Streamline analog-to-digital converter background calibration method based on rule optimization control

Abstract

The invention discloses a pipeline analog-to-digital converter background calibration method based on rule optimization control, which relates to the field of analog-to-digital converter conversion, and comprises a reference analog-to-digital converter, a fuzzy controller, a fuzzy rule construction module and a calibration output unit, wherein the fuzzy rule construction module adopts a symmetrical structure to reduce a half of fuzzy rules, so that the complexity of the fuzzy controller structure is reduced, and meanwhile, all the fuzzy rules are accurately and quickly initialized in a secondary initialization mode, so that the nonlinear fitting capability of the fuzzy controller is fully exerted. According to the method, the number of rules in the fuzzy control method can be effectively reduced, and the fitting capability of the method to nonlinear errors can be improved, so that the nonlinear errors in the assembly line fuzzy converter can be quickly and effectively calibrated.

Description

Technical Field

[0001] The present invention relates to the technical field of pipelined analog-to-digital converter calibration, and specifically to a background calibration method for a pipelined analog-to-digital converter based on rule optimization control. Background Art

[0002] An analog-to-digital converter (ADC), as a bridge between the analog domain and the digital domain, converts continuous analog signals into discrete digital signals. Pipelined ADCs have been widely used in fields such as communication, medical, consumer electronics, industrial control, automotive electronics, test and measurement, military and aerospace, and scientific research due to their high-speed and high-precision characteristics. However, with the reduction of process dimensions, the problem of device mismatch has intensified and the impact of noise on the system has increased, seriously affecting the performance of the circuit. Therefore, calibration techniques are needed to improve the effectiveness of the circuit. Digital calibration techniques have been widely studied due to their high precision, flexibility, reduction of hardware complexity and power consumption. For example, correlation-based calibration techniques and histogram-based calibration techniques. However, these calibration techniques can usually only calibrate specific errors and cannot achieve comprehensive calibration of errors.

[0003] Neural networks have become an effective way to solve the nonlinear problems of ADCs due to their strong fitting characteristics and generalization ability. In recent years, great progress has been made in using neural networks to calibrate the nonlinear problems in ADCs. For example, a neural network that superimposes dynamic branches and static branches is used to effectively calibrate dynamic distortion and static distortion in ADCs. There is also an application of ANN to implement a bijective vector recovery mapping (VRM) for nonlinear calibration, which effectively suppresses harmonic distortion and spurs, and a method of using NCN and MCN to calibrate the nonlinearity in a single channel and the mismatch between channels is proposed. To improve the calibration performance, multi-dimensional features are used as inputs to increase the amount of information and achieve effective fitting of non-monotonic transfer functions. There are also papers that effectively reduce the hardware overhead by reducing the parameters of the input layer and the number of neurons in the hidden layer. And during the training process of the neural network, to avoid falling into local minima, a method of combining PSO and SGD can be used to reduce the computational amount while finding the optimal solution. The initial parameters of the neural network can also be configured through the GA algorithm to ensure the calibration effect of the neural network, but this will increase the complexity of the overall structure.

[0004] Although neural networks have achieved good results in the non - linear calibration task of ADCs, they still face problems such as the structure, number of parameters, overfitting, and the balance of hardware implementation for some simple tasks. At the same time, the backpropagation process of neural networks is very challenging in hardware implementation. Therefore, it is necessary to find a simpler calibration method for specific tasks. The fuzzy control method is a non - linear control method widely used in the field of control systems. It relies on the operator's experience knowledge or operation data to effectively control complex objects, with simple design and easy implementation. Applying it to the calibration of pipelined ADCs is a good choice. Summary of the Invention

[0005] (1) Technical Problems to be Solved

[0006] In view of the problem that the pipelined analog - to - digital converter is affected by capacitor mismatch, comparator offset, gain error, and non - ideal factors, resulting in non - linear output of the analog - to - digital converter, the present invention proposes a background calibration method for a pipelined analog - to - digital converter based on a rule - optimized fuzzy controller. By using a symmetric structure and a two - stage initialization method to optimize the fuzzy controller rules, the number of fuzzy rules is reduced, and the complexity of the system is also reduced, in order to quickly calibrate the non - linear error of the pipelined fuzzy converter, thereby effectively improving the performance of the circuit.

[0007] (2) Technical Solutions

[0008] To achieve the above object, the present invention is realized through the following technical solutions: A background calibration method for a pipelined analog - to - digital converter based on rule - optimized control, which is applied to a calibration system composed of a reference analog - to - digital converter, a fuzzy controller, a fuzzy rule construction module, and a data output unit;

[0009] The pipelined analog - to - digital converter to be calibrated and the reference analog - to - digital converter are connected to the same signal source, and after quantifying the input signal V in of the same signal source, the M (M≥6) - stage quantization digital codes D1, D2,..., D M of the pipelined analog - to - digital converter to be calibrated are obtained, as well as the actual output value D out1 of the pipelined analog - to - digital converter to be calibrated and the ideal output value D out2 of the reference analog - to - digital converter, so as to obtain the quantization output error value E error =D out2 -D out1 ;

[0010] The fuzzy controller adopts a four - input and three - output structure, which takes the second - stage to fifth - stage quantization digital codes D2, D3, D4, D5 as inputs, infers three outputs according to the constructed fuzzy rule base, and then calculates the error compensation value Ecal ;

[0011] The calibration output unit adds the actual output value D of the pipelined analog-to-digital converter to be calibrated out1 and the error compensation value E cal to obtain the calibration output value D of the pipelined analog-to-digital converter to be calibrated cal ;

[0012] The fuzzy rule construction module reduces the number of fuzzy rules through a symmetric structure, that is, according to the quantization digital codes D2, D3, D4, D5 of the second to fifth levels and the quantization output error value E error constructs rules, uses the symmetric structure to reduce the number of rules in the fuzzy rule base to half of the original rule base, and adopts a two-stage initialization method to give full play to the fitting characteristics of the fuzzy controller;

[0013] The steps of the two-stage initialization are as follows:

[0014] Step e0: Initialize the error compensation value of all rules to 0, that is, the first-stage initialization;

[0015] Step e1: Input the signal and determine whether the rule corresponding to the input signal has been updated after the first-stage initialization;

[0016] Step e2: If it has been updated, adjust the rule according to the current input signal;

[0017] Step e3: If it has not been updated, update the current corresponding rule according to the output error value E of the current input signal error and at the same time use this output error value E error to update the rules of other fuzzy subsets corresponding to the fourth input;

[0018] The fuzzy rule construction module is used to construct the fuzzy rule base R ule and keep it updated in real time. If the update switch is turned on, the symmetric structure and the two-stage initialization method are used to simplify the number of the fuzzy rule base while increasing the fitting characteristics of the fuzzy controller; if the update switch is turned off, the original rules are maintained;

[0019] where the fuzzy rule base R ule is constructed and updated according to D2, D3, D4, D5 of the input signal and the quantization output error value E error , and is constructed and updated according to the following steps:

