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About Meters.
By Brian, MW0GKX.

In this article I'll discuss meters. I'm not going to mention electrostatic meters, or oscilloscopes, just the analogue and digital type of meters that are in common use and readily available, some quite cheaply, in most electronics (and other) retailers.

What is a meter?

A meter is any device built to accurately detect and display an electrical quantity in a form readable by a human being. Usually this "readable form" is visual: motion of a pointer on a scale, a series of lights arranged to form a bargraph, or some sort of display composed of numerical figures. In the analysis and testing of circuits, there are meters designed to accurately measure the basic quantities of voltage, current, and resistance. There are many other types of meters as well, but this article primarily covers the design and operation of these basic three.

Most modern meters are digital in design, meaning that their readable display is in the form of numerical digits. Older designs of meters are mechanical in nature, using some kind of pointer device to show quantity of measurement. In either case, the principles applied in adapting a display unit to the measurement of (relatively) large quantities of voltage, current, or resistance are the same.

The display mechanism of a meter is often referred to as the movement, borrowing from its mechanical nature to move a pointer along a scale, so that a measured value may be read. Though modern digital meters have no moving parts, the term "movement" may be applied to the same basic device performing the display function. The design of meter movements is beyond the scope of this article.

Meter movements.

general layout of an analogue, permanent-magnet meter movement

Until recently meter design usually used what is known as a permanent-magnet, moving coil, or PMMC movement, shown on the right.

In the picture the meter movement "needle" is shown pointing somewhere around 35 percent of full-scale, zero being full to the left and full-scale being completely to the right. An increase in measured current will drive the needle to point further to the right and a decrease will cause the needle to drop back down toward its resting point on the left. The arc on the meter display is labeled with numbers to indicate the value of the quantity being measured, whatever that quantity is. In other words, if it takes 50 microamps of current to drive the needle fully to the right (making this a "50μA full-scale movement"), the scale would have 0μA written at the very left end and 50μA at the very right, 25μA being marked in the middle of the scale. Usually the scale would be divided into much smaller graduations, probably every 5 or 1μA, with small, vertical (in relation to the arc baseline) lines, to allow whoever is viewing the movement to get a more precise reading from the needle's position.

centre zero meter movement display

The meter movement will have a pair of metal connection terminals on the back for the current to flow through. Most meter movements are polarity-sensitive, one direction of current driving the needle to the right and the other driving it to the left. Some meter movements have a needle that is spring-centered in the middle of the scale sweep instead of to the left, thus enabling measurements of either polarity.

Some meter movements are polarity-insensitive, relying on the attraction of an unmagnetised, movable iron vane toward a stationary, current-carrying wire to deflect the needle. Such meters are ideally suited for the measurement of alternating current (AC). A polarity-sensitive movement would just vibrate back and forth uselessly if connected to a source of AC.

DC Voltmeters.

Whatever the type of meter or size of meter movement there will be a rated value of voltage or current necessary to give full-scale indication. In electromagnetic movements, this will be the "full-scale deflection current" necessary to rotate the needle so that it points to the exact end of the indicating scale. In digital movements, it is the amount of voltage resulting in a "full-count" indication on the numerical display, when the digits cannot display a larger quantity.

The meter designer has to take a given meter movement and design the necessary external circuitry for full-scale indication at some specified amount of voltage or current. Most meter movements are quite sensitive, giving full-scale indication at only a small fraction of a volt or an amp. This is impractical for most tasks of voltage and current measurement, the meter needs to be capable of measuring a range of voltages and currents, either that or a seperate meter will be required for each range to be measured.

By making the sensitive meter movement part of a voltage or current divider circuit, with resistors in series with the movement, the movements' useful measurement range may be extended to measure far greater levels than could be indicated by the movement alone. Precision resistors are used to create the divider circuits necessary to divide voltage appropriately. The design is touched upon in the Voltmeter impact on measured circuit section.

AC Voltmeters.

