CN105322962A - Frequency oscillator stability optimizing device and method - Google Patents

Abstract

The invention discloses a device for optimizing the stability of a frequency oscillator based on self-reference, which includes: a frequency oscillator for generating a frequency signal; a phase storage unit for storing the current phase of the frequency signal generated by the frequency oscillator, And delay a fixed time unit; the phase locking unit is used to lock the phase of the frequency signal generated by the frequency oscillator to the phase at the moment before the delay time unit stored in the phase storage unit.

Description

Frequency oscillator stability optimization device and method

technical field

The invention relates to the field of frequency oscillators, in particular to a self-reference-based frequency oscillator stability optimization device and method.

Background technique

The development of artificial clock timekeeping has gone through thousands of years, from sundials to atomic clocks. Early timekeeping was mainly used for the prediction of astronomical phenomena, etc.; in the mid-18th century, timekeeping began to be applied to the measurement of longitude in navigation; through unremitting efforts, people gradually realized that the main purpose of accurate timekeeping is to keep time synchronized, and the timekeeping Stability becomes the determining factor of positioning accuracy.

Modern atomic clock timekeeping began in the 1950s. The birth of the world's first cesium beam atomic frequency standard led to the establishment of a new international "second" definition in 1967, that is, the "astronomical second" defined by the movement of celestial bodies was changed to the "atomic second" reproduced by atomic clocks , and ushered in a new era of human time measurement and punctuality.

After the cesium beam frequency standard is put into practical application, whether it is the physical characteristics such as the principle and structure of the equipment, or the technical indicators such as frequency accuracy and stability, it is constantly improving and improving. In the 1980s, people developed a cesium atomic fountain clock based on the theory of laser cooling and ion trapping, with a stability of 2.8×10 ^-15 τ ^-1/2 , which greatly improved the accuracy of time measurement and became the main timing and time keeping clock. tool. At present, there have been breakthroughs in the research of optical clocks, but long-term continuous efforts are still needed.

A typical passive frequency standard uses the electromagnetic wave frequency radiated by atomic specific energy level transitions as the reference frequency of the local oscillator, and performs frequency or phase locking to obtain a standard frequency signal. Its relative frequency stability is characterized by the Allan deviation, which can be expressed as

${\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\sqrt{<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; v</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ></span>}}{{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; Q</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; SNR</span>}}\sqrt{\frac{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}}$

Here, v ₀ is the nominal frequency of the frequency signal; <Δv ² (τ)> is the infinite time average of the first-order difference of the frequency; SNR is the signal-to-noise ratio; T _c is the frequency discrimination period; Q is the quality factor; τ is Integration time. The main method to improve the stability of this frequency standard is to increase the signal-to-noise ratio SNR or increase the free evolution time T _R =T _c /2. where the signal-to-noise ratio SNR is proportional to N is the number of atoms. However, in practical applications, the frequency fluctuation of the local oscillator is much higher than the phase noise introduced by atomic decoherence, which becomes an important factor affecting the frequency stability.

For the active frequency standard, its relative frequency stability can be expressed as

${\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\sqrt{<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; v</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ></span>}}{{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\sqrt{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&pi;Q</span>}}\sqrt{\frac{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; P\&tau;</span>}}}$

Here, k _B is Boltzmann's constant; T is the ambient temperature; P is the actual power of the frequency oscillator; τ is the integration time. The frequency stability is mainly determined by the phase fluctuation caused by thermal noise, and is proportional to

From the above analysis, it can be seen that the frequency stability of the currently used frequency standards in the short-term integration time is as follows: The characteristics of the frequency drift, that is, as time goes on, random noise, temperature, etc. will cause frequency drift, and its stability will gradually decrease.

Contents of the invention

The object of the present invention is to propose a self-reference-based frequency oscillator stability optimization device and method, which continuously locks the phase of the current moment of the frequency oscillator to the phase of the previous moment separated by a fixed time, thereby improving the frequency The frequency drift of the oscillator over time, caused by random noise, temperature, aging, etc., has significantly improved the stability of the frequency oscillator.

In order to achieve the above object, the present invention adopts the following technical solutions:

A device for optimizing the stability of a frequency oscillator based on self-reference, said device comprising: a frequency oscillator for generating a frequency signal; a phase storage unit for storing the current phase of the frequency signal generated by the frequency oscillator, and delaying A fixed time unit; a phase locking unit, which is used to lock the phase of the frequency signal generated by the frequency oscillator to the phase at a moment before a delay time unit stored in the phase storage unit.

