Probing pointers -

Probing pointers

The wrong probe can cause your circuit to fail or even physically destroy components. Here are some of the issues.

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Back when the Earth was starting to cool and the first creatures were crawling from the slime, we were building a very fast system using plenty of discrete logic because the processors of those Paleozoic years couldn't keep up with our data rates. I was probing a pair of signals on a fabulously-expensive oscilloscope, but their relationship made no sense. Eventually I realized that one of the scope probe leads was a full meter longer than the other. This was the first, but certainly not the last, time I cursed light's snail-like pace. And it was the first time I was forced to think about scope probes, other than the routine of compensating them.

Eons later I still see engineers rooting around in a bin and untangling a random, often abused, probe, carelessly connecting it to the scope that they spent a week evaluating and comparing to a host of other products. But that $10k or $20k instrument (or more; I read a press release for a nifty $400k model this week) can be completely hobbled by a lousy or poorly-selected probe.

A scope probe is not a wire. Sure, it's an electrical connection between a node on a board and the oscilloscope. But its resistance, capacitance, and inductance have serious consequences as speeds increase.

Plenty of white papers talk about proper probe selection, but to my knowledge none show how the wrong probe can either cause your circuit to fail or even physically destroy components. Let's look at some of the issues.

For readers without an EE, here's a bit of background. There will be a little math, but fear not! Mostly this is as simple as Ohm's Law, which is:

E is voltage, I current, and R resistance. But there's really no such thing as a perfect resistor. Every component, be it a wire, resistor, or anything else has some amount of capacitance and inductance associated with it. So, while Ohm's Law holds true, as frequencies increase we need to include these effects in our thinking about resistance.

A capacitor passes AC but not DC, and the higher the frequency, or the larger the capacitance, the more easily it passes current. This is known as capacitive reactance, which is a form of resistance to alternating current. It's expressed as:

C is the capacitance in farads and f is the frequency in Hz. If f is zero–DC–the reactance is infinity and a perfect capacitor completely blocks current flow. As the signal gets faster, its reactance drops.

Inductors are similar:

In this case L is the inductance. So an inductor, too, has a resistive-like effect, although it is inverse of that of the capacitor.

If a circuit has inductance and capacitance, the total reactance is, well, it's thankfully not important to this discussion, but suffice it to say that one can compute a net reactance. Toss in pure resistance and the total impedance–which is merely resistance to waveforms–in a parallel circuit is:

Ohm's Law still holds, except we now replace R with Z . So it's possible to compute current flow in a complicated circuit at any given frequency if one knows the voltage and impedance.

Figure 1
Click on image to enlarge.

I said there's no such thing as a perfect resistor. A typical ¼ watt resistor has 0.5 pF of shunt capacitance. A wire-wound resistor is a coil and has inductance (although some have reverse windings to limit this). A normal film or carbon resistor has very little inductance.

A scope probe has capacitance, resistance and some inductance (mostly in that black ground wire), and looks something like Figure 1 .
A scope probe, because of its impedance, is rather like a resistor that gets placed in parallel with the node you're testing. The net impedance of two in parallel is:

Thus, placing a probe on a node reduces the impedance of that point. Whatever drives the node must, in effect, push harder or the signal will degrade.

But is this really a big deal? Scope probes are typically specified at 10 million ohms, which is an enormous value. Put that in parallel with a digital device, whose resistance is orders of magnitudes lower, and there will be no measurable effect.

But what's important is impedance, not resistance, and as noted earlier, impedance depends on frequency. If you're probing a digital circuit odds are that things are switching pretty quickly. The frequency may be quite high.

Figure 2
Click on image to enlarge.

That's where the second part of a probe's spec, the tip capacitance, comes in. This ranges from under a pF to 100 pF or more. And that has a huge effect on the probe's impedance. Tektronix is one of the few vendors that gives graphs of probe impedance. Their TPP1000, a 1-GHz passive probe, has the impedance vs. frequency curve in Figure 2 .

At 100 MHz the impedance appears to be around 500 ohms. The probe's capacitance is 4 pF; running the reactance numbers we get 400 ohms at that frequency, pretty darn close. At low frequencies the reactance gets very large so the 10-MΩ resistor dominates.