Passing AC through a DC-style meter movement such as a PMMC, the alternating current must be rectified into DC or it would cause useless flutter of the needle.

pmmc movement showing rectifier for AC readings

This rectification is most commonly and easily accomplished through the use of devices called diodes. Without going into elaborate detail over how and why diodes work as they do, just remember that they each act like a one-way valve for electrons to flow, acting as a conductor for one polarity and an insulator for another. Arranged in a bridge, four diodes will serve to steer AC through the meter movement in a constant direction throughout all portions of the AC cycle. AC voltage can now be read on a DC meter.

When a sensitive meter movement needs to be re-ranged to function as an AC voltmeter, series-connected "multiplier" resistors and/or resistive voltage dividers may be employed just as in a DC meter design so both AC and DC ranges can use the same components, thus putting 2 instruments into 1 handy device.

With AC, capacitors may be used instead of resistors to make AC voltmeter divider circuits. This strategy has the advantage of being non-dissipative (no true power consumed and no heat produced).

waveforms: sine, square and triangle

There is another factor crucially important for the designer and user of AC metering instruments to be aware of. This is the issue of RMS measurement. As we already know, AC measurements are often cast in a scale of DC power equivalence, called RMS (Root-Mean-Square) for the sake of meaningful comparisons with DC and with other AC waveforms of varying shape. None of the meter movement technologies so far discussed measure the RMS value of an AC quantity directly. Meter movements relying on the motion of a mechanical needle ("rectified" D'Arsonval and iron-vane) tend to mechanically average the instantaneous values into an overall average value for the waveform. This average value is not necessarily the same as RMS, although many times it is mistaken as such. Average and RMS values rate against each other as such for the three common waveform shapes, Sine, Square and Triangular.

Since RMS seems to be the kind of measurement most people are interested in obtaining with an instrument, and electromechanical (analogue) meter movements naturally deliver average measurements rather than RMS, what are AC meter designers to do? Cheat, of course! Typically the assumption is made that the waveform shape to be measured is going to be sine (by far the most common, especially for power systems), and then the meter movement scale is altered by the appropriate multiplication factor. For sine waves we see that RMS is equal to 0.707 times the peak value while Average is 0.637 times the peak, so we can divide one figure by the other to obtain an average-to-RMS conversion factor of 1.109:

calculation for average to rms calculation: 0.707 over 0.637 (equals 1.1099)

In other words, the meter movement will be calibrated to indicate approximately 1.11 times higher than it would ordinarily (naturally) indicate with no special accommodations. It must be stressed that this "cheat" only works well when the meter is used to measure pure sine wave sources. Note that for triangle waves, the ratio between RMS and Average is not the same as for sine waves!

With square waves, the RMS and Average values are identical! An AC meter calibrated to accurately read RMS voltage or current on a pure sine wave will not give the proper value while indicating the magnitude of anything other than a perfect sine wave. This includes triangle waves, square waves, or any kind of distorted sine wave. With harmonics becoming an ever-present phenomenon in large AC power systems, this matter of accurate RMS measurement is no small matter. (Digital meters do the math in the chip, but still, usually, only give the sine wave RMS value). The design is touched upon in the next section.

Voltmeter impact on measured circuit.

Every meter impacts the circuit it is measuring to some extent. While some impact is inevitable, it can be minimised through good meter design.

diagram

Since voltmeters are always connected in parallel with the component or components under test, any current through the voltmeter will contribute to the overall current in the tested circuit, potentially affecting the voltage being measured. A perfect voltmeter has infinite resistance, so that it draws no current from the circuit under test. However, perfect voltmeters only exist in the pages of textbooks, not in real life! Take the voltage divider circuit as an extreme example of how a realistic voltmeter might impact the circuit its measuring:

Looking at DC exmaples:
With no voltmeter connected to the circuit, there should be exactly 12 volts across each 250 MΩ resistor in the series circuit, the two equal-value resistors dividing the total voltage (24 volts) exactly in half. However, if the voltmeter in question has a lead-to-lead resistance of 10 MΩ (a common amount for a modern digital voltmeter), its resistance will create a parallel subcircuit with the lower resistor of the divider when connected:





diagram

This effectively reduces the lower resistance from 250 MΩ to 9.615 MΩ (250 MΩ and 10 MΩ in parallel), drastically altering voltage drops in the circuit. The lower resistor will now have far less voltage across it than before, and the upper resistor far more.

