TDLAS (Tunable Diode Laser Absorption Spectroscopy) second harmonic detection system and method adopting fixed frequency

By adopting a fixed frequency second harmonic detection system in the TDLAS system, using signal preprocessing, frequency matching, fixed frequency conversion and orthogonal phase locking modules, the output instability caused by modulation frequency drift and bandpass filter pass are solved. The problem of excessive bandwidth achieves more stable second harmonic detection.

CN119470337APending Publication Date: 2025-02-18NANJING UNIV OF AERONAUTICS & ASTRONAUTICS
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Patent Information

Application Number
CN202411603522.0
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-11-11
Publication Date
2025-02-18

AI Technical Summary

Technical Problem

In TDLAS applications, the output is unstable due to the modulation frequency drift, and the bandpass filter has too wide passband, which leads to excessive interference signals.

Method used

Using a fixed frequency TDLAS second harmonic detection system, the second harmonic frequency of the photoelectric signal to be measured is converted into Fixed frequency to achieve stable demodulation.

Benefits of technology

It improves the stability of the system output second harmonics, reduces the bandpass filter pass band, and enhances the noise filtering effect.

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Abstract

The invention provides a TDLAS (Tunable Diode Laser Absorption Spectroscopy) second harmonic detection system and method adopting a fixed frequency, belonging to the field of circuit design and signal processing, and comprising a signal preprocessing module, a frequency matching module, a frequency generation module, a fixed frequency conversion module and an orthogonal phase locking module, wherein the input signal is divided into a modulated and absorbed optical electric signal to be measured and a modulation frequency synchronizing signal, the modulation frequency synchronizing signal passes through the frequency matching module to obtain a signal of which the frequency is twice the modulation frequency plus one fixed frequency, and the modulation frequency synchronizing signal and the optical electric signal to be measured are input into the fixed-frequency conversion module to obtain a fixed-frequency detection signal; the intermediate frequency signal generated by the frequency generation module and the fixed frequency detection signal are subjected to orthogonal phase locking demodulation to obtain the amplitude and phase of the second harmonic of the optical electric signal to be detected. And through fixed frequency detection, the influence of unstable demodulation signals caused by modulation frequency drift is reduced, and meanwhile, the defect that the transmission band of a traditional phase-locked amplifier band-pass filter is too wide is overcome.
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Description

Technical Field

[0001] The present invention relates to the field of circuit design and signal processing, and in particular to a TDLAS second harmonic detection system and method using a fixed frequency. Background Art

[0002] Tunable laser absorption spectroscopy (TDLAS) is a highly sensitive and selective spectral analysis technology that utilizes the wavelength scanning and current tuning characteristics of a diode laser and measures gas concentration by demodulating the second harmonic. It is currently widely used in environmental monitoring, industrial process control, natural gas detection and other fields.

[0003] Demodulating the second harmonic is a key step in TDLAS detection technology. The method of high-frequency modulation of the wavelength and detecting the second harmonic can greatly suppress the influence of system noise. The demodulation of the second harmonic mainly adopts the phase-locked amplification technology. The phase-locked amplifier is an amplifier that can separate a specific carrier frequency signal from an environment with great interference. The current phase-locked amplifiers need to undergo pre-processing such as bandpass filtering before phase-sensitive detection. When the modulation frequency of the laser drifts or needs to be adjusted, the frequency of the photoelectric signal may be at the edge of the filter passband, resulting in unstable output. If the passband is too wide, it will cause too many interference signals to affect the demodulation. Summary of the invention

[0004] The purpose of the present invention is to solve the problem of output instability caused by modulation frequency drift and excessive passband of the bandpass filter in TDLAS applications, and to propose a TDLAS second harmonic detection system and method using a fixed frequency.

[0005] The present invention solves the above problems through the following technical solutions:

[0006] A TDLAS second harmonic detection system using a fixed frequency comprises a signal preprocessing module, a frequency matching module, a frequency generating module, a fixed frequency conversion module and an orthogonal phase locking module. The signal preprocessing module receives a photoelectric signal from an external photodetector and is connected to an input end of the fixed frequency conversion module. The fixed frequency conversion module is connected to an input end of the orthogonal phase locking module. A CPU in the orthogonal phase locking module is connected to an input end of a frequency generating module. The frequency generating module is connected to an input end of a frequency matching module. An output end of the frequency matching module is connected to the fixed frequency conversion module.

