A pipeline ADC adaptive PN injection amplitude background calibration method and system based on a rear-stage digital code redundancy state reconstruction

Abstract

The application discloses a pipeline ADC adaptive PN injection amplitude background calibration method and system based on a rear-stage digital code redundancy state reconstruction. A monotone mapping is performed on the rear-stage digital code which is aligned with the first-stage MDAC residual sample delay and located before the variable inter-stage weight application, and a digital boundary proximity is formed in combination with quantization, gain and non-linear error tolerance; the reconstruction represents the state of the rear-stage redundancy processable code domain relative to the residual safety boundary, rather than the accurate value of the recovered analog residual; the PN peak amplitude is closed-loop adjusted according to the early warning event rate, and the real over-range interrupts the window statistics with a higher priority and is immediately reduced in amplitude. The LMS step size is linked with the LMS normalized PN amplitude a_L according to the inverse power law of 0<β<2, and is constrained by C / a_L²(k) determined by the upper bound of the input correlation matrix eigenvalue. The application does not increase the analog residual detection channel, and can consider the convergence speed, residual safety and loop stability.

Description

Technical Field

[0001] This invention relates to the field of integrated circuits and analog-to-digital converter digital calibration technology, and in particular to a pipelined ADC background calibration method and system that does not require the addition of an analog residual detection circuit, utilizes subsequent digital codes to reconstruct the redundant state of the first-stage MDAC, and adjusts the PN injection amplitude in a closed loop. Background Technology

[0002] Pipeline ADCs are widely used in communications, measurement, and image processing due to their combination of high conversion speed and high accuracy. However, the linearity and effective bit depth of pipelined ADCs are reduced due to capacitor mismatch, finite operational amplifier gain, and inter-stage gain errors caused by deep submicron processes. A background digital calibration method that can be performed during normal conversions is to use pseudo-random sequence PN injection and estimate inter-stage errors through correlation operations or the LMS algorithm.

[0003] In PN injection calibration, if the peak amplitude of PN is normalized to the LMS normalized amplitude a_L = A_PN / A_norm using a fixed non-zero amplitude reference A_norm, the approximate convergence rate is related to the dimensionless effective excitation amount μ·a_L², where μ is the LMS iteration step size. Increasing A_PN usually increases the observable calibration component, but at the same time compresses the residual margin of the first-stage MDAC. If the injected signal, combined with the input signal and circuit errors, exceeds the processing range of subsequent stages, it will cause clipping, saturation, or calibration deviation. Therefore, a closed-loop trade-off needs to be made between the calibration excitation strength and the residual safety margin.

[0004] Existing solutions include fixed-amplitude injection, adjusting jitter amplitude based on input amplitude, selecting injection based on quantization range or residual threshold, and adjusting random excitation amplitude based on saturation indication. These solutions typically use single-sample thresholding or direct detection of simulated residuals, but fail to simultaneously address the following issues: how to determine the code acquisition position of subsequent digital codes and strictly align them with the first-stage residual samples; how to conservatively reconstruct the safety boundary from subsequent digital codes while considering quantization, subsequent nonlinearity, PVT, and gain estimation errors; how to differentiate between statistical warnings that have not yet exceeded the range and actual over-range responses that require immediate action; and how to ensure that the effective excitation of LMS increases while satisfying calculable stability constraints when the PN amplitude changes. Summary of the Invention

[0005] The technical problem to be solved by this invention is: without adding analog residual sampling or comparison circuits, to clarify the code extraction node, sample correspondence, monotonic mapping condition and error tolerance of the subsequent digital code, and to conservatively reconstruct the degree to which the residual of the first-stage MDAC approaches the safety boundary; to find a larger PN peak amplitude that satisfies the residual safety constraint through a two-layer mechanism of "statistical early warning closed loop + real overrange hard protection"; and when using LMS calibration, to balance the effective excitation quantity and iterative stability by using the inverse power law candidate step size and the hard upper limit of stability determined by the upper bound of the eigenvalues ​​of the input correlation matrix. Technical solution

[0006] To address the aforementioned technical problems, this invention provides a pipelined ADC adaptive PN injection amplitude background calibration method based on post-stage digital code redundancy state reconstruction, comprising the following steps.

[0007] Step S1: During normal conversion of the pipelined ADC, inject a PN sequence with a peak amplitude of A_PN(k) into the residual path of the first-stage MDAC.

[0008] Step S2: Obtain the original quantization code and original overrange state of the subsequent stage before applying the first-stage interstage weights that vary with the current background calibration parameters. Compensate according to the subsequent stage pipeline delay L_B. Record the compensated code and state as D_B(n) and O(n) respectively, and align them with the normalized PN reference sequence u(n) and the same first-stage MDAC residual sample.

[0009] Step S3: Based on the monotonic transmission mapping of the subsequent quantization path in the unsaturated region, distinguish between the actual equivalent transmission gain G_B,true and the estimated value G_B,est used for boundary calculation. Combine the subsequent quantization step size Δ_B and the preset PVT range and code domain design tolerance E_B under the target confidence level to form a conservative safety boundary code span D_sec and calculate the digital boundary proximity ρ. When ρ≥θ_H and O(n)=0, it is recorded as a warning event.

[0010] Step S4: Independently latch the overrange state O(n). When any conversion sample exceeds the range, the normal decision-making of the current window is interrupted with the highest control priority, and a rapid decrease control is output without waiting for the current window to end, so that subsequent executable conversion samples adopt a reduced PN peak amplitude; when no overrange occurs, p_w(k) is statistically analyzed within N conversion samples, and the statistical result of the k-th window determines the gradual increase, rapid decrease, or maintenance of the amplitude control cycle for the next executable cycle.

