Oscilloscope probes: 10:1, and why the ground lead rings

An oscilloscope probe is a circuit. Tektronix’s primer on the subject says so in its first pages — probes “are circuits composed of distributed resistance, inductance, and capacitance” — and everything that goes wrong with a probe measurement follows from one of those three. The resistance is 10 MΩ for a 10:1 probe and rarely matters. The capacitance is 8–13 pF at the tip and loads the node. The inductance is the ground lead, and with the tip capacitance it makes a resonance that rings on every fast edge: “an 11 pF passive probe with 6-inch ground lead will ring at about 140 MHz”. On a 100 MHz scope that is above the bandwidth and invisible; on a 200 MHz scope it is on the screen, sitting on top of the signal, looking exactly like overshoot in the circuit.

That one figure from Tek pins the ground lead’s inductance at about 117 nH, 0.77 nH per millimetre, and from it the probe loading calculator computes where any lead rings against any scope, what the tip capacitance does to the node, and what rise time the screen will show for the edge that is actually there. This article is what a probe is, what the three elements do, and the test Tek gives for telling the probe’s ringing from the circuit’s.

What a 10:1 probe is

A 1X probe is a shielded cable: 1 MΩ at the scope and, in Tek’s table, 100 pF at the tip — the cable’s capacitance, all of it on the node. A 10X probe puts a 9 MΩ resistor in the tip, in parallel with a small capacitor, to form a 10:1 divider with the scope’s 1 MΩ and its input capacitance; the tip capacitance falls to 8–13 pF and the resistance rises to 10 MΩ. The signal arrives at the scope a tenth the size, which Tek notes is why “for general-purpose use, 10X probes are preferred, both because of their higher input resistance and lower capacitance”, with the 1X setting kept for small, slow signals. The division is only right when the tip capacitor is trimmed to the scope’s input, which is what the compensation adjustment is: “always compensate probes right after connecting them to the oscilloscope and check compensation frequently.” Over- or under-compensated, the probe reports a wrong edge before any of the following applies.

Loading: the probe changes the circuit

Tek’s simplest example is resistive. A 100 V battery with 100 Ω inside, driving 100 kΩ, delivers 99.9 V; probe it with a 100 kΩ probe and the load halves, the output is 99.8 V, and “this loading effect … is only 0.1% and is negligible for most purposes”. With 10 MΩ it is negligible on nearly everything. “Usually, the loading of greatest concern is that caused by the capacitance at the probe tip”:

For low frequencies, this capacitance has a reactance that is very high, and there’s little or no effect. But, as frequency increases, the capacitive reactance decreases. The result is increased loading at high frequencies. This capacitive loading affects the bandwidth and rise time characteristics of the measurement system by reducing bandwidth and increasing rise time.

— Tektronix, ABCs of Probes

Against a node with source impedance R_s, 11 pF is an RC that slows the node’s own edge by about 2.2·R_s·C — 1.2 ns on a 50 Ω line, 24 ns on a 1 kΩ one. Keysight’s second hint is the bench test for it: “connect your probe tip to a point on your circuit and then connect your second probe to the same point. Ideally, you should see no change on your signal. If you see a change, it is caused by the probe loading.” Its example is a 600 ps edge: a 500 MHz passive probe with a 15 cm alligator lead loaded it to 740 ps and displayed 1.4 ns “with resonance”; a 2 GHz active probe with a 1.8 cm lead left it at 630 ps and read 555. Keysight’s conclusion is that above about 600 MHz “active probes are the way to go”, because of “their significantly lower capacitive loading”.

Ringing: the ground lead

The ground lead is the element nobody draws. Tek’s equivalent circuit puts it in series with the probe’s input, and its chapter on grounding explains what that does:

Also, notice that the ground lead L and C_in forms a series resonant circuit with only R_in for damping. When this series resonant circuit is hit with a pulse, it will ring. Not only will there be ringing, but excessive ground-lead L will limit the charging circuit to C_in and, thus, will limit the rise time of the pulse.

Without going into the mathematics, an 11 pF passive probe with 6-inch ground lead will ring at about 140 MHz when excited by a fast pulse. With a 100 MHz oscilloscope, this ringing is well above the bandwidth of the oscilloscope and may not be seen at all. But, with a faster oscilloscope, say 200 MHz, the ground lead induced ringing will be well within the oscilloscope’s bandwidth and will be apparent on the display of the pulse.