[0020] Step f0: In the first-level initial stage, initialize the error compensation value of all rules to 0;

[0021] Step f1: Obtain the sub-level quantization codes D2, D3, D4, D5 of the input signal quantized by the pipelined analog-to-digital converter and the output error value E error ;

[0022] Step f2: Calculate the MINUS values of the current child quantization codes D2, D3, D4, D5, and map the current child quantization codes D2, D3, D4, D5 and the output error value E error to the region where MINUS is positive at the same time, as shown in Equations 1 and 2, to obtain the mapped subset quantization codes D 2s , D 3s , D 4s , D 5s and the output error value E errors ;

[0023] (D 2s , D 3s , D 4s , D 5s ) = (D2, D3, D4, D5) * MINUS 1

[0024] E errors = E error * MINUS 2

[0025] Step f3: Calculate the fuzzy subsets P 2s , D 3s , D 4s , D 5s corresponding to D 2s , P 3s , P 4s , P 5s and the membership values L p2s , L p3s , L p4s , L p5s ;

[0026] Step f4: Obtain the third to fifth digits after the decimal point P errors of this error value according to the output error value E o3 , P o4 , P o5 , and obtain the output fuzzy subsets T1, T2, T3 corresponding to the third to fifth digit values P o3 , P o4 , P o5 ;

[0027] Step f5: Determine whether the rules corresponding to the fuzzy subsets P 2s , P 3s , P 4s , P 5s have been updated after the first-level initialization; if not, perform the second-level initialization and execute Step f6, otherwise execute f7 to f11;

[0028] Step f6: If the corresponding rule has not been updated after the first-level initialization, perform secondary initialization; use the output error value E errors The corresponding output fuzzy subsets T1, T2, T3 update all the fuzzy subsets of the fourth input of the fuzzy controller, set the counting number Num of the corresponding rule to 1, and then return to f1. The constructed rule is as shown in Equation 3;

[0029] if E1 = P 2s , E2 = P 3s , E3 = P 4s , E4 = P then U1 = T1, U2 = T2, U3 = T3 (P =..., NB, NS, ZO, PS, PB,...) 3

[0031] Step f7: Obtain the current P 2s , P 3s , P 4s , P 5s The corresponding rule and the counting number Num of this rule. If Num is less than or equal to N, execute f8~f11; otherwise, do not update the rule and return to f1;

[0032] Step f8: Calculate the error value A of the combination (P 2s , P 3s , P 4s , P 5s ) corresponding to the fuzzy rule using Equation 4 error ;

[0033] A error = K3 * N um3 + K4 * N um4 + K5 * N um5 4

[0034] In Equation 4, N um3 , N um4 , N um5 represent the values corresponding to the three output fuzzy subsets T1, T2, T3 of this fuzzy rule respectively; K3, K4, K5 represent three proportionality factors;

[0035] Step f9: Obtain the average value C using Equation 5 error ;

[0036] C error = (A error * Num + E errors ) / (Num + 1) 5

[0037] Step f10: According to the fuzzy subsets W1, W2, W3 corresponding to the third to fifth decimal place values F3, F4, F5 after the decimal point of C error , use Equation 6 to construct the combination (P2s , P 3s , P 4s , P 5s ) The new fuzzy rule R ule :

[0038] if E1 = P 2s , E2 = P 3s , E3 = P 4s , E4 = P 5s then U1 = W1, U2 = W2, U3 = W3 6

[0039] Step f11: After adding 1 to the Num value of this rule, return to Step f1.

[0040] Preferably, the fuzzy controller obtains the error compensation value E according to the following steps cal :

[0041] Step 1: The fuzzy controller adopts the Mamdani model and uses a four-input and three-output structure. Its main modules are: fuzzification, fuzzy rule base, fuzzy inference engine, and defuzzification;

[0042] Step 2: After the fuzzy controller performs fuzzification processing on D2, D3, D4, and D5, it obtains four-input fuzzy subsets P1, P2, P3, P4 and four membership values L p2 , L p3 , L p4 , L p5 ;

[0043] Step 3: According to the fuzzy rule R in the fuzzy rule base ule , for the four-input corresponding fuzzy subsets P1, P2, P3, P4 and the four membership values L p2 , L p3 , L p4 , L p5 perform fuzzy inference to obtain the three-output fuzzy subsets Q1, Q2, Q3 of the fuzzy controller and the three-output membership degrees S Q1 , S Q2 , S Q3 ;

[0044] Step 4: After defuzzifying the three-output fuzzy subsets Q1, Q2, Q3 and the three-output membership degrees S Q1 , S Q2 , S Q3 and then calculating, obtain the error compensation value E output by the fuzzy controller cal .

[0045] Preferably, the four-input structure of the fuzzy controller in Step 2 is:

[0046] Step 2.1.1: Set the number of fuzzy subsets of each of the four inputs of the fuzzy controller to be the same as the number of types of corresponding level quantization digital code outputs;

[0047] Step 2.1.2: Set the fuzzy universe of discourse range of each of the four inputs of the fuzzy controller to be the same as the range of the corresponding level quantization digital code outputs;

[0048] Step 2.1.3: Trapezoidal membership functions are selected for all four inputs of the fuzzy controller.

[0049] Preferably, the calculation steps of the fuzzy subsets and membership values in Step 2 are as follows:

[0050] Step 2.2.1: Map D2, D3, D4, D5 to the region where the polarity factor MINUS is positive to obtain D′2, D′3, D′4, D′5;

[0051] Step 2.2.2: After D′2, D′3, D′4, D′5 of the pipeline analog-to-digital converter to be calibrated are respectively multiplied by the quantization factor "1", the values mapped to the fuzzy universe of discourse are X2, X3, X4, X5. Thus, the corresponding input fuzzy subsets P2, P3, P4, P5 are obtained according to the four fuzzy universes of discourse X2, X3, X4, X5;

[0052] Step 2.2.3: According to X2, X3, X4, X5, use Equation 7 to obtain the i-th membership value L pi :

[0053] L pi =trapmf(X i ), i = 2, 3, 4, 5 7

[0054] In Equation 7, trapmf represents the trapezoidal membership function; X i represents the i-th fuzzy universe of discourse value.

[0055] Preferably, the three-output structure of the fuzzy controller in Step 3 is as follows:

[0056] Step 3.1.1: Each of the three outputs of the fuzzy controller represents different decimal places of the error, and the scale factors of different decimal places are K3, K4, K5 respectively; the number of fuzzy subsets of the first output is determined by the error range, and the number of fuzzy subsets of the second to third outputs is 19, which are respectively defined as [R -9 , R -8 ,..., R0,..., R8, R9], corresponding to the values [-9, -8,…, 0,…, 8, 9] respectively;

[0057] Step 3.1.2: For the three outputs of the fuzzy controller, the fuzzy domain range of the first output is determined by the error range, and the fuzzy domains of the second to third outputs are [-9, 9];

[0058] Step 3.1.3: Triangular membership functions are used for all three outputs of the fuzzy controller.