A voltage divider with resistance values of 250 MΩ and 9.615 MΩ will divide 24 volts into portions of 23.1111 volts and 0.8889 volts, respectively. Since the voltmeter is part of that 9.615 MΩ resistance, that is what it will indicate: 0.8889 volts.

Now, the voltmeter can only indicate the voltage its connected across. It has no way of "knowing" there was a potential of 12 volts dropped across the lower 250 MΩ resistor before it was connected across it. The very act of connecting the voltmeter to the circuit makes it part of the circuit, and the voltmeter's own resistance alters the resistance ratio of the voltage divider circuit, consequently affecting the voltage being measured. The less current drawn by a voltmeter to actuate the needle, the less it will burden the circuit under test.

This effect is called loading, and it is present to some degree in every instance of voltmeter usage. The scenario shown above is worst-case, with a voltmeter resistance substantially lower than the resistances of the divider resistors. But there always will be some degree of loading, causing the meter to indicate less than the true voltage with no meter connected. Obviously, the higher the voltmeter resistance, the less loading of the circuit under test, and that is why an ideal voltmeter has infinite internal resistance.

Voltmeters with electromechanical movements are typically given ratings in "ohms per volt" of range to designate the amount of circuit impact created by the current draw of the movement. Because such meters rely on different values of multiplier resistors to give different measurement ranges, their lead-to-lead resistances will change depending on what range they're set to. Digital voltmeters, on the other hand, often exhibit a constant resistance across their test leads regardless of range setting (but not always!), and as such are usually rated simply in ohms of input resistance, rather than "ohms per volt" sensitivity.

basic multi range meter schematic

What "ohms per volt" means is how many ohms of lead-to-lead resistance for every volt of range setting on the selector switch. Let's take our example voltmeter from the last section as an example:

On the 1000 volt scale, the total resistance is 1 MΩ (999.5 kΩ + 500Ω), giving 1,000,000 Ω per 1000 volts of range, or 1000 ohms per volt (1 kΩ/V). This ohms-per-volt "sensitivity" rating remains constant for any range of this meter:

math example

The observant will notice that the ohms-per-volt rating of any meter is determined by a single factor: the full-scale current of the movement, in this case 1 mA. "Ohms per volt" is the mathematical reciprocal of "volts per ohm," which is defined by Ohm's Law as current (I=V/R). Consequently, the full-scale current of the movement dictates the Ω/volt sensitivity of the meter, regardless of what ranges the designer equips it with through multiplier resistors. In this case, the meter movement's full-scale current rating of 1 mA gives it a voltmeter sensitivity of 1000 Ω/V regardless of how we range it with multiplier resistors.

To minimise the loading of a voltmeter on any circuit, the designer must seek to minimise the current draw of its movement. This can be accomplished by re-designing the movement itself for maximum sensitivity (less current required for full-scale deflection), but the tradeoff here is typically ruggedness: a more sensitive movement tends to be more fragile.

amplified volt meter, simplified

Another approach is to electronically boost the current sent to the movement, so that very little current needs to be drawn from the circuit under test. This electronic circuit is known as an amplifier, and the voltmeter thus constructed is an amplified voltmeter.

The internal workings of an amplifier are too complex to be discussed here, but the circuit allows the measured voltage to control how much battery current is sent to the meter movement. Thus, the movement's current needs are supplied by a battery internal to the voltmeter and not by the circuit under test. The amplifier still loads the circuit under test to some degree, but generally hundreds or thousands of times less than the meter movement would by itself.