[0011] Step S5: Update the background calibration parameters using the correlation between the PN sequence and the ADC digital output; when using the LMS algorithm, let a_L(k) = A_PN(k) / A_norm, the candidate step size is linked with a_L(k) according to the inverse power law of 0<β<2, and the actual step size is further restricted by C / a_L²(k), where C is determined by the upper bound of the largest eigenvalue of the correlation matrix of the normalized regression vector.

[0012] This invention also provides a system for implementing the above method, including a PN sequence generator, a codeword acquisition and delay alignment module, a digital redundancy state reconstruction module, a window statistics module, a hard protection module, an amplitude closed-loop control module, and a background calibration module. All of the above feedback and protection modules can be implemented using digital logic, eliminating the need to add a residual amplitude detection path at the MDAC analog output. Beneficial effects

[0013] First, by employing traceable code acquisition nodes, pipeline delay alignment, monotonic transmission mapping, and code domain error tolerance, the degree to which the residual of the first-stage MDAC approaches the safety boundary is conservatively inferred from the existing digital code of the subsequent quantizer, without increasing the analog detection load and reducing the risk of the digital correction loop inversely affecting the boundary judgment.

[0014] Second, samples with ρ≥θ_H but not yet exceeding the range are used as statistical warnings, while actual exceeding the range is used as an independent hard protection trigger condition. This approach can both utilize the target range to find larger safety incentives and avoid treating actual exceeding the range events as tolerable normal statistical events.

[0015] Third, by using the rate of warning events within the observation window rather than a single warning sample as the regular feedback quantity, statistical hysteresis is formed through the target interval. Combined with freezing the increase when the input envelope rises, continuous safe slow increase, rapid reduction when the warning exceeds the limit, and hard protection hold time, the erroneous amplitude adjustment caused by noise or non-stationary input can be reduced.

[0016] Fourth, the minimum residual peak margin that can be allocated to PN injection is defined by V_R=V_lim-V_0,max-V_guard, and the normalized amplitude upper and lower limits are set uniformly using the instantaneous peak caliber to avoid mixing the total residual boundary, additional PN margin, RMS value and peak value.

[0017] Fifth, define the amplitude closed-loop normalization quantity a_R=A_PN / V_R and the LMS normalization quantity a_L=A_PN / A_norm respectively to avoid mixing different amplitude references; the LMS candidate step size adopts an inverse power law linkage of 0<β<2, and the actual step size is directly limited by C / a_L²(k) determined based on the upper bound of the eigenvalue of the correlation matrix, so that the stability constant has a calculable design basis and the effective excitation quantity is improved in the non-limited working region. Attached Figure Description

[0018] Figure 1 This is a structural block diagram of the system of the present invention, which shows the codeword acquisition and delay alignment module and the overrange hard protection branch with higher priority than the window statistical closed loop.

[0019] Figure 2 This is a flowchart of the adaptive PN injection amplitude background calibration process of the present invention, which shows the priority coverage relationship between sample-level overrange hard protection and window-level statistical decision.

[0020] Figure 3 This is a behavioral-level diagram illustrating the variation of the warning event rate p_w(k) and the amplitude closed-loop normalized PN peak amplitude a_R(k) with the amplitude control period in an embodiment of the present invention. Since A_norm=V_R is taken in this embodiment, a(k) is used as an abbreviation of a_R(k)=a_L(k) in the figure. Detailed Implementation

[0021] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. The listed values ​​are used to illustrate the relationship between control quantities and do not constitute a limitation on the scope of protection; without departing from the scope of the claims, those skilled in the art can adjust the corresponding parameters according to the pipeline stage bit depth, redundancy structure, and subsequent quantization range.

[0022] Figure 1 The illustrated pipelined ADC includes a first-stage sub-ADC, a first-stage MDAC, and a subsequent quantizer. The instantaneous peak value of the total residual of the first-stage MDAC, allowed without subsequent saturation and with a predetermined protection margin, is defined as V_lim. The instantaneous peak value of the maximum residual of the first-stage MDAC, covering a preset input range, PVT angle, inter-stage gain error, and setup error without PN sequence injection, is defined as V_0,max. The protection margin is defined as V_guard. Therefore, the minimum residual peak margin that can be allocated to PN injection is V_R = V_lim - V_0,max - V_guard, requiring V_R > 0. Hereinafter, A_PN, V_lim, V_0,max, V_guard, and V_R all use the same MDAC output equivalent location and instantaneous peak value.

[0023] The PN sequence generator produces a zero-mean normalized PN reference sequence u(n) and injects the corresponding analog sequence with a peak amplitude of A_PN(k) into the first-stage MDAC summation node. The amplitude closed loop uses a_R(k) = A_PN(k) / V_R; the LMS update uses a fixed non-zero amplitude reference A_norm, employing a_L(k) = A_PN(k) / A_norm and x(n) = a_L(k)·u(n) as the regression variable. In this embodiment, A_norm = V_R is preferred, in which case a_R(k) = a_L(k). In the figures and tables, a(k) can be used as a shorthand for the common value of both. The codeword acquisition and delay alignment module, the digital redundancy state reconstruction module, the window statistics module, the hard protection module, the amplitude closed-loop control module, and the background calibration module constitute the digital closed loop. Figure 1 The hard protection module is shown as an independent highest priority branch, and its output can directly cover the conventional amplitude control results of the window statistical closed loop.

[0024] The term "redundant state reconstruction" in this invention refers to reconstructing the normalized proximity state ρ of the first-stage MDAC residual relative to a preset safety boundary using the existing redundant processable code domain information in the subsequent quantization path. This is used to determine the safety margin and control the PN injection amplitude. This term does not mean recovering the precise instantaneous value of the first-stage MDAC analog residual voltage.

