Frequency synchronization detection method based on adaptive frequency standard tracking

Xin Geng; Baoqiang Du; Jianwei Zhang; Erlin Tian

doi:10.1515/phys-2021-0044

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Frequency synchronization detection method based on adaptive frequency standard tracking

Xin Geng , Baoqiang Du , Jianwei Zhang und Erlin Tian

Veröffentlicht/Copyright: 29. Juli 2021

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Abstract

In order to achieve wide-band high-resolution frequency measurement, a frequency synchronization detection method based on adaptive frequency standard tracking is proposed based on the quantized phase processing. First, the nominal value of the measured frequency signal was obtained from the rough frequency measurement module. Then, the field programmable gate array generated the nominal value of the measured frequency. After that, the direct comparison between the tracking frequency and the measured signal was carried out. Finally, the group quantized processing module gave the final result according to the phase full-period change time. Experimental results showed that the method has a wide frequency measurement range and high accuracy and can obtain frequency stability of the order of 10⁻¹³/s.

Keywords: frequency measurement; phase processing; frequency standard tracking

1 Introduction

The research of precision frequency sources has become a research hotspot in the field of time-frequency transmission, navigation, and positioning. Its development and application have penetrated into many fields of society, such as time-service and timekeeping, deep-space detection, time synchronization, time-frequency measurement, etc. [1,2,3,4,5,6,7,8,9,10]. Frequency stability is the main performance index of precision frequency sources; the best way to evaluate frequency stability is to measure precision frequency sources with high accuracy [11,12]. There are mainly four commonly used frequency measurement methods: pulse counting method, beat method, phase comparison method, and dual mixer time difference method [13,14,15,16]. The pulse counting method is to measure the signal frequency by filling high-frequency pulses within the gate time and counting. The advantage is that a wide frequency range can be measured by changing the clock frequency of the counter, while the disadvantage is that it is affected by a count error of ±1 word and the measurement accuracy is relatively low. The beating method is to directly enhance or multiply the measured signal and the frequency standard signal, then low-noise mixing output the beating signal, and use a counter to count the beating signal without gaps in multiple cycles to realize the measurement of the frequency and its stability. Its merits are high-precision, high-resolution, and wide-band measurement (up to 18 GHz), while the drawbacks are that in addition to the ±1 word count error, the system measurement error also has errors caused by the noise of the multiplier and mixer. In the phase comparison method, the phase difference between the comparison signals is taken out by a phase comparator and converted into a digital voltage, and the frequency measurement is realized by measuring the digital voltage. It is easy to integrate, and the measurement dynamic range is large. However, the resolution is limited by the conversion rate and the bit width of the digital signal. The double-mixing time difference method uses an intermediate frequency source to mix the measured signal and the frequency standard signal with low noise to generate two difference frequency signals. After low-pass filtering and zero-crossing detection, they are sent to the time interval counter as a gate switch signal; gate time is the time difference between the two difference frequency signals [17]. The change of the time difference directly reflects the change of the relative frequency difference, from which the frequency difference and the frequency of the measured signal are measured [18,19,20,21,22,23,24,25]. In order to improve the measurement accuracy and solve the contradiction between wide frequency measurement range and high resolution, this paper proposed a frequency synchronization detection method based on adaptive frequency standard tracking based on the quantized phase processing of different frequency groups [26]. This method combines direct digital synthesizer (DDS) technology and field programmable gate array (FPGA) on-chip technology to achieve a wide frequency range measurement of the measured signal through frequency standard tracking [27,28,29,30]. At the same time, it uses the scientific law of the group quantized phase change between the frequency standard signal and the measured signal to effectively overcome ±1 word count error, which improves the accuracy and stability of frequency measurement.

2 Measurement principle and scheme

2.1 Principles of quantized phase processing in different frequency groups

The principle of inter-frequency group quantized phase processing is to directly compare the two frequency signals after digital processing, and directly obtain the phase difference between the two compared signals [31,32]. The result only depends on the time difference between the characteristic edges of the two comparison signals and has nothing to do with the length of the respective periods of the comparison signals.

If the measured signal and the frequency standard signal have the same nominal value and a slight relative frequency deviation, the feasibility and effectiveness of the inter-frequency phase comparison can be guaranteed, which is conducive to the phase synchronization between the two signals and the generation of group period and group quantized phase [33].

Suppose two signals with the same nominal value and frequency offset Δ f ≠ 0 are the frequency standard signal f 0 and the measured signal f x . The corresponding periods are T 0 and T x . Take the time difference between the rising edge of each full cycle of f 0 and the subsequent rising edge of f x , that is, the phase difference, as the result of direct phase comparison f out , i.e., [ P D 1 , P D 2 , P D 3 , … , P D n ] T , as shown in equation (1) and Figure 1.

(1) [ P D 1 P D 2 P D 3 ⋮ P D n ] = [ 1 T x − 1 T 0 2 T x − 2 T 0 3 T x − 3 T 0 ⋮ n T x − n T 0 ] = [ 1 T max c 2 T max c 3 T max c ⋮ n T max c ] = [ 1 2 3 ⋮ n ] T max c

where n is a positive integer, that is, each phase difference is quantized by T max c . T max c is the smallest and indivisible phase difference in inter-frequency phase processing, which is called phase quantization [34,35,36]. At this time, all n phase differences are regarded as a whole, called the phase group, and the phase difference within the group is called the group quantized phase.

