A digital-to-analog conversion method based on improved binary gold panning algorithm optimization

Abstract

This invention discloses a digital-to-analog converter (DAC) method based on an improved binary gold mining algorithm, comprising: setting initial parameters; employing and designing a binary method of the gold mining optimization algorithm and applying it to the Uc-ReDAC model to calculate the binary code corresponding to the target voltage; expanding the gold miner position matrix using a dimension factor-based dimension expansion strategy to enhance the influence of the current dimension on the gold miner's binary position; designing a variable slope convergence factor based on the RC circuit time constant in the Uc-ReDAC model and constraining the gold miner's movement step size through this factor; employing a dynamic update strategy for the gold miner position matrix, expanding the gold miner's decimal position matrix using a circular mapping random number generation method, and outputting a binary code that meets the accuracy requirements. This invention combines the improved gold mining optimization algorithm with the mathematical model of an unconstrained relaxation-type DAC, ensuring both data conversion efficiency and accuracy while achieving data conversion.

Description

Technical Field

[0001] This invention belongs to the field of digital-to-analog conversion, and relates to digital-to-analog converter technology, specifically to a digital-to-analog conversion method based on an improved binary gold mining algorithm. Background Technology

[0002] Digital-to-analog converters (DACs) are indispensable core components in modern electronic systems, widely used in audio and video processing, communication systems, industrial automation, scientific measurement, medical equipment, power management, and emerging technologies. With the popularization of digital signal processing technology, DACs convert discrete digital signals into continuous analog signals, enabling digital systems to efficiently interface with analog devices. Therefore, research on DACs is particularly important. With the development of DAC technology in recent years, DACs can be classified into various types according to different principles and application requirements, including resistor divider, current distribution, weighted current, integrating, charge distribution, pulse width modulation, and hybrid DACs.

[0003] Currently, integrating intelligent optimization algorithms into engineering applications and applying them to the field of DAC technology is an important research direction. Applying intelligent optimization algorithms to the mathematical model of DAC transforms the optimization problem into a problem of solving the DAC output voltage, which will greatly reduce the complexity of DAC while ensuring conversion time and accuracy.

[0004] Therefore, combining intelligent optimization algorithms with DAC mathematical models to solve the optimization problem of binary encoding in the model is of great significance. Improving the conversion rate and accuracy of DAC is an important topic in the field of digital-to-analog converter technology, and its research is of great significance. Summary of the Invention

[0005] Purpose of the invention: In order to overcome the shortcomings of the existing technology, a digital-to-analog conversion method based on an improved binary gold mining algorithm is provided. The improved gold mining optimization algorithm is combined with the mathematical model of an unconstrained-relaxation digital-to-analog converter (Uc-ReDAC) to ensure data conversion efficiency and accuracy while achieving data conversion.

[0006] Technical Solution: To achieve the above objectives, this invention provides a digital-to-analog conversion method based on an improved binary gold mining algorithm, comprising the following steps:

[0007] S1: Set the initial parameters for the Uc-ReDAC model and algorithm;

[0008] S2: Adopt and design a binary method for gold mining optimization algorithm and use it in the Uc-ReDAC model to calculate the binary code corresponding to the target voltage;

[0009] S3: The gold miner position matrix is ​​expanded using a dimension factor-based dimension expansion strategy. The dimension factor is used to enhance the influence of the current dimension on the binary position of the gold miner, ensuring that the gold miner moves correctly.

[0010] S4: Design a variable slope convergence factor based on the time constant of the RC circuit in the Uc-ReDAC model, and use this factor to constrain the gold miner's moving step size;

[0011] S5: A dynamic update strategy for the gold prospector position matrix is ​​adopted. The decimal position matrix of the gold prospector is extended by the circular mapping random number generation method, and the final output is a binary code that meets the accuracy requirements.

[0012] Furthermore, the initial parameters in step S1 include the Uc-ReDAC resolution n and the minimum permissible error. The number of gold miners N, the maximum number of iterations M, and the upper and lower limits of the gold miner search space ub and lb.

[0013] Furthermore, the Uc-ReDAC model in step S2 is...

[0014]

[0015] Among them, V C,n V represents the voltage across the capacitor at time nT. C,0 The initial voltage across the capacitor, V DD The circuit represents the power supply voltage of the RC circuit, T represents the system clock period, τ = RC represents the time constant, n represents the length of the binary sequence, and b represents the voltage of the RC circuit. k This represents the k-th item in the binary sequence.

