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Making Precision
Measurements
Low Voltage and Low Resistance
Introduction .......................................................................... 2
Low Voltage Measurements ............................................... 2
Offset Voltages .....................................................................2
Noise ......................................................................................6
Common-Mode Current and Reversal Errors ..................8
Low Resistance Measurements .......................................... 9
Lead Resistance and Four-Wire Method ...........................9
Thermoelectric EMFs & Offset Compensation Methods .....9
Non-Ohmic Contacts ......................................................... 12
Device Heating .................................................................... 12
Dry Circuit Testing .............................................................. 12
Testing Inductive Devices .................................................. 13
Applications
Low-V: Hall Effect Measurements ....................................... 14
Low-R: Superconductor Resistance Measurements ...... 17
Selector Guide .................................................................... 18
Glossary .............................................................................. 19
Contact Us................................................................................... 22
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Low Voltage Measurements
Introduction
Low voltage and low resistance measurements are
often made on devices and materials with low source
impedance. This e-handbook discusses several potential
sources of error in low voltage measurements and how
to minimize their impact on measurement accuracy,
as well as potential error sources for low resistance
measurements, including lead resistance, thermoelectric
EMFs, non-ohmic contacts, device heating, dry circuit
testing, and measuring inductive devices.
Significant errors may be introduced into low voltage
measurements by offset voltages and noise sources that
can normally be ignored when measuring higher voltage
levels. These factors can have a significant effect on low
voltage measurement accuracy.
Offset Voltages
Ideally, when a voltmeter is connected to a relatively low
impedance circuit in which no voltages are present, it
should read zero. However, a number of error sources
in the circuit may be seen as a non-zero voltage offset.
These sources include thermoelectric EMFs, offsets
generated by rectification of RFI (radio frequency
interference), and offsets in the voltmeter input circuit.
Figure 1: Effects of Offset Voltages on Voltage Measurement
Accuracy
As shown in Figure 1, any offset voltage (VOFFSET) will add
to or subtract from the source voltage (VS) so that the
voltage measured by the meter becomes:
VM = VS ± VOFFSET
The relative polarities of the two voltages will determine
whether the offset voltage adds to or subtracts from the
source voltage. Steady offsets can generally be nulled
out by shorting the ends of the test leads together,
then enabling the instrument’s zero (relative) feature.
Note, however, that cancellation of offset drift may
require frequent rezeroing, particularly in the case of
thermoelectric EMFs.
ThermoelecTric emFs
Thermoelectric voltages (thermoelectric EMFs) are
the most common source of errors in low voltage
measurements. These voltages are generated when
different parts of a circuit are at different temperatures
and when conductors made of dissimilar materials are
joined together, as shown in Figure 2. The Seebeck
coefficients (QAB) of various materials with respect to
copper are summarized in Table 1.
Figure 2: Thermoelectric EMFs
FeATured resources
n Troubleshooting
Low Voltage
Measurement
Problems
n Accurate Low-Resistance
Measurements Start with
Identifying Sources of Error
AddiTionAl resources
n Understanding Low Voltage
Measurements
n Problem: Errors in Low
Resistance Measurements
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Low Voltage Measurements
Table 1: Seebeck Coefficients
Paired materials* seebeck coefficient, QAB
Cu - Cu ≤0.2 μV/°C
Cu - Ag 0.3 μV/°C
Cu - Au 0.3 μV/°C
Cu - Pb/Sn 1–3 μV/°C
Cu - Si 400 μV/°C
Cu - Kovar ~40–75 μV/°C
Cu - CuO ~1000 μV/°C
* Ag = silver Au = gold Cu = copper CuO = copper oxide
Pb = lead Si = silicon Sn = tin
Constructing circuits using the same material for all
conductors minimizes thermoelectric EMF generation.
For example, crimping copper sleeves or lugs onto copper
wires results in copper-to-copper junctions, which generate
minimal thermoelectric EMFs. Also, connections must
be kept clean and free of oxides. Crimped copper-to-
copper connections, called “cold welded,” do not allow
oxygen penetration and may have a Seebeck coefficient
of ≤0.2μV/°C, while Cu-CuO connections may have a
coefficient as high as 1mV/°C.
Minimizing temperature gradients within the circuit also
reduces thermoelectric EMFs. A technique for minimizing
such gradients is to place corresponding pairs of junctions
in close proximity to one another and to provide good
thermal coupling to a common, massive heat sink. Electrical
insulators having high thermal conductivity must be used,
but, since most electrical insulators don’t conduct heat
well, special insulators such as hard anodized aluminum,
beryllium oxide, specially filled epoxy resins, sapphire, or
diamond must be used to couple junctions to the heat sink.