Before the advent of semiconductors known as "field-effect transistors," vacuum tubes were used as amplifying devices to perform this boosting. Such vacuum-tube voltmeters, or (VTVM's) were once very popular instruments for electronic test and measurement. Nowadays solid-state transistor amplifier circuits accomplish the same task in digital meter designs. While this approach (of using an amplifier to boost the measured signal current) works well, it vastly complicates the design of the meter, making it nearly impossible for the beginer to comprehend its internal workings.

Ammeters.

A meter designed to measure electrical current is popularly called an "ammeter" because the unit of measurement is "amps". Ammeters are placed in series with the circuit under test, not in parallel as a volt meter is.

1 ma meter graphic

Taking the same meter movement as the voltmeter example, we can see that it would make a very limited instrument by itself, full-scale deflection occurring at only 1mA! We can extend the current measurement range by the use of external resistors. As is the case with extending a meter movements' voltage-measuring ability, we would have to correspondingly re-label the movements' scale so that it read differently for an extended current range.

In ammeter designs, external resistors added to extend the usable range of the movement are connected in parallel with the movement rather than in series as is the case for voltmeters. This is because we want to divide the measured current, not the measured voltage, going to the movement, and current divider circuits are always formed by parallel resistances.

For example, if we wanted to design an ammeter to have a full-scale range of 5amps using the same meter movement as before (having an intrinsic full-scale range of only 1mA), we would have to re-label the movements' scale to read 0 A on the far left and 5A on the far right, rather than 0mA to 1mA as before. Whatever extended range provided by the parallel-connected resistors, we would have to represent graphically on the meter movement face.

1ma meter with shunt graphic

Using 5amps as an extended range for our sample movement, let's determine the amount of parallel resistance necessary to bypass or "shunt" the majority of current so that only 1mA will go through the movement with a total current of 5A

From our given values of movement current, movement resistance, and total circuit (measured) current, we can determine the voltage across the meter movement (Ohm's Law applied to the center column, V=IR). Knowing that the circuit formed by the movement and the shunt is of a parallel configuration, we know that the voltage across the movement, shunt, and test leads (total) must be the same. We also know that the current through the shunt must be the difference between the total current (5amps) and the current through the movement (1mA or 0.001A), because branch currents add in a parallel configuration. Then, using Ohm's Law (R=V/I), we can determine the necessary shunt resistance value of just over 100 milli-ohms (100mΩ).

schematic of a basic multi range ammeter

As is the case with multiple-range voltmeters, ammeters can be given more than one usable range by incorporating several shunt resistors switched with a multi-pole switch.

Notice that the range resistors are connected through the switch so as to be in parallel with the meter movement, rather than in series as it was in the voltmeter design. The five-position switch makes contact with only one resistor at a time, of course. Each resistor is sized accordingly for a different full-scale range, based on the particular rating of the meter movement (1mA, 500Ω). With such a meter design, each resistor value is determined by the same technique, using a known total current, movement full-scale deflection rating, and movement resistance.

Shunt resistor values are very low: 5.00005mΩ is 5.00005 millionths of an ohm, or 0.00500005 ohm! To achieve these low resistances, ammeter shunt resistors often have to be custom made from relatively large diameter wire or solid pieces of metal.

Another thing to be aware of when sizing ammeter shunt resistors is the factor of power dissipation. Unlike the voltmeter, an ammeters' range resistors have to carry large amounts of current. If those shunt resistors are not sized accordingly, they may overheat and suffer damage, or at the very least lose accuracy due to overheating. For the example meter above, the power dissipations at full-scale indication are approximately: R1 50W, R2 5W, R3 0.5W, R4 49.5mW. So an 1/8 watt resistor would work just fine for R4, a 1/2 watt resistor would suffice for R3 and a 5 watt for R2 (although resistors tend to maintain their long-term accuracy better if not operated near their rated power dissipation, so you might want to over-rate resistors R2 and R3), but precision 50 watt resistors are rare and expensive components indeed. A custom resistor made from metal stock or thick wire may have to be constructed for R1 to meet both the requirements of low resistance and high power rating!