[0007] The signal preprocessing module includes a flow-conversion circuit and an AC amplifier, which are used to preliminarily amplify the photoelectric signal to be tested. The modulated and absorbed photoelectric signal to be tested detected by the photodetector is converted into a photocurrent after the flow-conversion circuit, and then preliminarily amplified by the AC amplifier and input into the fixed frequency conversion module; the frequency generation module includes a digital frequency synthesizer and an oscillator, which is used to synthesize a fixed frequency fi The oscillator provides an external clock input for the digital frequency synthesizer, and the CPU controls the digital frequency synthesizer to output a fixed frequency f i Highly stable intermediate frequency signal.

[0008] The frequency matching module includes a phase detector, an integrator, a DC amplifier, a voltage-controlled oscillator, a multiplier, a low-pass filter and a divider, wherein the phase detector, the integrator, the DC amplifier and the voltage-controlled oscillator form a phase-locked loop circuit, the multiplier and the low-pass filter are connected in the feedback loop of the phase-locked loop and connected to the divider to match the second harmonic frequency 2f0 of the photoelectric signal to be measured; the output signal frequency of the voltage-controlled oscillator is f i +f0′, and the fixed frequency f generated by the frequency generation module i The highly stable intermediate frequency signal of is used as the input signal of the multiplier. The output signal of the multiplier passes through a low-pass filter to obtain a transition signal with a frequency of transition frequency f0′; the transition signal is input into a two-frequency divider to obtain an output signal frequency of f0′ / 2, which is input into the phase detector together with the modulation frequency f0 synchronization signal. After the phase-locked loop frequency matching, f0′=2f0, and the frequency matching module outputs a signal frequency of f i +2f0.

[0009] The fixed frequency conversion module includes a mixer and a bandpass filter, the mixer and the bandpass filter are connected to convert the detection frequency from the second harmonic frequency 2f0 to a fixed frequency f i The photoelectric signal to be tested after the signal preprocessing module and the output signal of the frequency matching module are input into the mixer together, and the mixed signal is obtained with a fixed frequency f i The signal is input into the bandpass filter to obtain a fixed frequency f i Fixed frequency detection signal.

[0010] Furthermore, the center frequency of the bandpass filter is fixed to f i .

[0011] The orthogonal phase-locked module includes a phase shifter, a first phase-sensitive detector, a second phase-sensitive detector, a first low-pass filter, and a second low-pass filter. The first phase-sensitive detector is connected to the first low-pass filter, the second phase-sensitive detector is connected to the phase shifter and the second low-pass filter, and the first and second low-pass filters are connected to the CPU; it is used to perform orthogonal phase-locked amplification on the fixed-frequency detection signal and output the amplitude and phase of the second harmonic of the photoelectric signal to be measured; wherein the fixed-frequency detection signal generated by the fixed-frequency conversion module is respectively sent to the first phase-sensitive detector and the second phase-sensitive detector, and the highly stable intermediate frequency signal generated by the frequency generation module is divided into two paths, one path is input to the first phase-sensitive detector, and the other path is phase-shifted by 90° through the phase shifter and sent to the second phase-sensitive detector. The output signals of the first low-pass filter and the second low-pass filter are finally analyzed and calculated by the CPU to output the amplitude and phase of the second harmonic of the photoelectric signal to be measured.

[0012] A TDLAS second harmonic detection method using a fixed frequency comprises the following steps:

[0013] S1, the photoelectric signal to be measured is first input into the signal preprocessing module, converted from current to voltage, and then output to the given frequency conversion module after AC amplification;

[0014] S2, the modulation frequency f0 synchronization signal is input into the phase detector of the frequency matching module;

[0015] S3, the digital frequency synthesizer in the frequency generation module is controlled by the CPU to generate a fixed frequency f i The highly stable intermediate frequency signal is input into the multiplier of the feedback loop of the frequency matching module phase-locked loop circuit and combined with the output frequency of the voltage-controlled oscillator f i +f0′, and the sum frequency component and the difference frequency component are obtained after multiplication. The sum frequency component is filtered out by a low-pass filter to obtain a transition signal with a transition frequency f0′;