[0025] The "post-stage quantizer" or "back-end quantization path" referred to in this invention can be a post-stage quantizer following the first-stage MDAC, or it can be a combined path consisting of multiple post-stage pipeline stages and a final-stage ADC, which continues to quantize the first-stage residual and forms a digital code monotonically corresponding to that residual. The "post-stage raw quantization code" referred to in this invention refers to the back-end digital result before applying digital correction that changes in real-time with the first-stage back-end calibration parameters; this code can include fixed-structure sub-stage decoding, redundant code concatenation, pipeline delay alignment, and fixed-ratio scaling.

[0026] Preferably, the raw quantized code for the subsequent stage is obtained before applying digital correction that varies with the current first-stage calibration weights, so that the mapping of this code to the first-stage MDAC residual is not affected by the immediate changes in the current LMS weights. Let the pipeline delay from the formation of the residual sample V_res(n) by the first-stage MDAC to the output of the corresponding digital code by the subsequent quantizer be L_B conversion cycles. Then, in the (n+L_B)-th conversion cycle, the raw quantized code D_B,raw(n+L_B) and the raw overrange state O_raw(n+L_B) of the subsequent stage are acquired. After delay compensation, they are renamed D_B(n) and O(n) respectively, and written into the same data record along with the normalized PN reference sequence u(n) of the nth conversion cycle. L_B can be determined by the timing of each stage during design, or it can be calibrated by the relevant peak values ​​of the known training sequence.

[0027] In implementations that require the use of digitally corrected codes, the scaling factor used for code domain reconstruction is fixed to the latch value of the previous observation window, and the same latch value is used to calculate the G_B,est, E_B, or security boundary code span; the new calibration weights generated in the current observation window only take effect in the next observation window. This decouples the calibration weight update from the boundary reconstruction in time, avoiding real-time algebra loops.

[0028] Within the operating range where the subsequent quantizer is not saturated and the propagation direction is known, the aligned subsequent digital code can be represented as: D_B(n)-D_0=G_B,true(k)·V_res(n) / Δ_B+η_0(n) Where D_0 is the codeword midpoint, G_B,true(k) is the actual signed equivalent transmission gain from the equivalent position of the first-stage MDAC residual to the input of the subsequent quantizer, G_B,est(k) is the estimated value used for digital boundary calculation, Δ_B is the subsequent quantization step size, and η_0(n) is the synthesis error after quantization rounding, bias, subsequent integral nonlinearity, and random noise are converted to the code domain. The above mapping remains monotonic in the unsaturated interval; for the piecewise nonlinear subsequent stage, D_B can be mapped to the equivalent code distance by finding a table through a single survey.

[0029] Decompose η_0(n) into a deterministic bounded term η_det(n) and a random noise term η_N(n). Denote the non-negative deterministic upper bounds of quantization rounding, bias drift, and subsequent integral nonlinearity in the code domain as E_q, E_off, and E_INL, respectively. Denote the upper bound of the magnitude of the difference between the actual gain and the estimated gain as δ_G,max, satisfying |G_B,true(k)-G_B,est(k)|≤δ_G,max, and denote this gain estimation error in the code domain. E_G=δ_G,max·V_lim / Δ_B If the implementation uses the relative error specification |G_B,true-G_B,est| / |G_B,est|≤ε_G,max, then δ_G,max=ε_G,max·|G_B,est| can be taken. Let E_det=E_q+E_off+E_INL+E_G.

[0030] Let σ_N denote the code domain standard deviation of random noise. For Gaussian noise or other random noise without a finite absolute upper bound used in behavioral-level models, E_N is not expressed as a mathematical hard upper bound that holds for all samples, but rather selected according to the quantile corresponding to the target tail probability α; under the Gaussian approximation, E_N can be taken as K·σ_N, where K is determined by the target confidence level 1-α. Under the worst-case deterministic superposition and probabilistic noise margin, the following approach is adopted: E_B≥E_det+E_N=E_q+E_off+E_INL+E_G+E_N When the statistical variation of deterministic error and random noise can be approximated as uncorrelated, root mean square budgeting can also be used, with an additional non-negative safety margin E_margin: E_B≥√(E_q²+E_off²+E_INL²+E_G²+E_N²)+E_margin E_B thus constitutes a conservative code domain design tolerance under a preset PVT range and a target confidence level of not less than 1-α, rather than an absolute bound for all samples of the ideal Gaussian variable; when tail perturbations exceeding this probability tolerance further lead to overrange or equivalent overrange states, they are quickly handled by sample-level hard protection corresponding to O(n). Specifically, a budget method is selected and verified through PVT angles, input range, and target tail probability. Then, the following calculations are performed: D_lim=|G_B,est(k)|·V_lim / Δ_B D_sec = D_lim - E_B, and D_sec > 0 ρ=|D_B-D_0| / D_sec D_lim is the nominal security boundary code span formed by the estimated gain, and D_sec is the conservative security boundary code span after deducting the code domain error tolerance. ρ is a dimensionless quantity, and ρ=1 corresponds to the conservative security boundary; 0<θ_H<1 is chosen as the lead amount, and e_w(n)=1 is set when ρ≥θ_H and O(n)=0, otherwise e_w(n)=0. Under the condition that the target confidence level and the given error budget hold, E_B is deducted to reduce the probability of security misjudgment caused by quantization error, subsequent non-ideals, and gain estimation error, rather than claiming to eliminate all random tail misjudgments.

[0031] G_B,est(k), E_B, or D_sec can be obtained from the factory calibration value, the lookup value corresponding to the current PVT index, the background gain estimate, or the converted value of the existing digital correction coefficient. To avoid parameter jitter, the update period is not shorter than the PN amplitude control period and is latched unchanged within an observation window. When the positive and negative directions are asymmetrical, D_sec+ and D_sec− are set respectively.

