Analog measuring instruments
How a current becomes the movement of a pointer, and how this one mechanism is used to build an ammeter, a voltmeter and an ohmmeter. Understanding the instrument from the inside is what lets you know when it is lying.
01Why study them when everything is digital today
Digital multimeters are more accurate, cheaper, and do not break if you connect them backwards. And yet the analog instrument remains in the curricula and in the workshop, for four specific reasons:
- The pointer shows trends. To adjust a trimmer to its maximum or minimum, or to see whether a voltage is fluctuating, a pointer beats a number that jumps around.
- The panel of industrial equipment is still analog: moving-iron ammeters and voltmeters in electrical switchboards, VU meters, process indicators.
- The concept of sensitivity and loading of an instrument is only truly understood once you see why an analog instrument disturbs the circuit.
- It is the basis of every pointer transducer: the moving-coil mechanism is the same one found in a speaker and in the motor of a hard drive.
02The moving-coil galvanometer
Also called the D'Arsonval movement. It is the heart of every analog direct-current instrument.
It works through three effects:
- Driving torque. The current flowing through the coil, immersed in the magnet's field, produces a force (Laplace's law, F = B·I·L) that tends to make it rotate. This torque is proportional to the current.
- Restoring torque. Two spiral springs oppose the rotation with a torque proportional to the angle. The pointer stops where the two are equal, that is, at an angle proportional to I. That is why the scale is linear. The springs also serve a second purpose: carrying the current to the coil.
- Damping. Without it the pointer would oscillate around the final value. It is provided by the coil's own aluminum frame: as it moves through the field, eddy currents are induced in it that brake the motion. The ideal setting is critical damping: the pointer arrives quickly and without bouncing.
Two figures, and everything else is calculated from them:
- Ifsd (full scale deflection): the current that drives the pointer to full scale. Typical values: 50 µA, 100 µA, 1 mA.
- Rm: winding resistance. Typically 1 kΩ to 2 kΩ in 50 µA movements.
Sensitivity
Sensitivity is the most important specification of an analog instrument. The resistance a voltmeter presents on a given range is S × (full-scale value): a 20,000 Ω/V instrument on the 10 V range presents 200 kΩ, and on the 2.5 V range only 50 kΩ. In other words, the load it introduces changes with the selected range, something that does not happen in a digital multimeter (always 10 MΩ).
Accuracy class
Analog instruments are classified by their class: 0.5 · 1 · 1.5 · 2.5. The number is the maximum error expressed as a percentage of full scale, not of the reading.
A class 1.5 instrument with a 100 V full scale has an error of ± 1.5 V at any point on the scale. If you measure 10 V, the relative error is 15 %. That is why you should always choose the range in which the pointer ends up past the midpoint: measuring 10 V on the 100 V range is almost useless.
03From galvanometer to ammeter: the shunt
A 50 µA galvanometer burns out with any real current. To measure amperes, a very small resistor, the shunt, is placed in parallel with it, diverting almost all of the current.
A galvanometer with Im = 50 µA and Rm = 2 kΩ. You want a 1 A ammeter at full scale.
- Voltage across the galvanometer at full scale: 50 µA × 2000 Ω = 0.1 V.
- Current the shunt must divert: 1 A − 0.00005 A = 0.99995 A.
- Rsh = 0.1 / 0.99995 = 0.1 Ω.
Note two things: the shunt has an extremely low value (it is made from a piece of calibrated wire or from manganin) and the total drop across the ammeter is only 0.1 V, which is why it hardly disturbs the circuit. This value is called the burden voltage and appears in multimeter datasheets.
In a multi-range ammeter, the shunt must never be opened while the instrument is connected: all of the current would flow through the coil and burn it out instantly. That is why multirange instruments use the Ayrton shunt, in which the selector switch distributes a chain of resistors without ever leaving the galvanometer on its own.
04From galvanometer to voltmeter: the multiplier resistor
To measure voltage, a large resistor is placed in series with the galvanometer, so that the voltage to be measured produces exactly Ifsd.
