Analysis and Design of Tuning-Less mm-Wave Injection-Locked Frequency Dividers With Wide Locking Range Using 8th-Order Transformer-Based Resonator in 40 nm CMOS

Three tuning-less ultra-wide locking range (LR) transformer-based millimeter-wave (mm-wave) injection-locked frequency dividers (ILFDs) are presented. An eighth-order transformer-based resonator is proposed to improve the LR without an extra tuning mechanism or chip area. The operation principle of high-order transformer-based resonator in ILFDs based on the impedance diagram is analyzed. By comparing different high-order transformer-based resonators, the proposed resonator is the best option for the ultra-wide LR ILFD design. Also, the design considerations and tradeoffs of the implemented resonator are discussed. Furthermore, an inductive gain peaking technique is adopted to ensure start-up conditions and achieve low power consumption. Three ILFDs are designed and fabricated in 40-nm CMOS technology. The first chip exhibits a best-in-class LR of 104.5% from 28.8 to 91.9 GHz while consuming 5.8 mW with a 0.9-V power supply. The second chip achieves the best figure of merit (FoM) up to 26.6 GHz/mW and 79.6% from 31- to 72-GHz LR with a 0.5-V power supply. The third chip obtains an LR of 108.9% from 20 to 67.8 GHz while consuming 4.9 mW with a 0.9-V power supply. Furthermore, 6-dB phase noise differences of the three chips are achieved, which is close to the theoretical value.