[0016] Furthermore, the binary method of the gold mining optimization algorithm in step S2, and its application in the Uc-ReDAC model, is as follows:

[0017] The gold mining optimization algorithm is binary-coded. In this algorithm, gold miners mainly determine the location of the gold mine through three steps: migration, cooperation, and panning. The update of the gold miner's location is then standardized.

[0018] x i+1 (t+1)=x i (t)+ε (2)

[0019] Where, x i+1 x iLet represent the new and previous positions of the gold prospector, respectively; ε is the step size for migration, cooperation, and gold prospecting, and the position update is related to ε. Mapping the gold prospector's step size ε to [0,1], the sigmoid function is...

[0020]

[0021] The larger the gold miner's step size ε, the closer s(ε) is to 1; otherwise, the closer it is to 0. After mapping, the gold miner's position is updated to...

[0022]

[0023] If s(ε) is greater than the random number r, then x id The value of x is 1; otherwise, x id The value is 0, thus completing the gold miner's location update.

[0024] Furthermore, the dimensional expansion strategy in step S3 includes: each row in the matrix represents a solution found by the algorithm, and only solutions that meet the accuracy requirements can be output; otherwise, the matrix will continue to expand to higher dimensions.

[0025] Minimum permissible error of the Uc-ReDAC model Determined by the model resolution, for

[0026]

[0027] Where N is the resolution of the Uc-ReDAC; P gd The optimal value found for gold prospectors; V C,n The voltage to be searched; Minimum permissible error;

[0028] Despite the conditional dimensional expansion, the randomness of the gold miner's binary position update according to equation (1) leads to an undesirable length of the output binary code; therefore, let V in equation (1) C,0 =0, simplified to

[0029]

[0030] make Rewrite equation (6) as follows:

[0031]

[0032] If b1 = 0, then b1 is an invalid start bit, and the valid start bit of the binary code is b2; if b1 = b2 = 0, then b1 and b2 are invalid start bits, and the valid start bit of the binary code is b3.

[0033] Furthermore, in the dimension expansion strategy of step S3, the dimension expansion of the binary position matrix will only stop when a solution that meets the accuracy requirements exists in the gold miner's binary position matrix; considering that changes in the matrix dimension can affect the current gold miner's binary position, a dimension influence factor affecting the gold miner's binary position is designed, and its calculation formula is as follows:

[0034]

[0035] Among them, V DD D represents the power supply voltage of the RC circuit. max V at this model resolution DD The shortest length of the corresponding binary code; V C,n d represents the voltage to be searched; d represents the current binary encoding dimension.

[0036] At this point, the mapping formula for the gold prospector's step size ε is:

[0037]

[0038] Where ε is the gold prospector's step size;

[0039] In the Uc-ReDAC model, the shortest number of binary code bits corresponding to the target voltage cannot be calculated, but V at this model resolution can be calculated. DD The corresponding shortest binary code length D max When expanding dimensions, the influence of the current dimension on the binary position of the gold miner can be increased to control the length of the binary code.

[0040] Furthermore, in step S4, the variable slope convergence factor l is based on the RC circuit time constant in the Uc-ReDAC model. * for

[0041]

[0042] Where α is the initial value of the factor change; β is the convergence coefficient; iter is the current iteration number of the algorithm; and T is the maximum iteration number.

[0043] Furthermore, when the decimal position matrix of the gold miners is expanded in dimension, the element values ​​of the newly expanded dimension are randomly generated. However, traditional random number generation methods may lead to clustering of some random positions, thus affecting the performance of the algorithm. To address this issue, in step S5, when expanding the dimension of the decimal position matrix, a random factor based on a circular mapping method is designed, and the calculation formula is as follows:

[0044]

[0045] Where rand(j+1) is the currently generated random factor; α is the nonlinearity factor; and β is the driving factor.

[0046] Furthermore, step S5 employs a random number generation method where the range of the circular mapping random number generation decreases non-linearly with the increase of the iteration count; the gold prospector's decimal position update formula is...

[0047]

[0048] Where, x id Let be the value of the i-th gold miner in the d-th dimension; iter is the iteration number; rate is the shrinkage coefficient, which can be adjusted according to the actual search situation. The larger this value, the more obvious the shrinkage effect on the range of random number values; ub and lb are the initial upper and lower limits of the search space. As the number of iterations increases, the update range of element values ​​in the newly expanded dimension of the gold miner decimal position matrix decreases non-linearly, reducing the blindness in the later stages of algorithm iteration and accelerating convergence.

