In this thesis, a second-order low pass square root domain filter (SRD filter) based on operational transconductors amplifiers (OTAs) is presented. The SRD filter consists of two translinear filters and four OTAs. Because the OTA has small voltage swings, which may violate the large signal natural of the SRD filter. We investigate the dynamic range of this compact SRD filter with different quality factor(Q). The circuit has fewer numbers of transistors and operate in low voltage, therefore, it has less power consumption and less chip area. The circuit has been fabricated with 0.35£gm CMOS technology. It operates with a supply voltage 1.5V and the biasing current varies from 10uA to 80uA. Measurement results lts show that Im/I0≥40% when the external capacitance C is 3.5pF¡B7pF and Im/I0≥53% when the external capacitance C is 3pF¡B8.5pF. The cutoff frequency of the filter can be tuned from 1.24MHz to 5.53MHz when the external capacitance C is 3.5pF¡B7pF and the cutoff frequency can be tuned from 900KHz to 4.46MHz when the external capacitance C is 3pF¡B8.5pF. The total harmonic distortion is 0.908% and the power consumption is 506£gW.

Two kinds of companding filters are presented in this dissertation. The first one is a square-root domain filter based on operational transconductance amplifier (OTA). This one is compact and simple. The total are of the circuit excluding pads is 0.013 mm2. The supply voltage is 1.5V and the cutoff frequency can be tuned from 1.1 kHz to 35.2 kHz when the external capacitance C is 1nF. The total harmonic distortions is 0.93% and the power consumption is 152.29 £gW for a 10£gA DC input current. The other one is a tunable log-domain filter. The log domain filters uses parasitic vertical bipolar junction transistor (VBJT) in standard CMOS process for high frequency. The cut-off frequency is from 8.6 MHz to 25.8 MHz and the power dissipation is 585 £gW. All experimental results in a TSMC 0.35 £gm 2P4M CMOS process confirm the feasibility of the methodology.

Conventional gm-c filters have limited voltage swings in low voltage operation. CMOS companding filters replace gm-c filters in low voltage environment for high dynamic range. The square-root domain filter and log-domain filter belongs to this companding filter category. In this thesis, a second order low pass square root domain filter (SRD filter) based on the up-down TL (translinear loop) circuit structure is presented. The SRD filter consists of four geometric-mean cells and three squarer/divider cells. The advantages of the proposed circuits are low supply voltage, low power consumption, high bandwidth, and low total harmonic distortion (THD). The circuit has been fabricated with 0.35£gm CMOS technology. It operates with a supply voltage of 1.5V, and the bias current varies from 0.5£gA to 30£gA. Measurement results show that the cutoff frequency can be tuned from 3.12MHz to 8.11MHz when the Capacitance (C) is 5pF.The total harmonic distortion is 0.28%, and the power consumption is 1.09mW.

Bimetric theory is an extension to general relativity that introduces a secondary symmetric rank-two tensor field. This secondary spin-2 field is also dynamical, and to avoid the Boulware-Deser ghost issue, the interaction between the two fields is obtained through a potential that involes the matrix square-root of the tensors. This square-root “quantity” is a linear transformation, herein referred to as the square-root isometry. In this work we explore the conditions for the existence of the square-root isometry and its group properties. Morever we study the conditions for the simultaneous 3+1 decomposition of two fields, and then, in terms of null-cones, give the (local) causal relations between fields coupled by the square-root isometry. Finally, we show the algebraic equivalency of bimetric theory and its vielbein formulation up to a one-to-one map relating the respective parameter spaces over the real numbers. / Den bimetriska teorin är en utökning av den allmänna relativitetsteorin som introducerar ett sekundärt symmetriskt tensorfält av rang-två. Det här sekundära spin-2 fältet är också dynamiskt, och för att undvika Boulware-Deser spöke, erhålls vaxelverkan mellan de två fältena genom en potential som er baserad på kvadratrotsmatris av två tensorfält. Den “kvadratroten” är en linjär avbildning som kallas kvadratrotsisometri. I detta arbete utforskas förutsättningar för existensen av kvadratrotsisometrin och ges dess egenskaper i termer av gruppteori. Därutöver utforskas förutsättningarna för den samtidiga 3+1 dekompositionen av två tensorfält och sedan, i termer av ljuskoner, ges de (lokala) kausala relationerna för tensorfält kopplade genom kvadratrotsisometrin. Slutligen bevisas den algebraiska ekvivalensen mellan den bimetriska teorin och dess vielbein formulering upp till en bijektiv relation mellan respektive parameterutrymmen över de reella talen. / <p>Summarizes the results from the project done between March 2014 and November 2014.</p>