[0016] S4, the transition signal is input into the binary divider, the frequency becomes f0′ / 2, and the frequency is matched with the modulation frequency f0 synchronization signal through the phase-locked loop circuit to obtain the output signal of the frequency matching module ②, the frequency is f i +2f0;

[0017] S5, input the output signal of the frequency matching module and the photoelectric signal to be measured after the pre-processing module into the fixed frequency conversion module, and obtain a fixed frequency f i Fixed frequency detection signal;

[0018] S6, taking the fixed frequency detection signal as the target signal, and inputting it together with the intermediate frequency signal in step S3 into the orthogonal phase-locked module, and obtaining the amplitude and phase of the second harmonic of the photoelectric signal to be measured through CPU analysis and calculation.

[0019] Furthermore, in step S3, the digital frequency synthesizer outputs a fixed frequency f i It is of the same order of magnitude as the second harmonic frequency 2f0.

[0020] Furthermore, the frequency matching method in step S4 specifically includes:

[0021] (1) If f0′<2f0, the phase detector outputs a negative voltage, increasing the output frequency f of the voltage-controlled oscillator. i +f0′, the transition frequency f0′ increases;

[0022] (2) If f0′>2f0, the phase detector outputs a positive voltage, reducing the output frequency f of the voltage-controlled oscillator. i +f0′, the transition frequency f0′ decreases;

[0023] (3) If f0′=2f0, the phase detector outputs zero voltage and the fixed voltage-controlled oscillator output frequency f i +f0′, the frequency matching module② output frequency is f i +2f0.

[0024] Furthermore, in step S5, only the second harmonic component of the photoelectric signal to be measured is mixed with the output signal of the frequency matching module to obtain a fixed frequency f i signal component, and other frequency components pass through the center frequency f i The bandpass filter will remove it.

[0025] The present invention provides a TDLAS second harmonic detection system and method using a fixed frequency, which has a gain effect of converting the detection frequency of the second harmonic of the photoelectric signal to be detected from the traditional second harmonic frequency 2f0 to a high stable fixed frequency f generated by the frequency generation module. i , so that no matter how the modulation frequency of the TDLAS system drifts or changes, the system demodulates at a fixed frequency, greatly improving the stability of the system output second harmonic; and the frequency fluctuation generated by the frequency generation module is small, which can reduce the passband of the bandpass filter and enhance the noise filtering effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 The system block diagram of a TDLAS second harmonic detection system using a fixed frequency.

[0027] Figure 2 The signal flow chart of a TDLAS second harmonic detection method using a fixed frequency. DETAILED DESCRIPTION

[0028] The technical solution of the present invention is further described in detail below through specific implementation methods.

[0029] A TDLAS second harmonic detection system using a fixed frequency, such as Figure 1 As shown, it includes a signal preprocessing module, a frequency matching module, a frequency generating module, a fixed frequency conversion module, and an orthogonal phase locking module. The signal preprocessing module receives a photoelectric signal from an external photodetector and is connected to the input end of the fixed frequency conversion module. The fixed frequency conversion module is connected to the input end of the orthogonal phase locking module. The CPU in the orthogonal phase locking module is connected to the input end of the frequency generating module. The frequency generating module is connected to the input end of the frequency matching module. The output end of the frequency matching module is connected to the fixed frequency conversion module.

[0030] The signal preprocessing module includes a flow-conversion circuit and an AC amplifier, which are used to preliminarily amplify the photoelectric signal to be measured. The modulated and absorbed photoelectric signal to be measured detected by the photodetector is converted into a photocurrent after the flow-conversion circuit, and then preliminarily amplified by the AC amplifier and input into the fixed frequency conversion module. The expression is:

[0031]

[0032] Among them, f0 is the wavelength modulation frequency, 2f0 is the second harmonic frequency, f1 and f2 are the frequencies of other frequency components, A, A1, and A2 are the second harmonic amplitudes and the amplitudes of the f1 and f2 frequency components, respectively. is the phase of the frequency component, and n(t) is the noise.

[0033] The frequency generation module includes a digital frequency synthesizer and an oscillator for synthesizing a fixed frequency f i The oscillator provides an external clock input for the digital frequency synthesizer, and the CPU controls the digital frequency synthesizer to output a fixed frequency f i The output signal is expressed as Ccos(2πf i t), C is the amplitude of the intermediate frequency signal.

