Introduction

When making measurements using a digital multimeter (DMM), common errors will crop up. The following step-by-step discussion will help users to eliminate potential measurement errors and achieve the greatest accuracy with a DMM. (NOTE: The HP 34401A, a 6½-digit DMM, will be used as an example throughout this article.)

System Cabling Errors

Radio Frequency Interference (RFI). Most voltage-measuring instruments can generate false readings in the presence of large, high-frequency signal sources such as nearby radio and television transmitters, computer monitors, and cellular telephones. High-frequency energy can also be coupled to the multimeter on the system cabling. To reduce interference, try to minimize the exposure of the system cabling to high-frequency RF sources. If the application is extremely sensitive to RFI actually radiating from the multimeter, use a common-mode choke in the system cabling (see Fig. 1) to attenuate multimeter emissions.

Figure 1

Noise Caused by Magnetic Fields. When making measurements near magnetic fields, precautionary steps should be taken to avoid inducing voltages in the measurement connections. Voltage can be induced by either movement of the input connection wiring in a fixed magnetic field or by a varying magnetic field. An unshielded, poorly dressed input wire moving in the earth’s magnetic field can generate several millivolts. The varying magnetic field around the ac power line can also induce voltages up to several hundred millivolts. Users should be especially careful when working near conductors carrying large currents.

Where possible route cabling away from magnetic fields, which are commonly present around electric motors, generators, televisions, and computer monitors. In addition, be certain that the input wiring has proper strain relief and is tied down securely when operating near magnetic fields. Use twisted-pair connections to the multimeter to reduce the noise pickup loop area, or dress the wires as closely together as possible.

Noise Caused by Ground Loops. When measuring voltages in circuits where the multimeter and the device-under-test (DUT) are both referenced to a common earth ground, a ground loop is formed. Any voltage difference (see Fig.3) between the two ground reference points (Vground) causes a current to flow through the measurement leads. This causes errors, such as noise and offset voltage (usually power-line related), which are added to the measured voltage.

R_L = lead resistance
R_i = multimeter isolation resistance
V_ground = voltage drop on ground bus

The best way to eliminate ground loops is to maintain the multimeter’s isolation from earth; do not connect the input terminals to ground. If the multimeter must be earth-referenced, be sure to connect it and the DUT to the same common ground point. This will reduce or eliminate any voltage difference between the devices. Also make sure the multimeter and DUT are connected to the same electrical outlet whenever possible.

Dc Voltage Measurement Errors

Common-mode Rejection. Ideally, a multimeter is completely isolated from earth-referenced circuits. However, there is finite resistance between the multimeter’s input LO terminal and earth ground (see Fig. 4.) This can cause errors when measuring low voltages which are floating relative to earth ground.

V_f = float voltage
R_s = DUT source resistance imbalance
R_i = multimeter isolation resistance (LO-Earth)
C_i = multimeter input capacitance (» 200 pF LO-Earth)
Error (v) = (V_f x R_s)/(R_s + R_i)

Noise Caused by Injected Current. Residual capacitances in the multimeter’s power transformer cause small currents to flow from the LO terminal to earth ground. The frequency of the injected current is the power line frequency or possibly harmonics of the power line frequency. The injected current is dependent upon the power line configuration and frequency (see Fig. 5.)

With Connection A (See Fig. 6) the injected current flows from the earth connection provided by the circuit to the LO terminal of the DMM, adding no noise to the measurement. However, with Connection B the injected current flows through the resistor R, thereby adding noise to the measurement. With Connection B, larger values of R will worsen the problem.

Note: The measurement noise caused by injected current can be significantly reduced by setting the integration time of the DMM to 1 power line cycle (PLC) or greater.

Loading Errors Due to Input Resistance. Measurement loading errors occur when the resistance of the DUT is an appreciable percentage of the multimeter’s own input resistance (see Fig. 7.)

V_s = ideal DUT voltage
R_s = DUT source resistance
R_i = multimeter input resistance (10 MW or >10 GW )
Error (%) = (100 x R_s)/ (R_s + R_i)

To reduce the effects of loading errors, and to minimize noise pickup, set the DMM input resistance to greater than 10 GW for the 100 mVdc, 1 Vdc, and 10 Vdc ranges. The input resistance is maintained at 10 MW for the 100 Vdc and 1000 Vdc ranges.

Loading Errors Due to Input Bias Current. The multimeter’s input capacitance will "charge up" due to input bias currents when the terminals are open-circuited (if the input resistance is 10 GW ). The multimeter’s measuring circuitry exhibits approximately 30 pA of input bias current for ambient temperatures from 0°C to 30°C. Bias current will double for every 8°C change in ambient temperature above 30°C. This current generates small voltage offsets dependent upon the source resistance of the DUT. This effect becomes evident for a source resistance of greater than 100 kW , or when the multimeter’s operating temperature is significantly greater than 30°C.

i_b = multimeter bias current
R_s = DUT source resistance
C_i = multimeter input capacitance
Error (v) @ i_b x R_s

Ac Voltage Measurement Errors

Many of the errors associated with dc voltage measurements also apply to ac voltage measurements. This section will cover additional errors that are unique to ac voltage measurements.

