Electrical Measurements
SAFETY CONCERNSIn the United States, electrical potentials more than
48V are considered dangerous to human life. Althoughpeople have survived electrical shocks exceeding
thousands of volts and lightning strikes carrying
millions of joules of energy, everyone should treat
electricity with caution and respect. Voltage is not
the only concern, however. Currents in the mA range
can stop a normal heart under certain conditions. For
example, NIOSH (National Institute for Occupational
Safety and Health) estimates that as little as 20 mA at
110 VAC, the common utility voltage, can paralyze
respiratory muscles.
All equipment and sources of voltage and current, suchas the item under test, should not be powered when
making connections between sensors, actuators or othercomponents and the data acquisition system. This isespecially critical when using current transformers andmeasuring high voltages and AC current.

MAKING VALID MEASUREMENTS

Accurate measurements depend on accurate equipment and robust connections. Poor connections
and noise picked up through unshielded leads andimproperly grounded circuits will certainly yield inaccurate data. Packaged sensors are typically designed toensure accurate output signals with proper component
placement, shielding, filtering, and bypassing powerand ground I/O connections. Unprotected sensors,
however, such as thermocouples and strain gages often
are exposed to numerous types of noise signals thatcan couple into the sensors and leads and contaminate
the desired signal. Those who install such sensors must
follow industry-accepted practices to ensure that thesensors’ output signals are reliable, unbiased, and freeof noise and interference.

Some systems are manually switched to the proper
range, while others select the range automatically.
In addition, after properly connecting the sensors,
the item under test, and the data acquisition system,
apply power first to the data acquisition system. Next
energize the sensors and finally, the item under test.
Some data acquisition systems can be damaged whenvoltages are applied to their inputs while unpowered.

High DC Voltage
Voltages greater than about 24 VDC are considered highvoltage in data acquisition system terms. Built-in or
external voltage dividers and special signal conditioners are needed for dividing tens or hundreds of volts
down to just 10V or less to protect the instrument’s
input circuitry. One critical consideration for the safetyof both the equipment and operators is to use highvoltage insulation in wires, terminals, connectors, leads,
sensors, and other components to prevent leakage andarcing to low-potential terminals and nearby objects.

Low DC Voltage
Compared to high voltages, successfully measuringlow-level DC signals depends upon appropriate wiring
techniques between the signal source and the dataacquisition device. Input amplifier stages in signal
conditioning equipment cannot distinguish between
the measured signal and a noise voltage coupled into
lead wires. When measuring signals less than one volt,
shielded or unshielded twisted pairs provide the bestprotection against noise voltage pickup. Best wiring
practices call for shields to be grounded at one end
only, preferably at the signal source.

AC VOLTAGE
Low AC Voltage

DC VOLTAGE

Instrumentation Level DC Voltage

Data acquisition systems usually contain integratedcircuit signal conditioners and multiplexers at their
input terminals. These ICs typically can’t handle morethan about ±10 VDC input, although some may tolerate
as much as ±25 VDC. One way around the limitation isto place a voltage divider on the system’s input terminals
that reduces the voltage to meet the IC’s specifications.

General-purpose data acquisition systems often measure
low-level AC voltages on the secondary of loaded current transformers, step-down potential transformers,
clamp-on current probes, current-sensing resistors, orsensors lacking galvanic isolation. All these low-level
AC voltages must have a low common-mode voltage
component with respect to earth ground or float withminimal AC leakage. Also, connect the voltage source
to earth ground when necessary.

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)High-Voltage Adapter
High-voltage adapter≈50 kΩ

C

5 MΩ

A≈50 kΩ

Channel 1

C

5 MΩ

10 MΩ

B
5 MΩ

Data acquisition system

10 MΩ

A

10 MΩ
≈50 kΩ

High-voltage adapter

Data acquisition system

10 MΩ≈50 kΩ

Differential Input Attenuation

B
5 MΩ

Channel 1

Fig. 4.02. A differential amplifier requires a resistor at both
inputs when running single-ended, but only one resistor in a
voltage-divider attenuator.

Fig. 4.01. A typical data acquisition system usually requires
an attenuator at its input to accept voltages that exceed 10 V.

Outlet Level AC Voltage

system measure a lower voltage referenced to analog common.
Because the outputs from amplifiers A and B are identical, they
can be considered a common-mode voltage that the differential
amplifier C rejects.

In the U.S. and Canada, utility wiring supports a nominal
110 VAC, 60 Hz, single-phase voltage, suppliedwith (6.11)
three wires;
Figure 4.01
hot, neutral, and ground. Europe typically uses 220 VAC, 50 Hz,
and Japan supplies 100 VAC; 50 Hz in Eastern Japan and 60 Hz
in Western Japan. In many factories, 220/230 to 460/480 VAC,
single and three-phase voltage, Wye and Delta configurations arealso distributed to electrical and electronic control equipment.
All these voltages are lethal and leads should be connected or
disconnected from the data acquisition system and the equipment under test with the power disconnected.

