Probing High-Speed Nets Without Measuring the Probe

A measurement is a circuit. The probe tip, its ground connection, the cable, and the scope’s input all connect to the node under test, and each contributes impedance. When the measurement’s own impedance is comparable to the node’s, the reported waveform is the response of the probe to the circuit rather than the circuit’s actual behaviour. The oscilloscope display is a valid waveform; it is just not the one the designer intended to measure.

The probe as a load

A passive probe’s tip presents a resistance and a capacitance. A typical 10:1 passive probe is 10 MΩ in parallel with about ten picofarads; the tip capacitor is chosen to match the cable’s capacitance through the divider, so that the division ratio holds at DC and at high frequency alike.

Ten megohms is irrelevant at any frequency of interest. Ten picofarads is not. At 1 GHz a 10 pF load is about 16 Ω, and a 50 Ω line probed at that point sees a load a third of its own impedance: a visible reflection, and a reported waveform shaped by it.

The capacitance also slows the edge being measured. A source impedance of 25 Ω driving 10 pF has a time constant of 250 ps, which adds a rise time of about 550 ps, and a 100 ps edge read through that probe against a 100 ps instrument comes out at about 570 ps. Even a 1 pF load — the tip of a good active probe — costs 25 ps of time constant and about 55 ps of rise time on the same source, which against the same edge and instrument gives roughly 150 ps in quadrature. The measured rise time is always slower than the real one, and the error grows as the edge approaches the probe’s own limit.

Active probes exist to reduce this. A FET-input probe has a tip capacitance of a picofarad or less, and a bandwidth that can reach several gigahertz, at the cost of a powered probe head, a limited voltage range, and a price that reflects the matching network inside the tip. For anything faster than a nanosecond edge, an active probe is not a luxury; it is the difference between measuring the circuit and measuring the probe.

Ground lead inductance is the dominant error

The probe’s ground connection is usually the largest single error term. The standard passive probe ships with a ground lead several centimetres long, and that lead is an inductor.

A wire in free space is roughly 1 nH per millimetre. A 10 cm ground clip is therefore about 100 nH. With a 1 ns edge and a 1 mA current into the probe’s capacitance, the voltage developed across that lead is 100 mV; with a faster edge or a larger capacitance, it is volts.

The mechanism is a series LC resonance between the ground lead’s inductance and the probe’s tip capacitance. The resonant frequency for 100 nH and 10 pF is about 160 MHz, and the ringing that appears on a fast edge probed with a long ground lead is that resonance, not the circuit’s. The observed overshoot and the flat-topped or double-peaked shape that follows are artifacts, and they appear on nodes that are perfectly well behaved.

The fix is geometric rather than electrical: shorten the ground path. A probe with a spring-loaded tip that contacts a ground pad a few millimetres from the signal via has a ground inductance of a few nanohenries instead of a hundred, and the resonance moves above the measurement bandwidth. Where a ground pad is not available next to the node, a small coaxial connector soldered to the board gives a controlled connection with known geometry.

A coaxial connector is worth the board space on any net that will be measured repeatedly. An SMA or a similar part soldered to a short stub, with its shield tied to the reference plane at the launch, presents a 50 Ω load to the line and a well-defined ground return. The measurement then has a calibratable reference plane rather than an unknown one, which is what allows the result to be compared with a simulation.

Bandwidth, sample rate, and the specification gaps between them

A scope’s bandwidth specification is the frequency at which its response falls by 3 dB. A signal with a rise time $t_r$ has a bandwidth requirement approximated by $0.35 / t_r$; a 100 ps edge needs about 3.5 GHz of analog bandwidth to be captured without significant smoothing. The usual rule is to choose a scope bandwidth three to five times that figure so that the displayed rise time is within a few percent of the true one.

Sample rate is a separate specification and is often confused with bandwidth. A scope with 20 GSa/s takes a sample every 50 ps; that is adequate for a 3 GHz bandwidth only because the analog front end has already band-limited the signal. Sampling a fast edge at a rate comparable to its rise time produces an aliased or undersampled record that can look plausible and be wrong.

