OE-5.2 Theory of Measurements & Measurement Hardware

What this is and why it exists

Accuracy and precision are not synonyms, and that difference is this whole unit in miniature.

A precise instrument that is consistently wrong is worse than an imprecise honest one. The first gives tight, repeatable, confidently wrong readings and no reason to doubt them. The second at least shows you its uncertainty.

The Wheatstone bridge survives in modern instrumentation for one reason worth understanding: it measures a small change against a reference, rather than an absolute value.

The vocabulary

• Accuracy — how close a reading is to the true value.
• Precision — how close repeated readings are to each other.
• Resolution — the smallest change the instrument can show.
• Range — the span it can measure at all.
• Linearity — how well output follows input in a straight line.
• Repeatability — whether the same input gives the same reading later.
• Scale factor — how much output you get per unit of input.
• Bridge — a circuit comparing two ratios, balanced when they match.
• Null measurement — measuring by adjusting until a difference reads zero.

The mental model

Start with the four words people use interchangeably and should not. Accuracy is closeness to truth. Precision is closeness of repeated readings to each other. Resolution is the smallest step the display can show. It can be far finer than the accuracy, which is how an instrument shows five digits of which two are meaningless. Repeatability is whether it still agrees with itself tomorrow.

A reading is only as good as the worst of those, and a specification quoting only the flattering one is telling you something by omission.

Linearity and scale factor describe the relationship between what went in and what came out. A sensor that is linear over a range and curves outside it is entirely usable, provided you know where the range ends. Most measurement mistakes of this kind are made by using a device outside the span its linearity was quoted over.

Then bridges, and the idea worth extracting. A bridge is two ratios compared. When they match, the difference reads zero. To measure, you adjust until it does — a null measurement. This persists because reading a zero accurately is much simpler than reading a large value accurately. Your detector only has to be sensitive near zero, and it does not have to be calibrated at all.

That is also why a bridge suits small changes. A strain gauge changes resistance by a tiny fraction. Measuring that fraction directly demands an extraordinary instrument. Detecting the imbalance it creates in a bridge does not.

Variable-voltage and frequency-based measurements are the other two families. Frequency has a practical advantage worth knowing. It survives a noisy or long cable far better than a small voltage does, because noise changes amplitude more readily than rate.

What you should now be able to explain or do

Define accuracy, precision, resolution, linearity and repeatability, and say why quoting one flatters an instrument. Explain how resolution can be finer than accuracy and what that display is really telling you. State the range over which a linearity figure applies. Explain a bridge as a comparison of ratios and a null measurement, and say why zero is the simplest thing to read. Say why a bridge suits small changes. Say why a frequency output survives a long cable.

Check yourself