Ohmmeters.

Though mechanical ohmmeter (resistance meter) designs are rarely used today, having largely been superseded by digital instruments, their operation is worthy of note.

The purpose of an ohmmeter, of course, is to measure the resistance placed between its leads. This resistance reading is indicated through a mechanical meter movement which operates on electric current. The ohmmeter must then have an internal source of voltage to create the necessary current to operate the movement, and also have appropriate ranging resistors to allow just the right amount of current through the movement at any given resistance.

When there is infinite resistance, or no continuity, between test leads there is zero current through the meter movement, and the needle points toward the far left of the scale. In this regard, the ohmmeter indication is "backwards" reletive to the Volt and Amp meters because maximum indication (infinity) is on the left of the scale, while voltage and current meters have zero at the left of their scales.

If the test leads of an ohmmeter are directly shorted together (measuring zero Ω), the meter movement will have a maximum amount of current through it, limited only by the battery voltage and the movement's internal resistance and, therefore, show 0 resistance.

ohm meter with shorted leads and series resistor

With 9 volts of battery potential and only 500Ω of movement resistance, our circuit current will be 18mA, which is far beyond the full-scale rating of the movement. Such an excess of current will likely damage the meter.Not only that, but having such a condition limits the usefulness of the device. If full left-scale on the meter face represents an infinite amount of resistance, then full right-scale should represent zero. Currently, our design "pegs" the meter movement hard to the right when zero resistance is attached between the leads. We need a way to make it so that the movement just registers full-scale when the test leads are shorted together. This is accomplished by adding a series resistance to the meters' circuit.

To determine the proper value for R, we calculate the total circuit resistance needed to limit current to 1 mA (full-scale deflection on the movement) with 9 volts of potential from the battery, then subtract the movements' internal resistance from that figure. Once the right value for R has been calculated, we're still left with a problem of meter range. On the left side of the scale we have "infinity" and on the right side we have zero. Besides being "backwards", as previously mentioned, this scale is strange because it goes from nothing to everything, rather than from nothing to a finite value (such as 10 volts, 1 amp, etc.). You may wonder, "what does middle-of-scale represent? What figure lies exactly between zero and infinity?" Infinity is more than just a very big amount: it is an incalculable quantity, larger than any definite number ever could be. If half-scale indication on any other type of meter represents 1/2 of the full-scale range value, then what is half of infinity on an ohmmeter scale?

logarithmic scale

The answer to this problem is a logarithmic scale. Simply put, the scale of an ohmmeter does not smoothly progress from zero to infinity as the needle sweeps from right to left. Rather, the scale starts out "expanded" at the right-hand side, with the successive resistance values growing closer and closer to each other toward the left side of the scale.

Infinity cannot be approached in a linear (even) fashion, because the scale would never get there! With a logarithmic scale, the amount of resistance spanned for any given distance on the scale increases as the scale progresses toward infinity, making infinity an attainable goal! We still have a question of range for our ohmmeter, though. What value of resistance between the test leads will cause exactly 1/2 scale deflection of the needle? If we know that the movement has a full-scale rating of 1mA, then 0.5mA (500 µA) must be the value needed for half-scale deflection.

log scale for example meter

Following our design with the 9 volt battery as a source, an internal movement resistance of 500Ω and a series range resistor of 8.5kΩ, this leaves 9kΩ for an external (lead-to-lead) test resistance at 1/2 scale. In other words, the test resistance giving 1/2 scale deflection in an ohmmeter is equal in value to the (internal) series total resistance of the meter circuit.

Using Ohm's Law a few more times, we can determine the test resistance value for 1/4 and 3/4 scale deflection as well and the scale for this ohmmeter would look like the picture.

