An Integrated Divide-by-Two Direct Injection-Locking Frequency Divider for Bands $S$ Through $K_{u}$

In this work, direct injection locking is applied to a ring oscillator topology to design a wideband divide-by-two frequency divider circuit with a locking range covering bands
$S$
through
$K_{u}$
, namely input frequencies from 2 to 16 GHz. A thorough analysis is carried out: a behavioral model is developed that allows us to capture the operation of the two-stage differential ring oscillator. The mixing operation inherent in the direct injection scheme is deeply investigated and compared with tail injection locking. The design guidelines leading to a wide locking range are derived and exploited. Prototypes implemented in a digital 65-nm CMOS technology draw 1.6 mA from a 1.2-V supply. Since the design is inductorless, the divider area is as low as 130
$\mu{\hbox {m}}^{2}$
. The output phase noise tracks the reference's one with the expected 6-dB difference over the entire range of operation frequencies.