A method for optimizing the stability of a frequency oscillator based on self-reference, the method includes: using a phase storage unit to store the current phase of the frequency signal generated by the frequency oscillator, and delaying a fixed time unit, while using a phase-locking unit to continuously The phase of the frequency signal generated by the frequency oscillator at the current moment is locked to the phase at the previous moment stored in the phase storage unit at an interval of one delay time unit.

Description of drawings

FIG. 1 shows a schematic structural diagram of a typical embodiment of the self-reference-based frequency oscillator stability optimization device of the present invention.

detailed description

In order to make the object, technical solution and advantages of the present invention clearer, the present invention will be further described in detail below in combination with specific embodiments and with reference to the accompanying drawings.

Fig. 1 has shown the frequency oscillator stability optimization device based on self-reference that the present invention proposes, and described device comprises: frequency oscillator 1, is used for generating frequency signal; Phase storage unit 2, is used for storing the frequency oscillator 1 produced The phase of the current moment of the frequency signal, and delay a fixed time unit; the phase lock unit 3 is used to lock the phase of the frequency signal generated by the frequency oscillator 1 to the front of the interval of a delay time unit stored in the phase storage unit 2 moment of phase.

The phase of the frequency signal generated by frequency oscillator 1 is expressed as

Wherein, ω ₀ is the nominal angular frequency of this frequency signal; is the phase change term of the frequency signal with time.

According to the definition of Allan deviation, the stability of the frequency signal can be expressed as

Among them, τ is the integration time of the Allan deviation; v ₀ = ω ₀ /2π is the nominal frequency of the frequency signal; 〈Δv ² (τ)〉 is the infinite time average of the first-order difference of the frequency data, which is defined as

$<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; v</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ></span><span\; class="notranslate">\; =</span>\underset{{\mathrm{<span\; class="notranslate">\; T</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; \&Right\; Arrow;</span><span\; class="notranslate">\; \&infin;</span>}{\mathrm{<span\; class="notranslate">\; lim</span>}}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}{<span\; class="notranslate">\; \&Integral;</span>}_{<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; T</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}^{{\mathrm{<span\; class="notranslate">\; T</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}<span\; class="notranslate">\; <</span>{<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ></span>\mathrm{<span\; class="notranslate">\; dt</span>}$

is the infinite time average of the first-order difference of the phase change term, which is defined as

It should be noted that, usually, it can be assumed that is a stationary random function, and its states are ergodic, and its infinite time average can be obtained from the time average of a single sample function.

The phase value of the frequency signal generated by the frequency oscillator 1 at time t is stored by the phase storage unit 2 And after delaying a fixed time unit T ₀ , the phase of the frequency signal generated by the frequency oscillator 1 at t+T ₀ is determined by the phase locking unit 3 Locked in the phase of the t moment stored in the phase storage unit 2 get

which is

Here, C is a definite and constant number; the phase-locking process of the frequency oscillator 1 by the phase-locking unit 2 is a steady process, and δθ(t) is a random error generated during the phase-locking process at time t. It should be noted that, usually, the random error δθ generated by the phase-locking process is much smaller than the change of the frequency oscillator phase disturbance item in the delay time unit which is And the delay time unit T ₀ is much longer than the time required for a phase-locking process of the frequency oscillator.

It should be noted that, in the present invention, as long as the phase at the current moment is locked relative to the stored phase, it is not strictly required that the phases are completely equal. Therefore, for the convenience of expression, the fixed phase difference term C is omitted in the present invention, so that the above formula can be simplified as

Let T ₀ =2kπ/ω ₀ , the above formula can be further simplified as

Here, k is any constant positive integer. It should be noted that the phase storage unit 2 of the present invention can generate any fixed delay time unit T ₀ , which is not included in the discussion of the present invention.

The integration time of any Allan deviation can be expressed as

τ=NT ₀ +τ′

Here, N is a positive integer, 0≤τ'<T ₀ . When the phase-locking unit 3 is locked, it can be calculated as

It should be noted, varies with the variation of τ′, It is the maximum value within the value range of τ'. For example, when The change of is a diffusion process, namely where D is the diffusion coefficient, then Thus, the Allan deviation of the frequency signal can be expressed as

make

Available

It can be seen from the above formula:

When τ<<τ ₀ , due to The stability of the frequency signal generated by the frequency oscillator 1 is determined by Plays a dominant role and varies with time as σ _y (τ)∝1/τ;

When τ=τ ₀ ,

When τ＞＞τ ₀ , The stability of the frequency signal generated by the frequency oscillator 1 is dominated by δθ ² /ω ₀ ² T ₀ τ, and the change over time is

The present invention also provides a self-reference-based frequency oscillator stability optimization method, which is implemented by the above-mentioned self-reference-based frequency oscillator stability optimization device.

