Enhanced dynamical response of derivative controlled third order phase locked loops

Robust stability analysis and improved design of phase‐locked loops with non‐monotonic nonlinearities: LMI‐based approach

“…Unlike several recent works where rigorous analyses are established for low order PLLs and PLLs with no integrators in the filters [10,12,16,34], the analysis presented in this paper is more general in the sense that not only it is applicable to both PLLs with analog mixer and XOR gate but also to PLLs without any order or type restriction. Unlike several recent works where rigorous analyses are established for low order PLLs and PLLs with no integrators in the filters [10,12,16,34], the analysis presented in this paper is more general in the sense that not only it is applicable to both PLLs with analog mixer and XOR gate but also to PLLs without any order or type restriction.…”

“…Both results in (b1) and (b2) are expressed in terms of convex LMIs, which are computationally tractable and more efficient than frequency-based methods. Unlike several recent works where rigorous analyses are established for low order PLLs and PLLs with no integrators in the filters [10,12,16,34], the analysis presented in this paper is more general in the sense that not only it is applicable to both PLLs with analog mixer and XOR gate but also to PLLs without any order or type restriction. In Section 4, several numerical examples are given where the result in (b1) is used to search for optimized value of K L in second and higher order Type-1 PLLs, and it is demonstrated that K L obtained can accurately estimate the corresponding lock-in range.…”

“…When the loop is limited to low order (i.e., first and second), the conventional phase-plane technique can be applied for a more rigorous analysis [10,18,19]. Nonetheless, analysis of higher order PLLs is equally important as they offer additional advantages such as the ability to track a wider variety of frequency inputs and suppressing the effects of double frequency components present in the loop error signals [1,2,12,16,17]. Nonetheless, analysis of higher order PLLs is equally important as they offer additional advantages such as the ability to track a wider variety of frequency inputs and suppressing the effects of double frequency components present in the loop error signals [1,2,12,16,17].…”

“…There has been a continuing growth in the studies of nonlinear analysis of PLL-based circuits such as operating frequency range, bifurcations, and self-oscillations [10][11][12][13][14][15][16][17]. When the loop is limited to low order (i.e., first and second), the conventional phase-plane technique can be applied for a more rigorous analysis [10,18,19].…”

“…This is particularly useful as a large preponderance of applications utilize second order PLLs. Nonetheless, analysis of higher order PLLs is equally important as they offer additional advantages such as the ability to track a wider variety of frequency inputs and suppressing the effects of double frequency components present in the loop error signals [1,2,12,16,17]. In a mobile communication system, for instance, signals are subject to the well-known Doppler effect when there is a relative motion between transmitting and receiving antennas, which leads to a frequency/Doppler shift in the signal frequency.…”