This scheme attenuates the high and low signals, and lets bothends float hundreds of volts above ground. For example, the highinput can be 110 VAC while the low end has a 50 VDC offset.
After attenuation, the peak voltage of the high side signal is 0.77V
and the low side signal is 0.25V, which are well within the readable range of the data acquisition system’s differential inputs.
When a single-ended measurement is attempted by attenuating
only the high signal and pulling the low signal to ground, two
problems can develop. First, when the data acquisition system
ground and the signal ground are different, tying them together
forms a ground loop, which can result in excessive current anddestroy the instrument or equipment. The second error component
comes from the bias currents Ib flowing through the input pinsof the two operational amplifiers, A and B shown in Figure 4.02.
The bias current produces a voltage drop through the divider on
the high side input, but the low side input has no matching drop.
The difference appears at the input to differential amplifier C andproduces an offset at its output.

When connecting these voltage sources to data acquisition systems,
problems often crop up in ground loops, which produce noise.
Voltage drops appear between the neutral wire and ground formany reasons, some of which cannot be eliminated easily or evenfound. Accepted practices for shielding, grounding, and isolation
should be followed rigorously. Refer to Chapter 10 for more detailed
information concerning ground loops and interference.

High Voltage
Similar to DC voltage levels, data acquisition system inputs typically can’t handle more than ±10 VAC peak. Higher AC voltages
are attenuated and scaled with a signal conditioning stage before
they are processed. Voltages up to 2,000V, peak-to-peak, can bemeasured with a fully differential attenuator, calibrated to matchthe buffered differential inputs of a data acquisition system. Attenuators are typically voltage divider networks connected fromthe high side input terminal to a common ground.

Effective, Peak, Average, and RMS Voltage
Dc voltages and currents are relatively easy to measure andcalculate with Ohm’s law. For example, DC power is mathematically equivalent to the product of DC voltage and current andgenerates a unique amount of heat energy or performs a uniqueamount of work. By comparison, power calculations for AC voltage and current includes an additional factor, the cosine of thephase angle between them, called the power factor. When thevoltage and current waves are in phase, the cosine of the angle
is unity, so the product of voltage and current is a valid power
value measured in watts. When they are out of phase, however,the power factor is less than unity, so the power generated is lessthan the simple product of voltage and current. In an extreme
case, 90˚ for example, the cosine of the phase angle is zero, so thewattage is also zero. However, the power is then totally reactive,
does not generate heat (theoretically), and is simply labeled VA(volt-amperes).

For systems with a true differential input, however, neither the
input’s low nor high side can be connected directly to ground.
Two matched resistor dividers attenuate the incoming signal, oneon the high side and the other on the low side. Only the low sideof the attenuator is grounded. For example, an accessory device
is required to provide a 200:1 attenuation without affecting theamplifier’s high input impedance. In a typical system, the two
matched buffer amplifiers, A and B (Figure 4.01), on the front
end of the data acquisition system draw almost identical input
bias current. Matched voltage dividers placed on the high andlow-side inputs provide symmetrical current limiting from either
input and let the quasi-differential input of the data acquisition

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Effective Voltage
V

Effective voltage

141.4(B) DC voltage

Amplitude (v)1000Typical Data Acquisition Input

270˚

+

Peak (B)(C)

AC sine wave
90˚

+15
Vout

Peak (A)

–
–15

t

450˚

(A)

13.8V
commonmode-100-141.4
-V

+

50A
50 mV
shunt

ALT
Alternator

Battery–

Fig. 4.03. The numerical value for the peak voltage of AC mustbe 1.414 times that of DC to produce the same heating effect.
Fig. 4.04. The battery charging current in an automobile electrical system is typically measured with a handheld diagnostic
voltmeter across a shunt resistor, which is totally isolated fromthe battery voltage. However, when a data acquisition input
amplifier is connected to the shunt, the input also must sustain
the common mode voltage represented by the battery.

EQN 4.01. DC Power

P=ExI
Where:
E and I are in phase
P = power, W
E = DC voltage, V
I = DC current, A

Figure 4.04 Alternate

are the same; therefore the peak-to-peak value in this example
is twice 141.4 or 282.8 Vp-p.

EQN 4.02. AC PowerThe rms voltage value of a sine wave is equal to the effective
value and is defined as the square root of the average of thesquares of the instantaneous voltages measured over a given
number of cycles.

P = E x I x Cos φ
Where:
P = power, W
E = AC voltage, V
I = AC current, A
φ = phase angle between voltage and current

EQN 4.03. Volts rms

V rms =

Effective Voltage

V 1 2 + V 2 2 + V 3 2 + ...V n 2

The AC voltage wave shape follows a sine function (ideally), andbecause it continually rises and falls over each cycle, the area
under the curve for AC is less than for DC over the same (peak)
amplitude and time period. Thus, 100 VAC peak generates less heatthan 100 VDC in the same load. (See Figure 4.03.) To compensate
for this, peak AC voltages must be higher than DC to generate anequivalent amount of heat. The value of AC voltage that produces
an equivalent amount of work as the DC value is called the effective
voltage and equals the DC value multiplied by 1.414. In otherwords, 141.4 peak VAC produces the same amount of heat in agiven load, as does 100 VDC.