The mathematics Tek skips is 1/(2π√LC), and it gives the lead’s inductance from the example: 117 nH for six inches. The remedy is stated just as directly — “the effects of ringing can be reduced by designing probe grounding so that the ringing frequency occurs beyond the bandwidth limit of the probe/oscilloscope system” — and “to avoid grounding problems, always use the shortest ground lead provided with the probe.”

A 20 mm ground spring on the same 11 pF probe rings near 390 MHz, above a 350 MHz scope. That is the whole reason the spring exists, and the reason Tek’s figure 1.13 — the standard clip extended with “a 28-inch lead” — is a textbook ringing waveform, and its figure 1.12 shows that even a two-inch wire soldered to the test point “changed [the rise time] from 4.74 ns to 5.67 ns”.

Telling the probe’s ringing from the circuit’s

The overshoot on the screen might be real. Tek’s chapter 6 gives the test:

To distinguish between the two situations, move the probe cable around. If placing your hand over the probe or moving the cable causes a change in the aberrations, the aberrations are being caused by the probe grounding system. A correctly grounded (terminated) probe will be completely insensitive to cable positioning or touch.

Its example is a 1 ns step on a 350 MHz scope with a six-inch ground lead: aberrations on the edge that changed when a hand was placed over the cable, and that vanished entirely when the lead was replaced by a board-mounted probe-tip adapter. Both conditions have to hold for the ground lead to ring visibly — the scope must be fast enough to show the ring frequency, and the signal must have “enough high-frequency information (fast rise time) to cause the ringing” — which is why the same probe and lead are fine on a slow signal and wrong on a fast one.

Rise time: what the screen shows

Every probe and every scope has a rise time, “T_r = 0.35/BW” when only the bandwidth is given, and “when a probe is attached to an oscilloscope, you get a new set of system bandwidth and rise time limits”. For the display to be a measurement of the signal rather than of the instrument, Tek asks that “the rise time of the probe and oscilloscope together should be three to five times faster than that of the pulse being measured”. The reason is arithmetic: rise times combine roughly in quadrature, so a 1 ns edge on a system with a 1 ns rise time reads 1.4 ns, and on a 350 MHz scope with a 350 MHz probe — 1 ns each — 1.7 ns.

Tek adds a caution about the sum: “the relationship between system bandwidth and the individual oscilloscope and probe bandwidths is not a simple one”, which is why “manufacturers of quality oscilloscopes specify bandwidth or rise time to the probe tip when the oscilloscope is used with specific probe models”. The quadrature estimate is what the calculator uses; the specified system figure is better where it exists.

Where to clip it

The ground lead goes to the ground the signal is referenced to, as close to the probe tip as the board allows, through the shortest path the probe kit offers. In order of preference: a board-mounted probe-tip adapter or a test point with its own ground pin, which Tek’s chapter 6 shows removing the aberrations entirely; a ground spring on the probe barrel touching a ground pad within a couple of centimetres of the signal; and, last, the clip lead — to a ground within a few centimetres of the node, never to the chassis across the board, never extended. Keysight’s hint 8 is to “damp the resonance” when a short lead is not possible; Tek’s is to make the resonance faster than the scope can see.

One thing the ground lead must not do is carry the scope’s earth into a circuit that is not earth-referenced: Tek’s chapter 6 treats ground loops and floating measurements as their own subject, and the ripple-measurement article is the practical case, where the same clip lead that rings is also an antenna.

Worked numbers

The calculator’s defaults — Tek’s probe, Tek’s lead, a 200 MHz scope — on a 5 ns edge from 50 Ω:

probe             11 pF, 10 MΩ, 300 MHz      lead 152 mm (6 in)      scope 200 MHz
lead inductance   152 mm × 0.77 nH/mm                        = 117 nH
ring              1 / (2π √(117 nH × 11 pF))                 = 140 MHz
system rise       √(1.75 ns² + 1.17 ns²)                     = 2.1 ns  (166 MHz)   → ring visible
lead to hide it   84 nH → 108 mm;  a 20 mm spring rings at 390 MHz
loading           2.2 × 50 Ω × 11 pF = 1.2 ns added;  corner 289 MHz
displayed rise    √(5² + 1.75² + 1.17² + 1.2²) ns             = 5.5 ns  (+11 %)
Tek's ratio       5 ns / 2.1 ns                               = 2.4×    (wants 3–5)

Three errors, none of them the signal’s: ringing from the lead, a slow reading from the instrument, and a node that is slower with the probe on it than off. The spring fixes the first, a faster scope the second, and an active probe the third.