[0032] Each observation window contains N consecutive conversion samples, and the number of early warning events within the window is B_w(k)=Σe_w(n), with the early warning event rate p_w(k)=B_w(k) / N. In this embodiment, N=256, θ_H=0.85, the target interval [p_L, p_H]=[0.5%, 2%], and M=4 can be adopted. The target interval constitutes a statistical hysteresis: a small number of early warning events that have not exceeded the range are allowed to find a larger safe excitation, but a true over-range is not allowed to be regarded as a normal statistical event. N, θ_H, p_L, p_H and M can be set according to the noise level, the peak-to-average ratio of the input signal and the desired protection margin.

[0033] The amplitude closed loop uses the normalized quantity a_R(k)=A_PN(k) / V_R, and is limited within [a_R,min, a_R,max], where 0<a_R,min<a_R,max<1. Since V_R is the minimum remaining peak margin obtained after deducting V_0,max and V_guard under the preset input range and PVT corner, a_R,max<1 ensures that the PN peak does not exceed the margin pre-allocated for PN injection; the online early warning closed loop and the over-range hard protection further cover model errors, burst inputs and unmodeled disturbances.

[0034] The k-th observation window is used for statistics, estimation and formation of the amplitude control result, and the window-level amplitude modulation result takes effect from the next executable amplitude control period. When p_w(k)<p_L appears in M consecutive observation windows, the slow increase rule a_R(k+1)=min[a_R,max, g_up·a_R(k)] is executed, where g_up>1; when p_w(k)>p_H appears in any observation window, the fast decrease rule a_R(k+1)=max[a_R,min, g_down·a_R(k)] is executed, where 0<g_down<1; when p_L≤p_w(k)≤p_H, a_R(k+1)=a_R(k) is maintained. By setting 1-g_down>g_up-1, the amplitude adjustment presents the characteristic of slow increase and fast decrease. The LMS update always uses the a_L value actually adopted by the corresponding conversion sample, so as to avoid misapplying the amplitude of the next cycle to the samples already completed in the current window.

[0035] The hard protection logic operates by the conversion samples, and the window statistics logic operates by the observation windows. As long as O(n)=1 is detected within the observation window, the hard protection state machine is immediately set, the current B_w count is cleared or frozen, and fast amplitude reduction control is output without waiting for the end of the current observation window; considering DAC update, register synchronization or control path delay, the reduced PN peak amplitude is adopted starting from the next executable conversion sample after the control takes effect through the amplitude execution path. Then, the system enters a protection hold state lasting for H observation windows, during which amplitude increase is prohibited. The term "immediately" herein means that the control decision does not wait for the end of the window, and does not mean that the analog amplitude changes with zero delay on the current completed sample.

[0036] To reduce the impact of high peak-to-average ratio, burst or non-stationary input on the event rate, digital cancellation can be performed on the all-digital output code according to the known PN reference sequence and the actually adopted A_PN of each conversion sample, and when the PN residual correlation after cancellation is not higher than the preset threshold, the post-cancellation codes are used to form the short-term input envelope estimate V_env,s(k) and the long-term input envelope estimate V_env,l(k); histogram tail probability, decorrelated peak-to-average ratio or other code domain statistics that are insensitive to PN components can also be adopted. When V_env,s(k)≥γ·V_env,l(k), the PN amplitude gradual increase rule is frozen, the accumulated count of consecutive M low warning event rate windows is cleared, and p_H is temporarily adjusted to p_H', where γ>1 and 0<p_H'<p_H; when the above condition is not satisfied for Q consecutive observation windows, the gradual increase rule and p_H are restored and the accumulation of M safe windows is restarted, where Q≥1. This avoids the PN amplitude's own variation from raising the envelope and forming self-excited freezing feedback.

[0037] If the output of the subsequent stage is a SAR code, several most significant bits and several least significant bits can be defined as the warning code set, and B_w(k) is calculated based on the number of times the code falls into this set; the positive and negative overrange flags are still connected to the hard protection latch respectively. If the subsequent stage quantizer does not provide an explicit overrange flag, the reserved code, illegal code or saturation code that exceeds the hard boundary corresponding to D_lim can be taken as the equivalent overrange state.

[0038] The inter-stage weight update for the nth conversion sample can be expressed as: W(n+1)=W(n)+μ(k)·ε(n)·x(n) Where W(n) is the inter-stage weight to be calibrated, and ε(n) is the calibration error signal formed based on the ADC digital output, the current inter-stage weight, and the digital reconstruction relationship. The normalized PN reference regression vector, synchronized with the analog injection sequence and independent of the injection amplitude, is denoted as u(n). A fixed non-zero amplitude reference A_norm is selected, and a_L(k) = A_PN(k) / A_norm is defined. The actual dimensionless regression vector x(n) is set to a_L(k)·u(n). In this embodiment, A_norm = V_R, therefore a_L(k) = a_R(k). When the two references are different, they are both defined and converted using the same actual amplitude A_PN(k).