Same galvanometer (50 µA, 2 kΩ, S = 20,000 Ω/V):
| Range | R total = S × V | Rs = R total − Rm |
|---|---|---|
| 10 V | 200 kΩ | 198 kΩ |
| 50 V | 1 MΩ | 998 kΩ |
| 250 V | 5 MΩ | 4.998 MΩ |
With a 1 mA galvanometer (S = 1000 Ω/V), the 10 V range would present barely 10 kΩ. Measuring with that instrument the base of a transistor biased with 47 kΩ resistors would completely ruin the measurement.
05The ohmmeter
It is the only one of the three that needs its own source: an internal battery. It measures indirectly, by injecting current and observing the deflection.
- With the probes shorted: I is at its maximum, the pointer goes to full scale → 0 Ω on the right.
- With the probes open: I = 0, the pointer does not move → ∞ on the left.
- The midpoint of the scale corresponds to Rx = Rint, and it is where the reading is most accurate. So it pays to choose the range (× 1, × 10, × 100, × 1 k) that leaves the pointer near the center.
Before each measurement, and every time you change range, you must touch the probes together and turn the “zero adjust” trimmer until the pointer reads exactly 0 Ω. This compensates for battery wear. If it does not reach zero with a new battery, the instrument has a fault; if the pointer never moves, the battery is dead.
06Moving-iron and electrodynamic instruments
The moving coil works only for direct current: with alternating current, the torque reverses direction 50 times per second and the pointer does not move (or just vibrates). Measuring AC directly requires other mechanisms.
| Mechanism | Principle | Works on | Scale | Typical use |
|---|---|---|---|---|
| Moving coil | Coil in the field of a permanent magnet | DC | Linear | Analog multimeters, VU meters |
| Moving iron | Two pieces of iron inside a fixed coil repel each other, magnetized with the same sign | DC and AC | Square-law (cramped at the start) | Electrical switchboards. Measures true RMS value |
| Electrodynamic | One fixed coil and one moving coil; the torque depends on the product of the two currents | DC and AC | Square-law or linear depending on use | Wattmeter: measures real power, including the power factor |
| Thermal | A wire expands as it heats from the Joule effect | DC and AC | Square-law | Radio frequency, RMS value at any frequency |
Because the two pieces of iron are magnetized always with the same polarity, regardless of the direction of the current: they always repel. The torque turns out proportional to I2, and since the average of I2 is what defines the RMS value, the instrument directly indicates the true RMS value, even if the waveform is distorted. That is what a cheap digital multimeter does not do: those that do not say “True RMS” assume the wave is a sine wave and calculate the RMS value from the average value.
How a moving-coil instrument measures AC
With a rectifier in front. But then what the pointer responds to is the average value of the rectified wave, not the RMS value. Since the scale is calibrated in RMS for a sine wave, the form factor is applied:
07Analog versus digital
- Shows trends: ideal for adjusting a maximum or a minimum.
- Needs no battery to measure voltage and current.
- Limited sensitivity: it loads the circuit, and differently on each range.
- Error referred to full scale: poor in the first third.
- Damaged by reversed polarity or overload.
- You have to read by interpolating between marks, with a risk of parallax error.
- High and constant input impedance (10 MΩ).
- Error referred to the reading: good across the whole range.
- Unambiguous reading, with automatic polarity.
- Many extra functions: capacitance, frequency, diode test, hFE, temperature.
- The digits “dance” if the signal is noisy: trends are hard to see.
- Needs a battery for everything.
In the workshop the sensible thing is to have both, and know which to use: the digital for values, the analog for adjustments.
08In the lab
Using a 1.5 V battery, a 100 kΩ trimmer in series (starting at maximum) and a reference microammeter: reduce the trimmer until you reach full scale and note the current. For Rm, place a resistance decade box in parallel with the galvanometer and adjust it until the pointer falls to half scale: at that point the decade box equals exactly Rm.
With the galvanometer characterized, calculate the multiplier resistor for a 10 V range and build it from series resistors (combining E12 values until you get close). Compare the instrument against a digital multimeter at several points: 2, 5, 8 and 10 V. Calculate the relative error at each point and check that it grows toward the start of the scale.