When the shape of the AC signal is not a near-perfect sine wave,
ordinary vane-type voltmeters will not indicate a true rms AC value.
Special meters and some data acquisition systems, however, aredesigned to compensate for the shape discrepancies and are calledtrue rms meters. They measure and indicate the true rms value ofthe AC signal, regardless of the distortion. The average value of theAC voltage is zero, because the positive half cycle magnitude equals
the negative half cycle of the wave shape.

RMS Voltage

Voltage drops are relatively easy to measure with most instruments
because the difference in voltage appears between any two points
in a circuit. The circuit does not need to be disturbed or changed(provided the measuring instrument’s impedance is high compared with the impedance of the measured circuit) to make themeasurement. By comparison, simple direct-connection current
measurements are more troublesome, because the current appears
within a loop and the loop must be opened to insert the ammeter.

CURRENT

Equation 4.03

A Fundamental Problem

In order to make AC and DC voltmeter scales read the same value
for the same amount of work done, the AC voltmeter scales arecalibrated in rms (root mean square) voltage values. When observing 100 VAC rms on the meter face, the voltage is actually
141.4 VAC peak, and the amount of work it does equals that of
100 VDC (in the same load). Moreover, for ac, the maximum(peak) positive excursion and the maximum negative excursions

3
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Ground Referenced Differential Measurement

Shunt Resistor Current Measurement

Channels
CH0 H

Current
source

CH0 L
CH1 H

Differential amplifier

R

CH1 L

Supply

i

CH2 H

Motor
Loads

–
+A

ADC

100 kW

CH2 L

ShuntsAnalogCommonGood for a low
signal reference

Bad for a low
signal reference

Fig. 4.06. Sensors with 4 to 20 mA outputs are typicallyplaced in series with a resistor to develop a voltage. The
resistor is then connected to the input of a differential amplifier to measure the voltage drop.

Mux Board

Fig. 4.05. High DC currents are often measured withshunts using differential inputs sharing a common ground.

Figure 4.06 (3.06)

a calibrated shunt resistor. Figure 4.05 shows a special application
for differential measurements where the three shunts have one
end placed in the common side of a three-motor circuit. This
arrangement provides a common ground that can be connected to
an inexpensive monitoring unit with a non-isolated, low-voltage
input. Unfortunately, not all circuits that need more than one
shunt will have one end of each shunt conveniently connected
to a common point. In these instances, more expensive, isolated
analog input amplifiers are recommended.

Moreover, the ammeter contains a characteristic resistance or
impedance that most often changes the circuit parameters andmust be compensated to obtain accurate measurements.
Some current measuring instruments, however, can couple
inductively and have little or no affect on the circuit parameters.
Such probes are designed for both AC and DC circuits.

Insertion Loss

Data acquisition systems also measure low-level DC currents
with shunts. Many sensors output a standard 4 to 20 mA current, which is linearly related to the quantity being measured.
The signal current passes through the shunt resistor, as shownin Figure 4.06, and the voltage drop across the shunt provides
the input for the ADC.

Inserting an instrument or device in series with the circuit causes thetotal series impedance to change. In many applications, the added
component or sensor requires some power to operate or drops somevoltage resulting in what is called insertion loss. Therefore, somesignal power may be consumed in making the measurement, whichmust be compensated to provide a more accurate measurement.

Ohms law defines the nature of this simple circuit where theproduct of resistance (R) and current (I) yields the voltage: V = IR.
Consequently, when the data acquisition system requires a 10V
input for a 20 mA full-scale reading, a 500 W resistor does the job:

Common-Mode Limitations

Most differential amplifiers used for signal conditioners in data acquisition systems can sustain only a limited common mode voltage,
typically about ±10 VDC. However, more expensive amplifiers or
signal conditioners are available for special applications that sustain
common mode voltages exceeding the 10 VDC limit.

EQN. 4.04. Shunt Resistor

R = V/I = 10V/0.02A = 500 W
The current loop provides higher noise immunity and accuracy
than does a voltage source when measuring with long leads ofrelatively high resistance. In this case, the lead resistance is part of
the 500 W, so in a simple series circuit, the shunt resistor is often
adjustable in order to calibrate the loop to exactly 20 mA full scale.

One application, for example involves measuring the voltage
drop across a calibrated shunt resistor in an alternator charging
circuit. When the amplifier input is connected to the shunt
resistor to measure mV scaled to charging current, the common
mode voltage seen by the amplifier input is the maximum battery
voltage, nominally 13.8 VDC, but may be as high as 18.5 VDC
during high-current charging. Therefore, the common-mode
voltage rating for the data acquisition system input must be
greater than 18.5 VDC.