Allowing test equipment to warm up and reach thermal
equilibrium in a constant ambient temperature also
minimizes thermoelectric EMF effects. The instrument zero
feature can compensate for any remaining thermoelectric
EMF, provided it is relatively constant. To keep ambient
temperatures constant, 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.
connecTions To Avoid ThermoelecTric emFs
Connections in a simple low voltage circuit, as shown in
Figure 3, will usually include dissimilar materials at different
temperatures. This produces a number of thermoelectric
EMF sources, all connected in series with the voltage source
and the meter. The meter reading will be the algebraic
sum of all these sources. Therefore, it is important that the
connection between the signal source and the measuring
instrument doesn’t interfere with the reading.
Figure 3: Connections from Voltage Source to Voltmeter
If all the connections can be made of one metal,
the amount of thermoelectric EMF added to the
measurement will be negligible. However, this may not
always be possible. Test fixtures often use spring contacts,
which may be made of phosphor-bronze, beryllium-
copper, or other materials with high Seebeck coefficients.
In these cases, a small temperature difference may
generate a large enough thermoelectric voltage to affect
the accuracy of the measurement.
If dissimilar metals cannot be avoided, an effort should
be made to reduce the temperature gradients throughout
the test circuit by use of a heat sink or by shielding the
circuit from the source of heat.
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Low Voltage Measurements
Measurements of sources at cryogenic temperatures
pose special problems since the connections between
the sample in the cryostat and the voltmeter are often
made of metals with lower thermal conductivity than
copper, such as iron, which introduces dissimilar
metals into the circuit. In addition, since the source
may be near zero Kelvin while the meter is at 300K,
there is a very large temperature gradient. Matching
the composition of the wires between the cryostat
and the voltmeter and keeping all dissimilar metal
junction pairs at the same temperature allows making
very low voltage measurements with good accuracy.
reversinG sources To cAncel
ThermoelecTric emFs
When measuring a small voltage, such as the difference
between two standard cells or the difference between
two thermocouples connected back-to-back, the
error caused by stray thermoelectric EMFs can be
canceled by taking one measurement, then carefully
reversing the two sources and taking a second
measurement. The average of the difference between
these two readings is the desired voltage difference.
In Figure 4, the voltage sources, Va and Vb, represent
two standard cells (or two thermocouples). The voltage
measured in Figure 4a is:
V1 = Vemf + Va – Vb
The two cells are reversed in Figure 4b and the measured
voltage is: V2 = Vemf + Vb – Va
The average of the dif ference between these two
measurements is:
V1 – V2 = Vemf + Va – Vb – Vemf – Vb + Va or Va – Vb 2 2
Figure 4: Reversing Sources to Cancel Thermoelectric EMFs
Notice that this measurement technique effectively
cancels out the thermoelectric EMF term (Vemf), which
represents the algebraic sum of all thermoelectric EMFs
in the circuit except those in the connections between Va
and Vb. If the measured voltage is the result of a current
flowing through an unknown resistance, then either the
current-reversal method or the offset-compensated ohms
method may be used to cancel the thermoelectric EMFs.
rFi/emi
RFI (Radio Frequency Interference) and EMI (Electro-
magnetic Interference) are general terms used to
describe electromagnetic interference over a wide range
of frequencies across the spectrum. RFI or EMI can be
caused by sources such as TV or radio broadcast signals
or it can be caused by impulse sources, as in the case
of high voltage arcing. In either case, the effects on the
measurement can be considerable if enough of the
unwanted signal is present.
RFI/EMI interference may manifest itself as a steady
reading offset or it may result in noisy or erratic readings.
A reading offset may be caused by input amplifier
overload or DC rectification at the input.
RFI and EMI can be minimized by taking several
precautions when making sensitive measurements. The
most obvious precaution is to keep all instruments, cables,
and DUTs as far from the interference source as possible.
Shielding the test leads and the DUT (Figure 5) will often
reduce interference effects to an acceptable level. Noise
shields should be connected to input LO. In extreme cases,
a specially constructed screen room may be necessary to
attenuate the troublesome signal sufficiently.
If all else fails to prevent RF interference from being
introduced into the input, external filtering of the device
input paths may be required, as shown in Figure 6. In
many cases, a simple one-pole filter may be sufficient;
in more difficult cases, multiple-pole notch or band-stop
filters may be required. In particular, multiple capacitors
of different values may be connected in parallel to
provide low impedance over a wide frequency range.
Keep in mind, however, that such filtering may have other
detrimental effects, such as increased response time on
the measurement.
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Low Voltage Measurements
Figure 5: Shielding to Attenuate RFI/EMI Interference
Figure 6: Shielded Connections to Reduce Inducted RFI/EMI
inTernAl oFFseTs
Nanovoltmeters will rarely indicate zero when no voltage
is applied to the input, since there are unavoidable voltage
offsets present in the input of the instrument. A short
circuit can be connected across the input terminals and
the output can then be set to zero, either by front panel
zero controls or by computer control. If the short circuit has
a very low thermoelectric EMF, this can be used to verify
input noise and zero drift with time. Clean, pure copper
wire will usually be suitable. However, the zero established
in this manner is useful only for verification purposes and
is of no value in the end application of the instrument.