Build a divider with two 470 kΩ resistors powered from 10 V (theoretical voltage at the midpoint: 5 V). Measure with the analog instrument you built and with the digital multimeter. The difference between the two readings is the loading effect, and it can be calculated in advance. Repeat with 4.7 kΩ resistors: now the two readings agree.
(a) Check the ohmmeter's zero adjustment on each range and measure five known resistors,
noting where on the scale the pointer falls and the resulting error.
(b) If a function generator is available: measure with an analog multimeter (or a digital one without True RMS) a
sine wave and a square wave of the same amplitude. The sine wave reads correctly; the square wave
gives an error of about 11 %, which is exactly the form factor.
09Common mistakes
| Symptom | Usual cause |
|---|---|
| The pointer pegs against the left stop | Reversed polarity. The pointer can bend: disconnect immediately. |
| The pointer pegs against the right stop | Range too low. Always start with the highest. |
| The reading changes depending on who reads it | Parallax error. Good instruments have a mirror on the scale: you read when the pointer hides its own reflection. |
| When measuring voltage, the circuit stops working | Loading effect: the instrument has too little sensitivity for that high-impedance circuit. |
| The ohmmeter does not reach zero with the probes together | Dead battery, or the zero adjustment for that range is needed. |
| Measuring 12 V reads 11 V on the 250 V range | Class error referred to full scale. On a 250 V range of class 1.5 the error is ± 3.75 V. |
| The pointer oscillates and does not settle | Damping fault (damaged aluminum frame), or the measured signal really is varying. |
10Self-assessment
Why is the scale of a moving-coil instrument linear?
Because the driving torque is proportional to the current and the restoring torque of the spring is proportional to the angle. When they balance, the angle turns out proportional to the current. The soft-iron core keeps the field radial, which is the condition for this to hold over the whole travel.
A galvanometer of 100 µA and 1 kΩ. What shunt is needed to measure 500 mA?
Voltage at full scale: 100 µA × 1000 Ω = 0.1 V.
Current through the shunt: 500 mA − 0.1 mA = 499.9 mA.
Rsh = 0.1 / 0.4999 = 0.2 Ω.
What is the sensitivity of that same galvanometer, and what resistance does it present on the 20 V range?
S = 1/100 µA = 10,000 Ω/V. On the 20 V range it presents 10,000 × 20 = 200 kΩ.
Why is the ohmmeter zero on the right side of the scale?
Because with the probes shorted (0 Ω) the maximum current flows and the pointer reaches full scale. The higher the resistance, the lower the current and the smaller the deflection: the scale ends up inverted and is also non-linear.
A class 2.5 instrument with a 300 V full scale. What is the error when measuring 30 V?
Absolute error: 2.5 % of 300 V = ± 7.5 V. On a 30 V reading that is a relative error of 25 %. You need to switch to a lower range.
Why does a moving-iron instrument work on AC and a moving-coil one does not?
Because in the moving-iron instrument the two pieces are always magnetized with the same polarity and repel each other regardless of the direction of the current: the torque does not reverse. In the moving coil, the torque changes direction with the current and its average on AC is zero.
What does a moving-coil instrument with a rectifier measure if the signal is not sinusoidal?
It responds to the average value of the rectified wave, but its scale is calibrated assuming a sine wave (form factor 1.11). With a square or clipped wave the reading has a gross error. Only a True RMS instrument (or a moving-iron or thermal one) measures the true RMS value.
What is parallax error and how is it avoided?
It is the error of reading the pointer from a side angle: the tip seems to fall on a different mark. It is avoided by looking perpendicularly, and in class instruments the scale mirror is used: the correct reading is when the pointer exactly hides its reflection.
Why does a wattmeter need an electrodynamic mechanism, instead of simply multiplying V by I?
Because in AC the real power depends on the phase shift between voltage and current: P = V·I·cos φ. The electrodynamic movement has one coil carrying the current and another the voltage, and its torque is proportional to the instantaneous product of the two, so the average gives the real active power, including the power factor.