The accuracy and stability of the measured voltage across the shunt
are only as accurate and stable as the shunt resistor itself. Resistor
accuracies are commonly 5, 1, 0.5, 0.1 and 0.01% and come with atemperature coefficient that specifies their stability over a specifictemperature range. In addition, a 0.1% resistor usually has a lower
temperature coefficient and better long-term stability than a resistor
with lower accuracy because of its construction, which is usuallywire wound or metal film vs. carbon film or carbon composition.

ShuntsData acquisition instruments usually measure high-level DC
currents (in the ampere range) as a 50 or 100 mV voltage drop across4
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Current Transformers

Hall-Effect Sensor Flux Meter
Flux lines

C.T.
ratio
100:1

High-current
conductor

0.01 W

Current
sourceVout = 50 mVrms

Semiconductor

Voltmeter
I = 500 Arms

Fig. 4.08. When either the voltage or current port is regulated and calibrated, the Hall-effect device can be used as amagnetic flux sensor. The unregulated port provides an output
signal proportional to the magnitude of unknown flux density.
However, a Hall-effect proximity sensor or switch is a more
widely used component based on this principle.

Fig. 4.07. Current transformers are a convenient means tomeasure high AC currents. The voltage dropped across theresistor is proportional to the current through the transformer.

Current Transformers

Figure 4.08 (4.09 A)

exposed to a magnetic field, and a calibrated current is injectedacross the other two opposite edges.

High AC currents can be measured with shunts under special
circumstances, but most often such direct connections to AClines are extremely dangerous to humans. One way to get aroundthe hazard is to use current transformers (CT) that isolate ACline voltages and reduce input current by a specified ratio.
(See Figure 4.07.) A 500:5 CT, for example, has a 100:1 ratio andgenerates a secondary current of 5 A with 500 A in the primary.
When a low value load resistor such as 0.01 W connects to the
output of the current transformer, the full load secondary current produces 50 mVrms, which can be easily read with the dataacquisition system’s analog input. Although this output voltage
seems low, higher resistance values will drive the CT out of its
calibrated range and reduce the accuracy of the measurement.
Moreover, a CT rated at 2 VA can handle only a maximum usable load resistance (including lead wires) of 0.08 W.

The Hall-effect sensor is ideal for measuring magnetic fields or AC
and DC power. For power applications, it becomes a multiplying
device. It automatically multiplies the voltage and current toyield power and includes the phase angle factor as an integral
property. An electromagnetic coil generates the Beta field with
its core perpendicular to the surface of the thin Hall element
inside a shielded package. The coil connects in series with theload to sense load current, and the load voltage connects acrossthe semiconductor element as shown in Figure 4.09. The resulting current vector drives a readout device calibrated in watts or
becomes a control signal to a power controller in a closed-loop
circuit. Because the Hall-element material is temperature sensitive, a packaged Hall-effect wattmeter contains temperaturecompensating circuits. The defining equation for the output isthe product of the vectors:

For safety, always make certain that the current loop is closed before
applying power. An open-circuit CT can generate many thousandsof volts at its terminals with lethal current levels. For example,
consider a 5,000:5-A current transformer with a turns ration of
1,000 to 1, and 10 VAC output signal developed across a calibrated
low impedance load. The open-circuit secondary voltage is then
1,000 X 10 = 10,000 VAC, a very dangerous level to be connecting or disconnecting to a data acquisition system shunt resistor.

EQN: 4.05. Hall-Effect Sensor PowerP = E x I x Cos (φ)
Where:
P = power in the load, W
E = load voltage, V
I = load current, A
φ = phase angle between load voltage and load current

Hall-Effect Sensors

In 1879, Dr. Edwin Hall discovered the fundamental operating
principle of the sensor named after him. The basic Hall-effect sensor
operates under the influence of three parameters; current, voltage,
and a magnetic field. Hall passed a constant current through a gold
foil conductor while exposing the surface of the conductor to amagnetic field. A voltage drop developed across the opposite sidesof the conductor with a magnitude dependent on the propertyof the sensor material (Hall coefficient) and proportional to theintensity of the magnetic field. (See Figure 4.08.)

A Hall-effect sensor intended to measure a magnetic field is constructed such that the flat surface of the sensor element is exposedto the magnetic field. A calibrated voltage or current is applied
to the edges of the semiconductor as described above, and theunit is calibrated to accurately measure a specific range of Beta
(magnetic flux) values. The same principle is widely used in aHall-effect switch, where the magnetic field bias may be appliedwith a permanent magnet and a slotted vane alternately interrupts
the flux path. The output of the sensor switches between a low
voltage and a high voltage as the flux path is interrupted. Sucha device had been used as a switch for many years in numerous
automobile distributors to replace the ignition points.