[0049] Beneficial effects: Compared with the prior art, the present invention has the following advantages:

[0050] 1. Mapping the movement step size in the GRO algorithm to realize the binary representation of the algorithm can better solve the optimization problem under the Uc-ReDAC model and improve the efficiency of the algorithm;

[0051] 2. A dimension expansion strategy based on dimension factor is proposed, which combines dimension changes to affect gold miners, enhances the influence on the binary position changes of gold miners, and further controls the binary encoding length.

[0052] 3. A variable slope convergence factor based on the time constant of the RC circuit is proposed. It is nonlinearly varied according to the number of iterations to control the time of the gold miner from global search to local search, while taking into account the time characteristics of the external RC circuit, thus ensuring the correctness of the UC-ReDAC output voltage value.

[0053] 4. Based on the characteristics of the Uc-ReDAC model and the inherent features of the GRO algorithm, a gold prospector position matrix update strategy is proposed. By synchronously updating, the algorithm's running efficiency is improved, and the correct operation of the algorithm is guaranteed.

[0054] 5. The algorithm provided by this invention can be better applied to the Uc-ReDAC model. It searches for the binary code corresponding to the target voltage with a short length and high accuracy, effectively reducing the code search time. While realizing data conversion, it can ensure data conversion efficiency and accuracy. Attached Figure Description

[0055] Figure 1 This is a flowchart of the binary gold mining optimization algorithm of the present invention;

[0056] Figure 2 Here is a structural diagram of the Uc-ReDAC model;

[0057] Figure 3 A schematic diagram of the expanded dimension of the binary position matrix for gold prospectors;

[0058] Figure 4 A schematic diagram of the expanded dimension of the binary position matrix for the improved gold miners;

[0059] Figure 5 The improved variable slope convergence factor function curve of this invention is compared with the original convergence factor function.

[0060] Figure 6 This is a schematic diagram illustrating the dynamic update of the position matrix in this invention;

[0061] Figure 7 Update the range of elements in the decimal position matrix;

[0062] Figure 8 The variation in the number of bits in the binary encoding of the 4-bit Uc-ReDAC model;

[0063] Figure 9 The number of bits in the binary encoding of the 6-bit Uc-ReDAC model varies;

[0064] Figure 10 The variation in the number of bits in the binary encoding of the 8-bit Uc-ReDAC model;

[0065] Figure 11 The graph shows a comparison of the static parameters of the two algorithms in 4-bit, 6-bit, and 8-bit Uc-ReDAC models. Detailed Implementation

[0066] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. After reading this invention, any modifications of the invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.

[0067] This invention provides a digital-to-analog conversion method based on an improved binary gold mining algorithm, referring to... Figure 1 It includes the following steps:

[0068] S1: Set the initial parameters for the Uc-ReDAC model and algorithm;

[0069] Including Uc-ReDAC resolution n, minimum permissible error Based on the model resolution n, the number of gold miners N is 50, the maximum number of iterations M is set to 100, and the upper and lower limits of the gold miner search space ub and lb are set to 10 and -10, respectively.

[0070] S2: Adopt and design a binary method for gold mining optimization algorithm and use it in the Uc-ReDAC model to calculate the binary code corresponding to the target voltage;

[0071] The essence of Uc-ReDAC is to use binary codes generated by an optimized algorithm to control the charging and discharging of capacitors through a three-state buffer, thereby generating the required analog voltage. The Uc-ReDAC structure diagram is shown below. Figure 2 As shown. The mathematical model expression for Uc-ReDAC is:

[0072]

[0073] Among them, V C,n V represents the voltage across the capacitor at time nT. C,0 The initial voltage across the capacitor, V DD The circuit represents the power supply voltage of the RC circuit, T represents the system clock period, τ = RC represents the time constant, n represents the length of the binary sequence, and b represents the voltage of the RC circuit. k This represents the k-th item in the binary sequence;

[0074] The gold mining optimization algorithm is binary-coded. In this algorithm, gold miners primarily determine the location of gold mines through three steps: migration, cooperation, and panning. The update of gold miner locations is then standardized.

