**A Study of Ring Amplifier Noise Performance**Scaling of integrated circuit technology into the submicron region has been driven by digital design parameters. Analog design
parameters have not universally improved. One consequence of these changes is that high performance operational amplifiers have become increasingly difficult to design efficiently. These amplifiers
are often needed in high-resolution analog-to-digital converters. Recently, ring amplifiers have emerged as a scalable amplification technique built on a three-stage uncompensated amplifier
featuring a dynamic gain-bandwidth product.

An important aspect of amplifiers in high-resolution applications is knowledge of their noise performance. The dynamic bandwidth of ring amplifiers has resulted in the noise performance of ring amplifiers remaining uncharacterized in literature. This work identifies the problem with traditional noise estimation techniques when used on a ring amplifier. Alternative methods of estimation are presented, and the results are shown with respect to key ring amplifier design parameters. A 15 bit pipelined analog-to-digital converter to investigate the veracity of the noise estimation techniques is then detailed including a novel circuit to improve noise performance in ring amplifiers.

Major Advisor: Un-Ku Moon

Committee: Arun Natarajan

Committee: Gabor Temes

Committee: Karti Mayaram

GCR: David Hackleman

An important aspect of amplifiers in high-resolution applications is knowledge of their noise performance. The dynamic bandwidth of ring amplifiers has resulted in the noise performance of ring amplifiers remaining uncharacterized in literature. This work identifies the problem with traditional noise estimation techniques when used on a ring amplifier. Alternative methods of estimation are presented, and the results are shown with respect to key ring amplifier design parameters. A 15 bit pipelined analog-to-digital converter to investigate the veracity of the noise estimation techniques is then detailed including a novel circuit to improve noise performance in ring amplifiers.

Major Advisor: Un-Ku Moon

Committee: Arun Natarajan

Committee: Gabor Temes

Committee: Karti Mayaram

GCR: David Hackleman

**Finite Element Analysis Modeling and Experimental Verification of Reflected Wave Phenomena in Variable Speed Machine Drive Cable**Modern variable speed machine drive (VSMD)
systems are used for a variety of purposes including generation, propulsion, pumps and compressors. They employ high switching frequency power electronics to drive the electric machine. The machine
is subject to large voltage overshoot if long power cables, are used, called Reflected Wave Phenomena (RWP), that can result in high electrical stress on the VSMD insulation system.

The adoption of higher switching speed wide bandgap (WBG) power semiconductor devices for increased VSMD system efficiencies will result in RWP, up to twice the DC bus voltage, occurring in shorter power cable lengths with likely occurrences of even larger over-voltage at previously acceptable cable lengths.

This work investigates the effects that VSMD inverter switching frequency, pulse rise time and cable length have on RWP. A 2D finite element analysis (FEA) cable model is proposed to account for the frequency dependent cable such as skin effect. The FEA model is then compiled into a circuit simulation component and simulated against varying VSMD system parameters. The accuracy of the modeling technique is experimentally verified by testing varying power cable lengths. Simulations and experimental testing show that PWM rise time, switching frequency and cable length all heavily impact the over-voltages seen at the output of the power cables. The simulation results were found to similarly match the experimental findings.

Co-Major Advisor: Annette von Jouanne

Co-Major Advisor: Julia Zhang

Committee: Eduardo Cotilla-Sanchez

GCR: Christopher Hagen

The adoption of higher switching speed wide bandgap (WBG) power semiconductor devices for increased VSMD system efficiencies will result in RWP, up to twice the DC bus voltage, occurring in shorter power cable lengths with likely occurrences of even larger over-voltage at previously acceptable cable lengths.

This work investigates the effects that VSMD inverter switching frequency, pulse rise time and cable length have on RWP. A 2D finite element analysis (FEA) cable model is proposed to account for the frequency dependent cable such as skin effect. The FEA model is then compiled into a circuit simulation component and simulated against varying VSMD system parameters. The accuracy of the modeling technique is experimentally verified by testing varying power cable lengths. Simulations and experimental testing show that PWM rise time, switching frequency and cable length all heavily impact the over-voltages seen at the output of the power cables. The simulation results were found to similarly match the experimental findings.

Co-Major Advisor: Annette von Jouanne

Co-Major Advisor: Julia Zhang

Committee: Eduardo Cotilla-Sanchez

GCR: Christopher Hagen

**A Formal Foundation for Variational Programming Using the Choice Calculus**

In this thesis, we present semantic equivalence rules for an extension of the choice calculus and sound operations for an implementation of variational lists. The choice calculus is a calculus for
describing variation and the formula choice calculus is an extension with formulas. We prove semantic equivalence rules for the formula choice calculus. Variational lists are functional data
structures for representing and computing with variation in lists using the choice calculus. We prove map and bind operations are sound for an implementation of variational lists. These proofs are
written and verified in the language of the Coq proof assistant. We also provide a general definition of soundness for variational functions which can be used to define soundness for other
operations on variational data structures.

Major Advisor: Eric Walkingshaw

Committee: Martin Erwig

Committee: Alex Groce

GCR: Maggie Niess

In this thesis, we present semantic equivalence rules for an extension of the choice calculus and sound operations for an implementation of variational lists. The choice calculus is a calculus for describing variation and the formula choice calculus is an extension with formulas. We prove semantic equivalence rules for the formula choice calculus. Variational lists are functional data structures for representing and computing with variation in lists using the choice calculus. We prove map and bind operations are sound for an implementation of variational lists. These proofs are written and verified in the language of the Coq proof assistant. We also provide a general definition of soundness for variational functions which can be used to define soundness for other operations on variational data structures.

Major Advisor: Eric Walkingshaw

Committee: Martin Erwig

Committee: Alex Groce

GCR: Maggie Niess