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3.3.2 Nonlinear Calibration of High Frequency Devices

Jack Wang, Kevin Coakley

Statistical Engineering Division, ITL

P. Hale and D. Larson

Optoelectronics Division, EEEL

We plan to calibrate photodiodes in the frequency domain up to 50 GHz. In the main experiment, a short laser pulse (50 fs) hits a photodiode. The output electrical signal is fed into a oscilloscope. The measured electrical signal is the convolution of the photodiode impulse response function and the oscilloscope impulse response function (plus noise). To characterize the photodiode, we need to know the impulse response function of the oscilloscope.

In a nose-to-nose oscilloscope calibration experiment, the kick out signal from oscilloscope i is fed into oscilloscope j. The measured pulse (Mij(t)) is ``approximately" the convolution of the oscilloscope impulse response function with itself. In the Fourier domain, the oscilloscope 1 impulse response function is

\begin{eqnarray*}\hat{H}_1(w) = \sqrt{ M_{12}(w) M_{13}(w) / M_{23}(w) }

. We divide the fourier transform of the measured electrical signal by the fourier transform of the oscilloscope impulse response function to get the transfer function of the photodiode in frequency space.

The nose-to-nose calibration data is affected by additive noise, random timing jitter noise and systematic timing errors known as time base distortion. Further, waveforms are affected by trime drift errors. Time base distortion errors can be estimated by complex demodulation. In this experiment, a sinusoid is fed into the oscilloscope. The output is demodulated. Alternatively, time base errors can be estimated using weighted least squares provided that multiple sinusoids at different frequencies are input into the oscilloscope. We also plan to measure time base distortion by time of flight methods with delta function pulses.

We plan to compare the nose-to-nose (magnitude and phase) characterization to alternative characterizations. One alternative characterization provides only `magnitude" information. The other technique yields phase information using the Hilbert Transform. Finally, we plan to measure the absolute time delay (linear phase distortion) of the photodiode.


Figure 15: A 2 GHz sinusoid is measured by an equivalent time sampling approach (top). The actual and desired time of each sample is perturbed by a time base distortion error. We estimate the time base distortion by a complex demodulation algorithm in the frequency domain (bottom).

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