[0075] x i+1 (t+1)=x i (t)+ε (2)

[0076] Where, x i+1 x i Let represent the new and previous positions of the gold miner, respectively, and ε be the step size for migration, cooperation, and gold mining. Position updates are related to ε. Mapping the gold miner's step size ε to [0,1], the sigmoid function is:

[0077]

[0078] The larger the gold miner's step size ε, the closer s(ε) is to 1; otherwise, the closer it is to 0. After mapping, the gold miner's position is updated to...

[0079]

[0080] If s(ε) is greater than the random number r, then x id The value of x is 1; otherwise, x idThe value is 0, thus completing the gold miner's location update.

[0081] S3: The gold miner position matrix is ​​expanded using a dimension factor-based dimension expansion strategy. The dimension factor is used to enhance the influence of the current dimension on the binary position of the gold miner, ensuring that the gold miner moves correctly.

[0082] Dimension expansion methods such as Figure 3 As shown, the number of rows in the matrix represents the number of gold prospectors, and the number of columns represents the dimension of the gold prospectors. Each row in this matrix represents a solution found by the algorithm; only solutions that meet the accuracy requirements are output; otherwise, the matrix continues to expand to higher dimensions. The minimum allowable error of the Uc-ReDAC model is... Determined by the model resolution, for

[0083]

[0084] Where N is the resolution of the Uc-ReDAC; P gd The optimal value found for gold prospectors; V C,n The voltage to be searched; This represents the minimum permissible error.

[0085] Despite the conditional dimensional expansion, the randomness of the gold miner's binary position update according to equation (1) leads to an undesirable length of the output binary code. Therefore, let V in equation (1) C,0 =0, simplified to

[0086]

[0087] make Rewrite equation (6) as follows:

[0088]

[0089] Where b1 = 0, then b1 is an invalid start bit, and the valid start bit of the binary code is b2; if b1 = b2 = 0, then b1 and b2 are invalid start bits, and the valid start bit of the binary code is b3. Therefore, y i1 ==1. The improved binary position matrix for gold prospectors has expanded dimensions as follows: Figure 4 As shown.

[0090] In the dimension expansion strategy proposed in this invention, the dimension expansion of the binary position matrix will only stop when a solution satisfying the accuracy requirement exists in the gold miner's binary position matrix. Considering that changes in the matrix's dimension can affect the current binary position of the gold miner, this invention designs a dimension influence factor affecting the gold miner's binary position, the calculation formula of which is as follows:

[0091]

[0092] Among them, V DD D represents the power supply voltage of the RC circuit. max V at this model resolution DD The shortest length of the corresponding binary code; V C,n Let be the voltage to be searched; d is the current binary encoding dimension. At this point, the mapping formula for the gold prospector's step size ε is:

[0093]

[0094] Where ε is the gold prospector's step size;

[0095] In the Uc-ReDAC model, the shortest number of binary code bits corresponding to the target voltage cannot be calculated, but V at this model resolution can be calculated. DD The corresponding shortest binary code length D max When expanding dimensions, the influence of the current dimension on the binary position of the gold miner can be increased to control the length of the binary code.

[0096] S4: Design a variable slope convergence factor based on the time constant of the RC circuit in the Uc-ReDAC model, and use this factor to constrain the gold miner's moving step size;

[0097] In the gold mining optimization algorithm, the migration vector coefficient A1 is adjusted to determine whether the gold miner performs a global search or a local search. The formula for calculating A1 is:

[0098]

[0099] Where l1 is the balance factor; r1 is a random number in the range [0,1]. When |A1|≤1, the gold prospector narrows their migration, searching for gold in a smaller local area. Since the value of |A1| changes with l1, the change of l1 affects the gold prospector's search ability. This invention combines the charging and discharging process of the RC circuit in Uc-ReDAC to design a variable slope convergence factor l based on the time constant of the RC circuit. * Instead of l1, the calculation formula is as follows:

[0100]

[0101] Where α is the initial value of the factor change, which is 2 in this embodiment; β is the convergence coefficient, which is 0.5 in this embodiment; iter is the current iteration number of the algorithm; and T is the maximum iteration number.

