A Novel LO Phase-Shifting System Based on Digital Bang-Bang PLLs With Background Phase-Offset Correction for Integrated Phased Arrays
Francesco Tesolin, Simone M. Dartizio, Francesco Buccoleri, Alessio Santiccioli, Luca Bertulessi, Carlo Samori, Andrea L. Lacaita, Salvatore Levantino
Abstract
An LO phase-shifting system based on digital fractional- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${N}$ </tex-math></inline-formula> bang-bang phase-locked loops (PLLs) in the 8.5–10.0-GHz range is presented. A direct phase modulation method is leveraged to perform LO phase-shifting directly within the frequency synthesizer, leading to an inherently linear phase-shifting characteristic, even in the presence of digital-to-time converter (DTC) nonlinearities. Synchronization between fractional- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${N}$ </tex-math></inline-formula> PLL cores is achieved by clocking with the same reference clock the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta \Sigma $ </tex-math></inline-formula> modulator driving the frequency divider of each core. The adoption of a digital phase-offset correction technique canceling out timing skews greatly simplifies the reference-clock distribution and DTC matching. A dual-core prototype is implemented in a standard 28-nm CMOS process, where each element occupies 0.23-mm2 area and dissipates 20-mW power. An arbitrary phase shift between the LO outputs can be set over the 360° range with a resolution of 0.7 millidegree (19 bits). The rms phase accuracy is 0.76°, and the peak-to-peak phase error is 2.1°, without requiring any linearity or gain calibration. Each LO element features a −58.7 dBc in-band fractional spur and a −70 dBc reference spur, with a jitter versus power figure-of-merit of −253.5 and −250.0 dB for integer- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${N}$ </tex-math></inline-formula> and fractional- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${N}$ </tex-math></inline-formula> channels, respectively. The combined outputs of the two PLL cores reach an absolute jitter integrated from 1 kHz to 100 MHz (including spurs) of 38.2 and 59.78 fs, in integer- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${N}$ </tex-math></inline-formula> and near-integer fractional- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${N}$ </tex-math></inline-formula> operations, respectively.