Formal Verification and In-Situ Test of Analog and Mixed-Signal Circuits

As CMOS technologies continuously scale down, designing robust analog and mixed-signal (AMS) circuits becomes increasingly difficult. Consequently, there are pressing needs for AMS design checking techniques, more specifically design verification and design for testability (DfT). The purpose of verification is to ensure that the performance of an AMS design meets its specification under process, voltage and temperature (PVT) variations and different working conditions, while DfT techniques aim at embedding testability into the design, by adding auxiliary circuitries for testing purpose. This dissertation focuses on improving the robustness of AMS designs in highly scaled technologies, by developing novel formal verification and in-situ test techniques. Compared with conventional AMS verification that relies more on heuristically chosen simulations, formal verification provides a mathematically rigorous way of checking the target design property. A formal verification framework is proposed that incorporates nonlinear SMT solving techniques and simulation exploration to efficiently verify the dynamic properties of AMS designs. A powerful Bayesian inference based technique is applied to dynamically tradeoff between the costs of simulation and nonlinear SMT. The feasibility and efficacy of the proposed methodology are demonstrated on the verification of lock time specification of a charge-pump PLL. The powerful and low-cost digital processing capabilities of today?s CMOS technologies are enabling many new in-situ test schemes in a mixed-signal environment. First, a novel two-level structure of GRO-PVDL is proposed for on-chip jitter testing of high-speed high-resolution applications with a gated ring oscillator (GRO) at the first level to provide a coarse measurement and a Vernier-style structure at the second level to further measure the residue from the first level with a fine resolution. With the feature of quantization noise shaping, an effective resolution of 0.8ps can be achieved using a 90nm CMOS technology. Second, the reconfigurability of recent all-digital PLL designs is exploited to provide in-situ output jitter test and diagnosis abilities under multiple parametric variations of key analog building blocks. As an extension, an in-situ test scheme is proposed to provide online testing for all-digital PLL based polar transmitters

A Methodology for Implementing RF BiSTs in Production Testing to Replace RF Conventional Tests

Production testing of Radio Frequency (RF) devices is challenging due to the complex nature of the tests that have to be performed to verify functionality. In this dissertation a methodology to replace the complex and expensive RF functional tests with defect-oriented Built-in Self Tests (BiSTs) is detailed. If a design has sufficient margin to RF specifications then RF tests can be replaced with structural tests using a new data analysis technique called quadrant analysis, which is presented. Data from the analysis of over one million production units of said System on Chip (SoC) is presented along with the results of the analysis. The BiST techniques that have been used are discussed and a Texas Instruments 65 nm RF SoC with a Bluetooth and a FM core was used as a case study. The defect models that were used to develop the BiSTs are discussed as well. The scenario in which a design does not have sufficient margin to specification is also discussed. The data analysis method required in such a case is a regression analysis and the data from such an analysis is shown. The results prove that it is possible to replace expensive RF conventional tests with structural tests and that modern RFCMOS process technology and advances in design like the Digital Radio Processor (DRPTM) technology enable this. The Defective Parts Per Million (DPPM) impact of making this replacement is 27 units and is acceptable for RFCMOS high volume products. Finally, data showing test cost reduction of about 38% that resulted from the elimination of RF conventional tests is presented