[0102] When the maximum number of iterations is 250, the convergence factor variation curve at τ = 100 ns is shown in Figure l. * like Figure 5As shown. Rapid decay in the early stages of iteration facilitates global searching for the gold miner, while slow decay in the later stages facilitates local searching, thus improving the gold miner's search accuracy. In the Uc-ReDAC model, a larger time constant means a longer charging and discharging time for the RC circuit, requiring a longer binary encoding to complete the charging. Therefore, the convergence factor l proposed in this invention is adopted. * By controlling the time it takes for the gold miner to switch from a global search to a local search, while also taking into account the timing characteristics of the external RC circuit, the correctness of the UC-ReDAC output voltage value is ensured.

[0103] S5: A dynamic update strategy for the gold miner position matrix is ​​adopted. The decimal position matrix of the gold miners is extended by the circular mapping random number generation method, and the final output is a binary code that meets the precision requirements.

[0104] In the process of binarying the gold mining optimization algorithm, the gold miner's movement step size cannot be calculated using the gold miner's binary position. Therefore, this invention designs a dynamic update strategy for the gold miner's position matrix to obtain the gold miner's movement step size. For example... Figure 6 The dynamic update strategy for the gold miner's position matrix is ​​described as follows: Process 1 represents the dynamic update of the gold miner's binary position matrix, and Process 2 represents the dynamic update of the gold miner's decimal position matrix. In the dimension expansion strategy, as shown in Process 1, all elements in the first dimension of the gold miner's binary position matrix are set to 1. When expanding the dimension of the binary position matrix, the position information of the new dimension is generated by updating the decimal position information of the previous dimension in the decimal position matrix. In Process 2, the algorithm randomly selects the migration, cooperation, or gold mining update method to calculate the gold miner's movement step size, and then uses the movement step size to calculate its binary position information. This process continues until the updated gold miner's binary position matrix contains binary codes that meet the required precision, at which point the dimension expansion stops.

[0105] In the dynamic update strategy of the gold prospector position matrix, when the decimal position matrix of the gold prospectors is expanded in dimension, the element values ​​of the newly expanded dimension are randomly generated. However, traditional random number generation methods may lead to clustering of some random positions, thus affecting the performance of the algorithm. To address this, this invention designs a random factor based on a circular mapping method when expanding the dimension of the decimal position matrix. The calculation formula is as follows:

[0106]

[0107] Where rand(j+1) is the currently generated random factor; α is the nonlinearity factor, which is 0.6 in this embodiment; β is the driving factor, which is 0.8 in this embodiment.

[0108] Because using a fixed range of circular mapping random numbers for dimensional expansion of the gold miner's decimal position matrix is ​​not conducive to fine-grained searching of local regions in the later stages of iteration, a random number generation method is adopted where the range of circular mapping random number generation decreases non-linearly with the number of iterations. The gold miner's decimal position update formula is as follows:

[0109]

[0110] Where, x id Let be the value of the i-th miner in the d-th dimension; iter be the iteration number; rate be the shrinkage coefficient, which can be adjusted according to the actual search situation. In this invention, the algorithm uses 0.01. The larger this value, the more significant the shrinkage effect on the range of random number values; ub and lb are the initial upper and lower limits of the search space. As the number of iterations increases, the update range of element values ​​in the newly expanded dimension of the miner's decimal position matrix decreases non-linearly, reducing the blindness in the later stages of algorithm iteration and accelerating convergence. In this invention, ub = 10 and lb = -10. As the number of iterations increases, the update range of elements in the miner's decimal matrix is ​​as follows: Figure 7 As shown, the shaded area represents the range of values ​​for the elements in the gold prospector's decimal position matrix.

[0111] To verify the effectiveness and results of the method of the present invention, the following experiments and results analysis were conducted in this embodiment:

[0112] The experimental computer was an Intel(R) Core i7-8750H CPU @ 2.5GHz with 16GB of RAM; the operating system was Windows 11, and the programming environment was MATLAB R2021b. To test the performance of the algorithm of this invention, the algorithm of this invention, AP-BPSO, and BPSO were simulated 10 times each under 4-bit and 6-bit Uc-ReDAC models. The average value of the experimental results was taken, and the algorithm performance was evaluated by two metrics: average number of bits in the generated binary code and algorithm search time. The average number of bits in the binary code refers to the average number of bits in the binary code that can represent each analog voltage under this model; the algorithm search time refers to the total time it takes for the algorithm to output the binary code that can represent each analog voltage under this model. Finally, a comparative experiment was conducted on the number of bits in the generated binary code of the three algorithms under 4-bit, 6-bit, and 8-bit Uc-ReDAC models, and the static parameters of the algorithm of this invention and AP-BPSO under 4-bit, 6-bit, and 8-bit Uc-ReDAC models were compared.