The major problem with this design is its reliance upon a stable battery voltage for accurate resistance reading. If the battery voltage decreases (as all chemical batteries do with age and use), the ohmmeter scale will lose accuracy. With the series range resistor at a constant value of 8.5kΩ and the battery voltage decreasing, the meter will no longer deflect full-scale when the test leads are shorted together (0Ω). Likewise, a test resistance of 9kΩ will fail to deflect the needle to exactly 1/2 scale with a lesser battery voltage.There are design techniques used to compensate for varying battery voltage, but they do not completely take care of the problem and are to be considered approximations at best. For this reason, and for the fact of the logarithmic scale, this type of ohmmeter is never considered to be a precision instrument.

One final, but important thing needs to be mentioned with regard to ohmmeters. They only function correctly when measuring resistance that is not being powered by a voltage or current source. In other words, you cannot measure resistance with an ohmmeter on a "live" circuit! The reason for this is simple, the ohmmeters' accurate indication depends on the only source of voltage being its internal battery. The presence of any voltage across the component to be measured will interfere with the ohmmeters' operation. If the voltage is large enough, it may even damage the ohmmeter!

Multimeters

Seeing as how a common meter movement can be made to function as a voltmeter, ammeter, or ohmmeter simply by connecting it to different external components, it should make sense that a multi-purpose meter (multimeter) could be designed in one unit with the appropriate switch(es), a battery and some resistors.

For general purpose electronics work, the multimeter reigns supreme as the instrument of choice. No other device is able to do so much with so little an investment in parts and elegant simplicity of operation. As with most things in the world of electronics, the advent of solid-state components like transistors and ICs has revolutionised the way things are done, and multimeter design is no exception to this rule.

anologue multimeter

The unit shown here is typical of an older handheld analog multimeter, with ranges for voltage, current, and resistance measurement. Note the many scales on the face of the meter movement for the different ranges and functions selectable by the rotary switch. The wires for connecting this instrument to a circuit (the test leads) are plugged into the two copper jacks (socket holes) at the bottom-center of the meter face marked "- TEST +", black and red.

A slightly different design approach uses more jacks into which the test leads may be plugged into. Each one of the jacks is labeled with a number indicating the respective full-scale range of the meter. digital multimeter

On the right is a digital multimeter. The familiar meter movement has been replaced by a blank, gray-colored display screen. When powered, numerical digits appear in that screen area, depicting the amount of voltage, current, or resistance being measured. This particular model of digital meter has a rotary selector switch and four jacks into which test leads can be plugged. Two leads -- one red and one black -- are shown plugged into the meter.

A close examination of this meter will reveal one "common" jack for the black test lead and three others for the red test lead. The jack into which the red lead is shown inserted is labeled for voltage and resistance measurement, while the other two jacks are labeled for current (A, mA, and μA) measurement. This is a wise design feature of the multimeter, requiring the user to move a test lead plug from one jack to another in order to switch from the voltage measurement to the current measurement function. It would be hazardous to have the meter set in current measurement mode while connected across a significant source of voltage because of the low input resistance, and making it necessary to move a test lead plug rather than just flip the selector switch to a different position helps ensure that the meter doesn't get set to measure current unintentionally.

Note, too, that the selector switch still has different positions for voltage and current measurement, so in order for the user to switch between these two modes of measurement they must switch the position of the red test lead and move the selector switch to a different position. On this meter, neither the selector switch nor the jacks are labeled with measurement ranges. In other words, there are no "250 volt", "25 volt" or "2.5 volt" ranges (or any equivalent range steps) on this meter. That is because this meter is "autoranging", it automatically picks the appropriate range for the quantity being measured. Autoranging is a feature only found on digital meters, but not on all digital meters.

No two models of multimeters are designed to operate exactly the same, even if they're manufactured by the same company. In order to fully understand the operation of any multimeter, the owner's manual must be consulted.

Obtaining a reading from an analogue multimeter when there is a multitude of ranges and only one meter movement may seem daunting to the new owner. On an analogue multimeter, the meter movement is marked with several scales, each one useful for at least one range setting. All that is required is a careful look to see which scale will be displaying the value you're looking for and concentrate on that.

Notes on meter useage.

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