A modern Hall device replaces the original conductor with a thinsheet of semiconductor material. The output voltage appears
between two opposite edges of the sheet when the flat surface is

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Hall-Effect Sensor Wattmeter
Load

Iron containing
magnetic flux
Hall device
IL = Load current

Voltmeter
Power calibrated inindicator Watts - PW

RC

Flux
lines

VL = Load voltage

Line

Transformer

VW = Voltage
proportional to power

PW = ILVL x Cos φ
where φ = phase angle between voltage and current

Fig. 4.09. A Hall-Effect sensor is an ideal wattmeter for measuring AC power. It inherently includes the phase angle between
the voltage and current vectors as a multiplying factor to convert VA to W.

Voltage Divider Method

Resistive Voltage Divider
Reference

Figure 4.09A (4.08)
Rk(known)

+

A

–

B
Out
Gnd

Ru
(unknown)

+

A

–

B

x1

Vs

Resistance voltage divider circuits can use either single-ended ordifferential-input amplifiers. (Refer to Figure 4.10.) The knownreference resistor should have a value that is close to the unknown
value, and the source voltage should be low enough to ensure thatthe current is within acceptable limits such as 1.0 mA or less. For
example, when measuring an unknown resistor near 1,000 W,
select a 1,000 W reference resistor and a supply of 2.0 VDC. This
produces a current of 2/2,000 = 1 mA. A 1,000 W reference resistor keeps the current relatively low and satisfactorily measuresunknown values down to the 100 W range. The unknown resistor
value is calculated from:

Data
acquisition
systemVs
Sourcex1

Vm

EQN. 4.06. Voltage Divider Resistor

Ru
Vm
=
Rk
Vs – Vm

Ru = (Rk)(Vm)/(Vs – Vm)
Where:
Vm = measured input voltage, V
Vs = source voltage channel, V
Rk = known resistance, W
Ru = unknown resistance, W

Fig. 4.10. Resistive voltage dividers work with single-ended
or differential amplifiers and a reference resistor whose
value is near the unknown resistor’s value.

RESISTANCE

For example:

Basic Measurements

Where:
Vs = 2V
Vm = 1.10V
Rk = 1,000 W
Ru = unknown resistor, W

Ordinary ohmmeters measure resistance indirectly by injecting asmall current into the resistor under test and measuring the resulting
voltage drop across its terminals. Precision reference resistors called
multipliers scale analog meters to read in the middle portion of its
face, while digital ohmmeters scale either manually or automatically to properly position the decimal point. Digital multimeters(DMMs) similarly apply a DC voltage across an unknown resistor
and a precision shunt resistor. The test current generates a voltage
drop across the shunt resistor, which is read by the ADC to output
a digital value of the unknown resistor. Data acquisition systems,
however, do not typically read ohms directly; they measure voltages and voltage ratios across known and unknown resistancedividers and compute equivalent resistor values.

Then:
Ru = (1 k)(1.10 V)/(2.0 – 1.10)
Ru = (1,100)/(0.90) = 1,222.2 W

Constant Current/Voltage Drop

Current source/voltage drop methods to measure unknown
resistances use both two and four-wire circuits. Two-wire circuits
should be avoided for measuring very low to moderately low

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Wheatstone Bridge
Precision resistor
decade box

Precision calibrated
dial or digital readout

Anderson Loop
Current loop

Rw

1.010

A

Rx
unknown
resistor

B

R

Rw
Null
meter

Vg
V1

∆R

Rw

Subtractor

R w2

Gage

+
Excitation
–

Rw

R w1

Current
source

A1

R w3

+
A3
–

R w4

Vout

V out

VREF
RF

Fig. 4.11. An unknown resistor placed in one arm of a
Wheatstone bridge typically unbalances the circuit symmetry
and produces an offset voltage across nodes A and B. But
adjusting a precision, variable resistor in the opposite arm
brings the circuit back into balance when it equals the unknown
resistor value, which may be read on a calibrated dial.

V2

A2

Fig. 4.12. The Anderson loop uses a unique subtractor circuit, which eliminates errors arising from lead wire resistance.
It measures only the sensing element’s resistance change.

Figure 4.12

resistances because the lead wires and connections can become
part of the total resistance (which is added to the unknown value).

resistor. The potentiometer comes with a precision, calibrated
readout device that indicates its resistance, which is also thevalue of the unknown resistor.

Small Deviations

Anderson Loop Alternative

Resistance measurement errors come from a number of sources.
The most common errors in low resistance circuits for simple
constant current/voltage drop methods using two wires comefrom the lead wire resistance and connections added to theunknown resistance. Keeping the lead wires short and using
four-wire circuits such as Kelvin connections can minimize theseerrors. Errors in high resistance measurements can come from theshunt resistance of insulation, such as in wiring and connector
bodies. When using a current source and measuring the voltage
drop, use high input impedance measuring devices, whether
they are voltmeters or signal conditioner inputs. For extremely
high resistor measurements, use a voltage source and measure
the current using short lead wires and robust connections.