[0034] The frequency matching module includes a phase detector, an integrator, a DC amplifier, a voltage-controlled oscillator, a multiplier, a low-pass filter and a divider, wherein the phase detector, the integrator, the DC amplifier and the voltage-controlled oscillator form a phase-locked loop circuit, the multiplier and the low-pass filter are connected in the feedback loop of the phase-locked loop, and are connected to the divider to match the second harmonic frequency 2f0 of the photoelectric signal to be measured; the output signal of the voltage-controlled oscillator is expressed as Bcos[2π(f i +f0′)t], B is the output signal amplitude, and the frequency generated by the frequency generation module is a fixed frequency f i The highly stable intermediate frequency signal of the multiplier is used as the input signal of the multiplier. According to the product-sum-difference formula, the output signal expression of the multiplier is:

[0035]

[0036] Furthermore, the multiplier output signal is filtered out by a low-pass filter to remove the frequency f0′+2f i The signal component is obtained, and the output signal only contains the transition signal with the transition frequency f0′. After the two-frequency divider, the output signal frequency is f0′ / 2, and it is input into the phase detector together with the modulation frequency f0 synchronization signal. At this time, the phase-locked loop circuit starts to work. If f0′<2f0, the output voltage of the phase detector is negative. After passing through the integrator and the amplifier, it is input into the voltage-controlled oscillator, so that the frequency of the voltage-controlled oscillator increases; if f0′>2f0, the output voltage of the phase detector is positive. After passing through the integrator and the amplifier, it is input into the voltage-controlled oscillator, so that the frequency of the voltage-controlled oscillator decreases; when f0′=2f0, the output frequency of the voltage-controlled oscillator remains unchanged, the phase-locked loop is in a locked state, and the output frequency is f i +2f0, the frequency matching module output signal expression is Bcos[2π(f i +2f0)t].

[0037] The fixed frequency conversion module includes a mixer and a bandpass filter, the mixer and the bandpass filter are connected to convert the detection frequency from the second harmonic frequency 2f0 to a fixed frequency f i , the photoelectric signal to be measured after the signal preprocessing module and the output signal of the frequency matching module are input into the mixer together. According to the product-sum-difference formula, the output signal expression can be obtained as follows:

[0038]

[0039] Furthermore, the mixer output signal is transmitted through the center frequency f i Bandpass filter, the output frequency is fixed frequency f i The fixed frequency detection signal is expressed as:

[0040]

[0041] Where n′(t) is the noise after bandpass filtering.

[0042] The orthogonal phase-locked module includes a phase shifter, a first phase-sensitive detector, a second phase-sensitive detector, a first low-pass filter, and a second low-pass filter. The first phase-sensitive detector is connected to the first low-pass filter, the second phase-sensitive detector is connected to the phase shifter and the second low-pass filter, and the first and second low-pass filters are connected to the CPU; and is used to perform orthogonal phase-locked amplification on the fixed-frequency detection signal and output the amplitude and phase of the photoelectric signal to be measured.

[0043] Furthermore, the fixed frequency detection signal is input into the first phase-sensitive detector and the second phase-sensitive detector respectively, and the highly stable intermediate frequency signal Ccos(2πf i t) is divided into two paths, one path is directly input into the first phase-sensitive detector, and the other path is phase-shifted by 90° through the phase shifter, and the expression is Csin(2πf l t), input to the second phase-sensitive detector.

[0044] The output signal of the first phase-sensitive detector is expressed as:

[0045]

[0046] After passing through the first low-pass filter, the DC component is output, which is the in-phase component of the second harmonic of the photoelectric signal to be measured. The expression is:

[0047]

[0048] The output signal of the second phase-sensitive detector is expressed as:

[0049]

[0050] After passing through the second low-pass filter, the DC component is output, which is the orthogonal component of the second harmonic of the photoelectric signal to be measured. The expression is:

[0051]

[0052] The in-phase component and the orthogonal component are input into the CPU, and the expression obtained after the square sum operation is:

[0053]

[0054] Calculate the amplitude of the second harmonic of the photoelectric signal to be measured Phase The CPU can output amplitude, phase, in-phase component and orthogonal component as needed.