[0039] To ensure that the effective excitation quantity actually increases after the PN amplitude is increased, while avoiding LMS loop instability, candidate step sizes are first calculated: μ_0(k)=clip[μ_ref·(a_L,ref / a_L(k))^β,μ_min,μ_max], 0<β<2 Then, calculate the actual iteration step size based on the hard upper limit of stability corresponding to the PN amplitude: μ(k)=min[μ_0(k),C / a_L²(k)] To provide a basis for determining C, let R_u = E[u(n)u^T(n)], then R_x = E[x(n)x^T(n)] = a_L²(k)·R_u. Assume that λ_max(R_u) ≤ λ_u,max is obtained through worst-case simulation, online power estimation, or the upper bound of the Gershgorin disk. Choose a stability margin of 0 < κ < 1, and take: C=2κ / λ_u,max From μ(k) ≤ C / a_L²(k), we can obtain μ(k) < 2 / λ_max(R_x). Under the standard analytical framework of u(n) wide stationarity and using the classical LMS independence approximation, the above relationship can serve as a sufficient condition for mean-stable design. For single-tap scalar LMS, R_u is a 1×1 correlation matrix, and the largest eigenvalue of the matrix is ​​the scalar regressor power; for implementations containing additional input components or multi-tap regression vectors, λ_u,max takes the upper bound covering its maximum input energy and correlation. This constraint is used to provide engineering design margin and does not represent a guarantee of absolute stability under arbitrary quantization nonlinearity, gradient noise, time-varying parameters, or strongly non-stationary input conditions. The upper limit of the LMS normalized PN peak amplitude allowed within the preset working range is denoted as a_L,max, and it satisfies μ_min·a_L,max²≤C, which can maintain the minimum update capability across the entire amplitude range.

[0040] When the candidate step size does not reach μ_min or μ_max and is not limited by C / a_L²(k), the effective excitation amount μ(k)·a_L²(k) is proportional to a_L^(2-β)(k), and therefore increases with the increase of a_L(k); after reaching the stability upper limit, μ(k)·a_L²(k) no longer increases. Therefore, the claims, theoretical derivation, and behavioral verification all explicitly use the LMS normalized amplitude a_L; amplitude safety control explicitly uses a_R.

[0041] The amplitude control state machine includes a statistical state, a slow-increment wait state, a fast-decrement state, and a hard-protection hold state. The hard-protection latch signal can directly select the amplitude control word after fast decrement and output a clear signal to the window counter. In a non-restrictive fixed-point implementation, D_B-D_0 use a signed number with the subsequent significant bits plus 1 bit, ρ uses Q2.10 format, p_w uses Q1.15 format, a_R and a_L use Q1.11 format, and μ uses Q2.18 format; when A_norm=V_R, both share the same amplitude register. 1 / D_sec, g_up, g_down, and the segmented step size coefficients are stored in registers or lookup tables. Comparing ρ≥θ_H and p_w with [p_L, p_H] does not require floating-point operations.

[0042] A set of unrestricted control parameters was set as follows: N=256, M=4, θ_H=0.85, p_L=0.5%, p_H=2%, a_R,min=0.10, a_R,max=0.60, g_up=1.01, g_down=0.90, hard protection hold time H=2 observation windows, β=1, μ_ref=0.010, a_L,ref=0.30, μ_min=0.003, μ_max=0.030, C=0.0015. The behavioral model was normalized with V_lim, and A_norm=V_R=0.42V_lim was taken, so a_R=a_L=a, and a_L was used in LMS regression, candidate step size, stability limiting, and result statistics. The i-th basic residual sample within the k-th window is s_k·sin(2πi / 67+0.013k)+0.055ξ, where ξ is a zero-mean, unit-variance Gaussian random number, and s_k takes the value 0.58 in the normal window, 0.76 in windows 330-349, and 0.71 in windows 610-624. Let u(i)∈{-1,+1}, the actual residual is the sum of the basic residual and a_R(k)·V_R·u(i), while the LMS dimensionless regressor is x(i)=a_L(k)·u(i). The nominal inter-level weight is 0.085, the LMS observation noise standard deviation is 0.010, and the initial weight is 0. All three schemes run for 900 observation windows, with 256 samples per window. Table 1 uses the reproducible nominal operating conditions with random seed 20260824.

[0043] The comparison schemes include: a conservative fixed amplitude scheme with a normalized PN amplitude fixed at 0.14; an overrange-only amplitude adjustment scheme starting from 0.24, which rapidly reduces the amplitude only during actual overrange and gradually increases it within a safety window; and the present invention's dual-layer closed-loop scheme employing statistical early warning and sample-level hard protection. The convergence criterion was that the normalized weight error did not exceed 5% of the initial error for the first time, and the root mean square of the normalized weight error over the last 100 observation windows was used to characterize the tail-end error, resulting in Table 1.

[0044] Table 1. Behavioral Comparison of Three PN Amplitude Control Schemes Fixed PN amplitude 24 0 1.068% 0.000420 Over-range amplitude adjustment only 15 25 0.500% 0.001500 This invention features a double-layer closed loop. 16 4 0.728% 0.001334 Note: A total of 230,400 transformation samples; the values ​​are the deterministic calculation results of the above unrestricted behavioral-level model.

[0045] As shown in Table 1, under this unified normalized behavioral model, the proposed solution reduces the number of windows reaching the 5% error threshold from 24 to 16 compared to the conservative fixed amplitude solution, a reduction of approximately 33%, and the root mean square error of the tail weighting is reduced from 1.068% to 0.728%. Compared to the overrange amplitude modulation solution only, it only adds one observation window to reach the threshold, while the number of overrange samples is reduced from 25 to 4, a reduction of 84%. These results demonstrate that the two-layer closed loop achieves a significantly lower overrange risk at a convergence speed close to that of the overrange amplitude modulation solution only. Table 1 is used to demonstrate the executability and relative trend of the control relationship and does not represent post-silicon performance indicators for a specific chip.