The basic Anderson loop is often compared to a passive bridge
circuit, but it provides higher accuracy measurements with lessexcitation voltage. Furthermore, it contains an amplifier, whichputs it in the class of an active device.
The basic Anderson loop is a series circuit composed of one sensing element in series with one reference element powered by aconstant-current source. A dual-differential operational amplifier
with high temperature stability and high CMRR, called a subtractor, delivers the output response from the sensing element.
(Refer to Figure 4.12.) The advantage of this topology lies in its
ability to ignore changes in lead wire resistance and to amplify
only the output changes of the sensing element.

WHEATSTONE BRIDGE

The output response Vout of a basic strain-gage circuit is defined by:

Basic Principle

EQN. 4.07. Anderson Loop Output

Wheatstone bridges often measure precise resistances andextremely small resistance changes. A typical bridge circuit isarranged in a symmetrical pattern of equal-value series-parallel
resistors across a power source as shown in Figure 4.11. When all
resistors are identical, the voltage drops across them are equal,
and the voltage between nodes A and B is zero. When one ormore resistors are not equal, which is usually the resistor under
test, the bridge unbalances and a null meter placed between thenodes measures the amount of unbalance. An adjustable resistor
or a potentiometer can be placed in one arm of the bridge tomanually rebalance the circuit. When the potentiometer drives
the meter back to zero, its value then equals that of the unknown

Vout = A1V1 – A2V2
Vout = Ir (∆Rg)
Where:
A1 = amplification factor of stage 1
A2 = amplification factor of stage 2
V1 = voltage across sensing strain gage, V
V2 = voltage across reference strain gage, V
Ir = constant current, A∆Rg = strain gage resistance change, W

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13

Anderson Loop for Multiple strain Gages
Current loop

Anderson
subtractors
+
Gage
V1
R1 + ∆R1 –i,electricalcurrent
sourceThermocouple

–

+
Gage
V2
R2 + ∆R2 –

+

+
Gage
V3
R3 + ∆R3 –

+

+
Gage
V4
R4 + ∆R4 –

+

+

Vref
–

A

V1out

+

ib
V2out

Differential
amplifierRb = 10 kW–

Fig. 4.14. The resistor is necessary for at least one input toprovide the path to ground for amplifier bias currents.

V3out

–
V4out

The significance of the output signal voltage, I∆Rn, is that it isprincipally a function of the change in resistance or impedanceof the sensing element, not it’s absolute terminal resistance.

Vref

SINGLE-ENDED AND DIFFERENTIAL
MEASUREMENTS–
Instrumentation
amplifiers

Rrefreference
impedance

Differential Thermocouple Measurement

Figure 4.14
Reference
input

Basic Principles

Data acquisition systems provide for both single-ended anddifferential-input connections. The basic difference between
the two is the choice of the common connection for analog
voltage inputs. Single-ended multi-channel measurements
require that all voltages be referenced to the same, well-chosencommon node to prevent certain types of measurement errors.
Sometimes, however, an ideal common point cannot be secured
and a differential input is needed.

AnalogcommonFig. 4.13. The Anderson loop may be connected to multiple sensors in series such as in this strain rosette.
The circuit is not limited to only one sensor; it can be expanded
to contain numerous sensors in series such as a strain rosette. It
may be connected to signal conditioners with only six wires plus
a common as illustrated in Figure 4.13. Additional advantages
include an output voltage that is linear for each gage response,
it requires only 1/4 the power needed by the conventional
bridge circuit, and the loop output voltage is twice that of aconventional strain gage. The fact that the output signal of theAnderson loop is twice that of a strain gage Wheatstone bridge
circuit accounts for a 6 dB increase in signal-to-noise ratio.

Differential connections cancel or ignore common-mode
voltages and can measure the difference between the twoconnected points. The rejected common mode voltages canbe steady DC levels or noise spikes. When given a choice,the differential input is preferred.

When to Make Single-Ended Measurements

When single-ended and differential input measurements areoffered in the same data acquisition system, the differential
inputs usually consume two of the single-ended inputs. That is,
16 single-ended input amplifier channels equal 8 differentialinput amplifier channels. When noise susceptibility and groundloops are not a concern, single-ended input measurements
may be satisfactory.

