Measuring Shadows

Try measuring the height of a building using its shadow. The building’s shadow is, at best, a distorted, fuzzy, and somewhat inaccurate impression of the real article, sometimes missing completely. It may be long or short according to the angle of the sun and the tilt of the street upon which the shadow falls. The entire procedure is plagued by a host of imprecise effects.

Would a surveyor’s transit level (Figure 1) give a more accurate measurement? Possibly, but it’s still not perfect. The accuracy of a transit depends on the level set of the instrument, the alignment of its spotting scope with the frame, careful adjustment by the operator, and a reference distance established between the instrument and the base of the building. All said and done, the operator isn’t really measuring the height of the building; he is reading a number from a protractor bolted to the side of the unit that shows the approximate position of the scope, which points generally in the direction of the top of the building. Measurements always work that way; they never reveal the thing you wish to know, only the shadow of that thing.

A surveyor's transit level measures both horizontal and vertical angles.Consider the measurement of voltage. Take a conductive sphere the size of a basketball, suspend it on a silk thread, and charge the sphere with respect to the earth to a potential of more than 10,000V. Stick your arm into the space between the earth and the sphere, touching neither. You can feel the potential on your skin; it makes the hairs on your arm stand straight out. You needn’t touch the sphere to know it is highly charged.

Now hold your best scope probe in the same space. It will not respond. A scope probe does not respond to voltage potential. It responds to the flow of current in its first stage of amplification. No current, no response. Even a high-quality FET amplifier requires current to charge its gate capacitance. Because the air surrounding the sphere cannot supply much current, the probe fails to respond unless you touch the sphere, which instantly destroys the probe.

In electrical-engineering language, a good scope probe gives a meaningful response only when the input impedance of the probe vastly exceeds the impedance of the device under test (DUT). When that impedance condition is not met, as in the sphere example, the probe gives no warning; it simply reports the shadow it sees, which gives a wrong answer.

In a perfect world, you would know the input impedance of your probe and the impedance of the DUT—both as functions of frequency—and you would apply a frequency-dependent correction factor to your results. In the real world, that situation rarely occurs.

Here is a practical way to test the impedance condition. Obtain a second probe of the same type. With the first probe connected to the DUT, apply the second probe to the same spot on the DUT. If the second probe changes the measured waveform in any noticeable way, you may assume that the first probe probably induced at least as much of a change. Keep trying different probe styles until you find the one that changes the signal the least. Thereafter, mark that probe with a yellow tag that says, “Do not use; needs calibration.” That way, the good probe will still be in your lab the next time you need it.