We propose a methodology of loop design optimization for fourth-order fractional-N phase locked loop (PLL) frequency synthesizers featuring a short settling time of 5 µsec for applications in an active RFID (radio frequency identification) and automobile smart-key systems. To establish the optimized design flow, equations presenting the relationship between the specification and PLL loop parameters in terms of settling time, loop bandwidth, phase margin, and phase noise are summarized. The proposed design flow overcomes the settling time inaccuracy in conventional second-order approximation methods by obtaining the accurate relationship between settling time and loop bandwidth with the MATLAB Control System Toolbox for the fourth-order PLLs. The proposed flow also features the worst-case design by taking account of the process, voltage, and temperature (PVT) variations in loop filter components, and considers the tradeoff between phase noise and area. The three-step optimization process consists of 1) the derivation of the accurate relationship between the settling time and loop bandwidth for various PVT conditions, 2) the derivation of phase noise and area as functions of area-dominant filter capacitance, and 3) the derivation of all PLL loop components values. The optimized design result is compared with circuit simulations using an actually designed fourth-order fractional-N PLL in a 1.8 V 0.18 µm CMOS technology. The error between the design and simulation for the setting time is reduced from 0.63 µsec in the second-order approximation to 0.23 µsec in the fourth-order optimization that proves the validity of the proposed method for the high-speed settling operations.

We propose a design optimization flow for a high-speed and low-power operational transconductance amplifier (OTA) using a gm/ID lookup table design methodology in scaled CMOS. This methodology advantages from using gm/ID as a primary design parameter to consider all operation regions including strong, moderate, and weak inversion regions, and enables the lowest power design. SPICE-based lookup table approach is employed to optimize the operation region specified by the gm/ID with sufficient accuracy for short-channel transistors. The optimized design flow features 1) a proposal of the worst-case design scenario for specification and gm/ID lookup table generations from worst-case SPICE simulations, 2) an optimization procedure accomplished by the combination of analytical and simulation-based approaches in order to eliminate tweaking of circuit parameters, and 3) an additional use of gm/ID subplots to take second-order effects into account. A gain-boosted folded-cascode OTA for a switched capacitor circuit is adopted as a target topology to explore the effectiveness of the proposed design methodology for a circuit with complex topology. Analytical expressions of the gain-boosted folded-cascode OTA in terms of DC gain, frequency response and output noise are presented, and detailed optimization of gm/IDs as well as circuit parameters are illustrated. The optimization flow is verified for the application to a residue amplifier in a 10-bit 125 MS/s pipeline A/D converter implemented in a 0.18 µm CMOS technology. The optimized circuit satisfies the required specification for all corner simulations without additional tweaking of circuit parameters. We finally explore the possibility of applying this design methodology as a technology migration tool, and illustrate the failure analysis by comparing the differences in the gm/ID characteristics.

Digital delta-sigma modulators (DDSMs) applied in fractional-N frequency synthesizers suffer from spurious tones which undermine the synthesizer's spectral purity. We propose a solution featuring no hardware overhead while achieving equivalent spur elimination effect as using LFSR-dithering. This method can be implemented on MASH and single-loop DDSMs of 3rd- and 2nd-order.