The self-reference-based frequency oscillator stability optimization method of the present invention includes the steps of: using the phase storage unit 2 to store the phase of the frequency signal at the current moment generated by the frequency oscillator 1, and delaying a fixed time unit, while using the phase locking unit 3 The phase of the frequency signal generated by the frequency oscillator 1 at the current moment is continuously locked to the phase at the previous moment stored in the phase storage unit 2 at an interval of one delay time unit.

In summary, the present invention aims to protect a device and method for optimizing the stability of a frequency oscillator based on self-reference, by continuously locking the phase of the frequency oscillator at the current moment to the phase at the previous moment with a fixed time interval, avoiding Over time, frequency drift due to random noise, temperature, aging, etc. is accounted for. Compared with the prior art, the present invention has the following advantages and effects:

(1) When the device is locked, the stability of the frequency oscillator at the integration time τ0 is _at Typically, the short-term stability of a free-running frequency oscillator is characterized by If its stability at τ ₀ can reach It can be calculated that its stability at T ₀ needs to be Considering the random error δθ generated by the phase-locking process, if only the uncertainty of phase measurement is included, the thermal noise can be minimized, expressed as

${\mathrm{<span\; class="notranslate">\; \&delta;\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; th</span>}}<span\; class="notranslate">\; =</span>\sqrt{\frac{\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; P</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}}$

Here, k _B is Boltzmann's constant; T is the ambient temperature; P is the actual power of the frequency oscillator. Take the common value ω ₀ =2π×10GHz, T ₀ =1ms, P=7dBm (5mW), calculate

${\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\sqrt{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}\mathrm{<span\; class="notranslate">\; T</span>}}}{{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\sqrt{\mathrm{<span\; class="notranslate">\; P</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}}<span\; class="notranslate">\; \&ap;</span>\mathrm{<span\; class="notranslate">\; 8.5</span>}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; 10</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 16</span>}}$

At τ=1s, the stability is This indicator is difficult to achieve at the current technical level. In the device and method described in the present invention, since the integration time is before τ ₀ , the stability varies with time as σ _y (τ) ∝ 1/τ, thus adopting a frequency oscillator with poor short-term stability can realize The stability _at τ0 reaches In other words, the short-term stability of the frequency oscillator is significantly improved when the device locks.

(2) When the device is locked, the frequency stability of the frequency oscillator is at τ<<τ ₀ , expressed as σ _y (τ)∝1/τ; at τ>>τ ₀ , expressed as The integration time corresponding to its turning point Can be changed by value to adjust. For frequency oscillators with worse short-term stability, the The larger the corresponding value, the greater the integration time τ ₀ corresponding to the turning point, and the greater the optimization of the frequency stability σ _y (τ ₀ ) at the corresponding turning point and the frequency stability corresponding to the integration time thereafter .

It should be understood that the above specific embodiments of the present invention are only used to illustrate or explain the principle of the present invention, and not to limit the present invention. Therefore, any modification, equivalent replacement, improvement, etc. made without departing from the spirit and scope of the present invention shall fall within the protection scope of the present invention. Furthermore, it is intended that the appended claims of the present invention embrace all changes and modifications that come within the scope and metesques of the appended claims, or equivalents of such scope and metes and bounds.

Claims (8)