Common-mode Errors. Errors are generated when the multimeter’s input LO terminal is driven with an ac voltage relative to earth. The most common situation where unnecessary common-mode voltages are created is when the output of an ac calibrator is connected to the multimeter "backwards." Ideally, a multimeter reads the same regardless of how the source is connected. However, both source and multimeter effects can degrade this ideal situation.

Because of the capacitance between the input LO terminal and earth (approximately 200 pF for the HP 34401A), the source will experience different loading depending on how the input is applied. The magnitude of the error is dependent upon the source’s response to this loading. The multimeter’s measurement circuitry, while extensively shielded, responds differently in the backward input case due to slight differences in stray capacitance to earth. The multimeter’s errors are greatest for high-voltage, high-frequency inputs. Typically, the multimeter will exhibit about 0.06% additional error for a 100-V, 100-kHz reverse input. You can use the grounding techniques described for dc common-mode problems to minimize ac common-mode voltages.

True RMS Ac Measurements. True RMS-responding multimeters measure the "heating" potential of an applied voltage. Unlike an "average responding" measurement, a true RMS measurement is used to determine the power dissipated in a resistor. The power is proportional to the square of the measured true RMS voltage, independent of waveshape. An average responding ac multimeter is calibrated to read the same as a true RMS meter for sinewave inputs only. For other waveform shapes, an average responding meter will exhibit substantial errors (See Fig.9.)

The multimeter’s ac voltage and ac current functions measure the ac-coupled true RMS value. This is in contrast to the ac+dc true RMS value shown above. Only the "heating value" of the ac components of the input waveform are measured (dc is rejected). For sinewaves, triangle waves and square waves, the ac and ac+dc values are equal since these waveforms do not contain a dc offset. Non-symmetrical waveforms such as pulse trains contain dc voltages, which are rejected by ac-coupled true RMS measurements.

Crest Factor Errors A common misconception is that "since an ac multimeter is true RMS, its sinewave accuracy specifications apply to all waveforms." Actually, the shape of the input signal can dramatically affect measurement accuracy. A common way to describe signal waveshapes is crest factor. Crest factor is the ratio of the peak value to the RMS value of a waveform.

For example, a pulse train’s crest factor is approximately equal to the square root of the inverse of the duty cycle (see Fig. 9.) In general, the greater the crest factor, the greater the energy contained in higher frequency harmonics. All multimeters exhibit measurement errors that are crest factor-dependent.

The following equation shows how to estimate the measurement error due to signal crest factor:

total error = error_sine + error_{crest factor} + error_bandwidth

Where:
error_sine = DMM’s sinewave accuracy
error_crest = DMM’s crest factor
error_bandwidth = estimated bandwidth error (see below):

Error_bandwidth = (– CF x f)/(4p x BW)

Where:
CF = signal crest factor
f = fundamental input signal frequency
BW = DMM's -3 dB bandwidth

Example: Calculating Crest Factor Error,

Calculate the approximate measurement error for a pulse train input with a crest factor of 3 and a fundamental frequency of 20 kHz. For this example, assume the multimeter’s 90-day accuracy specifications are ± (0.05% + 0.03%).

Total Error = 0.08% + 0.15% + 1.4% = 1.6%

Ac Loading Errors. In the ac voltage function, the input of the HP 34401A appears as a 1-MW resistance paralleled with 100 pF of capacitance. The cabling used to connect signals to the multimeter will also add additional capacitance and loading. The multimeter’s approximate input resistance at various frequencies is shown in Fig. 10.

For Low Frequencies:

Additional error for high frequencies:

Where:
R_s = source resistance
f = input frequency
C_in = input capacitance (100 pF) plus cable capacitance

Note: Be sure to use low-capacitance cable when measuring high-frequency signals.

Low-Level Ac Measurement Errors. When measuring ac voltages less than 100 mV, be aware that these measurements are especially susceptible to errors introduced by extraneous noise sources. An exposed test lead will act as an antenna and a properly functioning multimeter will measure the signals received. The entire measurement path, including the power line, act as a loop antenna. Circulating currents in the loop will create error voltages across any impedances in series with the multimeter’s input. For this reason, apply low-level ac voltages to the multimeter through shielded cables, and connect the shield to the input LO terminal.

Make sure the multimeter and the ac source are connected to the same electrical outlet whenever possible, and also minimize the area of any ground loops that cannot be avoided. A high-impedance source is more susceptible to noise pickup than a low-impedance source. To reduce the high-frequency impedance of a source, place a capacitor in parallel with the multimeter’s input terminals. There may be some experimentation involved to determine the correct capacitor value for the particular application.