[0113] In the experiment, the algorithm of this invention used 50 gold miners, with a maximum dimension of 100 and a maximum number of iterations of 100. The initial random range of elements in the decimal position matrix of the gold miners was [-10, 10]. AP-BPSO and BPSO used 50 particles, with a maximum particle dimension of 100 and a maximum number of iterations of 100. The maximum and minimum inertia weights were 8 and 4, respectively, and the particle velocity range was [-10, 10]. In the 4-bit Uc-ReDAC, 6-bit Uc-ReDAC, and 8-bit Uc-ReDAC models, V... C,0 The voltage is 0V, the RC circuit time constant is 100ns, the clock period T is 10ns, and the power supply voltage V dd It is 3.3V.

[0114] The average number of bits generated by the algorithm of this invention and two other algorithms under 4-bit Uc-ReDAC and 6-bit Uc-ReDAC models, along with the algorithm search time, are shown in Table 1. Since the BPSO algorithm does not converge to the swarm optimal particle, the generated binary number becomes increasingly random with each iteration, thus affecting the search for the optimal V. C,n Binary encoding can lead to excessively long encoding bits, resulting in a long algorithm search time. The AP-BPSO algorithm adds an adaptive incremental coefficient to the BPSO algorithm, thereby increasing the search voltage V. C,n The value of affects the particle position to some extent, reducing the number of bits in the binary code, but the search time of the algorithm is not significantly reduced compared to the BPSO algorithm under the 6-bit Uc-ReDAC model.

[0115] Table 1

[0116]

[0117] The algorithm of this invention generates shorter binary codes and faster search times under both 4-bit and 6-bit Uc-ReDAC models. Compared to the AP-BPSO and BPSO algorithms, the average number of bits in the 4-bit Uc-ReDAC model is reduced by 16.67% and 60%, respectively, and the search time is reduced by 47.31% and 79.22%, respectively. Under the 6-bit Uc-ReDAC model, the average number of bits in the 6-bit Uc-ReDAC model is reduced by 52% and 57.14%, respectively, and the search time is reduced by 56.41% and 56.46%, respectively, indicating that the algorithm of this invention has high performance under both models. The algorithm of this invention digitizes the GRO algorithm and designs a dimension expansion strategy based on the dimension factor according to the characteristics of the algorithm itself and the rules of the Uc-ReDAC model. When expanding the dimension of the gold miner's position matrix, the influence of the current dimension change on the binary position of the gold miner is added to enhance the directionality of the gold miner's movement. At the same time, in order to improve the search accuracy of the gold miner, the algorithm of this invention incorporates a variable slope convergence factor based on the RC circuit time constant according to the Uc-ReDAC model. Based on the above improvements, the binary position matrix of the gold miners is conditionally expanded to minimize the number of bits in the binary encoding and improve algorithm efficiency.

[0118] In the two models described above, experiments were conducted on the three algorithms to generate binary codes with varying bit lengths, such as... Figure 8 As shown, the algorithm generates a line graph illustrating the variation in the number of binary code bits in a 4-bit Uc-ReDAC model. When the target voltage to be searched is close to V... dd The bit variation in the binary code generated by the AP-BPSO algorithm is more gradual compared to the BPSO algorithm, when searching for the target voltage. and The BPSO algorithm generated a binary code with a maximum bit length of 100, but this did not meet the required precision. The higher the target voltage, the greater the variation in the number of bits in the binary code. The BPSO algorithm does not impose any constraints on the particle's position, resulting in strong randomness in particle position, which leads to issues when the search voltage is close to V. dd The binary code is too long. The number of bits generated by the algorithm of this invention changes more gradually compared to the BPSO algorithm, but the difference is not significant compared to the AP-BPSO algorithm.

[0119] Figure 9 This invention's algorithm generates a curve showing the change in the number of binary encoded bits in a 6-bit Uc-ReDAC model. The target voltage to be searched is close to... and At that time, the binary code generated by the BPSO algorithm reached the maximum number of bits (100) and still did not meet the accuracy requirements. As the resolution of the Uc-ReDAC model increased, the BPSO algorithm's performance improved when the search voltage approached V. dd It is easier to get stuck in the global optimum, while searching for nearby... When the target voltage is reached, the BPSO algorithm generates a binary code with a larger change in bit length compared to the other two algorithms. The algorithm of this invention exhibits a smaller change in binary code bit length compared to the AP-BPSO algorithm. This invention's algorithm not only meets the accuracy requirements but also has significant advantages in terms of the number of binary code bits generated, the degree of bit length variation, and the algorithm's search time.

