
3.2.4 Characterization of High Speed Oscilloscopes
C. M. Wang and K. J. Coakley
P. D. Hale and T. S. Clement The frequencydependent phase and magnitude response of a device are required to determine its timedomain response and are used in optoelectronic device metrology, nonlinear device metrology, and high speed digital circuit design. Frequencydomain network analyzers measure device amplitude and phase responses relative to a reference tone, but cannot measure the total phase relationship of the frequency components in a broadband waveform. Here timedomain methods are required. We are investigating the use of a high speed sampling oscilloscope, which has been calibrated using the nosetonose method, to measure the phase response of fast optical detectors and electrical comb generators. Actual measurements of the impulse response of a sampling oscilloscope are affected by various nonideal properties of the hardware. Calibration of an oscilloscope's frequency response requires estimation and correction of these effects, which include distortion, drift, and jitter components in the timebase, and mismatch. Timebase distortion (TBD) is a deterministic error in the delay generator that triggers a sample. Drift and jitter are random variations in the sample time which occur on a long and short time scale relative to one complete sweep of the display. Many waveforms must be averaged to achieve a low noise level. Before averaging, the waveforms are corrected for drift. Relative drifts are estimated from crosscorrelation analysis of all distinct pairs of signals. A manuscript on alignment of noisy signals has been submitted to IEEE Transactions on Instrumentation and Measurement. Error due to TBD must be compensated to give good corrections above 15 GHz. We developed an efficient leastsquares algorithm for estimation TBD. The method requires measurements of sinusoidal signals at multiple phases and frequencies. It can accurately estimate the order of the harmonic model that is used to account for the amplitude nonlinearity of the sampler. This work appears in the 1999 December issue of IEEE Transactions on Instrumentation and Measurement.
To completely characterize data acquisition channels, the additive and
jitter errors must also be estimated.
The additive and jitter errors are used in the weighting of
the TBD estimation procedure.
It's found, from a simulation study, that the reduction in rootmeansquare
error of TBD estimate by using the appropriate weighting is about 20%.
Therefore, it's important to obtain an accurate estimate of additive and
jitter errors.
The signal model is given by
where y_{i} the measured signal at time i is a function of actual time of sampling plus the additive noise. The actual sampling time consists of two parts; t_{i} is the sum of the ideal sample time and TBD, and is the jitter. We assume that and are independent zeromean random variables with variances and respectively. Making a firstorder approximation of , we can write and obtain This allows us to estimate and by solving a simple linear regression problem. In fact, this is the most popular method for obtaining estimates of additive and jitter variances.
Under the assumptions of Gaussian jitter errors and negligible harmonic
distortion, we have shown that
where A is the amplitude and f is the frequency of the sinusoidal signals. The result can be used to adjust for the bias of additive and jitter variance estimates obtained by the firstorder approximation. These biases can be large if is not small. The jitter and additive noises also appear in the pulse signals from detectors. The effect of jitter on an averaged signal is that of a lowpass filter. We are currently investigating nonparametric methods for estimating these error variances. Once is obtained, the estimated frequencydomain representation of the impulse response of the detector is then multipled by over the frequency range of interest to deconvolve the jitter effects. Preliminary results of repeated measurements on the magnitude and phase response of an ensemble of three 50 GHz oscilloscope plugins will be presented in the 55^{th} ARFTG Conference on June 2000.
Date created: 7/20/2001 