[0046] To test the sensitivity of the results to random noise and variations in PVT / input peak value, three operating conditions were further set up: nominal, high noise, and high peak value / PVT offset. For the high noise condition, the standard deviation of the basic residual noise was increased from 0.055 to 0.070; for the high peak value / PVT offset condition, the normal residual amplitude was increased from 0.58 to 0.61, and the two burst amplitudes were increased from 0.76 and 0.71 to 0.80 and 0.75, respectively. Five random seeds were used for each operating condition from August 20, 2026 to August 24, 2026, resulting in a total of 15 operating condition-seed combinations. The statistical results are shown in Table 2.

[0047] Table 2 Statistical Validation of Multiple Random Seeds and Operating Conditions Fixed PN amplitude 26.6 / 28 1.3 / 3 1.149% / 1.385% Over-range amplitude adjustment only 15.2 / 16 45.7 / 61 0.571% / 0.650% This invention features a double-layer closed loop. 16.2 / 17 6.6 / 10 0.903% / 1.233% Note: Three operating conditions × 5 random seeds, a total of 15 sets of operating condition-seed combinations are run; each set contains 230,400 transformation samples.

[0048] As shown in Table 2, the dual-layer closed-loop circuit of this invention reached the 5% error threshold in all 15 operating conditions, with the slowest convergence window being 17 windows. The average convergence window was only 1.0 window more than the over-range amplitude adjustment scheme. The average number of over-range samples was 6.6, which was about 85.6% lower than the 45.7 of the over-range amplitude adjustment scheme, and the 95th percentile decreased from 61 to 10. The average tail-end weighted error RMS was 0.903%, lower than the 1.149% of the fixed amplitude scheme, but higher than the 0.571% of the over-range amplitude adjustment scheme. Therefore, the technical effect of this invention should be described as a more favorable trade-off between convergence speed, tail-end error, and over-range risk, rather than being optimal in all individual indicators.

[0049] Figure 2 The complete process combining sample-level hard protection and window-level amplitude control is presented. The system first acquires and aligns D_B(n), O(n), and u(n). If O(n) = 1, it outputs rapid amplitude reduction control with the highest priority without waiting for the window to end, clears or freezes the current window count, and sets the protection hold count H, so that subsequent executable samples use the reduced A_PN. Only when O(n) = 0 does the system reconstruct the digital boundary proximity ρ, accumulate warning events within N samples, and calculate p_w(k). The result of this window determines whether the next executable amplitude cycle should be rapidly reduced, slowly increased, or held. After each branch merges, a_R amplitude limiting is executed, and updates are performed according to the a_L linkage step size and LMS weight. "Immediate rapid reduction" in the diagram refers to the abbreviation for the control decision being output instantly.

[0050] Figure 3 The closed-loop relationship between the warning event rate p_w(k) and the normalized peak amplitude of PN is illustrated using normalized coordinates. In the figure, p(k) is an abbreviation of p_w(k); since A_norm = V_R in this embodiment, a(k) is a common abbreviation of a_R(k) = a_L(k). When the warning event rate is consistently lower than p_L, a_R(k) gradually increases; when the warning event rate is higher than p_H, a_R(k) decreases rapidly; when the warning event rate is within the target range, a_R(k) remains constant. Figure 3 Tables 1 and 2 are used to illustrate the control logic and variable relationships, and provide behavioral-level verification with explicit model parameters. Example

[0051] This invention is not limited to a specific number of bits or a specific pipeline stage structure. Digital boundary proximity can be obtained from the normalized amplitude of the output code of the subsequent stage, or from the hit rate of the boundary code set, the tail probability of the codeword histogram, or a combination of the above quantities; the overrange state is always treated as an independent hard protection condition. The observation window can be a fixed window, a sliding window, or exponentially weighted statistics; amplitude adjustment can be achieved using additive step size, multiplicative coefficients, or lookup table mapping; the target interval can vary with the input peak-to-average power ratio or operating mode. Background calibration is not limited to LMS; it can also use correlation accumulation, symbolic LMS, or normalized LMS; when using inverse power-law step size linkage, β can be 0.

Claims

1. A pipelined ADC adaptive PN injection amplitude background calibration method based on post-stage digital code redundancy state reconstruction, characterized in that, include: During the normal conversion of the pipelined ADC, a pseudo-random PN sequence with a peak amplitude of A_PN(k) is injected into the residual path of the multiplication digital-to-analog converter (MDAC) of the first-stage pipeline, where k represents the amplitude control period; Obtain the digital output code D_B and overrange state O(n) of the subsequent quantizer located after the first pipeline stage. Align D_B with the residual sample of the first MDAC that generated D_B in the digital domain with a delay. Based on the predetermined monotonic transfer mapping between the subsequent quantizer and the first MDAC, form a digital boundary proximity ρ from D_B that characterizes the degree to which the residual sample approaches the preset safety boundary. The digital boundary proximity ρ constitutes a reconstruction of the redundant processable code domain of the subsequent quantization path relative to the safe boundary state of the first-stage MDAC residual, without directly sampling the analog residual voltage of the first-stage MDAC and without requiring the recovery of the precise value of the analog residual voltage. When ρ≥θ_H and O(n)=0, the corresponding transformation sample is recorded as an early warning event, and the early warning event rate p_w(k) is calculated within an observation window containing N transformation samples, where 0<θ_H<1; The overrange state is latched independently of the warning event; When any conversion sample has O(n)=1, the regular amplitude decision of the current observation window is interrupted with a higher priority than window statistical control, and the amplitude reduction control is output without waiting for the current observation window to end, so that subsequent executable conversion samples after the amplitude reduction control takes effect through the amplitude execution path adopt a reduced PN peak amplitude; when the overrange state does not occur in the current observation window, p_w(k) is compared with the target warning event rate interval [p_L, p_H], and the PN peak amplitude of the next executable amplitude control cycle is determined based on the comparison result; The background calibration parameters are updated using the actual PN peak amplitude used in each conversion sample, the PN sequence synchronized with it, and the digital output of the pipeline ADC.