[0055] A TDLAS second harmonic detection method using a fixed frequency comprises the following steps:

[0056] S1, the photoelectric signal to be measured is first input into the signal preprocessing module, converted from current to voltage, and then output to the given frequency conversion module after AC amplification;

[0057] S2, the modulation frequency f0 synchronization signal is input into the phase detector of the frequency matching module;

[0058] S3, the digital frequency synthesizer in the frequency generation module is controlled by the CPU to generate a fixed frequency f iThe highly stable intermediate frequency signal is input into the multiplier of the feedback loop of the frequency matching module phase-locked loop circuit and combined with the output frequency of the voltage-controlled oscillator f i +f0′, and the sum frequency component and the difference frequency component are obtained after multiplication. The sum frequency component is filtered out by low-pass filtering to obtain a transition signal with a transition frequency f0′;

[0059] S4, the transition signal is input into the binary divider, the frequency becomes f0′ / 2, and the frequency is matched with the modulation frequency f0 synchronization signal through the phase-locked loop circuit to obtain the output signal of the frequency matching module ②, the frequency is f i +2f0;

[0060] S5, input the output signal of the frequency matching module and the photoelectric signal to be measured after the pre-processing module into the fixed frequency conversion module, and obtain a fixed frequency f i Fixed frequency detection signal;

[0061] S6, taking the fixed frequency detection signal as the target signal, and inputting it together with the intermediate frequency signal in step S3 into the orthogonal phase-locked module, and obtaining the amplitude and phase of the second harmonic of the photoelectric signal to be measured through CPU analysis and calculation.

[0062] Furthermore, in step S3, the digital frequency synthesizer outputs a fixed frequency f i It is of the same order of magnitude as the second harmonic frequency 2f0.

[0063] Furthermore, the frequency matching method in step S4 specifically includes:

[0064] (1) If f0′<2f0, the phase detector outputs a negative voltage, increasing the output frequency f of the voltage-controlled oscillator. i +f0′, the transition frequency f0′ increases;

[0065] (2) If f0′>2f0, the phase detector outputs a positive voltage, reducing the output frequency f of the voltage-controlled oscillator. i +f0′, the transition frequency f0′ decreases;

[0066] (3) If f0′=2f0, the phase detector outputs zero voltage and the fixed voltage-controlled oscillator output frequency f i +f0′, the phase-locked loop circuit is in the locked state, and the frequency matching module ② outputs a frequency of f i +2f0.

[0067] Furthermore, the photoelectric signal to be measured in step S5 is a signal obtained after gas absorption, which contains various frequency components. Only the second harmonic component of the photoelectric signal to be measured can be mixed with the output signal of the frequency matching module to obtain a fixed frequency f i signal component, and other frequency components pass through the center frequency f iThe bandpass filter will remove it.

[0068] Furthermore, the system signal flow chart is as follows: Figure 2 As shown in the figure, the modulation frequency synchronization signal frequency is f0, which is converted to f by the frequency matching module. i +2f0, the photoelectric signal to be measured contains multiple frequency components, among which the second harmonic with a frequency of 2f0 and the second harmonic with a frequency of f i The frequency matching module output signal of +2f0 is mixed to get f i and f i +4f0 frequency term, other frequency components have no f after mixing i The frequency term is f i The frequency term is extracted to obtain a fixed-frequency detection signal, which is equal to the frequency f i The two mutually orthogonal intermediate frequency signals are phase-sensitively detected to obtain a phase-sensitive detection signal, the frequency of which includes DC term, 2f i The DC terms obtained through low-pass filtering are the in-phase component and quadrature component of the second harmonic of the photoelectric signal to be measured, and the amplitude and phase of the second harmonic are obtained through calculation.

[0069] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, ordinary technicians in the field should understand that the specific implementation methods of the present invention can still be modified or some technical features can be replaced by equivalents without departing from the spirit of the technical solution of the present invention, which should be included in the scope of the technical solution for protection of the present invention.

