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How can we make accurate dc measurements with long sensor leads?

Q: How can we make accurate dc measurements with long sensor leads? Experts from our sister publication, Control Engineering magazine from the US, answer this question.

A: We generally prefer to make voltage measurements rather than current measurements because, when set up properly, voltage measurements are safer for the equipment being measured. They are safer in the sense that they disturb the measured equipment less than current measurements do. This is particularly true when the meter is physically far away from the measurement point, forcing you to use long test leads.

How far “long” is can be judged by looking at test leads designed for use with hand held DMMs. They run from about 3 ft (1 m) to 6 ft (2 m) in length, with 6 ft being the most common. Experience has shown that test leads less than 3 ft long unnecessarily constrain technicians’ activities. They are used only in special semi-permanent and permanent installations, where application characteristics make it worthwhile to make up special test fixturing.

Test leads 6 ft long are the most popular because they are a good compromise between the annoyance of constrained activities, and that of tripping over tangled test leads. It’s no coincidence that 6 ft is approximately the maximum distance most adult humans can span with outstretched arms. (Imagine the test leads one of Robert Heinlein’s 12-foot-tall Red Planet martians would insist on!)

Experience has also shown that 6 ft leads seldom cause electrical problems at audio and sub-audio frequencies. This fact should tell you something about how long “far” is. If the distance from your sensor to your meter can be spanned by standard test leads, you need not worry about their measurement effects. If not, you should be concerned.

Advice for working with long test leads

The things to think about when making measurements with long test leads are:

– Lead resistance — which affects all frequencies from dc on up;

– Transmission line effects — which include lead inductance, which starts showing up at high audio frequencies; and

– Electromagnetic interference (EMI) — which jumps out at you starting in the extremely low frequency (ELF) band below 30 Hz.

For this tutorial, I’m going to concentrate on lead resistance, as it’s most pertinent to dc measurements, and the others could fill up blog entries of their own.

The basic dc measurement circuit consists of an excitation power source (imagined as an ideal voltage source) and three resistances: sensor output resistance, transmission line (test lead) resistance, and meter resistance. The only thing electrically connecting these elements is the circulating current. When you make a measurement, what you are really measuring is the voltage drop across the meter resistance due to the circulating current. When planning a dc measurement, the first question to ask is, “What controls the circulating current?”

Voltage sources have a low resistance, with an “ideal” source defined as one with zero resistance. A thermocouple, for example, has a Thevenin equivalent circuit comprising the excitation source and sensor resistance, with the source producing a voltage in the millivolt range that is proportional to the hot/cold junction temperature difference, and a resistance well below an ohm. It is the excitation source, therefore, that controls the circulating current.

A thermister, on the other hand, requires an outside excitation source, with the transducer element being the sensor resistance on the order of a hundred ohms. It’s Thevenin equivalent still comprises the excitation source and sensor resistance. Their roles, however, differ. The sensor resistance now controls the circulating current.

Typical test leads are made of #22 copper wire, which has a resistance of 0.019 ohms/ft. Test leads using 2 #22 wires, 6 ft long thus have a total resistance of 0.228 ohms. That’s tiny compared to the thermister’s resistance, but significant compared to the thermocouple’s resistance. Lead resistance, however, can make a big difference (approximately 2%) to the thermocouple measurement if the transmission line distance to the sensor grows to, say, 60 ft. (The transmission line distance is the distance the signal must travel along the lead-wire pair as routed to the meter.)

By the way, you should recognize that contact resistances at connectors typically run on the order of 1 ohm as well. I’m ignoring them here because they are independent of lead length.

Now, let’s look at the meter resistance. The rule of thumb is to always use a high impedance meter for voltage measurements and a low impedance meter for current measurements. This translates into having a meter resistance at the opposite end of the scale from your source resistance. Whether making current or voltage measurements, you always want the lead (transmission line) resistance to be relatively tiny. But, tiny relative to what? It should be tiny relative to the largest resistance among the other components.

For the voltage measurement, we want a high meter impedance. In fact, the higher the better. DMMs have input impedances at least on the order of 100 k ohms, and oscilloscope resistances run a couple of orders of magnitude higher. Using such instruments, lead resistance for even very long leads (hundreds of meters) disappears.

If you try to use a high-impedance meter for a thermocouple measurement, however, the meter resistance controls the circulating current. The meter will read the excitation voltage no matter what the temperature is. You have to treat the thermocouple measurement as a current measurement, even though the sensor resistance is only around 100 ohms! That means using a very low resistance meter, and paying close attention to lead resistance.

That explains why we prefer to use voltage measurements for all long-range applications. Properly set up, lead length largely becomes irrelevant. So if, for example, you want to measure the current through a dc motor from a separate control room, you need to find a way to change it from a current measurement to a voltage measurement.

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