modes results from reflection of light at the polished edges of the substrate. Channel waveguides supporting a single guided mode for TE and TM polarizations were fabricated in x-cut LiNbO3 substrates using titanium-indiffusion technique. The waveguides and modulators were characterized at a wavelength of 1.55 ??m using a distributed feedback laser. The modulators were driven with a sinusoidal voltage waveform. To minimize harmonics of the modulating frequency in the intensity output, the magnitude of the optical feedback and the substrate temperature were adjusted. The feedback level was altered by applying refractive index-matching liquid to one or both ends of the waveguide at the edges of the crystal. It was found that a high degree of response linearity in the presence of feedback was achievable at certain substrate temperatures. The spurious-free dynamic range (SFDR) relative to the noise floor was measured at different feedback levels and substrate temperatures in an effort to maximize the modulator response linearity. An SFDR of 68.04 dB, limited by third-order nonlinearity, was achieved by applying index-matching fluid to the input end of the substrate. This compares with an SFDR of 64.84 dB limited by second-order nonlinearity when index-matching fluid was applied at both ends of the substrate. By changing the temperature of the same substrate to adjust the phase shifts experienced by TE and TM polarizations, the SFDR with index-matching fluid at the input end increased to 71.83 dB, limited by third-order nonlinearity. In tests at constant modulation depth, an improvement of as much as 9.6 dB in SFDR vs. the theoretical value for an interferometric modulator without feedback was achieved.

Phase locked loops (PLL) are used in many applications. Application examples include clock and data recovery, clock synthesis, frequency synthesis, modulator, and de-modulator. In many circuits, PLL must provide an output clock to follow the input clock closely. For high speed environments, the noises also rise up. Noises mainly come from the power supply and substrate. They produce jitter. A low jitter design is important in PLL circuit. In this thesis, we discuss the Voltage Controlled Oscillator (VCO) which has the largest jitter in PLL system. We propose a low jitter voltage controlled oscillator designed in TSMC 0.35£gm 2P4M Mixed-Signal process technology. We include a regulator to reduce jitter by increasing the VCO PSRR. This structure also provides a high linearity gain (Kvco) which decreases the VCO jitter in the PLL circuit and improve the system stability.

The use of optical feedback for improving response linearity of electrooptic light modulators has been investigated. The modulator is configured as a straight channel waveguide flanked by electrodes in a lithium niobate (LiNbO3) substrate. Light is coupled into the waveguide in both TE and TM polarizations, and a voltage applied across electrodes causes a relative phase shift between two polarization components. An output analyzer converts the phase modulation to intensity modulation. Optical feedback of light in both polarization modes results from reflection of light at the polished edges of the substrate. Channel waveguides supporting a single guided mode for TE and TM polarizations were fabricated in x-cut LiNbO3 substrates using titanium-indiffusion technique. The waveguides and modulators were characterized at a wavelength of 1.55 ??m using a distributed feedback laser. The modulators were driven with a sinusoidal voltage waveform. To minimize harmonics of the modulating frequency in the intensity output, the magnitude of the optical feedback and the substrate temperature were adjusted. The feedback level was altered by applying refractive index-matching liquid to one or both ends of the waveguide at the edges of the crystal. It was found that a high degree of response linearity in the presence of feedback was achievable at certain substrate temperatures. The spurious-free dynamic range (SFDR) relative to the noise floor was measured at different feedback levels and substrate temperatures in an effort to maximize the modulator response linearity. An SFDR of 68.04 dB, limited by third-order nonlinearity, was achieved by applying index-matching fluid to the input end of the substrate. This compares with an SFDR of 64.84 dB limited by second-order nonlinearity when index-matching fluid was applied at both ends of the substrate. By changing the temperature of the same substrate to adjust the phase shifts experienced by TE and TM polarizations, the SFDR with index-matching fluid at the input end increased to 71.83 dB, limited by third-order nonlinearity. In tests at constant modulation depth, an improvement of as much as 9.6 dB in SFDR vs. the theoretical value for an interferometric modulator without feedback was achieved.