Claims

1. A TDLAS second harmonic detection system using a fixed frequency, characterized in that: It includes a signal preprocessing module ①, a frequency matching module ②, a frequency generating module ③, a fixed frequency conversion module ④, and an orthogonal phase locking module ⑤. The signal preprocessing module ① receives a photoelectric signal from an external photodetector and is connected to an input end of the fixed frequency conversion module ④. The fixed frequency conversion module ④ is connected to an input end of the orthogonal phase locking module ⑤. The CPU in the orthogonal phase locking module ⑤ is connected to an input end of the frequency generating module ③. The frequency generating module ③ is connected to an input end of the frequency matching module ②. The output end of the frequency matching module ② is connected to the fixed frequency conversion module ④. The signal preprocessing module ① includes a flow pressure circuit and an AC amplifier, which are used to preliminarily amplify the photoelectric signal to be measured; the frequency generation module ③ includes a digital frequency synthesizer and an oscillator, which are used to synthesize a fixed frequency f l Highly stable intermediate frequency signal; The frequency matching module ② includes a phase detector, an integrator, a DC amplifier, a voltage-controlled oscillator, a multiplier, a low-pass filter and a divider; wherein the phase detector, the integrator, the DC amplifier and the voltage-controlled oscillator form a phase-locked loop circuit, the multiplier and the low-pass filter are connected in the feedback loop of the phase-locked loop, and are connected to the divider; and is used to match the second harmonic frequency 2f0 of the photoelectric signal to be measured; The fixed frequency conversion module ④ includes a mixer and a bandpass filter, and the mixer is connected to the bandpass filter; it is used to convert the detection frequency from the second harmonic frequency 2f0 to a fixed frequency f i , get the fixed frequency detection signal; The orthogonal phase-locked module ⑤ includes a phase shifter, a first phase-sensitive detector, a second phase-sensitive detector, a first low-pass filter, and a second low-pass filter; The first phase-sensitive detector is connected to the first low-pass filter, the second phase-sensitive detector is connected to the phase shifter and the second low-pass filter, and the first and second low-pass filters are connected to the CPU; they are used to perform orthogonal phase-locked amplification on the fixed-frequency detection signal and output the amplitude and phase of the second harmonic of the photoelectric signal to be measured.

2. A TDLAS second harmonic detection method using a fixed frequency, characterized in that: The following steps are involved: S1, the photoelectric signal to be measured is first input into the signal preprocessing module ①, converted from current to voltage, and then output to the given frequency conversion module ④ after AC amplification; S2, the modulation frequency f0 synchronization signal is input into the phase detector of the frequency matching module ②; S3, the digital frequency synthesizer in the frequency generation module ③ is controlled by the CPU to generate a fixed frequency f i The highly stable intermediate frequency signal is input into the multiplier of the feedback loop of the frequency matching module ② phase-locked loop circuit, and the output frequency of the voltage-controlled oscillator is f i +f0′, and the sum frequency component and the difference frequency component are obtained after multiplication. The sum frequency component is filtered out by a low-pass filter to obtain a transition signal with a transition frequency f0′; S4, the transition signal is input into the binary divider, the frequency becomes f0′ / 2, and the frequency is matched with the modulation frequency f0 synchronization signal through the phase-locked loop circuit to obtain the output signal of the frequency matching module ②, the frequency is f i +2f0; S5, input the output signal of the frequency matching module ② and the photoelectric signal to be measured after the pre-processing module into the fixed frequency conversion module ④, and obtain a fixed frequency f i Fixed frequency detection signal; S6. The fixed-frequency detection signal is used as the target signal and input into the orthogonal phase-locked module ⑤ together with the intermediate frequency signal in step S3. The amplitude and phase of the second harmonic of the photoelectric signal to be measured are obtained through CPU analysis and calculation.

3. A TDLAS second harmonic detection method using a fixed frequency according to claim 2, characterized in that: The frequency matching method in step S4 specifically includes: (1) If f0′<2f0, the phase detector outputs a negative voltage, increasing the output frequency f of the voltage-controlled oscillator. i +f0′, the transition frequency f0′ increases; (2) If f0′>2f0, the phase detector outputs a positive voltage, reducing the output frequency f of the voltage-controlled oscillator. i +f0′, the transition frequency f0′ decreases; (3) If f0′=2f0, the phase detector outputs zero voltage and the fixed voltage-controlled oscillator output frequency f i +f0′, the frequency matching module② output frequency is f i +2f0.