Sampling oscilloscope

A sampling oscilloscope measures a signal that repeats, such as a clock, a periodic test pattern or a laser pulse train, by taking one sample (or a few) per trigger and moving the sampling instant a little later on each repetition. The display is assembled in equivalent time: a waveform lasting picoseconds is built from samples spread over milliseconds or seconds, taken at rates typically from tens of kilosamples to about a megasample per second. Because the sampler needs only a very short aperture, with a slow converter behind it, electrical sampling heads reach bandwidths of the 50–100 GHz class, and optical plug-ins with a built-in, calibrated photodiode and receiver cover the 1310 and 1550 nm bands at tens of gigahertz. It is the standard instrument for optical transmitter eyes, extinction ratio and TDECQ.

How equivalent-time sampling works

A trigger marks a fixed point of each repetition. After a programmable delay, a sampling gate (a diode bridge or a similar fast switch driven by a sharp strobe) opens for a few picoseconds and holds the instantaneous voltage, which a slow, high-resolution converter then digitizes. In sequential sampling the delay steps by a fixed increment after each trigger; in random or pattern-locked sampling the instrument records the time of each sample relative to the trigger and places it accordingly.

For a data signal, the trigger is a clock at the symbol rate or a submultiple, taken from the pattern generator or from a clock-recovery unit fed by the signal itself. A clock trigger alone overlays all symbol periods into an eye diagram. With pattern lock, the scope also knows the pattern length and can display each bit of a repeating pattern in order, which allows averaging and analysis of intersymbol interference. A pseudo-random pattern of length $2^{15}-1$ repeats every 617 ns at 53.125 GBd.

The method fails on anything that does not repeat: a single transient, a burst, or a non-periodic data stream with no available clock. Those need a real-time oscilloscope, which digitizes continuously and recovers the clock in software, at a much higher cost per gigahertz and with more noise at the highest bandwidths.

Bandwidth and rise time

The sampler, cables and any optical front end form a low-pass system whose rise time is approximately

$$t_r \approx \frac{0.35}{f_\text{3dB}} ,$$

so a 70 GHz head has $t_r \approx$ 5.0 ps and a 50 GHz head 7.0 ps. The instrument's response adds to the device's roughly in quadrature: a photodiode with a 10 ps rise time measured on the 70 GHz head reads about 11.2 ps. Pulse-response measurements of detector bandwidth therefore either use a much faster instrument or deconvolve its calibrated response, as described in the photodetector bandwidth article.

For compliance measurements the bandwidth is deliberately reduced. A reference receiver with a fourth-order Bessel-Thomson response is applied in hardware or software: a 3 dB bandwidth of 0.75 times the bit rate for NRZ eye masks (7.73 GHz at 10.3125 Gbit/s) and half the symbol rate for PAM4 TDECQ (26.5625 GHz at 53.125 GBd). The raw instrument bandwidth must be well above this so that the reference response, not the hardware, defines the result.

Jitter floor

Every sample is placed in time by the trigger and the delay generator, and their combined timing jitter, typically from below 100 fs to about 1 ps rms, blurs the waveform horizontally. At 106.25 GBd the unit interval is 9.41 ps, so 200 fs rms is 2.1% of it; the jitter the scope reports is the quadrature sum of its own floor and the signal's. Precision timebases that phase-lock to the data clock bring the floor to the low end of this range.

Optical eye measurements

With an optical plug-in, the scope reports power levels directly. The one and zero levels give the extinction ratio and the optical modulation amplitude, which the eye diagram entry relates to average power. Both depend on the dark level: a transmitter at 0 dBm average with a 10.0 dB extinction ratio has levels of 1.82 and 0.18 mW, and a 0.02 mW error in the dark-level offset makes it read 10.5 dB. Dark calibration with the input blocked, and a launch power high enough to keep the head's own noise small against the signal, are the two habits that most affect repeatability.

Related instruments

A sampling scope measures in the time domain. A network analyzer measures the same frequency response as swept sinusoids with greater dynamic range, and an electrical spectrum analyzer shows the spectrum of the signal without phase. Linear optical sampling applies the equivalent-time principle with femtosecond optical pulses as the sampling gate and recovers the optical field, including phase.

Common questions

What is the difference between a sampling and a real-time oscilloscope?

A real-time oscilloscope digitizes every point of a single acquisition and can capture one-off events. A sampling oscilloscope takes few samples per trigger and needs a repeating signal and a trigger, but for the same bandwidth it is cheaper and generally has lower noise and jitter.

Can it measure optical pulses shorter than its rise time?

Not directly. A 1 ps pulse viewed through 70 GHz of instrument bandwidth displays with roughly the head's own 5 ps response, so only an upper bound on duration is obtained. Picosecond and femtosecond pulses are measured with an autocorrelator or other optical gating methods.

References: G. P. Agrawal, Fiber-Optic Communication Systems, 4th ed. (Wiley, 2010); D. Derickson, ed., Fiber Optic Test and Measurement (Prentice Hall, 1998); B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 3rd ed. (Wiley, 2019).