[0059] Preferably, the steps for calculating the three outputs in Step 3 are as follows:

[0060] Step 3.2.1: According to the input fuzzy subsets P2, P3, P4, P5 of the fuzzy controller and the constructed fuzzy rule base R ule , the three output subsets Q1, Q2, Q3 of the fuzzy controller are inferred using Equation 7:

[0061]

[0062] In Equation 8, represents fuzzy inference;

[0063] Step 3.2.2: According to the membership degrees L p2 , L p3 , L p4 , L p5 of the input fuzzy subsets P2, P3, P4, P5, the membership degrees S Q1 , S Q2 , S Q3 of the three output fuzzy subsets Q1, Q2, Q3 are obtained using the max-min composition operator.

[0064] Preferably, the calculation method for the error compensation value E cal in Step 4 includes:

[0065] Step 4.1: According to the three output fuzzy subsets Q1, Q2, Q3 of the fuzzy controller and the membership degrees S Q1 , S Q2 , S Q3 the three output values U3, U4, U5 of the fuzzy controller are obtained by defuzzifying using the maximum membership average method;

[0066] Step 4.2: The error compensation value E cal of the fuzzy controller is obtained using Equation 9:

[0067] E cal = (K3 * U3 + K4 * U4 + K5 * U5) * MINUS 9

[0068] In Equation 9, K3, K4, and K5 respectively represent the proportionality factors of the three outputs of the fuzzy controller, and MINUS is the polarity factor.

[0069] Preferably, the fuzzy rule construction module determines whether the update switch is turned on according to the following steps:

[0070] Step a1: Initialize the state, and the update switch of the fuzzy controller is in the on state;

[0071] Step a2: Every time G input signals are input, use Equation 10 to calculate the calibration output D of the G data cal and the reference output D out2 of the difference mean value E mae :

[0072]

[0073] In Equation 10, D out2,g represents the calibration output of the g-th data, and D cal,g represents the reference output of the g-th data;

[0074] Step a3: Judge the magnitude between E mae and the set error mean value E exp . If E mae <E exp , then turn off the update switch and keep the rule base. Otherwise, turn on the update switch and update the fuzzy rule base. All values of the rule count Num greater than 5 are set to 3.

[0075] Preferably, the principle of using a symmetric structure in the process of constructing the fuzzy rule base is:

[0076] Step b0: The larger the value of the sub-level quantization code D M of the pipelined analog-to-digital converter, the greater the error introduced at this level;

[0077] Step b1: If the sub-level quantization codes D M of a certain sub-level of the pipelined analog-to-digital converter are opposite to each other, the errors introduced at this level are also approximately opposite;

[0078] Step b2: When the sub-level quantization codes D2, D3, D4, D5 are all opposite to each other, the corresponding quantization output error E error is also approximately opposite;

[0079] Step b3: Therefore, a symmetric structure can be used; construct rules with D2 = 0, D3 = 0, D4 = 0, D5 = 0 as the symmetry line. Therefore, the polarity factor MINUS = ±1 can be defined. When the input is before the symmetry line, MINUS = ±1 is negative, and when it is on and after the symmetry line, MINUS = ±1 is positive. If the input is before the symmetry line, both the input and the error are multiplied by MINUS and mapped to the region where MINUS is positive;

[0080] The steps of using a symmetric structure in the process of constructing the fuzzy rule base are:

[0081] Step c0: Obtain the second - fifth level quantization digital codes D2, D3, D4, D5 and the quantization output error value E of the input signal quantized by the pipelined analog - to - digital converter error ;

[0082] Step c1: Calculate the value of MINUS according to the values of the second - fifth level quantization digital codes D2, D3, D4, D5

[0083] Step c2: Multiply the second - fifth level quantization digital codes D2, D3, D4, D5 of the input signal and the quantization output error value E error by MINUS to map the input to the region where MINUS is positive

[0084] Preferably, the process of calculating the value of MINUS according to the values of D2, D3, D4, D5 is as follows

[0085] Step d0: The default value of MINUS is 1

[0086] Step d1: Starting from the second - level quantization code D2, if D2 < 0, then MINUS = - 1; if D2 = 0, then continue to judge the third - level quantization code D3. If D3 < 0, then MINUS = - 1; if D3 = 0, then continue to judge the fourth - level quantization code D4. If D4 < 0, then MINUS = - 1; if D4 = 0, then continue to judge the fifth - level quantization code D5. If D5 < 0, then MINUS = - 1; otherwise MINUS = 1

[0087] (III) Beneficial effects

[0088] Compared with the prior art, the beneficial effects of the present invention are as follows

[0089] 1. The present invention proposes a new error calibration method based on rule - optimized fuzzy control for pipelined analog - to - digital converters. This method constructs rules based on the sub - level quantization codes and errors of the pipelined ADC, and reduces the original fuzzy rules by half through a symmetric structure, while also reducing the complexity of the system and improving the operation speed of the system. In order to fully utilize the fitting performance of the fuzzy controller, a two - level initialization method is used to cover all rules, accelerating the rule construction speed and avoiding the problem of poor calibration effect when facing new data

[0090] 2. When constructing the fuzzy rule base, the present invention is extremely fast. Only 1*10 3 samples are required to complete the construction of the rules and maintain the stability of the calibration performance. When the error changes, the rules can be quickly adjusted and updated in real - time

[0091] 3. The background calibration method based on rule-optimized fuzzy control proposed by the present invention can achieve comprehensive calibration of linear and nonlinear errors caused by capacitance mismatch, comparator offset, gain error, parasitic capacitance, and non-ideal factors, etc.

[0092] 4. The calibration method proposed by the present invention has excellent calibration effect. The simulation results show that the signal-to-noise distortion ratio after calibration is increased from 54.8 dB to 84.6 dB, the spurious-free dynamic range is increased from 63.6 dB to 102.6 dB, and the number of effective bits is increased from 8.81 bits to 13.76 bits. BRIEF DESCRIPTION OF THE DRAWINGS

[0093] Figure 1 is the structural diagram of the pipelined analog-to-digital converter of the present invention;

[0094] Figure 2 is the overall calibration structural diagram of the fuzzy control method;

[0095] Figure 3 is the symmetric structure of the fuzzy rule base;

[0096] Figure 4 is the secondary initialization of the fuzzy rules;

[0097] Figure 5 is the output spectrum diagram of the analog-to-digital converter to be calibrated;

[0098] Figure 6 is the output spectrum diagram after calibration by the fuzzy control method. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0099] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0100] The calibration method based on rule-optimized fuzzy control is applied to a calibration system composed of a reference analog-to-digital converter, a fuzzy controller, a fuzzy rule construction module, and a calibration output unit.

