一种应用于高精度SAR ADC校准的剪枝神经网络算法

介绍了一种基于剪枝神经网络的后台校准算法,能够对高精度单通道SAR ADC的电容失配、偏移、增益等多个非理想因素同时进行校准,有效提高SAR ADC的精度。本算法不仅可以达到全连接神经网络校准效果,而且同时对贡献小的权重进行剔除,降低了校准电路的资源消耗,加快了神经网络校准算法速度。仿真结果表明,信号频率接近奈奎斯特频率的情况下,对16 bit 5 MS/s的 SAR ADC进行校准,校准后ADC的有效位数从7.4 bit提高到15.6 bit,无杂散动态范围从46.8 dB提高到126.2 dB。     

基于神经网络的数字校准技术综述

随着集成电路工艺的发展以及晶体管尺寸的不断减小,ADC转换率变得更快、功耗更低,但器件的失配误差随之变得更大,从而影响精度,因此引入校准电路已成必然趋势。文章首先介绍了几种ADC的常见误差及其校准方法,然后介绍了神经网络的工作原理,并总结了几种主要的基于神经网络的数字校准方法,分析了不同方法的优势和劣势。最后,针对14位流水线ADC,给出了神经网络校准算法的系统级仿真验证结果。经校准后,有效位数(ENOB)从10位提升到12.5位,无杂散动态范围(SFDR)从80 dB提升到100 dB。     

Variable-amplitude dither-based digital background calibration algorithm for linear and high-order nonlinear error in pipelined ADCs

Dither-based digital background calibration algorithm has been used to eliminate the influence of linear and nonlinear errors in pipelined ADC. However, this algorithm suffers from two disadvantages: too slow convergent speed and deduction of transmitting signal’s amplitude in analog circuits due to dither injection. Input-dependent variable-amplitude dither-based algorithm is used in this paper to conquer both disadvantages. This proposed algorithm is implemented in a 14-bit, 100 MHz sample-rate pipelined ADC. The simulation results illustrate signal-to-noise and distortion (SINAD) of 76.56 dB after calibration of linear and nonlinear errors. Furthermore, the convergent speed is improved much more.     

A low power and small area digital self-calibration technique for pipeline ADC

A digital self-calibration implementation with discontinuity-error and gain-error corrections for a pipeline analog-to-digital converter (ADC) is presented. In the proposed calibration method, the error owing to each reference unit capacitor of the multiplying D/A converter is measured separately using a calibration capacitor and an enhanced resolution back-end pipeline ADC acting as an error quantizer. The offset and finite open loop DC-gain of the operational amplifier and capacitor mismatches, the reference voltage mismatch can all be calibrated. The calibration can be achieved by that only used addition and subtraction. Hence, it needs low power and area consuming. A prototype ADC with the proposed calibration was fabricated on a 0.5 μm double-poly triple-metal CMOS process. The power consumption and area of the calibration circuit are only 10.1 mW and 1.05 mm², respectively. At a sampling rate of 30 MS/s, the calibration improves the DNL and INL from 2.59 LSB and 14.98 LSB to 0.72 LSB and 1.82 LSB, respectively. For a 1.25 MHz sinusoidal signal, the calibration improves the signal-to-noise-distortion ratio and spurious-free dynamic range from 43.1 dB and 52.1 dB to 75.51 dB and 83.61 dB, respectively. The 12.25 effective number of bits at 30 MS/s ADC consumes a total power of 136 mW.     

基于码密度统计的流水线模数转换器校准算法研究

本文提出了一种用于校准流水线模数转换器线性误差的数字后台校准算法。该算法不需要修改转换器级电路部分,只需要一部分用于统计模数转换器输出码的数字电路即可完成。通过分析流水线模数转换器输出的数字码,该算法可以计算出每一级级电路对应的权重。本文利用一个14位的流水线模数转换器来验证该算法。测试结果显示,转换器的积分非线性由90LSB下降到0.8LSB,微分非线性由2LSB下降到0.3LSB;信噪失真比从38dB提高到66.5dB,总谐波失真从-37dB下降到-80dB。转换器的线性度有很大提高。     