It was observed that many hydraulically fractured horizontal shale gas wells exhibit transient linear flow behavior. A half-slope on a type curve represents this transient linear flow behavior. Shale gas wells show a significant skin effect which is uncommon in tight gas wells and masks early time linear behavior. Usually 70-85 percent of frac water is lost in the formation after the hydraulic fracturing job. In this research, a shale gas well was studied and simulated post hydraulic fracturing was modeled to relate the effect of frac water to the early significant skin effect observed in shale gas wells. The hydraulically fractured horizontal shale gas well was described in this work by a linear dual porosity model. The reservoir in this study consisted of a bounded rectangular reservoir with slab matrix blocks draining into neighboring hydraulic fractures and then the hydraulic fractures feed into the horizontal well that fully penetrates the entire rectangular reservoir. Numerical and analytical solutions were acquired before building a 3D 19x19x10 simulation model to verify accuracy. Many tests were conducted on the 3D model to match field water production since initial gas production was matching the analytical solutions before building the 3D simulation model. While some of the scenarios tested were artificial, they were conducted in order to reach a better conceptual understanding of the field. Increasing the water saturation in the formation resulted in increasing water production while lowering gas production. Adding a fractured bottom water layer that leaked into the hydraulic fracture allowed the model to have a good match of water and gas production rates. Modeling trapped frac water around the fracture produced approximately the same amount of water produced by field data, but the gas production was lower. Totally surrounding the fracture with frac water blocked all gas production until some of the water was produced and gas was able to pass through. Finally, trapped frac water around the fracture as combined with bottom water showed the best results match. It was shown that frac water could invade the formation surrounding the hydraulic fracture and could cause formation damage by blocking gas flow. It was also demonstrated that frac water could partially block off gas flow from the reservoir to the wellbore and thus lower the efficiency of the hydraulic fracturing job. It was also demonstrated that frac water affects the square root of time plot. It was proven by simulation that the huge skin at early time could be caused by frac water that invades and gets trapped near the hydraulic fractures due to capillary pressure.

In this thesis, a brand new first-order low pass square root domain filter (SRD filter) based on operational transconductors amplifiers (OTAs) is presented. The SRD filter consists of a translinear filter and two OTAs. We improve Cruz¡¦s SRD filter [15], reduce the number of transconductors from 3 to 2, and replace Class-AB linear transconductors with OTAs. The circuit has the least number of transistors up to date, therefore, the least power consumption and least chip area. The circuit has been fabricated with 0.35£gm CMOS technology. It operates with a supply voltage 1.5V and the biasing current varies from 0.05uA to 15uA. Measurement results show that the cutoff frequency of the filter can be tuned from 250 Hz to 29 kHz when the external capacitance C is 1nF and the cutoff frequency can be tuned from 1.8 kHz to 237kHz when the external capacitance C is 100pF. The total harmonic distortion is 1.03% and 1.01% when the external capacitance C is 1nF and 100pF and the power consumption is 116£gW.

