A. I. Gushchin1, N. N. Udalov2, D. E. Lashchyov3
1, 3 JSC “Russian Space Systems” (Moscow, Russia)
1, 2 National Research University “MPEI” (Moscow, Russia)

1 sanyok.centr@yandex.ru, 2 UdalovNN@mpei.ru, 3 Lashev777@gmail.com

Frequency synthesizers are widely used in mobile and wireless communication systems, radar, medicine, measurement technology, and scientific experiments. These devices are often created on the basis of the phase-locked loops in which a voltage-controlled oscillator adjusts in frequency due to a filtered signal from the output of a phase detector comparing the oscillations of a voltage-controlled oscillator and a reference oscillator. The phase-frequency detector provides cheaper designs and has a linear characteristic without a phase dead zone, so its use in these systems is more profitable. However, this complicates the calculation of the dynamic characteristics of the devices under consideration.

The goal of this article is to study frequency transients in a frequency synthesizer based on a pulsed phase-locked loop with a phase-frequency detector. Based on the published methodology for calculating a system with a low-pass filter with integration, we derive expressions relating the dimensionless initial frequency detuning and frequency transition time for cases where the two other types of filters are used. The final formulas are obtained from the equation of a closed phase-locked loop. It includes frequency detuning, the slope of the voltage-controlled oscillator, the charge and discharge current of the integrating capacitance, the frequency division coefficient, the transfer function of the filter and the normalized static characteristic of the phase-frequency detector.

Next, the corresponding dependency graphs, when changing the switching-in coefficient and the time constant of the additional integrating circuit, have been plotted. An increase in these device parameters leads to an increase in the frequency transition time. If we also take into account the time delay of the error signal caused by the operation of the phase-frequency detector, then we get two curves with a shift by the value of the specified delay along the time axis. Synthesizer models are also being designed to compare the transition time obtained during the modeling process with the result of a theoretical calculation.

The research will be useful for developers of frequency synthesizers based on phase-locked loops with a phase-frequency detector and a charge-pump circuit. For scientists dealing with the problems of these systems the results of this article will also be useful in their further scientific research, including calculating the dynamics of all-digital phase-locked loops.

Gushchin A.I., Udalov N.N., Lashchyov D.E. Frequency transients in a frequency synthesizer with a phase-frequency detector // Antennas. 2026. № 3. P. 94–101. DOI: https://doi.org/10.18127/j03209601-202603-09

1. Makarov A.K., Udalov N.N. Dinamika sintezatora chastoty s chastotno-fazovym detektorom. Sbornik lektsij, obzornykh dokladov, tezisov dokladov 7-go nauch. soveshchaniya «Stabilizatsiya chastoty i formirovanie signalov radio- i opticheskogo diapazonov». 1992. S. 84–90. (in Russian)
2. Ostin Kh. Razrabotka tochnoj petli fazovoj avtopodstrojki chastoty s vysokovol'tnym GUN. Komponenty i tekhnologii. 2010. № 7. S. 138–142. (in Russian)
3. Tel'nov A.A. Proektirovanie sistemy fazovoj avtopodstrojki chastity. Izvestiya SPbGETU «LETI». 2022. T. 15. № 7. S. 37–46. DOI: 10.32603/2071-8985-2022-15-7-37-46. (in Russian)
4. Golub V.S. Neskol'ko slov o sisteme FAPCh: fazovaya avtopodstrojka chastity. Komponenty i tekhnologii. 2003. № 8. (in Russian)
5. Chen Q. et al. A low-power ADPLL with calibration-free RO-based injection-locking TDC for BLE applications. Electronics. 2022. V. 11. № 13. P. 1–17. DOI: 10.3390/electronics11131953.
6. Zikij A.N., Kochubej A.S., Pomazanov A.V. Sintezator chastoty detsimetrovykh voln. Radiotekhnika. 2025. T. 89. № 11. S. 193–197. DOI: 10.18127/j00338486-202511-24. (in Russian)