Phase-Locked Loop Stability Based on Stochastic Bounds

This is a post-peer-review, pre-copyedit version of an article published in Analog Integrated Circuits and Signal Processing. The final authenticated version is available online at: http://dx.doi.org/https://doi.org/10.1007/s10470-015-0606-zIn this paper we study the stability of a phase-locked loop (PLL) in the presence of noise. We represent the noise as Brownian motion and model the circuit as a nonlinear stochastic differential equation, with the noise lumped at the phase detector input. We show that for the PLL, the theory of asymptotics of singular diffusions can be applied and we use this theory to develop a new figure of merit which we call a stability margin. The stability margin provides easily computable bounds on the acceptable noise levels for which stability is guaranteed. Through simulation, we show that such a sufficient bound provides a realistic prediction for PLL stabilit

Challenges and Solutions for High Performance Analog Circuits with Robust Operation in Low Power Digital CMOS

In modern System-on-Chip products, analog circuits need to co-exist with digital circuits integrated on the same chip. This brings on a lot of challenges since analog circuits need to maintain their performance while being subjected to disturbances from the digital circuits. Device size scaling is driven by digital applications to reduce size and improve performance but also results in the need to reduce the supply voltage. Moreover, in some applications, digital circuits require a changing supply voltage to adapt performance to workloads. So it is further desirable to develop design solutions for analog circuits that can operate with a flexible supply voltage, which can be reduced well below 1V. In this thesis challenges and solutions for key high performance analog circuit functions are explored and demonstrated that operate robustly in a digital environment, function with flexible supply voltages or have a digital-like operation. A combined phase detector consisting of a phase-frequency detector and sub-sampling phase detector is proposed for phase-locked loops (PLLs). The phase-frequency function offers robust operation and the sub-sampling detector leads to low in-band phase noise. A 2.2GHz PLL with a combined phase detector was prototyped in a 65nm CMOS process, with an on-chip loop filter area of only 0.04mm². The experimental results show that the PLL with the combined phase detector is more robust to disturbances than a sub-sampling PLL, while still achieving a measured in-band phase noise of -122dBc/Hz which is comparable to the excellent noise performance of a sub-sampling PLL. A pulse-controlled common-mode feedback (CMFB) circuit is proposed for a 0.6V-1.2V supply-scalable fully-differential amplifier that was implemented in a low power/leakage 65nm CMOS technology. An integrator built with the amplifier occupies an active area of 0.01mm². When the supply is changed from 0.6V to 1.2V, the measured frequency response changes are small, demonstrating the flexible supply operation of the differential amplifier with the pulse-controlled CMFB. Next, models are developed to study the performance scaling of a continuous-time sigma-delta modulator (SDM) with a varying supply voltage. It is demonstrated that the loop filter and the quantizer exhibit different supply dependence. The loop noise performance becomes better at a higher supply thanks to larger signal swings and better signal-to-noise ratio, while the figure of merit determined by the quantization noise gets better at a lower supply voltage, thanks to the quantizer power dissipation reduction. The theoretical models were verified with simulations of a 0.6V-1.2V 2MHz continuous-time SDM design in a 65nm CMOS low power/leakage process. Finally, two design techniques are introduced that leverage the continued improvement of digital circuit blocks for the realization of analog functions. A voltage-controlled-ring-oscillator-based amplifier with zero compensation is proposed that internally uses a phase-domain representation of the analog signal. This provides a huge DC gain without significant penalties on the unity-gain bandwidth or area. With this amplifier a 4th-order 40-MHz active-UGB-RC filter was implemented that offers a wide bandwidth, superior linearity and small area. The filter prototype in a 55nm CMOS process has an active area of 0.07mm² and a power consumption of 7.8mW at 1.2V. The in-band IIP3 and out-of-band IIP3 are measured as 27.3dBm and 22.5dBm, respectively. A digital in-situ biasing technique is proposed to overcome the design challenges of conventional analog biasing circuits in an advanced CMOS process. A digital CMFB was simulated in a 65nm CMOS technology to demonstrate the advantages of this digital biasing scheme. Using time-based successive approximation conversion, the digital CMFB provides the desired analog output with a more robust operation and a smaller area, but without needing any stability compensation schemes like in conventional analog CMFBs. In summary, analog design techniques are continuously evolving to adapt to the integration with digital circuits on the same chip and are increasingly using digital-like blocks to realize analog functions in highly-integrated SOC chips. The signal representation in analog circuits is moving from traditional electrical signals such as voltage or current, to time and phase-domain representations. These changes make analog circuits more robust to voltage disturbances and supply variations. In addition to improved robustness, analog circuits based on timing signals benefit from the faster and smaller transistors offered by the continued feature scaling in CMOS technologies