A DPLL Method Applied to Clock Steering

Abstract

Several closed-loop control methods have dealt with clock steering problems, but parameters for these methods are not easy to choose. In this paper, we propose a new clock steering method, which uses a second-order type-2 digital phase-locked loop (DPLL) equivalent to a two-state Kalman filter with a delay. We derive the approximate expressions of the steady-state Kalman gains, which are equivalent to the DPLL gains. Then, we derive the transfer functions of the approximate DPLL. A brief and effective approach to choosing a parameter is also proposed. Simulation results show that the performance of the time steering error and the frequency stability is quite desirable, and can meet the requirements of generating a local representation of coordinated universal time or a global navigation satellite system time. IndexTerms-Clock steering, digital phase-locked loop (DPLL), frequency stability, Kalman filter, steering error.

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“…The time-frequency steering system adopts the Kalman filter shown in Equation (6), and the three-dimensional state-space model of phase difference, frequency difference and frequency drift established is [ 19 , 22 ]: In Equation (18), the first equation is the state equation, , , and respectively represent the three state variables of phase, frequency, and frequency change rate. , is process noise.…”

“… where are the z-transform forms of and , respectively. Through Equation (21), the closed-loop system transfer function structure consistent with the third-order type-three DPLL can be obtained [ 23 ], which is a further extension of the two-dimensional state-space model Kalman filter [ 22 ]. In order to ensure the normal and orderly output of the time-frequency steer value in the loop filter, it is considered to add a delay device .…”

“…The Kalman filter guarantees the stability of the system because of its complete observability, and the equivalent DPLL with a delay is represented by Equations (23) and (24); in addition, (25) has also been verified by simulation. The noise variance parameters and are only used to determine the steady-state Kalman gain equivalent to the DPLL gain when constructing the equivalent DPLL, WU Yi-wei [ 22 ] derived and verified the approximate relationship between the noise variance parameters , and the steady-state Kalman gain in the two-dimensional Kalman filter model. By analyzing the five steps of Kalman filtering, is the estimated covariance matrix, and is the predicted covariance matrix.…”

“…Use Equation (17) to draw the SSB phase noise spectral density curves and , use the frequency value of the intersection point of the two curves as a fixed reference value . Then, substituting into Equations (24) and (25), the amplitude–frequency response curves and of the system transfer function and system error transfer function in the frequency domain can be obtained [ 22 ].…”

“…The authors of references [ 20 , 21 ] selected the observable Kalman filter system, and verified the stability of the equivalent DPLL control system with a delay structure. In references [ 21 , 22 ], the standard second-order type 2 DPLL and the third-order type 3 DPLL are equivalently constructed. Because the adjustment parameters in references [ 21 , 23 ] need to be adjusted many times, there are precision limitations and self-adaptive approximate selection.…”