[0101] The pipelined analog-to-digital converter to be calibrated and the reference analog-to-digital converter are connected to the same signal source, and after quantifying the input signal V of the same signal source in the M (M≥6)-stage quantization digital codes D1, D2,..., D of the pipelined analog-to-digital converter to be calibrated are obtained M , and the actual output value D of the pipelined analog-to-digital converter to be calibrated out1 and the ideal output value D of the reference analog-to-digital converter out2, so as to obtain the quantization output error value E of the pipeline analog-to-digital converter to be calibrated and the reference analog-to-digital converter error = D out2 - D out1 ; In a specific embodiment, the structure of the pipeline analog-to-digital converter to be calibrated is as Figure 1 shown. The pipeline analog-to-digital converter to be calibrated is a 6-stage 14-bit structure, where the quantization accuracy of stages 1 to 5 is 2.5 bits, and the quantization accuracy of the last stage is 4 bits. The pipeline analog-to-digital converter to be calibrated quantizes the signal V in to obtain the quantization digital codes D1, D2, D3, D4, D5, D6 at each stage, and the quantization digital codes at each stage are superimposed bit by bit to obtain the actual output D out1 . The reference analog-to-digital converter adopts a Sigma-Delta analog-to-digital converter with an effective accuracy of 16 bits. The reference analog-to-digital converter also quantizes the signal V in to obtain the ideal output value D out2 , and the quantization output difference (D out2 - D out1 ) between the analog-to-digital converter to be calibrated and the reference analog-to-digital converter is the quantization output error value E error .

[0102] The fuzzy controller adopts a four-input three-output structure, which uses the quantization digital codes D2, D3, D4, D5 from the second stage to the fifth stage as inputs, infers three outputs according to the constructed fuzzy rule base, and then calculates the error compensation value E cal ; In a specific embodiment, the error compensation structure diagram inferred by the fuzzy controller according to the quantization codes from the second stage to the fifth stage is as Figure 2 shown. If the quantization digital codes from the second stage to the fifth stage after the input signal is quantized by the analog-to-digital converter to be calibrated are (-2, 0, 0, 1), the error compensation value E cal calculated by the fuzzy controller is -0.00241.

[0103] In this embodiment, the fuzzy controller obtains the error compensation value E cal as follows:

[0104] Step 1: The fuzzy controller adopts the Mamdani model and uses a four-input three-output structure. Its main modules are: fuzzification, fuzzy rule base, fuzzy inference engine, and defuzzification.

[0105] Step 2: After the fuzzy controller performs fuzzification processing on D2, D3, D4, D5, it obtains four-input fuzzy subsets P1, P2, P3, P4 and four membership values L p2 , L p3 , L p4 , L p5 ; Specific embodiment: As Figure 2As shown, the quantization digital codes (-2, 0, 0, 1) of the second to fifth stages of the analog-to-digital converter to be calibrated are respectively input into the fuzzy controller. After mapping and trapezoidal membership functions, the corresponding fuzzy subsets (PB, ZO, ZO, NS) and membership degrees (1, 1, 1, 1) are obtained.

[0106] Step 2.2.1: Map D2, D3, D4, and D5 to the region where the polarity factor MINUS is positive to obtain D2’, D3’, D4’, and D5’. Specific example: The quantization digital codes (-2, 0, 0, 1) of the second to fifth stages are mapped to the region where the polarity factor MINUS is positive to obtain (2, 0, 0, -1).

[0107] Step 2.2.2: After D2’, D3’, D4’, and D5’ of the pipelined analog-to-digital converter to be calibrated are respectively multiplied by the quantization factor "1", the values mapped to the fuzzy universe are X2, X3, X4, and X5. Thus, according to the four fuzzy universes X2, X3, X4, and X5, the corresponding input fuzzy subsets P2, P3, P4, and P5 are obtained; Specific example: After (2, 0, 0, -1) is multiplied by the quantization factor, (2, 0, 0, -1) is obtained, and thus the corresponding input fuzzy subsets (PB, ZO, ZO, NS) are obtained.

[0108] Step 2.2.3: According to X2, X3, X4, and X5, use Equation (7) to obtain the i-th membership degree value L pi :

[0109] L pi = trapmf(X i ), i = 2, 3, 4, 5 (7)

[0110] In Equation (7), trapmf represents the trapezoidal membership function; X i represents the i-th fuzzy universe value. Specific example: The membership degree values obtained from (2, 0, 0, -1) are (1, 1, 1, 1).

[0111] Step 3: According to the fuzzy rule R ule in the fuzzy rule base, perform fuzzy inference on the four-input corresponding fuzzy subsets P1, P2, P3, P4 and the four membership degree values L p2 , L p3 , L p4 , L p5 to obtain the three-output fuzzy subsets Q1, Q2, Q3 of the fuzzy controller and the three-output membership degrees S Q1 , S Q2 , S Q3; Specific embodiment: Fuzzy inference is performed on the four-input corresponding fuzzy subsets (PB, ZO, ZO, NS) and the four membership values (1, 1, 1, 1) to obtain the three-output fuzzy subsets (R2, R4, R1) and the three-output membership degrees (1, 1, 1).

[0112] Step 3.2.1: According to the input fuzzy subsets P2, P3, P4, P5 of the fuzzy controller and the constructed fuzzy rule base R ule , the three-output subsets Q1, Q2, Q3 of the fuzzy controller are obtained by inference using Equation (8):

[0113]

[0114] In Equation (8), represents fuzzy inference;

[0115] Specific embodiment: The four-input corresponding fuzzy subsets (PB, ZO, ZO, NS) are inferred according to the corresponding rules in the constructed fuzzy rule base: if E1 = PB, E2 = ZO, E3 = ZO, E4 = NS then U1 = R2, U2 = R4, U3 = R1, to obtain the three-output subsets (R2, R4, R1).

[0116] Step 3.2.2: According to the membership degrees L p2 , L p3 , L p4 , L p5 of the input fuzzy subsets P2, P3, P4, P5, the membership degrees S Q1 , S Q2 , S Q3 of the three-output fuzzy subsets Q1, Q2, Q3 are obtained using the max-min composition operator.

[0117] Specific embodiment: According to the membership degrees (1, 1, 1, 1) of the four-input corresponding fuzzy subsets (PB, ZO, ZO, NS), the membership degrees (1, 1, 1) of the three-output fuzzy subsets (R2, R4, R1) are obtained using the max-min composition operator.

[0118] Step 4: After defuzzifying the three-output fuzzy subsets Q1, Q2, Q3 and the three-output membership degrees S Q1 , S Q2 , S Q3 , the error compensation value E output by the fuzzy controller is calculated. cal . Specific embodiment: After defuzzifying the three-output fuzzy subsets (R2, R4, R1) and the membership degrees (1, 1, 1), the error compensation value -0.00241 output by the fuzzy controller is calculated.

