CN114742005B - Quartz crystal oscillator temperature frequency characteristic modeling method based on VPPM - Google Patents
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Abstract
The invention discloses a quartz crystal oscillator temperature frequency characteristic modeling method based on a variable parameter polynomial model, which comprises the steps of data acquisition, calculation of temperature derivative by using a difference method, calculation of frequency offset, construction of a random neural network model and acquisition of weight parameters from a hidden layer to an output layer in the random neural network. According to the method, the influence of complex temperature change is converted into the change of the model parameters, so that the frequency variation can be accurately estimated in different temperature variation intervals and different temperature variation conditions, and the stability of the frequency of the electronic product can be improved; the method utilizes the change of temperature and temperature derivative to realize the self-adaptive adjustment of model parameters, establishes a more reasonable variable parameter temperature-frequency characteristic model, calculates the frequency offset during temperature change more accurately, and improves the frequency offset compensation precision.
Description
Technical Field
The invention relates to a quartz crystal oscillator temperature frequency characteristic modeling method, in particular to a quartz crystal oscillator temperature frequency characteristic modeling method based on VPPM, and belongs to the technical field of electronic science.
Background
Quartz crystal resonator is made of quartz material, is a frequency source of many electronic communication systems, and is widely applied to various electronic products in modern industrial society. The frequency of the quartz crystal is affected by a plurality of factors such as noise, aging, temperature and the like, wherein the temperature is the most important factor affecting the stability of the frequency of the quartz crystal. The frequency of the quartz crystal oscillator changes with temperature, and the relationship between the temperature and the frequency is called as temperature frequency characteristic. The accurate temperature frequency characteristic model has important significance for developing the temperature compensation crystal oscillator, and is beneficial to improving the frequency stability of the electronic product.
The temperature frequency characteristic of the traditional quartz crystal oscillator is generally described by adopting a Polynomial Model (PM), and the traditional Polynomial Model has the advantages of simple structure and definite physical meaning, but has the disadvantages that the Model adopts fixed parameters, and the potential assumption is that the temperature frequency characteristic of the quartz crystal oscillator is unchanged in different temperature variation ranges and under different temperature variation conditions. However, in practical application and test scenarios, because of the complexity of the internal thermal characteristics of the crystal oscillator, the temperature frequency characteristics have large differences in the heating or cooling process, and certain differences exist in different temperature operation intervals, so that the traditional fixed parameter model is difficult to accurately estimate the frequency variation, and cannot realize accurate compensation. Therefore, for the situation of complex temperature change in practice, a quartz crystal oscillator temperature frequency characteristic modeling method based on a variable parameter polynomial model (Varying-Parameter Polynomial Model, VPPM) is researched, and the method has important significance for improving the analysis accuracy of the variable parameter quartz crystal oscillator temperature frequency characteristic.
Disclosure of Invention
The invention aims to provide a quartz crystal oscillator temperature frequency characteristic modeling method based on VPPM.
In order to solve the technical problems, the invention adopts the following technical scheme:
a quartz crystal oscillator temperature frequency characteristic modeling method based on VPPM comprises the following steps:
step 1: and (3) data acquisition: simulating a static change situation in a test environment, continuously changing the environment temperature, and acquiring test temperatures T (i), i=0, 1, … and N and corresponding output frequencies { f (i), i=0, 1, … and N } of the crystal;
step 2: calculating by using a difference method to obtain a temperature derivative:
dT(i)＝T(i)-T(i-1) (1)
step 3: calculating a frequency offset:
wherein f 0 Is the reference frequency
Step 4: constructing a random neural network model:
in the method, in the process of the invention,
the weight parameter from the hidden layer to the output layer in the random neural network is that m represents the number of hidden layer nodes; />
Fitting the variable parameters by test temperature and frequency offset; h (i) is an output vector of the parameter adjustment model, and the calculation method comprises the following steps:
wherein f (-) is a nonlinear activation function sigmoid function, W.epsilon.R m×2 And b.epsilon.R 2×1 Are all set to [ -1,1]Random parameter vectors uniformly distributed among the two;
step 5: acquiring weight parameters from a hidden layer to an output layer in a random neural network: the training takes the test temperature and the temperature derivative as model input, takes the variable parameter as model output, constructs a training data set, trains a random neural network model, and obtains the weight parameter from the hidden layer to the output layer in the random neural network.
Further, the method for testing the temperature and frequency offset fitting frequency offset in the step 4 is as follows:
Δf(i)＝a 1 (i)(T(i)-T 0 )+a 2 (i)(T(i)-T 0 ) 2 +a 3 (i)(T(i)-T 0 ) 3 (5)
wherein T is 0 Is the reference temperature.