2. The method according to claim 1, characterized in that, The post-stage quantizer is a back-end quantization path consisting of one or more post-stage pipeline stages and a final-stage analog-to-digital converter, used to continue quantizing the first-stage MDAC residual and forming a digital code monotonically corresponding to the residual. The post-stage raw quantization code is allowed to include fixed decoding, codeword concatenation, delay alignment, or fixed scaling, but has not yet been subjected to digital correction that changes in real time with the first-stage background calibration parameters, and is taken before the first-stage inter-stage weights that change with the background calibration parameters are applied. Let the pipeline delay of the back-end quantization path relative to the first-stage MDAC residual sample be L_B conversion cycles. The post-stage raw quantization code D_B,raw(n+L_B) and the raw overrange state O_raw(n+L_B) acquired in the n+L_B conversion cycle are delayed and compensated. The compensated code and state are recorded as D_B(n) and O(n) respectively, and together with the normalized PN reference sequence u(n) of the nth conversion cycle, they form the same conversion sample data group.

3. The method according to claim 2, characterized in that, Within the unsaturated operating range of the subsequent quantizer, the monotonic transfer mapping satisfies: D_B(n)-D_0=G_B,true(k)·V_res(n) / Δ_B+η_0(n), Where D_0 is the codeword midpoint, G_B,true(k) is the actual signed equivalent transmission gain from the equivalent position of the first-stage MDAC residual to the input of the subsequent quantizer, G_B,est(k) is the estimated equivalent transmission gain used for digital boundary calculation, Δ_B is the subsequent quantization step size, V_res(n) is the first-stage MDAC residual sample, and η_0(n) is the synthesis error after quantization rounding, bias, subsequent integral nonlinearity, and random noise are converted to the code domain. The instantaneous peak value of the preset first-stage MDAC residual safety boundary is denoted as V_lim. E_B is used as the code domain design tolerance under the preset PVT range and target confidence level. The estimated nominal safety boundary code span D_lim=|G_B,est(k)|·V_lim / Δ_B and the conservative safety boundary code span D_sec=D_lim-E_B are determined. When D_sec>0, ρ=|D_B(n)-D_0| / D_sec is calculated.

4. The method according to claim 3, characterized in that, The deterministic upper bounds of the code domain for quantization rounding, bias drift, post-integral nonlinearity, and equivalent transmission gain estimation errors are denoted as E_q, E_off, E_INL, and E_G, respectively, and E_det = E_q + E_off + E_INL + E_G. The upper bound of the magnitude of the difference between the actual equivalent transmission gain and the estimated equivalent transmission gain is denoted as δ_G,max, satisfying |G_B,true(k) - G_B,est(k)| ≤ δ_G,max, and the upper bound of the code domain for the gain estimation error is determined according to E_G = δ_G,max·V_lim / Δ_B. The code domain standard deviation of random noise is denoted as σ_N, and the upper bound of the code domain for the gain estimation error is determined according to the quantile corresponding to the preset tail probability α or E_N. _N=K·σ_N determines the probability noise margin E_N, and determines the conservative code domain design tolerance at a target confidence level not lower than 1-α according to E_B≥E_det+E_N; when the tail disturbance exceeding the probability tolerance further leads to overrange or equivalent overrange state, it is quickly handled by the hard protection branch corresponding to O(n); G_B,est(k), the above sub-items, E_B or D_sec are obtained through corner simulation, factory calibration, background estimation, digital correction coefficient conversion, temperature and voltage lookup table or a combination thereof, and are latched unchanged within an observation window; when a digitally corrected post-level code is used, the monotonic transmission mapping uses the correction coefficient latched in the previous observation window.

5. The method according to claim 1, characterized in that, p_w(k)=B_w(k) / N, where B_w(k) is the number of early warning events in the k-th observation window; when O(n)=1, the early warning count of the current observation window is cleared or frozen, a fast amplitude reduction control is output without waiting for the end of the current observation window, and increasing the PN peak amplitude is prohibited within the subsequent H observation windows after the fast amplitude reduction control takes effect, where H is an integer not less than 1; when the post-stage quantizer does not provide an explicit overrange flag, an equivalent O(n) is formed by reserved codes, illegal codes or saturation codes that exceed the hard boundary; p_w(k) of the k-th observation window is used to determine A_PN(k+1) that takes effect from the next executable amplitude control cycle; when p_w(k)<p_L occurs for M consecutive observation windows, A_PN(k+1) is slowly increased, when p_w(k)>p_H, A_PN(k+1) is rapidly decreased, and when p_L≤p_w(k)≤p_H, A_PN(k+1) is maintained; when multiplication coefficients are adopted, the increasing rule is A_PN(k+1)=g_up·A_PN(k), and the decreasing rule is A_PN(k+1)=g_down·A_PN(k), where g_up>1, 0<g_down<1, and 1-g_down>g_up-1.

6. The method according to claim 5, characterized in that, The short-term input envelope estimate V_env,s(k) and the long-term input envelope estimate V_env,l(k) are formed based on the all-digital output code of the pipeline ADC that performs digital cancellation using a known PN reference sequence and the PN peak amplitude actually adopted by each conversion sample, and the PN residual correlation after cancellation is not higher than a preset threshold, or based on a code domain statistic that is insensitive to the known PN component; when V_env,s(k)≥γ·V_env,l(k), the increasing rule is frozen, the cumulative count of M consecutive observation windows with low early warning event rate is cleared, and p_H is temporarily adjusted to p_H', where γ>1 and 0<p_H'<p_H; when the above condition is not satisfied for Q consecutive observation windows, the increasing rule and p_H are restored, where Q is an integer not less than 1.