[0119] Step 4.1: According to the three-output fuzzy subsets Q1, Q2, Q3 of the fuzzy controller and the membership degrees S Q1 , S Q2 , S Q3 Use the maximum membership average method to defuzzify and obtain the three output values U3, U4, U5 of the fuzzy controller; specific example: According to the three-output fuzzy subsets (R2, R4, R1) and the membership degrees (1, 1, 1), use the maximum membership average method to defuzzify and obtain the three output values U3 = 2, U4 = 4, U5 = 1 of the fuzzy controller.

[0120] Step 4.2: Use Equation (9) to obtain the error compensation value E of the fuzzy controller cal :

[0121] E cal = (K3 * U3 + K4 * U4 + K5 * U5) * MINUS (9)

[0122] In Equation (9), K3, K4, and K5 respectively represent the proportionality factors of the three outputs of the fuzzy controller, and MINUS is the polarity factor;

[0123] Specific example: According to Equation (9) E cal = (K3 * U3 + K4 * U4 + K5 * U5) * MINUS, calculate

[0124] E cal = (0.001 * 2 + 0.0001 * 4 + 0.00001 * 1) * (-1) = -0.00241 to obtain the error compensation value E cal is -0.00241.

[0125] The calibration output unit adds the actual output value D of the pipeline analog-to-digital converter to be calibrated out1 and the error compensation value E cal to obtain the calibration output value D of the pipeline analog-to-digital converter to be calibrated cal . Specific example: Add the actual output value 0.2528076171875 of the pipeline analog-to-digital converter to be calibrated and the error compensation value -0.00241 to obtain the calibration output value 0.2503976171875.

[0126] The fuzzy rule construction module is used to construct and maintain the fuzzy rule base in real time. If the update switch is turned on, it constructs rules according to the second-level to fifth-level quantization digital codes D2, D3, D4, D5 and the quantization output error value E error and simplifies the number of the fuzzy rule base and increases the fitting characteristics of the fuzzy controller through a symmetric structure and a two-level initialization method. If the update switch is turned off, the original rules are maintained.

[0127] The fuzzy rule construction module determines whether the update switch is turned on according to the following steps:

[0128] Step a1: Initialize the state. The update switch of the fuzzy controller is in the on state.

[0129] Step a2: When every G input signals are input, use Equation (10) to calculate the calibration output D of G data cal and the reference output D out2 of the difference mean value E mae :

[0130]

[0131] In Equation (10), D out2,g represents the calibration output of the g-th data, and D cal,g represents the reference output of the g-th data; specific embodiment: When every 1000 input signals are input, calculate the difference mean value of the calibration output and the reference output of 1000 data.

[0132] Step a3: Judge the magnitude between E mae and the set error mean value E exp . If E mae <E exp , then turn off the update switch and keep the rule base. Otherwise, turn on the update switch, update the fuzzy rule base, and set all values of the rule count number Num greater than 5 to 3.

[0133] Specific embodiment: Judge the difference mean value and the set error mean value E exp =0.00004. If the calculated error mean value is less than the set error mean value, then turn off the update switch and the rule base remains unchanged. If it is greater than the set error mean value, further update and adjust the rules are needed, and when the rule count number Num is greater than 5, all values are set to 3, so as to keep the rules updated continuously.

[0134] The steps of using a symmetric structure in the process of constructing the fuzzy rule base are as follows: as Figure 3 shown;

[0135] Step c0: Obtain the second-stage to fifth-stage quantization digital codes D2, D3, D4, D5 of the input signal quantized by the pipelined analog-to-digital converter and the quantization output error value E error .

[0136] Specific embodiment: Obtain the second-stage to fifth-stage quantization digital codes (-2, 0, 0, 1) and the quantization output error value -0.00241.

[0137] Step c1: Calculate the value of MINUS according to the values of the second-stage to fifth-stage quantization digital codes D2, D3, D4, D5.

[0138] The process of calculating the MINUS value is as follows:

[0139] Step d0: The default value of MINUS is 1.

[0140] Step d1: Starting from the second-level quantization code D2, if D2 is less than 0, then MINUS = -1; if D2 is equal to 0, then continue to judge the third-level quantization code D3. If D3 is less than 0, then MINUS = -1. If D3 is equal to 0, then continue to judge the fourth-level quantization code D4. If D4 is less than 0, then MINUS = -1. If D4 is equal to 0, then continue to judge the fifth-level quantization code D5. If D5 is less than 0, then MINUS = -1. Otherwise, MINUS = 1. Specific example: In the second-level to fifth-level quantization digital codes (0, 0, -1, 1), since D2 = 0 and D3 = 0, it is necessary to continue to judge the fourth-level quantization code D4. Since D4 = -1 is less than 0, MINUS = -1.

[0141] Step c2: Multiply the second-level to fifth-level quantization digital codes D2, D3, D4, D5 of the input signal and the quantization output error value E error by MINUS to map the input to the region where MINUS is positive. Specific example: (-2, 0, 0, 1) multiplied by the quantization output error value -0.00241 and MINUS = -1 maps the input to the region where MINUS is positive, obtaining (2, 0, 0, -1) and 0.00241.

[0142] The steps of using two-level initialization in the process of constructing the fuzzy rule base are as follows:

[0143] Step e0: Initialize the error compensation value of all rules to 0, that is, the first-level initialization.

[0144] Step e1: Input the signal and judge whether the rule corresponding to the input signal has been updated after the first-level initialization.

[0145] Step e2: If it has been updated, adjust the rule according to the current input signal.

[0146] Step e3: If it has not been updated, then according to the output error value E of the current input signal error update the current corresponding rule, and at the same time use this output error value E error to update the rules of other fuzzy subsets corresponding to the four inputs (fifth-level quantization code).

[0147] Specific example: Such as Figure 5As shown, if the fuzzy rule corresponding to the current input (PB, ZO, ZO, NS) has not been updated after the first-level initialization, then update the error of this rule and the rules of other fuzzy subsets corresponding to the four inputs, namely (PB, ZO, ZO, NB), (PB, ZO, ZO, ZO), (PB, ZO, ZO, PS), (PB, ZO, ZO, PB), as Figure 4 shown by the shaded part in

[0148] The fuzzy rule base R ule is constructed and updated according to D2, D3, D4, D5 of the input signal and the quantization output error value E error as follows: Specific embodiment: Execute the following steps in the initial stage or when the rule update switch is on. When the switch is off, rule update is not performed, so the following steps are not executed.

[0149] Step f0: First-level initialization, initialize the error compensation value of all rules to 0;

[0150] Step f1: Obtain the sub-level quantization codes D2, D3, D4, D5 of the input signal quantized by the pipelined analog-to-digital converter and the output error value E error .

[0151] Specific embodiment: Obtain the second-level to fifth-level quantization digital codes of the pipelined analog-to-digital converter as (-2, 0, 0, 1), and the output error value is E error =-0.00241.

[0152] Step f2: Calculate the MINUS value of the current sub-level quantization codes D2, D3, D4, D5, and map the current sub-level quantization codes D2, D3, D4, D5 and the output error value E error to the region where MINUS is positive at the same time, as shown in equations (1) and (2). Obtain the mapped subset quantization codes D 2s , D 3s , D 4s , D 5s and the output error value E errors .