The output responses of a multiple strain gage arrangement canbe expressed as:
EQN 4.08. Multiple Strain Gage Output

V1out – Vref = I∆R1
V2out – Vref = I∆R2
V3out – Vref = I∆R3
V4out – Vref = I∆R4
Where:
Rref = Rn, nominal gage resistance
Vnout = output voltage, V
I = constant current, A∆Rn = the change in resistance of the nth strain gage, W
Vref = reference voltage, V

When to Make Differential Measurements

Differential measurements call for a differential amplifier tomeasure the difference voltage between the two input signal leads. Differential amplifiers are preferred because they
provide greater noise rejection than single-ended amplifiers.
Furthermore, some sensors, particularly strain gages, requiremeasuring the voltage difference between the two signal
leads. Figure 4.14 depicts a differential amplifier configured
for a thermocouple. Although the amplifier measures thevoltage difference between the two inputs, a path to groundis required on at least one input of the amplifiers. The 10 kW
resistor between the low side and ground provides a path for
amplifier bias current. If the resistor is absent or too high in

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Differential Strain Gage Measurement

Differential Mode Noise Rejection

100 kW
R4

S1

R1
–
+A

Vexc
R3

+
Diff
–

R2
+

100 kW–

S1 – S2

S2

Excitation

Fig. 4.15. When the strain gage reference voltage and amplifier share the same common terminal, switched bias resistors
are not necessary.

Fig. 4.16. The differential amplifier rejects voltages that arecommon to both lines.

value, the bias current drives the input to one of the power
supply rail values, saturating the amplifier, which exceeds its
Figure 4.16
usual ±10V common-mode range.

when a DC path already exists at the sensor for bias current to flowfrom the amplifier inputs to analog common.
Consider the strain gage in Figure 4.15. When the excitation
voltage is referenced to the same common as the differential
amplifier, bias resistors are not required because the strain gage
itself provides a current path to ground for the instrumentation
amplifier. However, when the instrumentation amplifier is floatingor referenced to a different common, at least one bias resistor
is required. A balanced termination with a 100 kW resistor canalso be used.

The common-mode voltage generated by the bias current, ib, is:
EQN. 4.09. Common Mode Voltage

Vcm = 2ibRb
Where:
ib = bias current, A
Rb = bias resistor, W

Common-mode rejection ratio, CMRR, is a critical amplifier
specification and a measure of quality for instruments making
differential measurements. A large CMRR is necessary to accurately measure a small differential signal on a large common
mode voltage. The CMRR specifies the maximum effect of thecommon mode voltage on a differential measurement. Figure 4.16
shows the output signal free of the common mode input noise
after passing through the differential amplifier. The two noise
spikes entering the amplifier are equal in phase and amplitude,
so the difference amplifier cancels them.

The minimum value for Rb may be as low as a short circuit (onone side only), which reduces to a single-ended input configuration. Otherwise, under worse-case conditions, the voltage error inpercent of the applied voltage due to source resistance and Rb is:
EQN. 4.10. Voltage Error∆E(%) = 100( 2RRsb )Where:∆E = error, %Rs = source resistance, W
Rb = bias resistor, W

An amplifier’s CMRR is typically specified in decibels, dB, a ratioof two voltages that may differ by a large magnitude, and determined by:
EQN. 4.11. Common Mode Rejection Ratio

This applies to Rb for a balanced circuit where bias resistors are on
both inputs. Values for Rb typically range from 10 kW to 10 MW.
If both equations cannot be satisfied simultaneously, the source
resistance is too high to operate within specifications.

dB = 20log(V1/V2)
Where:
V1 = larger voltage, V
V2 = smaller voltage, V

Some amplifier inputs come with built-in bias resistors for differential
measurements, while users supply the bias resistors for extremely
high-impedance inputs. However, an incorrect user-supplied bias
resistor might dramatically lower the input impedance in nonisolated systems and load the circuits being measured. Other dataacquisition systems provide a suitable range of resistors that can beswitched to analog common (preventing users from selecting an
incorrect resistor). Alternatively, users can disconnect all resistors

For example, a ratio of 10 equals 20 dB, a ratio of 100 equals
40 dB and each additional factor of 10 adds another 20 dB to
the sum. Furthermore, an amplifier with a specification of 100
dB corresponds to a ratio of 100,000, so an instrument with a
CMRR of 100 dB measuring a signal on a common-mode voltageof 1 volt can have an error of 0.01 mV. If the common-mode

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7)

Optical Couplers
VinputR–+

Kelvin Connection
RL–+

Voutput

RL

R
Photo
diode

R1

LED
LED

R4
RL

Photo
diode

Input
groundExcitation andregulation++
Vexc Vsense––

R2

OutputgroundR3
RL
RL

Fig. 4.17. When making high common-mode voltage measurements, optical couplers provide a convenient and safemeans for connecting the voltage to data acquisition systems.