7. The method according to claim 1, characterized in that, The background calibration parameters are LMS inter-stage weights; a fixed non-zero amplitude reference A_norm is selected and the LMS normalized PN amplitude a_L(k) = A_PN(k) / A_norm is defined. The normalized PN reference regression vector, which is independent of the injected amplitude, is denoted as u(n). The calibration error signal formed by the pipeline ADC digital output and the current LMS inter-stage weights is denoted as ε(n). The actual dimensionless LMS regression vector x(n) = a_L(k)·u(n) is set, and the LMS inter-stage weights are updated according to W(n+1) = W(n) + μ(k)·ε(n)·x(n). First, determine the candidate step size according to μ_0(k)=clip[μ_ref·(a_L,ref / a_L(k))^β,μ_min,μ_max], then determine the actual iteration step size according to μ(k)=min[μ_0(k),C / a_L²(k)], where clip represents the amplitude limit between μ_min and μ_max, a_L,ref is the dimensionless reference amplitude, 0<β<2, and C is the dimensionless stability constant; when the amplitude limit and stability upper limit are not reached, μ(k)·a_L²(k) is proportional to a_L^(2-β)(k); Where R_u=E[u(n)u^T(n)], R_x=E[x(n)x^T(n)]=a_L²(k)·R_u; the upper bound of the maximum eigenvalue of R_u is denoted as λ_u,max, and 0<κ<1 is selected. The stability constant C is determined according to C=2κ / λ_u,max or a conservative value less than this value; the upper limit of the LMS normalized PN peak amplitude allowed within the preset working range is denoted as a_L,max, and μ(k)<2 / λ_max(R_x) and μ_min·a_L,max²≤C are used as design constraints under the standard analysis framework of u(n) width stationarity and classical LMS independence approximation; for single-tap scalar LMS, R_u is a 1×1 correlation matrix, and the matrix relationship degenerates into a scalar power relationship.

8. A pipelined ADC adaptive PN injection amplitude background calibration system based on post-stage digital code redundancy state reconstruction, characterized in that, include: A PN sequence generator is used to inject a controllable PN sequence with a peak amplitude of A_PN(k) into the residual path of the first-stage MDAC during normal conversion of the pipelined ADC. The codeword acquisition and delay alignment module is used to acquire the original digital output code and original overrange state of the subsequent quantizer, compensate according to the pipeline delay of the subsequent stage, and record the compensated code and state as D_B(n) and O(n) respectively, and make D_B(n), O(n) and the normalized PN reference sequence u(n) correspond to the same first-stage MDAC residual sample; wherein the subsequent quantizer is a back-end quantization path composed of one or more subsequent pipeline stages and a final stage analog-to-digital converter, and the original digital output code is allowed to include fixed decoding, codeword concatenation, delay alignment or fixed scaling, but has not yet been subjected to digital correction that changes in real time with the first-stage background calibration parameters; The digital redundancy state reconstruction module is used to generate a digital boundary proximity ρ from D_B based on a predetermined monotonic transmission mapping and code domain error tolerance, so as to reconstruct the state of the subsequent redundant processable code domain relative to the residual safety boundary of the first-stage MDAC, without directly sampling the analog residual voltage of the first-stage MDAC and without requiring the recovery of the accurate value of the analog residual voltage. The window statistics module is used to count the warning events with ρ≥θ_H and O(n)=0 and obtain the warning event rate; The hard protection module is used to independently latch the overrange state of any conversion sample and output a rapid reduction command with a higher control priority than the window statistics module without waiting for the current observation window to end. The amplitude closed-loop control module is used to respond to the rapid amplitude reduction command, so that subsequent executable conversion samples after the amplitude execution path takes effect adopt a reduced PN peak amplitude, or output the PN peak amplitude control word of the next executable amplitude control cycle according to the warning event rate of the current observation window when no overrange state occurs. The background calibration module is used to update the background calibration parameters based on the PN sequence and the pipelined ADC digital output.

9. The system according to claim 8, characterized in that, The midpoint of the codeword of the subsequent digital output code is denoted as D_0; when the code domain security boundaries in the positive and negative directions are asymmetrical, the conservative security boundary code spans in the positive and negative directions are denoted as D_sec+ and D_sec− respectively, and the corresponding boundaries are selected for normalization according to the sign of D_B-D_0; when the subsequent quantizer is a SAR quantizer, the highest and lowest codes form the warning code set; when the subsequent quantizer does not provide an explicit overrange flag, the reserved code, illegal code, or saturation code that exceeds the hard boundary is used as the equivalent overrange state.

10. The system according to claim 8, characterized in that, The background calibration module is an LMS weight update module. It selects a fixed non-zero amplitude reference A_norm and defines a_L(k) = A_PN(k) / A_norm. The normalized PN reference regression vector, independent of the injected amplitude, is denoted as u(n), and the calibration error signal is denoted as ε(n). Using x(n) = a_L(k)·u(n) as the LMS regression vector, the LMS inter-level weights are updated according to W(n+1) = W(n) + μ(k)·ε(n)·x(n), and the weights are updated according to μ_0(k) = clip[μ_ref·(a_L,ref The actual iteration step size is determined by [ / a_L(k))^β, μ_min, μ_max] and μ(k)=min[μ_0(k), C / a_L²(k)], where clip represents the amplitude limit between μ_min and μ_max, 0<β<2, and C is determined according to the upper bound of the largest eigenvalue of the u(n) correlation matrix; the upper limit of the allowed LMS normalized PN peak amplitude is denoted as a_L,max, and μ_min·a_L,max²≤C is used as the design constraint under the standard analysis framework of u(n) width stationarity and classical LMS independence approximation.

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