[0153] (D 2s , D 3s , D 4s , D 5s )=(D2, D3, D4, D5)*MINUS (1)

[0154] E errors =E error *MINUS (2)

[0155] Specific embodiment: Calculate MINUS = -1 for the current child quantization code (-2, 0, 0, 1), obtain the mapped subset quantization code as (2, 0, 0, -1), and output an error value of 0.00241.

[0156] Step f3: Calculate D 2s , D 3s , D 4s , D 5s respectively corresponding to the fuzzy subsets P 2s , P 3s , P 4s , P 5s and the membership degree values L p2s , L p3s , L p4s , L p5s . Specific embodiment: Calculate the membership degree values (1, 1, 1, 1) of the fuzzy subset (PB, ZO, ZO, NS) corresponding to (2, 0, 0, -1).

[0157] Step f4: According to the output error value E errors obtain the third to fifth digits after the decimal point of this error value P o3 , P o4 , P o5 , and obtain the third to fifth digit values P o3 , P o4 , P o5 corresponding to the output fuzzy subsets T1, T2, T3; Specific embodiment: According to the third to fifth digits after the decimal point (2, 4, 1) of the output error value and obtain the corresponding fuzzy subsets (R2, R4, R1).

[0158] Step f5: Determine whether the rules corresponding to the fuzzy subsets P 2s , P 3s , P 4s , P 5s have been updated after the first-level initialization. If not updated, perform second-level initialization, execute step f6, otherwise execute f7~f11.

[0159] Step f6: If the corresponding rule has not been updated after the first-level initialization, perform secondary initialization. Use the output fuzzy subsets T1, T2, T3 corresponding to the output error value E errors to update all the fuzzy subsets of the fourth input (fifth-level quantization code) of the fuzzy controller, and set the corresponding rule counting number Num to 1, then return to f1. The constructed rule is as shown in Equation (3).

[0160] if E1 = P 2s , E2 = P 3s , E3 = P 4s, if E4 = P then U1 = T1, U2 = T2, U3 = T3 (P =..., NB, NS, ZO, PS, PB,...) (3)

[0162] Specific embodiment: If the (PB, ZO, ZO, NS) corresponding rule has not been updated after the first-level initialization, then perform the second-level initialization. Use the fuzzy subsets (R2, R4, R1) corresponding to the output error value 0.00241 to update all the fuzzy subsets corresponding to the fourth input. That is:

[0163] if E1 = PB, E2 = ZO, E3 = ZO, E4 = NB then U1 = R2, U2 = R4, U3 = R1

[0164] if E1 = PB, E2 = ZO, E3 = ZO, E4 = NS then U1 = R2, U2 = R4, U3 = R1

[0165] if E1 = PB, E2 = ZO, E3 = ZO, E4 = ZO then U1 = R2, U2 = R4, U3 = R1

[0166] if E1 = PB, E2 = ZO, E3 = ZO, E4 = PS then U1 = R2, U2 = R4, U3 = R1

[0167] if E1 = PB, E2 = ZO, E3 = ZO, E4 = PB then U1 = R2, U2 = R4, U3 = R1

[0168] Step f7: Obtain the current P 2s , P 3s , P 4s , P 5s The corresponding rule and the counting times Num of this rule. If Num is less than or equal to N, then execute f8~f11. Otherwise, do not update the rule and return to f1. Specific embodiment: The rule counting times is set to N = 6. That is, each rule is updated 6 times and then no longer updated.

[0169] Step f8: Calculate the error value A of the fuzzy rule corresponding to the combination (P 2s , P 3s , P 4s , P 5s ) using Equation (4) error ;

[0170] A error = K3 * N um3 + K4 * N um4 + K5 * N um5 (4)

[0171] In formula (4), N um3 , N um4 , N um5 respectively represent the numerical values corresponding to the three output fuzzy subsets T1, T2, and T3 of this fuzzy rule; K3, K4, and K5 respectively represent three scaling factors;

[0172] Specific embodiment: If the current (PB, ZO, ZO, NS) corresponds to the rule

[0173] if E1 = PB, E2 = ZO, E3 = ZO, E4 = PS then U1 = R2, U2 = R3, U3 = R9; the numerical values corresponding to the three output fuzzy subsets (R2, R4, R9) are (2, 3, 9). Then the error value A error = 0.00239 is calculated, where K3 = 0.001, K4 = 0.0001, and K5 = 0.00001.

[0174] Step f9: Obtain the average value C using formula (5) error ;

[0175] C error = (A error * Num + E errors ) / (Num + 1) (5)

[0176] Specific embodiment: If Num = 2, then the average value C error = (0.00239 * 2 + 0.00241) / (2 + 1) = 0.00240 is calculated.

[0177] Step f10: According to the fuzzy subsets W1, W2, and W3 corresponding to the third to fifth decimal place values F3, F4, and F5 after the decimal point of C error , use formula (6) to construct a new fuzzy rule R 2s , P 3s , P 4s , P 5s : ule :

[0178] if E1 = P 2s , E2 = P 3s , E3 = P 4s , E4 = P 5s then U1 = W1, U2 = W2, U3 = W3 (6)

[0179] Specific embodiment: According to C errorThe numerical values 2, 4, 0 in the third to fifth decimal places correspond to the fuzzy subsets R2, R4, R0 to construct a new fuzzy rule: if E1 = PB, E2 = ZO, E3 = ZO, E4 = PB then U1 = R2, U2 = R4, U3 = R0.

[0180] Step f11: After adding 1 to the Num value of this rule, return to step f1.

[0181] In a specific embodiment of the present invention, a calibration system behavioral model is built for the above-mentioned analog-to-digital converter calibration method and device using MATLAB and Simulink. The input is a 1GHz single-frequency sine wave, and the pipeline analog-to-digital converter to be calibrated has a 6-stage 14-bit structure, where the quantization accuracy of stages 1 to 5 is 2.5 bits, and the quantization accuracy of the last stage is 4 bits. The output spectrum diagram of the analog-to-digital converter to be calibrated is as Figure 5 shown. The abscissa of the image represents the signal frequency, and the ordinate represents the signal amplitude.

[0182] The calibration output spectrum diagram of the pipeline analog-to-digital converter calibrated by the method of fuzzy control with rule optimization is as Figure 6 shown. After calibration, the SNDR is improved from 54.8dB to 84.6dB, the SFDR is improved from 63.6dB to 102.6dB, and the ENOB is improved from 8.81 bits to 13.76 bits.

