Observations Concerning the Locking Range in a Complementary Differential $LC$ Injection-Locked Frequency Divider—Part II: Design Methodology

Modeling, Analysis, and Experimental Validation of Frequency Dividers with Direct Injection

“…Finally, it should be highlighted that even if our experiments were performed in MHz range as in [8,16], similar results are expected at GHz range because it was shown in [5] that approximate models based on algebraic characteristics for the active parts of the divider can be effectively used at GHz frequencies.…”

“…These devices form the composite two-terminal shown in Figure 3(a), which is described by a nonlinear characteristic, nl (V) [14][15][16][17]. It is easy to realize that nl (0) = 0 and, due to the circuit symmetry, nl (V) is an odd function of V. Since the two-terminal sub-circuit in Figure 3(a) has to compensate the tank losses, it exhibits a negative resistance, and thus, it is locally active with a currentvoltage characteristic nl (V) lying into the second and fourth quadrants of the − V plane ( Figure 5).…”

An Experimental Method to Extract the Phase-Sensitivity of Oscillators to Noise Perturbations

“…Such a procedure consists in injecting small-amplitude sinusoidal signals whose frequency is close to the oscillator free-running frequency or to an integer multiple of it. When falls in a frequency range centered at , referred to as the locking range (LR), a synchronization effect (i.e., the injection locking) occurs for which the oscillating frequency exactly locks to the value [1], [15]- [17]. As we show in this paper, the size of the locking ranges depends ontheamplitudeoftheharmoniccomponentsofthe function.…”

Analysis and design of divide-by-three LC-CMOS frequency dividers

“…can be well approximated by a cubic polynomial [14]. On the other hand, the function ) ( 1 v g , calculated by approximating the derivative with a finite difference, can be modeled by a constant function (Fig.…”