The third specification, rarely quoted on the front panel, is the response shape. A scope with a maximally flat response and one with a sharper cutoff produce different amounts of overshoot on the same edge. Two instruments with the same 3 dB bandwidth can still disagree visibly on the peak overshoot of a fast edge. When a measurement is used to judge compliance against a mask, the instrument’s response is part of the measurement and must be characterised.

import math

def measured_rise(true_ps, probe_ps, scope_ps):
    # independent, approximately Gaussian contributions add in quadrature
    return math.sqrt(true_ps**2 + probe_ps**2 + scope_ps**2)

def probe_cap_time_constant(z_source_ohm, c_pf):
    # 10-90% rise of an RC charging curve is about 2.2 tau
    tau_ps = z_source_ohm * c_pf * 1e-12 * 1e12
    return 2.2 * tau_ps

print(f"10 pF probe RC rise: {probe_cap_time_constant(25, 10):.0f} ps")
print(f"1 pF probe RC rise:  {probe_cap_time_constant(25, 1):.0f} ps")
print(f"true 100 ps, probe 55 ps, scope 100 ps -> {measured_rise(100, 55, 100):.0f} ps")

The quadrature addition is an approximation that assumes each contribution is Gaussian, which is not exactly true for real instruments. It is still the right way to think about it: the errors do not add linearly, and the largest one dominates.

Where to put the probe

Probing the wrong point produces a correct measurement of the wrong thing.

Probing at the driver’s pin measures the driver’s output plus the probe’s loading plus the reflection from the line, all at a point where the waveform has not yet settled. Probing at the receiver’s pin measures the arriving waveform, which is what the receiver sees and therefore what determines whether the link works. For eye-diagram work the receiver’s pin is the only meaningful point.

Probing a via or a test pad that hangs off the line as a stub adds the stub’s own resonance to the measurement. A test point that is a 5 mm trace ending in a pad is a quarter-wave resonator at several gigahertz, and the measurement at the pad will show that resonance as a ripple on the signal. Test points should be placed on the line, not on branches, or should be designed as matched launches.

The reference point matters as much as the signal point. A single-ended probe measures the node relative to its own ground lead, and if the ground lead is connected to a point on the plane that is not at the same potential as the receiver’s reference, the difference appears in the measurement. This is the ground-bounce mechanism from Return Current Paths and Why Loop Area Sets Trace Inductance appearing in the instrument rather than on the board. A differential probe, or a pair of probes with a common-mode subtraction, removes the ambiguity at the cost of more setup.

Measuring jitter without inventing it

Jitter measurement is where the instrument’s own noise becomes the result. Total jitter is the sum of deterministic components — duty-cycle distortion, periodic jitter from power supply ripple, data-dependent jitter from intersymbol interference — and random jitter, which is unbounded and described statistically.

A scope’s trigger system contributes jitter of its own, and so does the probe’s noise. A measurement that reports 5 ps of random jitter from a link may be reporting the instrument’s trigger noise if the instrument’s contribution is of that order. The check is to measure a source with known jitter, or to measure the same signal through two different setups and compare.

The other trap is the record length. A jitter histogram built from a short record has statistical uncertainty that grows as the square root of the sample count, and the tails of the distribution — which are what determine the bit error rate — are exactly where the samples are fewest. A record long enough to populate the tails is long enough that the measurement takes time, and the temptation to extrapolate from a short record is the source of most optimistic jitter reports.

Correlating measurement with simulation

The value of a measurement is highest when it can be compared with a prediction. That requires the measurement to have a defined reference plane, a known probe impedance, and a calibration.

A vector network analyser measurement of a channel gives S-parameters with a reference plane at the calibration plane, and the calibration — short, open, load, thru — removes the fixture’s contribution. The resulting model can be cascaded with the transmitter and receiver models to predict the eye, and the prediction can be compared with a scope measurement made at the same point with a matched launch.

Without the calibration, the fixture is part of the model, and the comparison is between two unknowns. That is the practical reason test coupons and characterised launches exist on production boards: they give the measurement a place to start.

The limits of the measurement are the limits of the instrument, and they are worth stating before a result is used to accept or reject a design. A 1 GHz probe cannot adjudicate a 3 GHz edge; a 20 GSa/s scope cannot resolve a 20 ps feature; a ground lead cannot be ignored above a few hundred megahertz. The board design described in Power Delivery Network Impedance and the Target It Must Hold is verified by these instruments, and a measurement that cannot see the resonance it is looking for will report a passing rail.