一种前后台结合的SAR ADC的校准算法

提出了一种数字前台校准技术,即电容重组技术,并将该技术与LMS数字后台校准技术相结合,提高了LMS算法的收敛速度。提出的算法使用RC混合结构的14位SAR ADC进行建模。仿真结果表明,LMS算法的收敛速度可以提高到1 k个转换周期内,同时校准后ADC的ENOB平均值从10.59 bit提高到13.79 bit。SFDR平均值从71.33 dB提高到112.93 dB,DNL最大值的平均值从1.88 LSB提高到0.97 LSB。INL最大值的平均值从8.01 LSB提高到0.88 LSB。     

A background digital calibration of split-capacitor 16-bit SAR ADC with sub-binary architecture

The paper introduces a sub-binary architecture in 16-bit split-capacitor successive-approximation register (SAR) analog-to-digital converters (ADCs). The redundancy in sub-binary capacitors array provides ways to correct the dynamic errors in conversion procedure with a smaller overall conversion time. So the redundancy can be used to solve the mismatch or parasitic problems in split-capacitor CDAC SAR. A background digital calibration method with perturbation is utilized to calibrate the conversion errors. The behavioral simulation and measured results show that the 16-bit SAR ADC performance can be improved after the digital calibration. The prototype was fabricated in 0.18 μm CMOS process. The INL are −6/7.813 LSB, the DNL are −0.925/1.313 before calibration. After calibration, the INL are −0.813/0.938, the DNL are −0.625/0.688. The measured ENOB is 11.42 bit and SFDR is 79.95 dB before calibration, while the ENOB is 14.46 bit and SFDR is 95.65 dB after calibration.     

A statistics-based digital background calibration technique for pipelined ADCs

This paper introduces a digital background calibration technique for pipelined analog-to-digital converters (ADCs). The proposed method continuously measures and digitally corrects conversion errors resulting from residue amplifier gain error and nonlinearity. It is based on modulation of the residue voltage using a pseudorandom-noise sequence (PN). A least-mean-squares (LMS) algorithm is utilized to correct conversion errors arising from the residue amplifier non-idealities. Besides, a new statistics-based digitized residue distance estimation (DRDE) algorithm is proposed that allows the LMS algorithm to operate in the background without interrupting the normal operation of the ADC. The DRDE method extracts the residue amplifier non-idealities by evaluating the digitized residue voltage probability density function (PDF). Behavioral simulation results verify the usefulness of the proposed calibration technique and show that the signal-to-noise-and-distortion-ratio (SNDR) is improved from 43 to 71.9 dB, in a 12-bit pipelined ADC.     

A digital processor for full calibration of pipelined ADCs

In this paper, a digital processor is presented for full calibration of pipeline ADCs. The main idea is to find an inverse model of ADC errors by using small number of the measured codes. This approach does not change internal parts of the ADC and most known errors are compensated simultaneously by digital post-processing of the output bits. Some function approximation algorithms are tested and their performances are evaluated. To verify the algorithms, a 12-bit pipelined ADC based on 1.5-bit per stage architecture is simulated with 1%-2% non-ideal factors in the SIMULINK with a 20 MHz sinusoidal input and a 100 MS/s sampling frequency. The selected algorithm has been implemented on a Virtex-4 LX25 FPGA from Xilinx. The designed processor improves the SNDR from 45 to 69 dB and increases the SFDR from 45.5 to 90 dB. The calibration processor also improves the integral nonlinearity of the ADC.     

一种基于统计的流水线ADC数字后台校准方法

高精度流水线ADC的设计需要校准技术来提高其转换精度.基于统计的数字后台校准方法无需校准信号,直接通过对输出的统计得到误差值的大小,将其从数字输出中移除从而消除了ADC输出非线性.将该校准方法应用于14bit流水线ADC中,仿真结果表明校准后信噪失真比SNR为76.9dB,无杂散动态范围SFDR为73.9dB,有效精度ENOB从9bit提高到12.5bit.     