If the instrument is being used to measure a small
voltage drop resulting from the flow of current through
a resistor, the following procedure will result in a proper
zero. First, the instrument should be allowed to warm up
for the specified time, usually one to two hours. During
this time, the connections should be made between
the device under test and the instrument. No current
should be supplied to the device under test to allow the
temperature gradients to settle to a minimum, stable
level. Next, the zero adjustment should be made. In some
instruments, this is done by pressing REL (for Relative) or
ZERO button. The instrument will now read zero. When
the test current is applied, the instrument will indicate the
resulting voltage drop. In some applications, the voltage
to be measured is always present and the preceding
procedure cannot be used. For example, the voltage
difference between two standard cells is best observed
by reversing the instrument connections to the cells
and averaging the two readings. This same technique
is used to cancel offsets when measuring the output of
differential thermocouples. This is the same method used
to cancel thermoelectric EMFs.
Zero driFT
Zero drift is a change in the meter reading with no input
signal (measured with the input shorted) over a period
of time. The zero drift of an instrument is almost entirely
determined by the input stage. Most nanovoltmeters use
some form of chopping or modulation of the input signal
to minimize the drift.
The zero reading may also vary as the ambient temperature
changes. This effect is usually referred to as the temperature
coefficient of the voltage offset. In addition, an instrument
may display a transient temperature effect. After a step
change in the ambient temperature, the voltage offset may
change by a relatively large amount, possibly exceeding the
published specifications.
The offset will then gradually decrease and eventually
settle to a value close to the original value. This is the
result of dissimilar metal junctions in the instrument with
different thermal time constants. While one junction will
adjust to the new ambient temperature quickly, another
changes slowly, resulting in a temporary change in
voltage offset.
To minimize voltage offsets due to ambient temperature
changes in junctions, make measurements in a
temperature controlled environment and/or slow down
temperature changes by thermally shielding the circuit.
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Low Voltage Measurements
Noise
Significant errors can be generated by noise sources,
which include Johnson noise, magnetic fields, and ground
loops. An understanding of these noise sources and the
methods available to minimize them is crucial to making
meaningful low voltage measurements.
Johnson noise
The ultimate limit of resolution in an electrical measure-
ment is defined by Johnson or thermal noise. This noise
is the voltage associated with the motion of electrons due
to their thermal energy at temperatures above absolute
zero. All voltage sources have internal resistance, so all
voltage sources develop Johnson noise. The noise voltage
developed by a metallic resistance can be calculated from
the following equation:
where: V = rms noise voltage developed in source resistance
k = Boltzmann’s constant, 1.38 × 10–23 joule/K
T = absolute temperature of the source in Kelvin
B = noise bandwidth in hertz
R = resistance of the source in ohms
For example, at room temperature (290K), a source
resistance of 10kΩ with a measurement bandwidth of
5kHz will have almost 1μV rms of noise.
Johnson noise may be reduced by lowering the
temperature of the source resistance and by decreasing
the bandwidth of the measurement. Cooling the sample
from room temperature (290K) to liquid nitrogen
temperature (77K) decreases the voltage noise by
approximately a factor of two.
If the voltmeter has adjustable filtering and integration,
the bandwidth can be reduced by increasing the amount
of filtering and/or by integrating over multiple power line
cycles. Decreasing the bandwidth of the measurement
is equivalent to increasing the response time of the
instrument, and as a result, the measurement time is
much longer. However, if the measurement response
time is long, the thermoelectric EMFs associated with
the temperature gradients in the circuit become more
important. Sensitive measurements may not be achieved
if the thermal time constants of the measurement circuit
are of the same order as the response time. If this occurs,
distinguishing between a change in signal voltage and a
change in thermoelectric EMFs becomes impossible.
mAGneTic Fields
Magnetic fields generate error voltages in two circum-
stances: 1) if the field is changing with time, and 2) if there
is relative motion between the circuit and the field. Voltages
in conductors can be generated from the motion of a
conductor in a magnetic field, from local AC currents caused
by components in the test system, or from the deliberate
ramping of the magnetic field, such as for magneto-
resistance measurements. Even the earth’s relatively
weak magnetic field can generate nanovolts in dangling
leads, so leads must be kept short and rigidly tied down.
Basic physics shows that the amount of voltage a magnetic
field induces in a circuit is proportional to the area the
circuit leads enclose and the rate of change in magnetic
flux density, as shown in Figure 7. The induced voltage is
proportional both to the magnitude of A andBB , as well as
to the rate of change in A and BB , so there are two ways to
minimize the induced voltage:
n Keep both A andBB to a minimum by reducing loop
area and avoiding magnetic fields, if possible; and
n Keep both A andBB constant by minimizing vibration
and movement, and by keeping circuits away from
AC and RF fields.
To minimize induced magnetic voltages, leads must be
run close together and magnetically shielded and they
should be tied down to minimize movement. Mu-metal,
a special alloy with high permeability at low magnetic flux
densities and at low frequencies, is a commonly used
ma