﻿ 任意波形失真度的一种评价方法
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1. 北京航空航天大学 仪器科学与光电工程学院, 北京 100191;
2. 北京长城计量测试技术研究所, 北京 100095

Evaluation method for distortion of arbitrary waveform
SUN Jingyu1,2, WANG Zhongyu1 , LIANG Zhiguo2
1. School of Instrumentation Science and Opto-electronics Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China;
2. Beijing Changcheng Institute of Metrology and Measurement, Beijing 100095, China
Abstract:The index of distortion to evaluate the total quality of waveforms has special advantages and has been accepted widely by most people. Based on the analyses of the distortion definition of arbitrary waveform, a method using nonlinear-curve-fitting to evaluate the distortion of arbitrary waveform was discussed. Firstly, by moving the model in time domain, the“similar-fitting” model to the arbitrary waveform to be evaluated can be obtained. Then, using the least-square fitting method, the fitting curve on amplitude domain can be gotten, and this is just the best fitting curve to the arbitrary waveform to be evaluated. Thus, the distortion of the arbitrary waveform can be calculated. The results of the experiment show that this method has obviously practicability and flexibility, and can resolve the problem of evaluation for the distortion of arbitrary waveform. And then, it can resolve the problem of calibration for arbitrary waveform and arbitrary waveform generator (AWG).
Key words: arbitrary waveform     distortion     evaluation     calibration     metrology

1 任意波形失真度的定义与评价前提 1.1 任意波形失真度的定义

f(t)=G·x(t-t0)+Q

DT=ρ/fr

1.2 任意波形失真度评价的基本前提与假设

1) 谈论到任意波形,人们通常的理解是“任意”给定的波形,或者按照人们的意志“随意”给定的波形.这在通常意义下是对的,也就体现了“任意”性.但谈到对于任意波形的校准,这样的任意显然是行不通的,因为假如人们事先对于所要校准的任意波形一无所知,则校准根本无从谈起.因此,谈到对任意波形的校准,事先必须已知被校准任意波形的模型或参数,然后才能针对这一模型或参数进行校准.

2) 本文后续的讨论,均认为研究的任意波形是周期性的.实际上,对于“单次”的任意波形,可以通过周期延拓的办法将其拓展为周期波形,因此不影响相应的讨论过程与结论的得出.

3) 用于评价的采样设备的参数或性能指标已知.包括采样使用的采样速率、有效位数、量程等,以及相应参数的不确定度.

2 任意波形失真度评价的过程

1) 对于已知模型的目标任意波形,选取采集系统适当的量程(一般使任意波形的峰峰值达到其80%~90%)、采集速率rs(根据采样定律,理论上采样速率应高于被校任意波形最高谐波频率的2倍;实际中根据需要选择可接受的将被忽略的最高谐波频率)进行采样,获得相应的采样序列y(k),k=1,2,…,m.

2) 由于此时采集的y(k)相对于式(1)所示目标波形的“初始位置”一般不会一致,因此需要将目标波形进行相应的平移,亦即对目标波形延迟τ0得到x(t-τ0),使二者在起始时间上“对准”.这一过程,就是要对目标波形x(t)延迟时间τ,使用相同的采样速率rs进行采样得到x(k),并与实际采样序列y(k)进行非线性最小二乘拟合运算,找出“最佳的”延迟时间τ0,并得到此时的目标波形x0(t)的采样序列为x0(k),k=1,2,…,m.

3) 为叙述方便，以下将x0(t)简记为x(t);并令与测量波形y(t)最小二乘最优的期望函数为f(t)=G·x(t)+Q.即,选取合适的GQ,使得

3 实验验证

 图 1 正常心电图示意图Fig. 1 Sketch of normal electrocardiogram

1) 按照上述评价过程,首先使用Tektronix AWG20212任意波发生器模拟产生该波形(实际模拟发生时将幅度放大3 000倍,即:峰值2.1 V,峰峰值3.3 V),并使用Tektronix TDS7104数字存储示波器进行采集,获得采样波形y(k),见图 2中序列1.

 图 2 采样波形与拟合序列Fig. 2 Sample waveform and fit waveform

2) 使用相同的采样速率采样x(t-τ),并与上述采样波形进行非线性最小二乘拟合,得到拟合波形x(t-τ0),如图 2中序列2.

3) 构造f(t)=G·x0(t)+Q,并与y(k)进行最小二乘拟合;按照式(2)、式(3)得:G=2.995 2,Q=-0.016 7 V,如图 2中序列3.从而根据式(4)计算:

DTs=ρ/fr=0.027 89/0.415 3=6.7%

4) 修正测量设备的A/D位数DB的影响(使用数字存储示波器的量程为5V,DB的位数为6.1位),根据式(5)计算:

4 结 论

1) 文献[14]所描述的任意波形失真度的一般定义具有广泛的适应性,可以从时域角度定量描述被测波形与其期望波形之间的差异,并且在现实中是完全可以实现的.

2) 经过理论推导,可以使用简便的方法,通过波形非线性拟合,得到被测任意波形的最佳拟合波形,从而得出被测波形的失真度.

3) 由于该方法使用时域计算就能完成整个评价过程,对数据采样没有整周期或者同步的要求,可以完全避免频谱分析方法所固有的栅栏效应或频谱泄漏带来的评价误差问题,从而使所有采集到的数据均得到有效利用.同时,也因为避免了繁琐的频域计算与时频域转换过程,而且步骤简单易行,甚至在目前的技术条件下,使用普通的个人计算机就能够达到实时评价的程度.

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#### 文章信息

SUN Jingyu, WANG Zhongyu, LIANG Zhiguo

Evaluation method for distortion of arbitrary waveform

Journal of Beijing University of Aeronautics and Astronsutics, 2015, 41(1): 33-37.
http://dx.doi.org/10.13700/j.bh.1001-5965.2014.0079