In this thesis, a first order low pass square root domain filter (SRD filter) based on the novel operational transconductor amplifiers (OTAs) is presented. The SRD filter consists of a translinear filter and two OTAs. Because the conventional OTA has small input voltage swings, which violates the large signal operation of a SRD filter. We propose the novel OTA which is based on the large signal behaviors of MOSFETs, and the OTA also has large signal operation. We improve Cruz¡¦s SRD filter [22], reduce the number of the transconductors from 3 to 2, and replace Class-AB linear transconductors with the proposed OTAs. The MOSFET count of whole circuit can be reduced. Therefore, the OTAs have many advantages: wider input voltage swing, low supply voltage, low power consumption, and small chip area. The circuit has been fabricated with 0.35£gm CMOS technology. It operates with a supply voltage 1.5V and the bias current varies from 0.3£gA to 15£gA. Measurement results show that the cutoff frequency can be tuned from 1.1kHz to 35.2kHz when the external capacitance C is 1nF and the cutoff frequency can be tuned from 8.7kHz to 310.4kHz when the external capacitance C is 100pF. The total harmonic distortions are 0.93% and 0.91% when the external capacitances C are 1nF and 100pF, and the power consumption is 152.29£gW.

International Telemetering Conference Proceedings / October 21, 2002 / Town & Country Hotel and Conference Center, San Diego, California / As frequency allocation restrictions are tightening, and data rates are increasing, it is becoming necessary to incorporate higher order modulation techniques to make more efficient use of available spectrum. When used with Square Root Raised Cosine filtering, 8-ary Phase Shift Keyed modulation is a spectrally efficient technique that makes better use of today’s RF spectrum in comparison to standard formats. This paper will discuss 8-ary PSK modulation and its spectral efficiency with a SRRC filter, along with comparisons to BPSK, QPSK, and FSK.

The growing interest in computing structured matrix functions stems from the fact that preserving and exploiting the structure of matrices can help us gain physically meaningful solutions with less computational cost and memory requirement. The work presented here is divided into two parts. The first part deals with the computation of functions of structured matrices. The second part is concerned with the structured error analysis in the computation of matrix functions. We present algorithms applying the inverse scaling and squaring method and using the Schur-like form of the symplectic matrices as an alternative to the algorithms using the Schur decomposition to compute the logarithm of symplectic matrices. There are two main calculations in the inverse scaling and squaring method: taking a square root and evaluating the Padé approximants. Numerical experiments suggest that using the Schur-like form with the structure preserving iterations for the square root helps us to exploit the Hamiltonian structure of the logarithm of symplectic matrices. Some type of matrices are nearly structured. We discuss the conditions for using the nearest structured matrix to the nearly structured one by analysing the forward error bounds. Since the structure preserving algorithms for computing the functions of matrices provide advantages in terms of accuracy and data storage we suggest to compute the function of the nearest structured matrix. The analysis is applied to the nearly unitary, nearly Hermitian and nearly positive semi-definite matrices for the matrix logarithm, square root, exponential, cosine and sine functions. It is significant to investigate the effect of the structured perturbations in the sensitivity analysis of matrix functions. We study the structured condition number of matrix functions defined between smooth square matrix manifolds. We develop algorithms computing and estimating the structured condition number. We also present the lower and upper bounds on the structured condition number, which are cheaper to compute than the "exact" structured condition number. We observe that the lower bounds give a good estimation for the structured condition numbers. Comparing the structured and unstructured condition number reveals that they can differ by several orders of magnitude. Having discussed how to compute the structured condition number of matrix functions defined between smooth square matrix manifolds we apply the theory of structured condition numbers to the structured matrix factorizations. We measure the sensitivity of matrix factors to the structured perturbations for the structured polar decomposition, structured sign factorization and the generalized polar decomposition. Finally, we consider the unstructured perturbation analysis for the canonical generalized polar decomposition by using three different methods. Apart from theoretical aspect of the perturbation analysis, perturbation bounds obtained from these methods are compared numerically and our findings show an improvement on the sharpness of the perturbation bounds in the literature.

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