[0120] Figure 10 Extracting data from the 8-bit Uc-ReDAC model for three algorithms to The graph shows the change in the number of bits in the binary code under different voltages. As the voltage to be searched increases, the 8-bit Uc-ReDAC model under the BPSO algorithm performs better in the search... The generated binary code had already reached the specified maximum number of bits (100) and did not meet the precision requirements. The 8-bit Uc-ReDAC model under the AP-BPSO algorithm, in the search... and The maximum number of bits was 100. As the voltage to be searched increases and the model resolution improves, the number of bits in the binary code corresponding to the voltage to be searched will become larger and larger.

[0121] The algorithm of this invention searches for all target voltages in the 8-bit Uc-ReDAC model without exceeding the specified maximum number of bits and meets the accuracy requirements. This algorithm has significant advantages over the other two algorithms in both the number of bits and the range of bit variation. Because this invention incorporates the influence of dimensionality on the search direction, especially when the binary code corresponding to the voltage to be searched in the model is long, the dimensionality influence factor further strengthens its impact on the binary position of the searcher, making the generated binary code as short as possible and effectively improving the algorithm's efficiency and running speed.

[0122] Figure 11 This paper presents a comparison of the static parameters of the proposed algorithm and the AP-BPSO algorithm under 4-bit Uc-ReDAC, 6-bit Uc-ReDAC, and 8-bit Uc-ReDAC models. Figure 11 (a) and (b) show the integral nonlinearity (INL) and differential nonlinearity (DNL) of the two algorithms under the 4-bit Uc-ReDAC model, respectively; (c) and (d) show the comparison of INL and DNL of the two algorithms under the 6-bit Uc-ReDAC model, respectively; (e) and (f) show the comparison of INL and DNL of the two algorithms under the 8-bit Uc-ReDAC model, respectively. In (e) and (f), when the voltage to be searched is close to V... ddAt that time, the static parameters of the 11-bit Uc-ReDAC model under the algorithm of this invention are significantly better than those of the AP-BPSO algorithm.

[0123] Table 2 shows the static parameters of the binary codes generated by the algorithm of this invention and the AP-BPSO algorithm under 4-bit Uc-ReDAC, 6-bit Uc-ReDAC, and 8-bit Uc-ReDAC models, respectively. Under the 4-bit Uc-ReDAC model, the rms(DNL) of the algorithm of this invention is 0.355, slightly better than the AP-BPSO algorithm. This is because the model resolution is lower, and the seekable voltages of both algorithms are limited. Under the 6-bit Uc-ReDAC model, all static parameters of the algorithm of this invention are better than those of the AP-BPSO algorithm. In the higher-resolution 8-bit Uc-ReDAC model, the max(DNL) of the model under the algorithm of this invention is reduced by 57.56%, rms(DNL) by 18.87%, max(INL) by 84.63%, and rms(INL) by 39.26% compared to the AP-BPSO algorithm. The algorithm of this invention employs a variable slope convergence factor based on the time constant of the RC circuit during the optimization process. In the early stage of iteration, the convergence factor decreases rapidly, which is beneficial for the searcher to perform a global search. In the later stage of iteration, the convergence factor decreases slowly, which is beneficial for the searcher to perform a local search. This improves the search accuracy of the algorithm of this invention. Especially in the higher resolution Uc-ReDAC model, the higher resolution means that more iterations are needed when searching for a certain voltage, and the search accuracy of the algorithm of this invention will be higher.