캘리브레이션이 필요없는 위상고정 루프의 설계

학위논문 (박사)-- 서울대학교 대학원 : 전기·컴퓨터공학부, 2017. 2. 김재하.A PVT-insensitive-bandwidth PLL and a chirp frequency synthesizer PLL are proposed using a constant-relative-gain digitally-controlled oscillator (DCO), a constant-gain time-to-digital converter (TDC), and a simple digital loop filter (DLF) without an explicit calibration or additional circuit components. A digital LC-PLL that realizes a PVT-insensitive loop bandwidth (BW) by using the constant-relative-gain LC-DCO and constant-gain TDC is proposed. In other words, based on ratiometric circuit designs, the LC-DCO can make a fixed percent change to its frequency for a unit change in its digital input and the TDC can maintain a fixed range and resolution measured in reference unit intervals (UIs) across PVT variations. With such LC-DCO and TDC, the proposed PLL can realize a bandwidth which is a constant fraction of the reference frequency even with a simple proportional-integral digital loop filter without any explicit calibration loops. The prototype digital LC-PLL fabricated in a 28-nm CMOS demonstrates a frequency range of 8.38~9.34 GHz and 652-fs,rms integrated jitter from 10-kHz to 1-GHz at 8.84-GHz while dissipating 15.2-mW and occupying 0.24-mm^2. Also, the PLL across three different die samples and supply voltage ranging from 1.0 to 1.2V demonstrates a nearly constant BW at 822-kHz with the variation of ±4.25-% only. A chirp frequency synthesizer PLL (FS-PLL) that is capable of precise triangular frequency modulation using type-III digital LC-PLL architecture for X-band FMCW imaging radar is proposed. By employing a phase-modulating two-point modulation (TPM), constant-gain TDC, and a simple second-order DLF with polarity-alternating frequency ramp estimator, the PLL achieves a gain self-tracking TPM realizing a frequency chirp with fast chirp slope (=chirp BW/chirp period) without increasing frequency errors around the turn-around points, degrading the effective resolution achievable. A prototype chirp FS-PLL fabricated in a 65nm CMOS demonstrates that the PLL can generate a precise triangular chirp profile centered at 8.9-GHz with 940-MHz bandwidth and 28.8-us period with only 1.9-MHz,rms frequency error including the turn-around points and 14.8-mW power dissipation. The achieved 32.63-MHz/us chirp slope is higher than that of FMCW FS-PLLs previously reported by 2.6x.CHAPTER 1 INTRODUCTION 1 1.1 MOTIVATION 1 1.2 THESIS ORGANIZATION 5 CHAPTER 2 CONVENTIONAL PHASE-LOCKED LOOP 7 2.1 CHARGE-PUMP PLL 7 2.1.1 OPERATING PRINCIPLE 7 2.1.2 LOOP DYNAMICS 9 2.2 DIGITAL PLL 10 2.2.1 OPERATING PRINCIPLE 11 2.2.2 LOOP DYNAMICS 12 CHAPTER 3 VARIATIONS ON PHASE-LOCKED LOOP 14 3.1 OSCILLATOR GAIN VARIATION 14 3.1.1 RING VOLTAGE-CONTROLLED OSCILLATOR 15 3.1.2 LC VOLTAGE-CONTROLLED OSCILLATOR 17 3.1.3 LC DIGITALLY-CONTROLLED OSCILLATOR 19 3.2 PHASE DETECTOR GAIN VARIATION 20 3.2.1 LINEAR PHASE DETECTOR 20 3.2.2 LINEAR TIME-TO-DIGITAL CONVERTER 21 CHAPTER 4 PROPOSED DCO AND TDC FOR CALIBRATION-FREE PLL 23 4.1 DIGTALLY-CONTROLLED OSCILLATOR (DCO) 25 4.1.1 OVERVIEW 24 4.1.2 CONSTANT-RELATIVE-GAIN DCO 26 4.2 TIME-TO-DIGITAL CONVERTER (TDC) 28 4.2.1 OVERVIEW 28 4.2.2 CONSTANT-GAIN TDC 30 CHAPTER 5 PVT-INSENSITIVE-BANDWIDTH PLL 35 5.1 OVERVIEW 36 5.2 PRIOR WORKS 37 5.3 PROPOSED PVT-INSENSITIVE-BANDWIDTH PLL 39 5.4 CIRCUIT IMPLEMENTATION 41 5.4.1 CAPACITOR-TUNED LC-DCO 41 5.4.2 TRANSFORMER-TUNED LC-DCO 45 5.4.3 OVERSAMPLING-BASED CONSTANT-GAIN TDC 49 5.4.4 PHASE DIGITAL-TO-ANALOG CONVERTER 52 5.4.5 DIGITAL LOOP FILTER 54 5.4.6 FREQUENCY DIVIDER 55 5.4.7 BANG-BANG PHASE-FREQUENCY DETECTOR 56 5.5 CELL-BASED DESIGN FLOW 57 5.6 MEASUREMENT RESULTS 58 CHAPTER 6 CHIRP FREQUENCY SYNTHESIZER PLL 66 6.1 OVERVIEW 67 6.2 PRIOR WORKS 71 6.3 PROPOSED CHIRP FREQUENCY SYNTHESIZER PLL 75 6.4 CIRCUIT IMPLEMENTATION 83 6.4.1 SECOND-ORDER DIGITAL LOOP FILTER 83 6.4.2 PHASE MODULATOR 84 6.4.3 CONSTANT-GAIN TDC 85 6.4.4 VRACTOR-BASED LC-DCO 87 6.4.5 OVERALL CLOCK CHAIN 90 6.5 MEASUREMENT RESULTS 91 6.6 SIGNAL-TO-NOISE RATIO OF RADAR 98 CHAPTER 7 CONCLUSION 100 BIBLIOGRAPHY 102 초록 109Docto