Digital background calibration of charge pump based pipelined ADC

In the presented work, digital background calibration of a charge pump based pipelined ADC is presented. A 10-bit 100 MS/s pipelined ADC is designed using TSMC 0.18 µm CMOS technology operating on a 1.8 V power supply voltage. A power efficient opamp-less charge pump based technique is chosen to achieve the desired stage voltage gain of 2 and digital background calibration is used to calibrate the inter-stage gain error. After calibration, the ADC achieves an SNDR of 66.78 dB and SFDR of 79.3 dB. Also, DNL improves to +0.6/–0.4 LSB and INL improves from +9.3/–9.6 LSB to within ±0.5 LSB, consuming 16.53 mW of power.     

一款结合数字校正技术的流水线ADC设计

基于65 nm CMOS工艺、1.2 V供电电压,设计了一款结合偏移双通道技术的流水线模数转换器(analog-to-digital convertor,ADC)。芯片的测试结果表明,该校正方法有效地消除和补偿了电容失配、级间增益误差和放大器谐波失真对流水线ADC综合性能的制约。流水线ADC在125 MS/s采样率、3 MHz正弦波输入信号的情况下,信噪失真比(signal-and-noise distortionratio,SNDR)从校正前的28 dB提高到61 dB,无杂散动态范围(spurious-free dynamic range,SFDR)从校正前的37 dB提高到62 dB。ADC芯片的功耗为72 mW,面积为1.56 mm2。偏移双通道数字校正技术在计算机软件上实现,数字电路在65 nm CMOS工艺、125 MHz时钟下估计得出的功耗为12 mW,面积为0.21 mm2。     

A 12-bit 100 MS/s pipelined ADC with digital background calibration

This paper presents a 12-bit 100 MS/s CMOS pipelined analog-to-digital converter (ADC) with digital background calibration. A large magnitude calibration signal is injected into the multiplying digital-to-analog converter (MDAC) while the architecture of the MDAC remains unchanged. When sampled at 100 MS/s, it takes only 2.8 s to calibrate the 12-bit prototype ADC and achieves a peak spurious-free dynamic range of 85 dB and a peak signal-to-noise plus distortion ratio of 66 dB with 2 MHz input. Integral nonlinearity is improved from 1.9 to 0.6 least significant bits after calibration. The chip is fabricated in a 0.18μm CMOS process, occupies an active area of 2.3×1.6 mm~2, and consumes 205 mW at 1.8 V.     

PN-assisted digital background calibration of two-step ADC to over 14-bit accuracy

A new non-binary multiplying digital-to-analog converter (MDAC) structure with signal-dependent dithering scaling technique is proposed in this paper. A full digital background calibration algorithm based on pseudo-random dithers injection is used to calibrate the nonlinear errors of MDAC. By measuring sampling capacitor mismatch and op-amp gain errors of the pipelined analog-to-digital converter (ADC) in background, the errors will be greatly reduced by the proposed calibration algorithm. At the same time, the signal-dependent dithering scaling technique provides a swing margin to the injected pseudo-random signal. By using this technique, the errors caused by the capacitor mismatch and op-amp gain errors can be calibrated at the same time. What’s more, this method greatly accelerates the convergence speed. A two-stage 14-bit pipelined ADC is used to simulate and verify the proposed algorithm. The simulation results indicate the effectiveness of the technique, in which the signal-to-noise plus distortion (SNDR) and the spurious-free dynamic range (SFDR) performance of a 14-bit two-step ADC are improved from 49.12 and 56.25 to 85.68 and 102.23 dB with the input frequency being 0.06 * f _s , respectively. The SFDR is more than 98 dB. The SNDR reaches 84 dB in the whole Nyquist bandwidth after calibration. Integral nonlinearity is improved from 80 to 1.5 least significant bits after calibration.     