RL

Figure 4.18

Where Adiff = differential gain = 10
Acm = common mode gain = 0.001553
EQN. 4.12. Common Mode Rejection Ratio

CMRR = Adiff/Acm
CMRR = 10/0.001553
CMRR = 6,439
Find CMRR in dB:
EQN. 4.13. CMRR Example

CMRRdB = 20 log 6439 = 20(3.820) = 76.4 dB

High Common-Mode Voltage Measurements

Often, a small voltage riding on a much larger voltage must
be measured. For example, when a thermocouple sits on one
terminal of a battery, the signal conditioner input must be able
to measure the millivolt output of the thermocouple while suppressing the battery voltage. When the common-mode voltage
is less than 15V, an instrument amplifier with differential inputs
can read the thermocouple voltage while ignoring the battery
voltage. When the common-mode voltage is higher than 15V,
however, an isolation amplifier is usually required. (Also refer
to Figure 4.04.)
Although isolation does not protect amplifiers against excessive
normal-mode input voltage (voltage across a pair of inputs), it
does protect against excessive common-mode voltage. Isolation
eliminates a potentially large and damaging current that would
flow from the signal source due to the common-mode voltage.

–A

Signalconditioning

Fig. 4.18. The Kelvin connection eliminates lead resistancefrom altering the excitation voltage by using a second pair ofwires. The measuring device has relatively high input impedance so it does not draw current and develop a voltage drop
across its leads that would add an error.

voltage is larger, or if greater accuracy is needed, an amplifier
with a CMRR of at least 120 dB would be needed, a ratio of one
million to one.
Calculate the CMRR for a differential amplifier given in a data
sheet:+

Several isolation methods inherently include high common-mode
voltage rejection. Each channel can have an isolation amplifier,or a group of channels (not isolated from each other) can be
multiplexed and digitized by an ADC before the digital data are
isolated. Isolation barriers can be optical, magnetic, or capacitive.
The most common types are optocouplers composed of infrared(IR) light-emitting diodes (LEDs) detected by photodiodes on the
opposite side of a high-voltage, quartz barrier. Optocouplers cantransmit numerical data in serial pulse trains or sine waves andpulse trains whose frequency or pulse width can be modulatedwith analog signals. Varying LED current, as shown in Fig. 4.17,
can also transmit analog information. Magnetic barriers usingtransformers and capacitive barriers are generally internal andused in monolithic or hybrid isolation amplifiers.
In frequency-coupled isolation, a high-frequency carrier signal is
inductively or capacitively coupled across the isolation barrier.
The signal is modulated on the input side and demodulated on
the output side to reproduce the original input signal.
Isolated ADCs and their accompanying signal conditioning
circuits float. The ADC converts the input signal to a digital signal,and the interface for transferring the digital code is digitally
isolated. (See Chapter 6.)

KELVIN CONNECTIONSBasic Principle

Wheatstone bridge circuits are accurate, simple, sensitive, andconvenient ohmmeters to operate when the bridge, the unknown
resistance, and the readout are all located near one another. But
when the excitation and regulation circuit are located several
meters away from the bridge circuit, the lead resistance, RL, maycause an error in the excitation voltage.

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Common Ohmmeter Circuits
Basic Ohmmeter Circuit
Rw

+
+

+

V
–

–

i

+
Ru
–

Is
Rm

Rw

–
V≈Ω

Examples of Kelvin-Type Measurements

Kelvin Connection: Ohmmeter Circuit

Vs

A

+

Rw

+

I
Ru

–

One way around the problem is to use a Kelvin connection, amethod that connects the excitation and regulator circuits tothe bridge with four wires. Two wires carry the excitation current, and the other two, the sense lines, measure the excitation
voltage at the bridge and carry no current. Because the signal
conditioning circuit has high input impedance, little current
flows in the input leads, so their resistance does not introduce
significant errors. (See Figure 4.18.)

Rw

V

An example of the Kelvin circuit illustrates an ohmmeter composed of a current source and a voltmeter. (See Figure 4.19.) The
voltmeter measures the voltage dropped by the load resistor so thevalue of the resistor is simply V/I. The accuracy of the calculated
resistance in this configuration is directly proportional to the accuracy of the ammeter and voltmeter. The resistance is calculatedwith Ohms law:
EQN: 4.14. Kelvin Connection Resistance–

Ru = V/I
Where:
Ru = unknown resistance, W
V = voltmeter reading, V
I = ammeter reading, A
Rw = lead resistanceVs = voltage sourceV≈Ω

Kelvin Connection for Remote Voltmeter
I

Vs

Rw

A

Rw

+
–

V

i≈0
Rw

Ru

I

Rw
V≈Ω

Voltmeter calibrated in ohms
Rm = Multiplier resistors
Rw = Lead resistance
Ru = Unknown resistor
Vs = Voltage source
Is = Current source

Although the load or unknown resistor may be located a considerable distance from the ammeter and voltmeter, the long voltmeter
leads in the Kelvin equivalent circuit do not drop significant
voltage because they draw negligible current. Moreover, speciallydesigned Kelvin clips are available that connect to the load withminimal voltage drop at the jaw hinges and contact surfaces.

­ ig. 4.19. The basic ohmmeter circuit contains a currentF
source and multiplier resistors so the voltmeter scale may becalibrated in W. The Kelvin connection uses more than one setof leads to eliminate the lead resistance as a variable in theequation for both local and remote measurements.

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