[0183] Although the embodiments of the present invention have been shown and described, for those of ordinary skill in the art, it can be understood that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A background calibration method for a pipelined analog-to-digital converter based on rule optimization control, characterized in that Applied to a calibration system composed of a reference analog-to-digital converter, a fuzzy controller, a fuzzy rule construction module, and a data output unit; Connect the pipeline analog-to-digital converter to be calibrated and the reference analog-to-digital converter to the same signal source, and for the input signal V of the same signal source in After quantization, obtain the M (M≥6) - stage quantization digital codes D1, D2,..., D of the pipeline analog-to-digital converter to be calibrated M , as well as the actual output value D of the pipeline analog-to-digital converter to be calibrated out1 and the ideal output value D of the reference analog-to-digital converter out2 , so as to obtain the quantization output error value E between the pipeline analog-to-digital converter to be calibrated and the reference analog-to-digital converter error = D out2 - D out1 ; The fuzzy controller adopts a four-input and three-output structure, which takes the quantization digital codes D2, D3, D4, and D5 from the second level to the fifth level as inputs, infers three outputs according to the constructed fuzzy rule base, and then calculates the error compensation value E cal ; The calibration output unit adds the actual output value D of the pipelined analog-to-digital converter to be calibrated out1 and the error compensation value E cal to obtain the calibration output value D of the pipelined analog-to-digital converter to be calibrated cal ; The fuzzy rule construction module reduces the number of fuzzy rules through a symmetric structure, that is, according to the quantization digital codes D2, D3, D4, D5 from the second level to the fifth level and the quantization output error value E error Construct rules, use the symmetric structure to reduce the number of rules in the fuzzy rule base to half of the original rule base, and adopt a two-level initialization method to give full play to the fitting characteristics of the fuzzy controller; The steps of the secondary initialization are as follows: Step e0: Initialize the error compensation values of all rules to 0, that is, the first-level initialization; Step e1: Input a signal and determine whether the rule corresponding to the input signal has been updated after the first-level initialization; Step e2: If it has been updated, adjust the rule according to the current input signal; Step e3: If there is no update, then according to the output error value E of the current input signal error Update the current corresponding rule, and at the same time use this output error value E error Update the rules of other fuzzy subsets corresponding to the fourth input; The fuzzy rule construction module is used to construct the fuzzy rule base R ule And keep it updated in real time. If the update switch is turned on, the number of fuzzy rule bases is simplified and the fitting characteristics of the fuzzy controller are increased through a symmetric structure and a secondary initialization method; if the update switch is turned off, the original rules are maintained; wherein the fuzzy rule base R ule is constructed and updated according to D2, D3, D4, D5 of the input signal and the quantization output error value E error , by the following steps: Step f0: In the first-level initial stage, initialize the error compensation values of all rules to 0; Step f1: Obtain the sub-level quantization codes D2, D3, D4, D5 of the input signal quantized by the pipelined analog-to-digital converter and the output error value E error ; Step f2: Calculate the MINUS values of the current child quantization codes D2, D3, D4, D5, and map the current child quantization codes D2, D3, D4, D5 and the output error value E error to the region where MINUS is positive at the same time, as shown in Equations 1 and 2, to obtain the mapped subset quantization codes D 2s , D 3s , D 4s , D 5s and the output error value E errors ; (D 2s , D 3s , D 4s , D 5s ) = (D2, D3, D4, D5) * MINUS1 E errors = E error * MINUS2 Step f3: Calculate D 2s , D 3s , D 4s , D 5s respectively corresponding fuzzy subsets P 2s , P 3s , P 4s , P 5s and membership values L p2s , L p3s , L p4s , L p5s ; Step f4: According to the output error value E errors obtain the third to fifth digits P after the decimal point of this error value o3 , P o4 , P o5 , and obtain the third to fifth digit values P o3 , P o4 , P o5 corresponding to the output fuzzy subsets T1, T2, T3; Step f5: Determine the fuzzy subset P 2s , P 3s , P 4s , P 5s Whether the corresponding rule has been updated after the first-level initialization; if not, perform the second-level initialization and execute step f6, otherwise execute f7 to f11; Step f6: If the corresponding rule has not been updated after the first-level initialization, perform secondary initialization; use the output error value E errors Update all the fuzzy subsets of the fourth input of the fuzzy controller with the corresponding output fuzzy subsets T1, T2, T3, set the counting number Num of the corresponding rule to 1, and then return to f1. The constructed rule is as shown in Equation 3; if E1 = P 2s , E2 = P 3s , E3 = P 4s , E4 = P then U1 = T1, U2 = T2, U3 = T3(P =..., NB, NS, ZO, PS, PB,...)3 Step f7: Obtain the current P 2s , P 3s , P 4s , P 5s , the corresponding rule, and the counting times Num of this rule. If Num is less than or equal to N, then execute f8 to f11; otherwise, do not update the rule and return to f1; Step f8: Calculate the error value A 2s , P 3s , P 4s , P 5s ) corresponding to the fuzzy rule error ; A error = K3 * N um3 + K4 * N um4 + K5 * N um5 4 In Equation 4, N um3 , N um4 , N um5 respectively represent the output fuzzy subsets T1 of this fuzzy rule three, The values corresponding to T2 and T3; K3, K4, and K5 respectively represent three scaling factors; Step f9: Obtain the average value C using Equation 5 error ; C error = (A error * Num + E errors ) / (Num + 1)5 Step f10: According to C error The fuzzy subsets W1, W2, W3 corresponding to the third to fifth digit values F3, F4, F5 after the decimal point, use Equation 6 to construct the combination (P 2s , P 3s , P 4s , P 5s ) new fuzzy rule R ule : if E1 = P 2s , E2 = P 3s , E3 = P 4s , E4 = P 5s then U1 = W1, U2 = W2, U3 = W3 6 Step f11: After adding 1 to the Num value of this rule, return to Step f1.

2. The background calibration method of a pipelined analog-to-digital converter based on rule optimization control according to claim 1, characterized in that The fuzzy controller obtains the error compensation value E according to the following steps cal : Step 1: The fuzzy controller adopts the Mamdani model and uses a four-input three-output structure. Its main modules are: fuzzification, fuzzy rule base, fuzzy inference engine, and defuzzification; Step 2: After the fuzzy controller performs fuzzy processing on D2, D3, D4, and D5, four-input fuzzy subsets P1, P2, P3, P4 and four membership values L are obtained p2 , L p3 , L p4 , L p5 ; Step 3: According to the fuzzy rule R in the fuzzy rule base ule , for the four-input corresponding fuzzy subsets P1, P2, P3, P4 and the four membership values L p2 , L p3 , L p4 , L p5 , perform fuzzy inference to obtain the fuzzy subsets Q1, Q2, Q3 of the three outputs of the fuzzy controller and the membership degrees S Q1 , S Q2 , S Q3 ; Step 4: After defuzzifying the three-output fuzzy subsets Q1, Q2, Q3 and the membership degrees S Q1 , S Q2 , S Q3 , calculate the error compensation value E output by the fuzzy controller cal .

