Investigation on Locking and Pulling Modes in Analog Frequency Dividers

Figure 2

Comparison of the boundaries of the locking range (Arnold’s tongue) for a frequency divider with saturation-like nonlinearity, obtained by formulas and by numerical simulations. Δ_{𝑀_PA} is shown in (10), Δ_{𝑀_BL} in (22), Δ_{𝑀_AD} in (9), and Δ_{𝑀_𝑉𝑅𝐿} in (12). Numerical simulations are obtained by using the following parameters of the circuit in Figure 1: 𝐿=4nH, 𝑅=400, 𝜔₀=1.8GHz, 𝐼₀=2mA, and 𝑘=2.6/𝑉.