[0124] Table 2

[0125]

Claims

1. A digital-to-analog conversion method based on an improved binary gold mining algorithm, characterized in that, Includes the following steps: S1: Set the initial parameters for the Uc-ReDAC model and algorithm; S2: Adopt and design a binary method for gold mining optimization algorithm and use it in the Uc-ReDAC model to calculate the binary code corresponding to the target voltage; S3: The gold miner position matrix is ​​expanded using a dimension factor-based dimension expansion strategy, and the influence of the current dimension on the binary position of the gold miner is enhanced by the dimension factor. S4: Design a variable slope convergence factor based on the time constant of the RC circuit in the Uc-ReDAC model, and use this factor to constrain the gold miner's moving step size; S5: A dynamic update strategy for the gold miner position matrix is ​​adopted. The decimal position matrix of the gold miners is extended by the circular mapping random number generation method, and the final output is a binary code that meets the precision requirements. In step S2, the Uc-ReDAC model is Among them, V C,n V represents the voltage across the capacitor at time nT. C,0 The initial voltage across the capacitor, V DD The circuit represents the power supply voltage of the RC circuit, T represents the system clock period, τ = RC represents the time constant, n represents the length of the binary sequence, and b represents the voltage of the RC circuit. k This represents the k-th item in the binary sequence; The dimensional expansion strategy in step S3 includes: each row in the matrix represents a solution found by the algorithm, and only solutions that meet the accuracy requirements can be output; otherwise, the matrix will continue to expand to higher dimensions. Minimum permissible error of the Uc-ReDAC model Determined by the model resolution, for Where N is the resolution of the Uc-ReDAC; P gd The optimal value found for gold prospectors; V C,n The voltage to be searched; Minimum permissible error; Let V in equation (1) C,0 =0, simplified to make Rewrite equation (6) as follows: If b1 = 0, then b1 is an invalid start bit, and the valid start bit of the binary code is b2; if b1 = b2 = 0, then b1 and b2 are invalid start bits, and the valid start bit of the binary code is b3.

2. The digital-to-analog conversion method based on an improved binary gold mining algorithm as described in claim 1, characterized in that, The initial parameters in step S1 include the Uc-ReDAC resolution n and the minimum permissible error. The number of gold miners N, the maximum number of iterations M, and the upper and lower limits of the gold miner search space ub and lb.

3. The digital-to-analog conversion method based on an improved binary gold mining algorithm as described in claim 1, characterized in that, The binary method of the gold mining optimization algorithm in step S2, and its application in the Uc-ReDAC model, is as follows: The gold mining optimization algorithm is binary-coded. In this algorithm, prospectors determine the location of a gold mine through three steps: migration, cooperation, and panning. The update of prospector locations is then standardized. x i+1 (t+1)=x i (t)+ε (2) Where, x i+1 x i Let represent the new and previous positions of the gold prospector, respectively; ε is the step size for migration, cooperation, and gold prospecting, and the position update is related to ε. Mapping the gold prospector's step size ε to [0,1], the sigmoid function is... After mapping, the gold prospector's location will be updated to... If s(ε) is greater than the random number r, then x id The value of x is 1; otherwise, x id The value is 0, thus completing the gold miner's location update.

4. The digital-to-analog conversion method based on an improved binary gold mining algorithm as described in claim 1, characterized in that, In the dimension expansion strategy of step S3, the dimension expansion of the binary position matrix will only stop when a solution that meets the accuracy requirements exists in the gold miner's binary position matrix; a dimension influence factor affecting the gold miner's binary position is designed, and its calculation formula is as follows: Among them, V DD D represents the power supply voltage of the RC circuit. max V at this model resolution DD The shortest length of the corresponding binary code; V C,n d represents the voltage to be searched; d represents the current binary encoding dimension. At this point, the mapping formula for the gold prospector's step size ε is: Where ε is the gold prospector's step size.

5. The digital-to-analog conversion method based on an improved binary gold mining algorithm as described in claim 4, characterized in that, In step S4, the variable slope convergence factor l is based on the RC circuit time constant in the Uc-ReDAC model. * for Where α is the initial value of the factor change; β is the convergence coefficient; iter is the current iteration number of the algorithm; and T is the maximum iteration number.

6. The digital-to-analog conversion method based on an improved binary gold mining algorithm as described in claim 1, characterized in that, In step S5, when expanding the dimension of the decimal position matrix, a random factor based on a circular mapping method is designed, and the calculation formula is as follows: Where rand(j+1) is the currently generated random factor; α is the nonlinearity factor; and β is the driving factor.

7. The digital-to-analog conversion method based on an improved binary gold mining algorithm as described in claim 6, characterized in that, Step S5 employs a random number generation method where the range of the circular mapping random number generation decreases non-linearly with the increase of the iteration count; the gold prospector's decimal position update formula is... Where, x id Let be the value of the i-th gold miner in the d-th dimension; iter is the iteration number; rate is the shrinkage coefficient.

Images