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3.2.6 Estimation of Time Base Distortion

C. M. Wang and K. J. Coakley
Statistical Engineering Division, ITL

P. D. Hale and T. S. Clement
Optoelectronics Division, EEELD. C. DeGroot
Radio-Frequency Technology Division, EEEL

As part of a program to characterize photodiodes, we characterize the time base distortion (TBD) of high speed oscilloscopes. A discrete time signal model is given by

\begin{displaymath}Y_i = f\left( (i-1)T_s + g_i + \tau_i\right) + \epsilon_i

where Yi the measured signal at time i is a function of actual time of sampling plus the additive noise, and (i-1)Ts is the ideal sample time with Ts being the sampling interval. Deviations between the ideal and actual times have two components: a deterministic part, gi, called TBD and a random component, $\tau_i$, called jitter. We study several methods for estimating TBD gi based on waveforms at multiple phases and frequencies. The waveforms are given by

   \begin{displaymath}Y_{ij} = \alpha_j + \sum_{k=1}^{h}\left[ \beta_{jk} \cos\left...
...k} \sin\left(2\pi k f_j t_{ij}\right) \right] +

where Yij is the measured signal at time tij (the ith sample time of the jth experiment), fj is the frequency used in the jth experiment, and $\beta_{jk}$ and $\gamma_{jk}$ are the amplitudes of the kth harmonic of the jth experiment. The number of harmonics h is assumed to be finite. The harmonic model is used to account for amplitude nonlinearity of the sampling channel. The model also assumes that tij is given by

\begin{displaymath}t_{ij} = (i - 1)T_s + g_i + \tau_{ij}

There are m experiments with n samples for each experiment, that is, $i = 1,\,2,\cdots,n$, and $j = 1,\,2,\cdots,m$.

We develop an efficient least squares algorithm for estimating TBD gi. We study several practical problems related to TBD estimation. One of the problems is the estimation of the harmonic order. Another problem is the determination of the number of experiments. Use of proper harmonic order and sufficient number of experiments are important for accurate TBD estimation. We also study the relative performance of various methods for estimating TBD using the simulated and measured waveforms. The methods developed will be used to correct the sampled signals.


Figure 12: This plot displays the estimated TBD of a sampling oscilloscope in a 4 nanosecond window. The number above each subplot corresponds to the number of experiments used. Each experiment consists of 4096 samples. The measurement uses frequencies 9.75 GHz and 10.25 GHz. The discontinuity is not uncommon in the real TBD.

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Date created: 7/20/2001
Last updated: 7/20/2001
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