A Low-Voltage 30-GHz CMOS Divide-by-Three ILFD With Injection-Switched Cross-Coupled Pair Technique

A Novel Single-Inductor Injection-Locked Frequency Divider by Three With Dual-Injection Secondary Locking

“…Otherwise, the resulting tank current would be delayed with respect to V out,d and the oscillation frequency would depart from resonance [8]. As a result, combining (16) and (14), the following condition holds:…”

“…Note that the simpler (14) corresponds to the first term of (24). Despite the presence of more terms in (24), all of them become synchronous with (ωt + ϕ) for γ = 3ϕ, as in the ohmic-regime approximation.…”

“…The actual orientation of I inj,1 depends instead on the magnitude and the signs of A inj,1,h , B inj,1,h . However, from a practical standpoint, since the amplitude of the beat tones quickly vanishes by increasing its order, the injection current is expected to retain the same orientation of (14). To clearly assess the orientation of I inj,1 , circuit simulations of the real floating-source injector were performed using the simulation set-up in Fig.…”

“…3(b) shows a tone at 2 f osc = 10.0 GHz [which is essentially due to V (2 • ) cm in (9)], and a tone at f in − f osc = 10.1 GHz, which is due to intermixing with the input signal [term V (2 ) cm in (9)]. The injector current has a tone at f osc = 5.0 GHz, resulting from resistive conduction, while intermixing generates the dominant component at f in − 2 f osc = 5.1 GHz in (14). The other higher order beat tones at [.…”