Research On TIADC Error And Correction Method Based On Nonlinear Modeling

With the increasing diversity,complexity,non-stationarity and transient nature of modern electronic signals,higher and higher requirements are put forward for the sampling rate and accuracy of ADC.Single-channel ADCs are difficult to meet high sampling rate and high resolution requirements simultaneously under current manufacturing process conditions.Time interleaving more than one ADC is an effective way to substantially increase sampling rate beyond a certain process technology limit,which makes the TimeInterleaved ADC(TIADC)structure a practical solution to meet the growing demand of modern electronic systems.However,non-ideal circuit implementations and mismatches among different channels cause a significant degradation in performance of TIADC system.In order to fully realize the value of TIADC in practice,it is vital to calibrate errors of TIADC system.During my Ph.D research process,I dedicate myself to analyze and eliminate errors in TIADC system.Combining with the research projects granted by National Nature Science Foundation of China,a thorough study of the nonlinear mismatch errors in TIADC system is made.In this thesis,the nonlinear mismatch error model of TIADC is proposed firstly.On this basis,the nonlinear mismatch error is divided into static nonlinear mismatch error and dynamic nonlinear mismatch error.The performance of various mismatch errors in TIADC under different conditions are analyzed,and the corresponding estimation and correction algorithms are proposed.This thesis mainly conducts thorough researches from the following aspects:(1)A behavioral model based on Volterra series is proposed to model the dynamic nonlinear behaviors in TIADC.The expressions of Hybrid Volterra series for TIADC are given and discrete-time equivalent model is obtained by transforming Hybrid TIADC model to a discrete time one.The derivations give a theoretical foundation to use discretetime Volterra series to model TIADC system.We also summarize some special cases of Volterra series.By combining these simplified models with the derived TIADC formula,a large number of brand-new TIADC mismatch error models can be obtained.Different models have their own characteristics,so different estimation and calibration methods can be proposed.(2)Fast TIADC calibration methods for offset,gain and time mismatch errors are proposed,where three mismatch errors are corrected separately.Firstly,the estimation and calibration of the offset mismatch error is performed using a statistical-based method with the input signal being zero.Next,the difference of the main spectral amplitude among different channels of TIADC are utilized as the objective function,and the STPNM algorithm is used to iteratively calibrate the gain mismatch error.After that,the frequency of the input signal is set equal to the sampling rate of the TIADC system.The difference of the average value of samples from different channels are used as the objective function,and the STPNM algorithm is used to calibrate the time mismatch error.The algorithm is implemented in a 5GSPS digital storage oscilloscope.(3)A comprehensive calibration method for offset,gain and time mismatch errors is proposed for 10 GSPS digital phosphor oscilloscope.The method uses an adaptive algorithm to achieve comprehensive calibration of three mismatches.The core formula of the method is deduced in detail,and the iterative formulas of the correction algorithm are given.What's more,the hardware implementation of the adaptive calibration algorithm in FPGA is proposed,where the polyphase filtering method is adopted to design the filters in the calibration algorithm to solve the contradiction between TIADC output signal rate and FPGA processing rate.(4)Two algorithms for correcting TIADC static nonlinear mismatch errors are proposed.The principles of both methods are based on compensating the nonlinearity with inverse system.The difference is that the first method needs to estimate the nonlinear parameters of the system firstly,and then solve the parameters of the inverse system according to the analytic expression of the polynomial's -th order inverse.The second method is to correct the nonlinear error in TIADC by periodic time-varying adaptive method.This method does not need to estimate the parameters of the nonlinear system itself,but can directly calculate the parameters of the inverse system by adaptive method.(5)The estimation and correction method for dynamic nonlinear mismatch errors of TIADC are proposed,which takes Volterra series as an example to illustrate the estimation and correction method of TIADC dynamic nonlinear mismatch error from a general perspective.These methods are applicable to all TIADC models based on Volterra series' special forms given in this thesis.It is only necessary to use the relationship between these models and Volterra series to obtain the error estimation and correction methods of these TIADC models.At the same time,models,methods and conclusions applied to single-channel nonlinear problems can be transformed into the methods suitable for TIADC based on the core formulas derived from this thesis.Therefore,the methods presented in this paper are universal and expansive.