Digital Voltage

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Digital Voltage

Solutions for Low Voltage Measurement Errors

Many research and production applications require low level voltage measurements to characterize materials and devices. At microvolt levels and lower there are a number of potential error sources that can have a negative impact on measurement integrity. Broadly speaking, these error sources cause voltage offsets and noisy readings, regardless of the type of instrument you are using – digital multimeter (DMM), sensitive source-measure unit (SMU), nanovoltmeter, or electrometer. Thermal effects are normally the largest source of error in low voltage measurements, but recognizing their symptoms can help prioritize your troubleshooting and improve measurement accuracy.

Offset Voltages. Ideally, when a voltmeter is connected to a relatively low impedance test circuit where no voltage is present, it should read zero. However, test circuit thermal effects may be seen as a non-zero offset on the meter. The principal causes are thermoelectric EMFs and offsets in the voltmeter's input circuitry.

Any offset voltage (VOFFSET) between the device under test (DUT) and the voltmeter will add to or subtract from the source voltage (VS), so that the voltage measured by the meter becomes:

VM = VS ±VOFFSET.

For example, assume VS = 5μV and VOFFSET = 250nV. If the voltage polarities are in opposition, the voltmeter reading will be:

VM = (5 × 10–6) – (250 × 10–9)

VM = 4.75 × 10–6

VM = 4.75μV (an error of –5%)

Internal Zero Offset. A sensitive instrument such as a nanovoltmeter will rarely indicate zero when no voltage is applied to the input, since there are unavoidable offset voltages present in the input circuitry. The first step in troubleshooting, or preparing for voltage measurements, is to check the instrument's zero offset after it has warmed up thoroughly. This is done by disconnecting it from the external measurement circuit, selecting the desired measurement range, and shorting the test leads together. If the meter does not read zero, the offset voltage can be "nulled out" by pressing the REL (for Relative) or ZERO button, or by adjusting the ZERO control knob if the instrument has one. In computer controlled instruments, this is done by invoking the ZERO function from the computer.

When measuring a small voltage across a DUT resulting from current flow through it, start by letting the voltmeter warm up for one to two hours. The measurement connections should be made between the DUT and the instrument during this time, but no current should be supplied to the DUT until temperature gradients have settled to a minimum. When the instrument display has stabilized, make the zero adjustment, then quickly apply the test current and take the voltage reading across the DUT.

In some applications, the voltage to be measured is always present and this procedure can't be used. One example is measuring the voltage difference between two standard cells or two thermocouples. In such cases it is best to take two measurements, one with the test leads reversed, and then average the two readings. This will be described in more detail later.

Zero Drift. An instrument's input stage voltage offset is apt to change with the operating temperature. A change in the meter reading over time with no input signal and test leads shorted is referred to as zero drift. The magnitude of this effect is usually referred to as the temperature coefficient of voltage offset. Good measurement practice dictates periodic checking and adjustment of the zero offset.

In some measurement environments, a rapid change in ambient temperature can cause a large shift in an instrument's zero offset, possibly exceeding the manufacturer's voltage offset specifications. If you are measuring a stable voltage source, you might see the voltmeter reading shift rapidly up or down. This transient offset will then gradually decrease and the meter reading eventually settles close to the original value. This effect results from dissimilar metal junctions in the instrument that have different thermal time constants, with some reacting more slowly than others. In environments prone to rapid temperature changes, it's a good idea to monitor them with a fast acting temperature sensor, or even record voltage and temperature measurements simultaneously. Once the temperature has settled to a steady value, you can check the zero offset again.

Minimizing Thermoelectric EMF Errors Steady thermoelectric EMFs can be nulled out by shorting an instrument's input leads and using its ZERO or REL feature. The most common cause of a thermally generated voltage in a test circuit is a connection between two different metals that act as a thermocouple pair. The magnitude of the generated voltage depends on the ambient temperature and the metals' Seebeck coefficient (QAB in Table 1). Still, if an instrument's shorted input leads actually encompass such a thermal EMF source, ambient temperature variations can require frequent meter zeroing

To diagnose this problem, start with a "cold" test instrument that has been turned off overnight. Then locate the parts of the test circuit where there are connections between different metallic conductors. Short the instrument input leads across the portion of the test circuit that encompasses these connections. Turn on all the test equipment and observe the voltmeter reading as it and the ambient temperature increases. When the voltmeter reaches thermal equilibrium and the meter reading has stabilized, any remaining thermoelectric EMF can be nulled out with the ZERO feature.

