Over the past 50 years, the integrated circuit (IC) industry has grown rapidly, following the famous ``Moore's law." The process feature size keeps shrinking, whereby the performance of digital circuits is constantly enhanced and their cost constantly decreases. However, with the system integration and the development of system on chip (SoC), nearly all of today's ICs contain analog/mixed-Signal circuits. Although a mixed-signal SoC is primarily digital, the analog circuit design and verification consume most of the resources, and the dominant source of IC breakdowns is attributable to the analog circuits.

One important reason for the high cost and risk of breakdowns of analog circuits is that the technology advancement does not benefit many analog and mixed-signal circuits, and in fact imposes higher requirements on their performance. With process scaling, many important parameters of integrated circuit components degrade, which cause a drop in many key aspects of performance of analog circuits. Many analog circuits rely on matched circuit components (transistors, resistors, or capacitors) to achieve the required linearity performance; examples are amplifiers, digital-to-analog converters (DACs), etc. However, shrinking of the feature sizes increases the circuit components mismatch, thereby making it more difficult to maintain circuit accuracy.

Therefore, to reduce the cost of analog circuit design, designers should propose new structures whose key performance can be improved by the technology scaling. In this dissertation, we propose a low-cost, high-precision DAC structure based on ordered element matching (OEM) theory. High matching accuracy can be achieved by applying OEM calibration to the resistors in unary weighted segments and calibrating the gain error between different segments by calibration DAC (CalDAC). As a design example to verify the proposed structure, a high-precision DAC is designed in a 130 nm Global Foundry (GF) CMOS process. The 130 nm GF process features high-density digital circuits and is a typical process which is constantly enhanced by the scaling of device dimensions and voltage supply; implementation of a high-precision DAC in such process is important to decreasing the costs of high-precision DAC designs. As a result, our proposed DAC structure is demonstrated to be able to significantly lower the cost of high-precision DAC design.

Another reason for the high cost and risk of breakdowns of analog circuits arises from the complexity of analog circuit working states. Most digital circuits serve as logic functions, so that digital transistors work in only two states, either low or high. In contrast, analog circuits have much more complicated functions; they may work in multiple operating points, since various feedback approaches are applied in analog circuits to enhance their performance. Circuits with undetected operating points can be devastating, particularly when they are employed in critical applications such as automotive, health care, and military products. However, since the existing circuit simulators provide only a single operating point, recognizing the existence of undesired operating points depends largely on the experiences of designers. In some circuits, even the most experienced designers may not be aware that a circuit they designed has undesired operating points, which often go undetected in the standard simulations in the design process.

To identify undesired operating points in an analog circuit and reduce its risk of breakdowns, a systematic verification method against undesired operating points in analog circuits is proposed in this dissertation. Unlike traditional methods of finding all operating points, this method targets only searches for voltage intervals containing undesired operating points. To achieve this, our method first converts the circuit into a corresponding graph and locates the break point to break all the positive feedback loops (PFLs). For one dimensional verification, divide and contraction algorithms could be applied to identify undesired operating points. Two dimensional vector field methods are used to solve the two dimensional verifications. Based on the proposed verification methods against undesired operating points, an EDA tool called ``ITV" is developed to identify undesired operating points in analog and mixed-signal circuits. Simulation results show ITV to be effective and efficient in identifying undesired operating points in a class of commonly used benchmark circuits that includes bias generators, voltage references, temperature sensors, and op-amp circuits.