About Instrumentation Engineering
Instrumentation questions are about measuring well: the chain from sensor to display, the resistance of a resistance thermometer, the emf of a thermocouple, the current on a 4 to 20 mA loop, an error quoted against the span, the flow through an orifice plate, the level read from a pressure, and the smallest change a converter can resolve. This topic covers all of those on one page, so that the subject can be practised as a whole rather than in fragments.
What you need to understand
- A measurement chain runs from sensor to signal conditioning to conversion to display, and every stage adds its own error. The chain is as good as its worst link, not its best.
- Accuracy is how close a reading is to the true value; precision is how close repeated readings are to each other. A precise instrument can be consistently wrong, which is why calibration matters.
- An error is normally quoted as a percentage of the span rather than of the reading, because the span is what the instrument was bought to cover. An error of one per cent of span is the same number of units wherever in the range it occurs.
- Span is the upper range value less the lower, and zero is where the lower value sits. Changing the zero moves the whole range; changing the span stretches it.
- A 4 to 20 mA loop carries the reading as a current, which is immune to the resistance of the cable. The four milliamps at the bottom are a live zero: zero current means a broken loop, not a low reading.
- A resistance thermometer follows R = R0 (1 + alpha T). A Pt100 is 100 ohms at zero degrees Celsius, and about 138.5 ohms at a hundred degrees.
- A thermocouple produces a small emf proportional to the difference in temperature between its two junctions. The cold junction has to be compensated, because the emf depends on the difference and not on the hot junction alone.
- An orifice plate produces a differential pressure that goes as the square of the flow, so the flow goes as the square root of the differential. A square root extractor turns that back into a linear reading.
- The pressure at the bottom of a column of liquid is the density times g times the height. It does not depend on the shape of the vessel or on how wide it is, which is exactly why it can be used to read level.
- A converter of n bits divides its range into two to the n levels, so the smallest change it can resolve is the range divided by that. Each extra bit halves the step.
- Absolute pressure is measured from a vacuum and gauge pressure from the atmosphere, so absolute is the gauge reading plus the barometer. Vacuum gauges work the other way and their readings are subtracted.
- Calibration checks the instrument at several points across the range, up scale and down scale, so that hysteresis shows up as a difference between the two. A single point check proves nothing.
- Dead band is the smallest change that produces a movement of the output at all, and it is why an instrument can appear stuck when it is merely inside its band.
- The response time of a sensor is how long it takes to reach about 63 per cent of a step change, in the same way as a time constant. Damping smooths a noisy reading at the cost of making the response slower.
How to work through these questions
- Write down the range, the span and the value before doing anything, and check that the value lies inside the range. A reading outside it is a sign the numbers have been read the wrong way round.
- For a 4 to 20 mA question, work out the fraction of span first, then apply four plus sixteen times it. Doing it in that order keeps the live zero in the right place.
- For an error, decide first whether the question wants the error in units or as a percentage, and then whether against the span or against the reading. A question says which, and the two answers differ.
- For anything with a square root law, ask whether the quantity given is the differential or the flow, and which one is being asked for. The square and the square root are easy to apply the wrong way round.
- For a level from a pressure, remember that only the height matters. If the tank tapers, the volume is not proportional to the pressure, but the level is.
- Check the size of every answer. A loop current outside 4 to 20 mA, a resolution coarser than a tenth of the range, or an error above a few per cent of span all point to a slip.
Mistakes that cost marks
- Multiplying the temperature coefficient by the temperature and forgetting the one in R0 (1 + alpha T), which gives a resistance a hundred times too small.
- Dividing the emf of a thermocouple by the sensitivity instead of multiplying, or leaving the answer in microvolts when millivolts were asked for.
- Leaving the four milliamps out of a 4 to 20 mA calculation and reporting sixteen times the fraction of span.
- Quoting an error against the reading when the question asked for it against the span, which flatters the instrument near the top of its range.
- Treating the flow through an orifice plate as a straight proportion of the differential pressure.
- Forgetting to divide by a thousand when a pressure in pascals is wanted in kilopascals, or the other way round.
- Dividing a converter range by the number of bits rather than by two to the power of the bit count, which understates the resolution badly.
- Subtracting the barometer reading from a gauge when the gauge was reading above the atmosphere, or adding it when the question was about a vacuum.
Worked example
A transmitter is calibrated from 0 to 200 cubic metres per hour and sends 4 to 20 mA. What current does it send at 50 cubic metres per hour? A 12 bit converter has a range of 0 to 10 V: what is the smallest change it can resolve?
- For the loop, the span is 200 and the measurement of 50 sits a quarter of the way up it: 50 / 200 = 0.25.
- The output is four milliamps at the bottom plus sixteen milliamps of travel: 4 + 16 x 0.25 = 8 mA.
- Check it against the sense of the loop: a quarter of the range should be a quarter of the way from four to twenty, and 8 mA is exactly halfway between four and twenty, which is a quarter of the travel. The live zero is what makes that so.
- For the converter, 12 bits give 2 to the 12 levels, which is 4096.
- The resolution is the range divided by the number of levels: 10000 mV / 4096 = 2.44 mV. A 10 bit converter over the same range would resolve 9.77 mV, so the two extra bits buy a fourfold improvement - each bit halves the step.
Answer: 8 mA on the loop; 2.44 mV for the converter
Practice questions with answers
A few Instrumentation Engineering questions with the full solution shown, so you can see
how the method is applied before you attempt the timed set.