Further, the weight parameter identification method from the hidden layer to the output layer in the random neural network in the step 5 is as follows:
Δf(i)＝v 11 h 1 (i)ΔT(i)+…+v 1m h m (i)ΔT(i)+v 21 h 1 ΔT(i) 2 +…+v 2m h m (i)ΔT(i) 2 +v 31 h 1 (i)ΔT(i) 3 +...+v 3m h m (i)ΔT(i) 3 (6)
in the above formula, Δt (i) =t (i) -T 0 An input matrix X and an output matrix Y of model parameter identification are established:
the least square method is utilized to obtain the identified model parameters:
wherein X is + Representing a generalized inverse of the X matrix.
The beneficial effects of adopting above-mentioned technical scheme to produce lie in:
(1) According to the method, the influence of complex temperature change is converted into the change of the model parameters, so that the frequency variation can be accurately estimated in different temperature variation intervals and different temperature variation conditions, and the stability of the frequency of the electronic product can be improved;
(2) According to the invention, the self-adaptive adjustment of model parameters is realized by utilizing the change of temperature and temperature derivative, a more reasonable variable parameter temperature-frequency characteristic model is established, the frequency offset during temperature change is calculated more accurately, and the frequency offset compensation precision is improved.
Drawings
FIG. 1 is a functional block diagram of the present invention;
fig. 2 is a frequency offset estimation result diagram of the PM method according to the embodiment of the invention;
fig. 3 is a frequency offset estimation result diagram of the VPPM method according to an embodiment of the invention;
fig. 4 is a frequency deviation estimation error diagram of the PM method and VPPM method of an embodiment of the invention;
fig. 5 is a comparison chart of frequency deviation estimation results of the PM method and the VPPM method according to the embodiment of the invention.
Detailed Description
Example 1:
a quartz crystal oscillator temperature frequency characteristic modeling method based on VPPM comprises the following steps:
step 1: and (3) data acquisition: simulating a static change situation in a test environment, continuously changing the environment temperature, and acquiring test temperatures { T (i), i=0, 1, …, N } and corresponding output frequencies { f (i), i=0, 1, …, N } of the crystal;
step 2: calculating by using a difference method to obtain a temperature derivative:
dT(i)＝T(i)-T(i-1) (1)
step 3: calculating a frequency offset:
wherein f 0 Is the reference frequency
Step 4: constructing a random neural network model:
in the method, in the process of the invention,
is a weight parameter from a hidden layer to an output layer in a random neural network, and m represents hiddenThe number of layer nodes; />
Fitting the variable parameters by test temperature and frequency offset; h (i) is an output vector of the parameter adjustment model, and the calculation method comprises the following steps: />
Wherein f (-) is a nonlinear activation function sigmoid function, W.epsilon.R m×2 And b.epsilon.R 2×1 Are all set to [ -1,1]Random parameter vectors uniformly distributed among the two;
step 5: acquiring weight parameters from a hidden layer to an output layer in a random neural network: the training takes the test temperature and the temperature derivative as model input, takes the variable parameter as model output, constructs a training data set, trains a random neural network model, and obtains the weight parameter from the hidden layer to the output layer in the random neural network.
The method for testing the temperature and frequency offset fitting frequency offset in the step 4 is as follows:
Δf(i)＝a 1 (i)(T(i)-T 0 )+a 2 (i)(T(i)-T 0 ) 2 +a 3 (i)(T(i)-T 0 ) 3 (5)
wherein T is 0 For reference temperature f 0 Is the reference frequency.
The weight parameter identification method between the hidden layer and the output layer in the random neural network comprises the following steps:
Δf(i)＝v 11 h 1 (i)ΔT(i)+…+v 1m h m (i)ΔT(i)+v 21 h 1 ΔT(i) 2 +…+v 2m h m (i)ΔT(i) 2 +v 31 h 1 (i)ΔT(i) 3 +...+v 3m h m (i)ΔT(i) 3 (6)
in the above formula, Δt (i) =t (i) -T 0 An input matrix X and an output matrix Y of model parameter identification are established:
the least square method is utilized to obtain the identified model parameters:
wherein X is + Representing a generalized inverse of the X matrix.
Aiming at the defects of the prior PM technology, the invention provides a quartz crystal oscillator temperature frequency characteristic model building method based on a VPPM model, and a schematic block diagram is shown in figure 1. The model includes two links: and a basic temperature frequency characteristic model and a parameter adjustment model. The invention characterizes the change of the model under the condition of complex temperature change as the change of the model parameters, and is beneficial to improving the accuracy of crystal oscillator frequency offset estimation.