3. A background calibration method for a pipelined analog-to-digital converter based on rule optimization control according to claim 2, characterized in that, The four-input structure of the fuzzy controller in Step 2 is as follows: Step 2.1.1: Set the number of fuzzy subsets of each input in the four inputs of the fuzzy controller to be the same as the number of types of corresponding-level quantization digital code outputs; Step 2.1.2: Set the fuzzy domain range of each input in the four inputs of the fuzzy controller to be the same as the range of the corresponding-level quantization digital code outputs; Step 2.1.3: All four inputs of the fuzzy controller use trapezoidal membership functions.

4. A background calibration method for a pipelined analog-to-digital converter based on rule optimization control according to claim 2, characterized in that, The calculation steps of the fuzzy subsets and membership values in Step 2 are as follows: Step 2.2.1: Map D2, D3, D4, and D5 to the region where the polarity factor MINUS is positive to obtain D2’, D3’, D4’, and D5’; Step 2.2.2: After multiplying D2’, D3’, D4’, and D5’ of the pipeline analog-to-digital converter to be calibrated by the quantization factor "1" respectively, the values mapped to the fuzzy domain are X2, X3, X4, and X5. Thus, according to the four fuzzy domains X2, X3, X4, and X5, the corresponding input fuzzy subsets P2, P3, P4, and P5 are obtained; Step 2.2.3: Calculate the membership value L of the i-th according to X2, X3, X4, X5 using Equation 7 pi : L pi = trapmf(X i ), i = 2, 3, 4, 5, 7 In Equation 7, trapmf represents the trapezoidal membership function; X i represents the i-th fuzzy domain value.

5. A background calibration method for a pipelined analog-to-digital converter based on rule optimization control according to claim 2, characterized in that, The three-output structure of the fuzzy controller in Step 3 is as follows: Step 3.1.1: Each of the three outputs of the fuzzy controller represents different decimal places of the error, and the scaling factors for different decimal places are K3, K4, and K5 respectively; the number of fuzzy subsets of the first output is determined by the error range, and the number of fuzzy subsets of the second to third outputs is 19, which are respectively defined as [R -9 , R -8 ,..., R0,..., R8, R9], corresponding to the values [-9, -8,..., 0,..., 8, 9] respectively; Step 3.1.2: For the three outputs of the fuzzy controller, the fuzzy domain range of the first output is determined by the error range, and the fuzzy domains of the second to third outputs are [-9, 9]; Step 3.1.3: All three outputs of the fuzzy controller use triangular membership functions.

6. A background calibration method for a pipelined analog-to-digital converter based on rule optimization control according to claim 5, characterized in that The calculation steps of the three outputs in Step 3 are as follows: Step 3.2.1: According to the input fuzzy subsets P2, P3, P4, P5 of the fuzzy controller and the constructed fuzzy rule base R ule , the three output subsets Q1, Q2, Q3 of the fuzzy controller are obtained by inference using Equation 8: In Formula 8, represents fuzzy inference; Step 3.2.2: According to the membership degrees L p2 , L p3 , L p4 , L p5 of the input fuzzy subsets P2, P3, P4, P5, use the max-min composition operator to obtain the membership degrees S Q1 , S Q2 , S Q3 of the three-output fuzzy subsets Q1, Q2, Q3.

7. A background calibration method for a pipelined analog-to-digital converter based on rule optimization control according to claim 2, characterized in that The error compensation value E in step 4 cal The calculation method includes: Step 4.1: According to the three-output fuzzy subsets Q1, Q2, Q3 of the fuzzy controller and the membership degrees S Q1 , S Q2 , S Q3 Use the average value method of the maximum membership degree to defuzzify and obtain the three output values U3, U4, U5 of the fuzzy controller; Step 4.2: Obtain the error compensation value E of the fuzzy controller using Equation 9 cal : E cal = (K3 * U3 + K4 * U4 + K5 * U5) * MINUS 9 In Equation 9, K3, K4, and K5 respectively represent the scaling factors of the three outputs of the fuzzy controller, and MINUS is the polarity factor.

8. A background calibration method for a pipelined analog-to-digital converter based on rule optimization control according to claim 1, characterized in that, The fuzzy rule construction module determines whether the update switch is turned on according to the following steps: Step a1: Initialize the state, and the update switch of the fuzzy controller is in the on state; Step a2: When every G input signals are input, calculate the calibration output D of G data by using Equation 10 cal and the reference output D out2 to obtain the mean value E of the difference mae : In Equation 10, D out2,g represents the calibrated output of the g-th data, and D cal,g represents the reference output of the g-th data; Step a3: Determine E mae and the set error mean value E exp to check their magnitudes. If E mae < E exp , then turn off the update switch and keep the rule base. Otherwise, turn on the update switch, update the fuzzy rule base, and set all values of the rule count Num greater than 5 to 3.

9. A background calibration method for a pipelined analog-to-digital converter based on rule optimization control according to claim 1, characterized in that The principle of using a symmetric structure in the process of constructing the fuzzy rule base is: Step b0: Sub - level quantization code D of the pipelined analog - to - digital converter M The larger the value, the greater the error introduced at this level; Step b1: If the quantization codes D of a certain sub - stage of the pipelined analog - to - digital converter M are opposite to each other, the corresponding introduced errors at this stage are also approximately opposite; Step b2: When the child quantization codes D2, D3, D4, D5 are all opposite to each other, the corresponding quantization output error E error is also approximately opposite; Step b3: Therefore, a symmetric structure can be used; the rules are constructed with D2 = 0, D3 = 0, D4 = 0, D5 = 0 as the symmetry lines. Thus, the polarity factor MINUS = ±1 can be defined. When the input is before the symmetry line, MINUS = ±1 is negative, and when it is on or after the symmetry line, MINUS = ±1 is positive. If the input is before the symmetry line, both the input and the error are multiplied by MINUS to map them to the region where MINUS is positive; The steps of using the symmetric structure in the process of constructing the fuzzy rule base are as follows: Step c0: Obtain the second to fifth stage quantization digital codes D2, D3, D4, D5 obtained by quantizing the input signal by the pipelined analog-to-digital converter, and the quantization output error value E error ; Step c1: Calculate the value of MINUS according to the values of the quantization digital codes D2, D3, D4, D5 from the second level to the fifth level; Step c2: Multiply the second to fifth quantization digital codes D2, D3, D4, D5 of the input signal and the quantization output error value E error by MINUS to map the input to the region where MINUS is positive.

10. A background calibration method for a pipelined analog-to-digital converter based on rule optimization control according to claim 9, characterized in that, The process of calculating the value of MINUS according to the values of D2, D3, D4, D5 is as follows: Step d0: The default value of MINUS is 1; Step d1: Starting from the second-level quantization code D2, if D2 < 0, then MINUS = -1. If D2 = 0, then continue to judge the third-level quantization code D3. If D3 < 0, then MINUS = -1; If D3 = 0, then continue to judge the fourth-level quantization code D4. If D4 < 0, then MINUS = -1; If D4 = 0, then continue to judge the fifth-level quantization code D5. If D5 < 0, then MINUS = -1; Otherwise, MINUS = 1.

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