Figure 1

Two frequency signals with the same nominal value and slight relative frequency deviation.

From equation (1), it can be seen that the quantized phase step value of any adjacent group in the phase group is T max c , that is equation (2):

(2) | P D n − P D n − 1 | = T max c

When the step value of any group quantized phase accumulation is equal to an integer number of cycles T 0 of the frequency standard signal f 0 , that is equation (3):

(3) n T max c = m T 0

The group quantized phase will undergo a full-period change, return to the initial state, and move in cycles. The time for any group quantized phase to undergo a full-period change is called group period T gp , and at the same time, equation (4) can be obtained:

(4) Δ f = 1 T gp

2.2 Frequency synchronization detection scheme of adaptive frequency standard tracking

The scheme is shown in Figure 2 and is mainly composed of a rough frequency measurement module, a DDS frequency standard tracking circuit module, a different frequency phase comparison module, a group quantized processing module, and a data processing result display module. The rough frequency measurement module mainly adopts the method of pulse filling and counting to obtain the nominal value of the measured frequency signal and then generates the control signal of the DDS frequency standard tracking circuit module through FPGA to output the same signal as the nominal value of the measured frequency [37]. Because the DDS frequency standard tracking circuit module uses the frequency standard signal as an external clock, the signal output by the module maintains the accuracy and stability of the frequency standard signal, and there is a slight relative frequency deviation from the actual value of the measured signal.

Figure 2

Frequency synchronization detection scheme of adaptive frequency standard tracking.

The output signal of the DDS frequency standard tracking circuit module and the measured signal are sent to the inter-frequency phase comparison module at the same time, and the phase difference that changes with time is obtained after direct phase discrimination and comparison [38]. The group quantized processing module measures each phase difference value in real time and saves the result. The data processing result display module determines the time interval at which two identical phase difference values occur successively, that is, the group period T gp , the frequency offset Δ f is calculated by equation (4), and the final result is displayed in combination with the rough measurement nominal value.

3 Frequency measurement experiment

The experiment is shown in Figure 3. The BVA OCXO8607-B 10 MHz high-stable crystal oscillator was used as the frequency standard signal and the clock source of the DDS frequency synthesizer. The KEYSIGHT E8663D frequency synthesizer produced a series of frequency signals as the measured signal; the measurement results are shown in Table 1.

Figure 3

A simplified block diagram of the experiment.

Table 1

Experimental results of frequency measurement

Measured signal (MHz)	Frequency standard signal (MHz)	Actual measured signal (MHz)	Frequency stability σ (s)
47.0000100	10	47.00000971	8.74403 × 10⁻¹³
44.0000100	10	44.00000894	8.62075 × 10⁻¹³
38.0000100	10	38.00000868	7.85734 × 10⁻¹³
33.0000100	10	33.00000981	7.56542 × 10⁻¹³
26.0000100	10	26.00000874	7.38754 × 10⁻¹³
22.0000100	10	22.00000861	6.15675 × 10⁻¹³
18.0000100	10	18.00000953	5.06854 × 10⁻¹³
11.0000100	10	11.00000883	3.46806 × 10⁻¹³
8.0000010	10	8.00000087	2.94948 × 10⁻¹³
5.0000010	10	5.00000084	2.73543 × 10⁻¹³
1.0000010	10	1.00000090	2.35785 × 10⁻¹³

According to the data in Table 1, the frequency stability of the frequency synchronization detection scheme of adaptive frequency standard tracking in the radio frequency range can easily reach the order of 10⁻¹³/s and the highest theoretical accuracy of the double-mixing time difference method is consistent. The theoretical values of the other three commonly used frequency measurement methods are all below 10⁻¹²/s.

The measurement range of the dual mixer time difference method is generally 1–30 MHz. If the frequency measurement range is widened, a certain number of mixers must be added, which in turn introduces the superposition of additional noise, and the system frequency stability decreases. The frequency synchronization detection method of adaptive frequency standard tracking can realize frequency measurement in a wide range and high precision without reducing the stability and accuracy.

4 Conclusion

Based on the research on the principle of quantized phase processing of different frequency groups, a frequency synchronization detection method of adaptive frequency standard tracking is proposed. The paper mainly has following three innovation points: (1) based on the adaptive frequency standard tracking technology, the frequency measurement range is greatly expanded. This scheme can realize the direct measurement, comparison, and processing of the phase of any frequency signal in the radio frequency range. (2) On the basis of the characteristic law of the full-period change of the group quantized phase, the small frequency deviation of the tracking frequency signal is calculated, which effectively overcomes the ±1 word count error. This method can obtain frequency stability of the order of 10⁻¹³/s. (3) Compared with the four commonly used measurement methods, it has simple structure, low cost, low additional noise, and high measurement resolution.

Acknowledgment

This work was supported by National Natural Science Foundation of China (No. U1304618) and Scientific and Technological Project of Henan Province (No. 202102210145) and Hunan Province Natural Science Foundation (No. S2021JJMSXMO268).

Conflict of interest: Authors state no conflict of interest.
Data availability statement: The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Received: 2021-03-18

Revised: 2021-04-27

Accepted: 2021-05-20

Published Online: 2021-07-29

This work is licensed under the Creative Commons Attribution 4.0 International License.

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frequency measurement; phase processing; frequency standard tracking

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