In the embodiment, a certain quartz crystal at 19.2MHz is taken as an experimental object, and model training data and test data of frequency are carried out by adopting a conventional PM method and a VPPM method at different temperatures. The PM method performs frequency deviation estimation, and the result is shown in fig. 2, and it can be seen that the frequency estimation error is still large at the point where the temperature gradient changes greatly. The VPPM method performs frequency deviation estimation, and the result is shown in fig. 3, and it can be seen that the estimation result is relatively close to the actual experimental result, and the large deviation is eliminated. The estimated error for the frequency deviation is plotted in fig. 4, and it can be seen that the maximum estimated error for the PM method can reach 1.1ppm, while the maximum deviation estimated error for the VPPM method is less than 0.5ppm. The comparative results of the root mean square error RMSE are shown in table 1, it can be seen that the RMSE of the PM process exceeds 0.5ppm, while the RMSE of the VPPM process is less than 0.2ppm. Fig. 5 is a graph showing frequency deviation of different modeling methods, and it can be seen that when the VPPM method is used, the estimated value and the true value of the frequency deviation are basically on the same straight line, so that the consistency is good, and the estimated error of the conventional PM method changes significantly along with the temperature rise and fall. From the experimental results, the VPPM method can better describe the temperature-frequency characteristic change rule of the quartz crystal oscillator and reduce the frequency deviation prediction error.
TABLE 1
| Polynomial Model (PM) | Variable Parameter Polynomial Model (VPPM) | |
| RMSE | 0.5456 | 0.1837 |
Claims (1)
1. A quartz crystal oscillator temperature frequency characteristic modeling method based on a variable parameter polynomial model is characterized by comprising the following steps of: the method comprises the following steps:
step 1: and (3) data acquisition: simulating a static change situation in a test environment, continuously changing the environment temperature, and carrying out N sampling to obtain a test temperature { T (i), i=0, 1,. N } and a corresponding output frequency { f (i), i=0, 1,. N } of the crystal;
step 2: calculating by using a difference method to obtain a temperature derivative:
dT(i)＝T(i)-T(i-1) (1)
step 3: calculating a frequency offset:
wherein f 0 Is the reference frequency
Step 4: constructing a random neural network model:
in the method, in the process of the invention,
the weight parameter from the hidden layer to the output layer in the random neural network is that m represents the number of hidden layer nodes; />
Fitting the variable parameters by test temperature and frequency offset; h (i) is an output vector of the parameter adjustment model, and the calculation method comprises the following steps:
where f (-) is a nonlinear activation function sigmoid function,
W∈R m×2 and b.epsilon.R 2×1 Are all set to [ -1,1]Random parameter vectors uniformly distributed among the two;
the method for obtaining the variable parameters by fitting the test temperature and the frequency offset comprises the following steps:
Δf(i)＝a 1 (i)(T(i)-T 0 )+a 2 (i)(T(i)-T 0 ) 2 +a 3 (i)(T(i)-T 0 ) 3 (5)
wherein T is 0 Is the reference temperature;
step 5: acquiring weight parameters from a hidden layer to an output layer in a random neural network: training, namely inputting a test temperature and a temperature derivative as a model, outputting a variable parameter as a model, constructing a training data set, training a random neural network model, and obtaining a weight parameter from a hidden layer to an output layer in the random neural network;
the weight parameter identification method between the hidden layer and the output layer in the random neural network comprises the following steps:
Δf(i)＝v 11 h 1 (i)ΔT(i)+...+v 1m h m (i)ΔT(i)+v 21 h 1 ΔT(i) 2 +...+v 2m h m (i)ΔT(i) 2 +v 31 h 1 (i)ΔT(i) 3 +...+v 3m h m (i)ΔT(i) 3 (6)
in the above formula, Δt (i) =t (i) -T 0 ，h 1 (i) And h m (i) Respectively representing the 1 st element and the m-th element in the h (i) vector, and establishing an input matrix X and an output matrix Y for model parameter identification:
the least square method is utilized to obtain the identified model parameters:
wherein X is + Representing a generalized inverse of the X matrix.
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| CN102082548A (en) * | 2010-11-12 | 2011-06-01 | 成都天奥电子股份有限公司 | High-accuracy microcomputer-compensated surface-mounted temperature compensation crystal oscillator |
| CN112713881A (en) * | 2020-12-10 | 2021-04-27 | 国网四川省电力公司电力科学研究院 | Synchronous clock maintaining system and method based on edge calculation |
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| US7692499B2 (en) * | 2007-12-31 | 2010-04-06 | Integrated Device Technology, Inc. | Digitally compensated highly stable holdover clock generation techniques using adaptive filtering |
| CN110879302B (en) * | 2019-11-26 | 2022-02-22 | 西安石油大学 | Temperature compensation method for quartz resonance differential accelerometer |
| CN112380774B (en) * | 2020-11-23 | 2022-04-15 | 青岛柯锐思德电子科技有限公司 | Dynamic modeling method and system based on residual echo state network |
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| CN102082548A (en) * | 2010-11-12 | 2011-06-01 | 成都天奥电子股份有限公司 | High-accuracy microcomputer-compensated surface-mounted temperature compensation crystal oscillator |
| CN112713881A (en) * | 2020-12-10 | 2021-04-27 | 国网四川省电力公司电力科学研究院 | Synchronous clock maintaining system and method based on edge calculation |
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