Allowing adequate warm up time for test equipment and stabilizing ambient temperatures minimizes thermoelectric EMFs. Equipment should be kept away from direct sunlight, exhaust fans, and similar sources of heat flow or moving air. Wrapping connections in insulating foam (e.g., polyurethane) also minimizes ambient temperature fluctuations caused by air movement.

Constructing test circuits using the same material for all conductors further reduces thermoelectric EMF generation. For example, connections made by crimping copper sleeves or lugs on copper wires results in cold-welded copper-to-copper junctions that generate minimal thermoelectric EMFs. Also, keep connections clean and free of oxides. For example, clean Cu-Cu connections typically have a Seebeck coefficient of ≤ 0.2μV/°C, while Cu-CuO connections may have a coefficient as high as 1mV/°C.

Sometimes, dissimilar metals cannot be avoided. For example, test fixtures often use spring contacts, which may be made of phosphor-bronze, beryllium-copper, or other materials with high Seebeck coefficients that can cause significant measurement errors. In that case an effort should be made to reduce temperature gradients throughout the test circuit by placing all junctions in close proximity to one another and shielding the circuit from heat sources.

Another technique is to provide good thermal coupling between the text fixtures and a common, massive heat sink. Electrical insulators having high thermal conductivity must be used. Since most electrical insulators do not conduct heat very well, special insulator materials such as hard anodized aluminum, beryllium oxide, specially filled epoxy resins, sapphire, or diamond are needed to couple junctions to the heat sink.

Reversing Sources to Cancel Thermoelectric EMFs. There may be cases where it's not practical to eliminate all thermoelectric EMFs in a test circuit, and a low voltage measurement will be prone to error. Measuring a small voltage difference between two standard cells is one example of where this problem can occur. However, the thermoelectric EMF can be cancelled by taking one measurement, and then carefully reversing the two voltage sources and taking a second measurement. The average of the difference between these two readings is the desired voltage difference between the cells.

If Va and Vb represent two standard cells, the voltage measured the first time is:

V1 = Vemf + Va – Vb

With the two cells reversed the second measured voltage is:

V2 = Vemf + Vb – Va

The average of the difference between these two measurements cancels out Vemf, i.e.:

(V1 – V2) / 2 = (Vemf + Va – Vb – Vemf – Vb + Va) / 2 = Va – Vb

Input Offset Current Loading. Another consideration when measuring voltages from sources with high impedance is the input offset current of a voltmeter. The input offset current develops an error voltage (offset) across the source resistance (Rs). This causes the actual measured voltage to differ from the source voltage, i.e.,

Vm = Vs ± (Ioffset x Rs)

For instance, if the offset current is 1pA into a source resistance of 10Gohm, and the source voltage is 10V, then the actual voltage measured by the instrument is:

Vm = 10V ± (10-12A x 1010Ω)

Vm = 10V ± 0.01V

The error caused by the input offset current in this example is about 0.1%.

Digital multimeters and nanovoltmeters have offset currents from about 1pA to 1nA. Electrometers are known for their low input offset current, from about 10fA (10-14A) down to 50aA (5 x 10-17A). The lower the input offset current the more accurate the voltage measurement. Electrometers are the instruments to use for precise voltage measurements with high source resistance.

Input offset current errors will not be obvious. The solution is to get the instrument specifications from the manufacturer, find the source impedance, and calculate the potential measurement error.

Other Error Sources to Consider. There are many other potential error sources in low voltage measurements, such as Johnson Noise, RFI/EMI noise, ground loops, etc. However, thermal EMFs are the most common sources of error and tend to have largest magnitude. Following the guidelines in this article can help you identify and correct these error sources more quickly, resulting in more accurate measurements.

References. More techniques and tips on low voltage measurements are available at http://www.keithley.com/data?asset=54358.

About the Author

Dale Cigoy is a Senior Application Engineer at Keithley Instruments in Cleveland, OH. With 25 years of experience in instrument applications, his major responsibility is helping customers with electrical measurements that include Keithley equipment. Prior to this he wrote technical instruction manuals for Keithley products. Cigoy joined Keithley in 1976 after earning a Bachelor of Science degree in Electronic Technology from Capitol College in Laurel, MD.