Intra-periodic fluctuations of dynamic tracking errors in digital pll with frequency-phase control

Аuthors

Zhodzishskii D. M.

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

e-mail: DZhodzishsky@topcon.com

Abstract

With third-order astatism a phase-locked-loop frequency control system can be described by the following equations

Here is the adjustment period; i are phase and frequency of NCO (Numeral Control Oscillator) after completing the i-th adjustment period;

is the number in the third integrator of the PLL loop filter equal (in a steady-state mode with no noise) to the derivative of the incoming signal frequency ; is the signal at the output of the PLL discriminator; are coefficients of the loop filter determining dynamic and noise properties of the system.

These equations are still valid for the second order if .

Incoming signal phase instability results in PLL tracking errors which we will name dynamic ones. Here is the phase of the incoming signal, is the NCO phase at any random time instant t.

The paper considers dynamic errors in a steady-state mode. Such mode occurs after transient processes completion when , where n is PLL astatism order, and m is the order of the polynomial describing . In steady-state mode the tracking error averaged over the adjustment period when and when . However, tracking error instantaneous magnitude  can vary within the adjustment period, i.e., intra-periodic fluctuations occur.

The paper presents analytical equations for such intra-periodic fluctuations.

The results obtained can be implemented for PLL systems design to determine ultimate dynamic effects possible for such systems.

Keywords:

phase-locked loops, intra-periodic fluctuations, synchronization system

References

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