Question 1
A platinum resistance thermometer has a resistance of 1000 ohms at zero degrees Celsius and a temperature coefficient of 0.00385 per degree. At 160 degrees Celsius, what is its resistance, in ohms?
-
A
384
-
B
1616
-
C
618.81
-
D
616
Answer: Option B — with explanation
A metal resistance thermometer works because its resistance rises with temperature, and over the range a sensor is used the rise is very nearly a straight line: R = R0 (1 + alpha T), where R0 is the resistance at zero degrees and alpha is the temperature coefficient.
The bracket is 1 + 0.00385 x 160 = 1.6160, so the resistance is 1000 x 1.6160 = 1616 ohms.
It is the coefficient times the temperature that is small, not the resistance: multiplying the two together and forgetting the one is the usual slip, and it gives a resistance a hundred times too small.
Common mistakes
- 616 is not the answer: 616
- 384 is not the answer: 384
- 618.81 is not the answer: 618.81
Question 2
A thermocouple has a sensitivity of 50 microvolts per degree Celsius. Its measuring junction is 200 degrees Celsius hotter than its reference junction. What emf does it produce, in millivolts?
Answer: Option C — with explanation
A thermocouple produces a voltage in proportion to the difference in temperature between its two junctions, and the constant of that proportion is the sensitivity of the pair of metals.
The emf is the sensitivity times the difference: 50 x 200 = 10000 microvolts, which is 10 millivolts.
The division by a thousand is the whole of the second step. Leaving the answer in microvolts, or dividing the temperature by the sensitivity instead of multiplying, is what the other answers are built on.
Common mistakes
- 0.25 is not the answer: 0.25
- 10000 is not the answer: 10000
- 4 is not the answer: 4
Question 3
A transmitter is calibrated from 100 to 2100, and its output is 4 mA at 100 and 20 mA at 2100. What current does it send, in milliamps, when the measurement is 700?
-
A
15.20
-
B
4.80
-
C
6
-
D
8.80
Answer: Option D — with explanation
A 4 to 20 mA transmitter uses the current itself to carry the reading, and the four milliamps at the bottom are the live zero: they tell the receiver that the loop is working even when the measurement is at the bottom of its range.
The measurement of 700 sits 600 above the lower range value in a span of 2000, which is 3/10 of the range.
The output is 4 + 16 x 3/10 = 8.80 mA. Taking the sixteen milliamps of travel and forgetting the four at the bottom is the usual slip, and it gives a current that is too low by exactly four.
Common mistakes
- 4.80 is not the answer: 4.80
- 6 is not the answer: 6
- 15.20 is not the answer: 15.20
Question 4
The span of an instrument is 50. Checked at 100 it reads 110. What is the error as a percentage of the span?
Answer: Option A — with explanation
An instrument is judged against its span, not against the reading, because the span is what it was bought to cover. The error is therefore the difference between the reading and the true value, divided by the span.
The difference here is 110 - 100 = 10, and the span is 50, so the error is 10 / 50 x 100 = 20 per cent.
Dividing by the reading instead of the span gives a larger figure that flatters or damns the instrument depending on where in its range the check was made, and it is the mistake the other answers are built on.
Common mistakes
- 220 is not the answer: 220
- 500 is not the answer: 500
- 10 is not the answer: 10
Question 5
A flow of 72 cubic metres per hour through an orifice plate gives a differential of 100 kPa. What flow, in cubic metres per hour, gives a differential of 900 kPa?
Answer: Option D — with explanation
The flow through an orifice plate goes as the square root of the differential pressure across it, because the differential is what the plate turns into kinetic energy and that energy goes as the square of the velocity.
The differential has gone from 100 kPa to 900 kPa, a factor of 9, so the flow changes by the square root of that, which is 3.
The new flow is 72 x 3 = 216 cubic metres per hour. Treating the flow as a straight proportion of the differential is the usual error, and it overstates the flow whenever the differential rises.
Common mistakes
- 648 is not the answer: 648
- 24 is not the answer: 24
- 72 is not the answer: 72
Frequently asked questions
Why is the loop current used rather than a voltage?
Because a current is the same all the way round the loop, whatever the resistance of the cable and the connections, while a voltage is divided by them. A current signal can be sent hundreds of metres and still arrive unchanged.
What is the live zero and why four milliamps?
The four milliamps at the bottom of the range mean that a genuine zero reading still carries a current, so a broken wire, which carries none, can be told apart from a true zero. That is why the range starts at four rather than at nought.
Why quote an error against the span rather than the reading?
Because the span is fixed and the reading is not. An instrument quoted against its span has a bounded error wherever it is used, while an error against the reading grows as the reading falls, which makes comparisons between instruments meaningless.
Why does the level of a tank not depend on its shape?
Because the pressure at the bottom comes from the weight of the column above the tapping, and a wider tank simply has more water spread over a larger area. The two effects cancel exactly, so only the height matters.
How many bits do I need for a given resolution?
Divide the range by the resolution you want, and find the power of two that covers it. A range of 10 V wanting 1 mV needs ten thousand steps, and 14 bits give 16384, so 14 bits will do it.
Why does a thermocouple need cold junction compensation?
Because the emf depends on the difference between the two junctions, not on the measuring junction alone. If the reference junction warms up with the cabinet, the reading drifts, so the instrument measures the terminal temperature and corrects for it.