Foreground calibration technique of a pipeline ADC using capacitor ratio of Multiplying Digital-to-Analog Converter (MDAC)

A foreground calibration technique of a pipeline analog-to-digital converter (ADC) has been presented in this paper. This work puts an emphasis on erroneous ADC output occurring due to device mismatch, which, in any standard CMOS process boils down to capacitor mismatch. Deviation of gain of a multiplying digital-to-analog converter (MDAC), also known as the radix of a pipeline ADC stage, from its ideal values adds to the non-linearity of the ADC output. Capacitor mismatch is a major contributor for such an error. The proposed foreground calibration technique makes use of a simple arithmetic unit to extract the radix value from the ADC output for calibration. It uses a sinusoidal signal at the input for calibration purposes. The input sinusoidal signal can be sampled by the ADC clock at any rate for the calibration algorithm to be successful. Behavioral simulation of a pipeline ADC with 5% capacitor mismatch supports the established technique. To verify the calibration algorithm further, pipeline ADCs of different resolutions have been designed and simulated in a 0.18 μm CMOS process.     

应用于流水线ADC的LMS自适应校准算法与FPGA实现

研究了应用于流水线模数转换器(ADC)的LMS自适应数字校准算法及其FPGA实现。该校准算法可用于校准大多数已知的误差,包括非线性运算放大器的有限增益、电容失配,以及比较器的失调等。通过Simulink软件,对一个12位160 MS/s的流水线ADC进行建模。采用LMS自适应校准算法对该流水线ADC进行校准,并将算法在Virtex-5上实现了硬件设计。实验结果表明, 输入信号频率为58.63 MHz时,流水线ADC的无杂散动态范围(SFDR)和有效位(ENOB)分别由校准前的46.31 dB和7.32位提高到校准后的82.03 dB和11.12位。     

MOSFET-only pipelined analogue-to-digital converters: non-linearity compensation by digital calibration

In this study, a 12-bit 65MS/s MOSFET-only pipelined analogue-to-digital converter (ADC) is successfully designed and implemented in 0.18 µm standard digital complementary metal–oxide–semiconductor (CMOS) technology. In the proposed ADC, constant capacitors of the analogue pipeline stages are replaced with anti-parallel depletion-mode metal–oxide–semiconductor (MOS) devices and their non-linearity is modelled and calibrated digitally. Simulations show that the proposed digital calibration algorithm improves the ADC signal-to-noise plus distortion ratio and spurious-free dynamic range from 43 dB and 44 dB to 70 dB and 78 dB, respectively.     

Offset-injection digital background calibration for VCO-based ADC

A new offset-injection digital background calibration technique for VCO-based ADC is proposed to compensate for VCO nonlinearity. By injecting a predetermined offset signal, the new technique suppresses in-band distortions caused by VCO nonlinearity successfully. The offset-injection technique draws support from orthogonal polynomials least mean square algorithm to improve the computation efficiency. A dual-path all-standard-cell VCO-based ADC is also proposed to inject the calibration signal. The proposed VCO-based ADC achieves 71.9 dB of signal to noise and distortion ratio and 11.65 bits of effective number of bit.     

A background calibration in pipelined ADCs

In this paper, a novel background calibration is presented. The proposed scheme continuously measures and digitally compensates conversion errors caused by residue amplifier nonlinearity. This scheme can be used to relax analog circuit requirements for high-precision residue amplifier, accordingly decreasing the power consumption and/or increasing sampling rates in pipelined ADCs. The proposed scheme employs a fifth-order polynomial to eliminate conversion errors. One unique feature of the proposed scheme is that a single pseudorandom sequence, pn, is exploited. The simulation results show that, using the proposed calibration technique, the signal-to-noise-and-distortion-ratio (SNDR) is improved from 40 to 66 dB and the spurious-free-dynamic-range (SFDR) is increased from 48 to 80 dB.     

Inter-channel offset and gain mismatch correction for time-interleaved pipelined ADCs

This paper presents a digital background calibration technique to compensate inter-channel gain and offset errors in parallel, pipelined analog-to-digital converters (ADCs). By using an extra analog path, calibration of each ADC channel is done without imposing any changes on the digitizing structure, i.e., keeping each channel completely intact. The extra analog path is simplified using averaging and chopping concepts, and it is realized in a standard 0.18‐μm CMOS technology. The complexity of the analog part of the proposed calibration system is same for a different number of channels.Simulation results of a behavioral 12-bit, dual channel, pipelined ADC show that offset and gain error tones are improved from −56.5 and −58.3 dB before calibration to about −86.7 and −103 dB after calibration, respectively.