This is a $900 probe. Cheap probes may be considerably worse. The capacitance of Pomona's $117 5812A, rated for 300 MHz, is listed as “<17 pF." Let's assume 17. That's 93 ohms at 100 MHz. In a 5-volt circuit, the probe will add a 54-ma load. Surfing the net one finds lots of cheapies at 100 pF or worse, which nets a terrifying 20 ohms at 100 MHz. To put that into perspective, in a 2-volt circuit it would take 100 ma to drive the probe alone, and few gates can do that. Even at 10 MHz we're talking 10 ma. 74HCT gates, for instance, are generally rated at 4 ma. Other parts, notably processors, may be capable of driving less current. TI's OMAP35xx parts are spec'd at 2 ma on most pins. In other words, connect one of these puppies to your board and the circuit may very well stop working. I think some of those homeless people I see in Baltimore are engineers who cracked when they found their troubleshooting tools made troubleshooting impossible. The important take-away is this: when buying a probe don't be seduced by the 10-MΩ rating. Think impedance, which is related to tip capacitance. (A side note for those working with analog. Generally analog signals aren't as fast as digital so the probe-loading issues may be less severe. On the other hand, many analog nodes have a much higher impedance than digital. Even at DC putting a 10-MΩ probe across a 10-MΩ node will zap half the signal). Better probes exist. Tek's 4 GHz P7240 has a tip capacitance of only 0.85 pF. Running the numbers we get 2 KΩ at 100 MHz, which exactly matches the chart in the device's manual. But this is an active probe, one loaded with electronics, and it'll set you back $5,000. Which explains the sign held aloft by one gaunt street person last week: “Please help. Will work for a pair of P7240s.” Logic analyzer probes also exhibit capacitive characteristics. Agilent, for instance, sells sets that range from 0.7 pF to 3 pF per tip. The probe sets for their MSOs run 8 to 12 pF. Cheapies advertised on the Internet have higher capacitances, and an astonishing number don't have a rating at all. Never connect a logic analyzer to a circuit unless you've thought through the probe impedance issues.
Fourier fits
But it gets worse.

Joseph Fourier

In 1822, Joseph Fourier released his Théorie analytique de la chaleur (The Analytic Theory of heat ) . That seminal work has tormented generations of electrical engineering students (and no doubt others). Discontinuous functions–like square waves–are very resistant to mathematical analysis with calculus unless one does horrible things like use unit step functions. But Fourier showed that one can represent many of these periodic functions as the sum of sine waves of different amplitudes and frequencies. The Fourier Series for a square wave is:

The series goes on forever, so all square waves have frequency components going to infinity. However, the amplitude of these decrease rapidly due to the division by an ever-larger odd number. The point, though, is that the “frequency” of a square wave is composed of many frequencies higher than that of the baseband.

Pulses, like the ones that race around every digital board, the ones we probe with our scopes and logic analyzers, are square-wave-ish. The good news is that they're not perfect square waves: obviously, with the exception of clocks, they rarely have a 50% duty cycle. Pulses are also, happily, imperfect. Fourier's analysis assumed that the signal transitions between zero and one instantaneously. In the real world every pulse has a finite rise and fall time. If Tr is the rise time, then the frequency components above F in the following formula will be so far down they're not important:

This does mean that, assuming a 1-nsec rise time, even if your clock is ticking along at a leisurely rate about the same as a Florida old-timer's speedometer, the signals have significant frequencies up to 500 MHz.

Those unseen but very real frequency components will interact with the scope probe.

Ad hoc formulas
Long troubleshooting sessions often see a board covered with connections to test equipment, data loggers, etc. Long lengths of wire-wrap wire get soldered between a node and an instrument. These connections all change the AC properties of the nodes by adding inductance and capacitance. Here are some useful formulas with which one can estimate the effects. These are derived from book High-Speed Digital Design (Howard Johnson and Martin Graham, 1993 PTR Prentice-Hall Inc, Englewood Cliffs, NJ), and there's much more useful data in that book.

Most of us use multilayer PCBs that have one or more ground and power planes. Solder a wire to a node and drape it across the board as it runs to a scope or other instrument, and you'll add capacitance. If d is the diameter of the wire in inches, h is the height above the PCB, and l is the length of the wire, then the capacitance in pF is:

(A better solution is to run the wire straight up from the node, perpendicular to the PCB.)

AWG 30 wire-wrap wire is 0.0124 inches in diameter. Typical hook-up wires are AWG 20 (0.036 inches), AWG 22 (0.028 inches), and AWG 24 (0.022 inches).

The inductance of the same wire in nanohenries is:

The inductance of a round loop of wire (for example a scope probe's ground lead) in nH is, if d is the diameter of the wire and x is the diameter of the loop:
Next month we'll look at some real-world data.

Jack Ganssle () is a lecturer and consultant specializing in embedded systems development. He has been a columnist with Embedded Systems Design and for over 20 years. For more information on Jack, click here.

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This material was first printed in March 2012 Embedded Systems Design magazine.
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