1. A frequency oscillator stability optimization device, the device comprising: a frequency oscillator for generating a frequency signal; The phase storage unit is used to store the phase of the frequency signal generated by the frequency oscillator at the current moment, and delay a fixed time unit; The phase locking unit is used to lock the phase of the frequency signal generated by the frequency oscillator to the phase at a moment before one delay time unit stored in the phase storage unit. 2. The device according to claim 1, wherein the phase of the frequency signal produced by the frequency oscillator is expressed as Among them, _ω0 is the nominal angular frequency of the frequency signal, is the phase change item of the frequency signal with time, according to the definition of the Allan deviation, the stability of the frequency signal can be expressed by the Allan deviation as: Among them, τ is the integration time of the Allan deviation, v ₀ = ω ₀ /2π is the nominal frequency of the frequency signal, <Δv ² (τ)> is the infinite time average of the first-order difference of the frequency data, which is defined as: $<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; v</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ></span><span\; class="notranslate">\; =</span>\underset{{\mathrm{<span\; class="notranslate">\; T</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; \&Right\; Arrow;</span><span\; class="notranslate">\; \&infin;</span>}{\mathrm{<span\; class="notranslate">\; lim</span>}}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}{<span\; class="notranslate">\; \&Integral;</span>}_{<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; T</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}^{{\mathrm{<span\; class="notranslate">\; T</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}<span\; class="notranslate">\; <</span>{<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ></span>\mathrm{<span\; class="notranslate">\; dt</span>}$ is the infinite time average of the first-order difference of the phase change term, which is defined as: assumed It is a stationary random function, and its states are ergodic, and its infinite time average is obtained by the time average of a single sample function. 3. The device according to claim 2, characterized in that, the phase value of the frequency signal produced by the frequency oscillator at time t is stored by the phase storage unit And after a fixed time unit T ₀ is delayed, the phase locking unit will set the phase of the frequency signal generated by the frequency oscillator at t+T ₀ Locked in the phase of the t moment stored in the phase storage unit 2 get which is Wherein C is a fixed number, the phase-locking process of the frequency oscillator by the phase-locking unit is a stable process, and δθ(t) is the random error generated during the phase-locking process at time t. 4. The device of claim 3, wherein: Will Simplifies to: ω ₀ T ₀ Let T ₀ = 2kπ/ω ₀ , the above formula can be further simplified as: k is any constant positive integer, and the integration time of any Allen deviation is expressed as: τ=NT ₀ +τ′ N is a positive integer, 0≤τ′<T ₀ , when the phase-locked unit is locked, it can be calculated as follows: varies with the variation of τ′, It is the maximum value within the value range of τ′, thus, the Allan deviation of the frequency signal can be expressed as make Available When τ<<τ ₀ , due to The stability of the frequency signal generated by the frequency oscillator is determined by Plays a dominant role and varies with time as σ _y (τ)∝1/τ; When τ=τ ₀ , When τ＞＞τ ₀ , The stability of the frequency signal generated by the frequency oscillator is dominated by δθ ² /ω ₀ ² T ₀ τ, and the change over time is 5. A method for optimizing the stability of a frequency oscillator based on self-reference, the method comprising: using a phase storage unit to store the phase of the frequency signal at the current moment produced by the frequency oscillator, and delaying a fixed time unit, while using a phase-locked unit The phase of the frequency signal generated by the frequency oscillator at the current moment is continuously locked to the phase at the previous moment stored by the phase storage unit at an interval of one delay time unit. 6. method according to claim 5, is characterized in that, the phase of the frequency signal that described frequency oscillator produces is expressed as Among them, _ω0 is the nominal angular frequency of the frequency signal, is the phase change item of the frequency signal with time, according to the definition of the Allan deviation, the stability of the frequency signal can be expressed by the Allan deviation as: Among them, τ is the integration time of the Allan deviation, v ₀ = ω ₀ /2π is the nominal frequency of the frequency signal, <Δv ² (τ)> is the infinite time average of the first-order difference of the frequency data, which is defined as: $<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; v</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ></span><span\; class="notranslate">\; =</span>\underset{{\mathrm{<span\; class="notranslate">\; T</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; \&Right\; Arrow;</span><span\; class="notranslate">\; \&infin;</span>}{\mathrm{<span\; class="notranslate">\; lim</span>}}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}{<span\; class="notranslate">\; \&Integral;</span>}_{<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; T</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}^{{\mathrm{<span\; class="notranslate">\; T</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}<span\; class="notranslate">\; <</span>{<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ></span>\mathrm{<span\; class="notranslate">\; dt</span>}$ is the infinite time average of the first-order difference of the phase change term, which is defined as: assumed It is a stationary random function, and its states are ergodic, and its infinite time average is obtained by the time average of a single sample function. 7. method according to claim 6, it is characterized in that, store the phase value of the frequency signal that frequency oscillator produces at time t by phase storage unit And after a fixed time unit T ₀ is delayed, the phase locking unit will set the phase of the frequency signal generated by the frequency oscillator at t+T ₀ Locked in the phase of the t moment stored in the phase storage unit 2 get which is Wherein C is a fixed number, the phase-locking process of the frequency oscillator by the phase-locking unit is a stable process, and δθ(t) is the random error generated during the phase-locking process at time t. 8. The method of claim 7, wherein, Will Simplifies to: Let T ₀ =2kπ/ω ₀ , the above formula can be further simplified as: k is any constant positive integer, and the integration time of any Allen deviation is expressed as: τ=NT ₀ +τ′ N is a positive integer, 0≤τ′<T ₀ , when the phase-locked unit is locked, it can be calculated as follows: varies with the variation of τ′, It is the maximum value within the value range of τ′, thus, the Allan deviation of the frequency signal can be expressed as make Available When τ<<τ ₀ , due to The stability of the frequency signal generated by the frequency oscillator is determined by Plays a dominant role and varies with time as σ _y (τ)∝1/τ; When τ=τ ₀ , When τ＞＞τ ₀ , The stability of the frequency signal generated by the frequency oscillator is dominated by δθ ² /ω ₀ ² T ₀ τ, and the change over time is