digital multimeter theory and usage

Arguably the most commonly used tool within the electrical industry, the digital multimeter (D.M.M.) offers a suite of capabilities enabling users to troubleshoot circuits, measure voltages, currents, resistances, etc. Solid construction and high reliability are critical as D.M.M.s are often used to check for hazardous voltages (live-dead checks).

Incorrect usage and interpretation of readings is seemingly common; often stemming from a lack of understanding on the underlying circuitry within the D.M.M..

ANALOG FRONT-END / INPUT

Given how popular and rugged the tried and trusted Fluke 87V D.M.M. is, this particular meter shall be used as a good example during the analysis portion of this article. Other D.M.M.s will feature similar designs / theory.

To the left is a block diagram from the Fluke 83, 85, 87 service manual. Clearly, two sections must exist (analog, digital) given this is, after all, a D.M.M.. Most commonly, the misunderstanding arises from the analog portion of the meter.

Shown below is the schematic of the major front-end / input circuitry for the Fluke 87V. Aside from some clever compensation components / portions of the circuit, the voltage measurement portion is relatively simple.

PRECISION RESISTOR NETWORK

In essence, the Fluke 87V has four voltage ranges based on the configuration of the precision resistor network "Z1" (voltage divider):

400 [mVAC] & 4 [VAC] / 4 [VDC] 10:1 Division Ratio
40 [V] 100:1 Division Ratio
400 [V] 1000:1 Division Ratio
1000 [V] 10000:1 Division Ratio

A critical note within the service manual explains the use of the seemingly odd 9.996 [MΩ] resistor within Z1. The switch resistance which connects the resistors within Z1 is roughly 4 [kΩ] - thus combining to a total of 10 [MΩ].

THE EFFECTS OF INPUT IMPEDANCE ON MEASUREMENTS

We shall consider a few common scenarios with analysis based on the following assumptions:

Input Impedance: 10 [MΩ]
D.M.M. AC & DC Measurement Circuits Equivalent (ie. simplified)
Impedance = Resistance (no reactive effects considered)

Let's assume in this instance we're measuring a heating element on a phase of a three-phase system. We can assume:

Now we can perform an analysis to compare both versions of the circuit to see the impact of our D.M.M. measurement. Given the high voltages, our meter will be in the 1000 V range and thus utilize the highest division range in the resistor network Z1.

SCENARIO 1: LOW IMPEDANCE

This situation is most typical, especially in any sort of power / mains circuitry. Both the source and load are relatively low impedance compared to the multimeter input impedance. If we re-draw the circuit to include the internals of the D.M.M. we can begin to see what's really going on. Shown below is a more accurate reflection of a real-world multimeter.

Since we assume our meter has infinite input impedance:

Given our D.M.M. has a definite input impedance, some current must flow through our meter in addition to the load:

SCENARIO 2: HIGH IMPEDANCE

3: CONTACT / SWITCH READINGS

Because continuity checking (using the D.M.M. function) cannot be used on live circuits, a common technique is to measure the differential voltage across a contact / switch. This offers a safe and generally reliable method to determine if a set of contacts is open / closed. A closed contact will obviously have no practically measurable voltage across it; conversely an open contact will.

This technique is only recommended when a known, significant load is present downstream of the measured contact. We can demonstrate the issues that arise if this is not realized.

Redrawing the D.M.M. to account for its input impedance, we have the following circuit on the left. We can further simplify this circuit for analysis by removing the switch entirely. The switch being activated merely shorts out our meter, which is the trivial case and thus unimportant. From the further simplified circuit on the right hand side we can clearly see the D.M.M. is actually connected in series with the downstream load. We can now investigate the effect the downstream load has on our meter reading.

We shall assume the following:

120 [VAC] Control Circuit
D.M.M. AC & DC Measurement Circuits Equivalent (ie. simplified)
Impedance = Resistance (no reactive effects considered)
400V Meter Range

Now let:

The voltage seen by the D.M.M. A.D.C. (Analog to Digital Converter) and thus (after scaling) the meter display value can be calculated as:

This is a very important observation! Despite the fact that the circuit is live / energized with 120 volts, the D.M.M. displays zero volts across the switch. Such measurements (across devices) should never be used to verify energy isolation within systems.

We will now consider a more typical case where the switch has significant downstream loading (ie. resistance is relatively small).

Let's assume the switch controls a 60 [W] lightbulb. The nominal bulb resistance is then calculated as:

Now let:

Similar to before, the D.M.M. measured voltage is calculated as:

We have now proven that even for low power electrical loads, the high input impedance of the D.M.M. dominates the voltage distribution and allows for essentially unaffected readings.

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