Most extraneous noise is not correlated with the input signal. The equation below shows how to determine the error:

Correlated noise, while rare, is especially detrimental because it will always add directly to the input signal. Measuring a low-level signal with the same frequency as the local power line is a common situation that is prone to this error.

Temperature Coefficient and Overload Errors. The HP 34401A uses an ac measurement technique that measures and removes internal offset voltages when selecting a different function or range. If the multimeter is left in the same range for an extended period of time, and the ambient temperature changes significantly (or if the multimeter is not fully warmed up), the internal offsets may change. This temperature coefficient is typically 0.002% of range per °C, and is automatically removed when changing functions or ranges.

When manual ranging to a new range in an overload condition, the internal offset measurement may be degraded for the selected range. Typically, an additional 0.01% of range error may be introduced. This additional error is automatically removed when removing the overload condition and then changing functions or ranges.

Resistance Measurement Errors

Two methods can be offered for measuring resistance: 2-wire and 4-wire ohms. For both methods, the test current flows from the input HI terminal and then through the resistor being measured. For 2-wire ohms, the voltage drop across the resistor being measured is sensed internal to the multimeter. Therefore, test lead resistance is also measured. For 4-wire ohms, separate "sense" connections are required. Since no current flows in the sense leads, the resistance in these leads does not give a measurement error.

The errors mentioned earlier for dc voltage measurements also apply to resistance measurements. However, there are additional error sources that are unique to resistance measurements.

Power Dissipation Effects. When measuring resistors designed for temperature measurements (or other resistive devices with large temperature coefficients), be aware that the multimeter will dissipate some power in the DUT. If power dissipation is a problem, select the multimeter’s next higher measurement range to reduce the errors to acceptable levels (see Fig. 11 for examples.)

Settling Time Effects. The ability to insert automatic measurement settling delays can be available. These delays are adequate for resistance measurements with less than 200 pF of combined cable and device capacitance, which is particularly important when measuring resistances above 100 kW . Settling due to RC time constant effects can be quite long. Some precision resistors and multi-function calibrators use large parallel capacitors (1000 pF to 0.1 m F) with high resistor values to filter out noise currents injected by their internal circuitry. Non-ideal capacitances in cables and other devices may have much longer settling times than expected just by RC time constants due to dielectric absorption (soak) effects. Errors will be measured when settling after the initial connection and after a range change.

High-Resistance Measurement Errors. When measuring large resistances, significant errors can occur due to insulation resistance and surface cleanliness. Users should take the necessary precautions to maintain a "clean" high-resistance system. Test leads and fixtures are susceptible to leakage due to moisture absorption in insulating materials and "dirty" surface films. Nylon and PVC are relatively poor insulators (10⁹ W ) compared to PTFE Teflon insulators (10¹³ W ). Leakage from nylon or PVC insulators can easily contribute a 0.1% error when measuring a 1 MW resistance in humid conditions. (Note: Teflon is a registered trademark of E.I.duPont deNemours and Company)

Dc Current Measurement Errors

When connecting the multimeter in series with a test circuit to measure current, a measurement error is introduced, the cause being the multimeter’s series burden voltage. A voltage is developed across the wiring resistance and current shunt resistance of the multimeter (see Fig. 12.)

V_s = source voltage
R_s = DUT source resistance
V_b = multimeter burden voltage
R = multimeter current shunt
Error (%) = (-100% x V_b)/V_s

Ac Current Measurement Errors

Burden voltage errors, which apply to dc current, also apply to ac current measurements. However, the burden voltage for ac current is larger due to the multimeter’s series inductance and the measurement connections. The burden voltage increases as the input frequency increases. Some circuits may oscillate when performing current measurements due to the multimeter’s series inductance and the specific measurement connections.

Frequency and Period Measurement Errors in the HP 34401A

A reciprocal counting technique is used to measure frequency and period to generate constant measurement resolution for any input frequency. The ac voltage measurement section performs input signal conditioning. All frequency counters are susceptible to errors when measuring low-voltage, low-frequency signals. The effects of both internal noise and external noise pickup are critical when measuring "slow" signals. The error is inversely proportional to frequency. Measurement errors will also occur when attempting to measure the frequency (or period) of an input following a dc offset voltage change. To avoid this, allow the multimeter’s input dc blocking capacitor to fully settle before making frequency measurements.

For more information about the HP 34401A click here.

Biographical Information

David Heintz has been a technical writer with HP’s Electronic Measurements Division in Loveland, Colorado, since 1984. He has written customer documentation for numerous test and measurement instruments, and his work has been recognized by the Society for Technical Communication.

Scott Stever is an R&D Section Manager with HP’s Electronic Measurements Division in Loveland, Colorado. He has been with HP since 1979 and has held numerous positions in the R&D environment.

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