Download The effects of resistor matching on common

CMR
The effects of resistor matching
on common-mode rejection
By Stephen Lee,
applications engineer,
Analog Devices
Process control and data acquisition systems often make differential measurements so that they
can isolate the desired differential
signal from unwanted commonmode signals. For example, when
measuring a strain gauge in a factory environment, the signal of
interest is the differential voltage
at the output of the strain gauge,
not the 50/60Hz common-mode
signal that is picked up by the
wires connecting the sensor to
the instrument.
Most differential signals are
measured using an instrumentation amplifier or difference
amplifier. This article will discuss
how these circuits achieve high
common-mode rejection, CMR.
More importantly, however, it
will discuss how to quickly calculate the level of performance
one can expect from off the
shelf components.
What is CMR and Why it is
Important
Common mode voltages are the
signals that are the same at both
inputs. Often, these signals are
unwanted because it is the differential signal that is of interest.
Figure 1: Electromagnetic interference and ground potentials can be rejected because they are common to both
inputs. The differential signal from the sensor is amplified.
Sensors that output differential
signals include load cells, strain
gauges and pressure sensors.
Measuring current across a
shunt resistor also requires a differential measurement. Figure 1
shows a schematic of an instrument measuring a Wheatstone
Bridge. The wires are far from the
sensor, and they pick up electromagnetically induced, 50/60Hz
signals from the power mains.
Since it is the sensor that is
of interest and not the 50/60Hz
signal, the data acquisition system will measure the difference
across the sensor and reject the
50/60Hz signal that manifests
itself at both inputs.
Difference Amplifiers and
Three Op Amp
In-Amps share a similar topology Either a difference amplifier
or instrumentation amplifier can
condition differential signals.
Figure 2 illustrates the differences. Difference amplifiers are used
when the input signal is larger
than the supply voltage of the op
amp. When higher impedance
is needed, an instrumentation
amplifier is selected, because it
has buffered inputs which offer
Figure 2: Difference Amplifier (left) and a three op-amp instrumentation amplifier (right).
high input impedance, typically
in the GigaOhm range. A classic
three op amp instrumentation
amplifier incorporates a difference amplifier. This is relevant,
because the same equations are
used to calculate CMR for both
types of amplifiers.
Figure 3 illustrates how an input signal is composed of a differential-mode component and
a common-mode component. By
calculating the gain of the difference amplifier and substituting
the differential and commonmode components, the gain of
each respective component is
obtained. Common-mode rejection ratio is a comparison of the
amplifier’s differential gain vs. its
common-mode gain. Amplifiers
specify this as common-mode
rejection and express this as a
value in decibels.
How Resistors affect
Common-Mode Rejection
When using a monolithic difference amplifier, such as Analog
Devices’AD628, or a monolithic
instrumentation amplifier, such
as the company’s AD8221,
a common-mode rejection
specification is listed in the
EE Times-India | July 2007 | eetindia.com
Similarly, using four discrete resistors will worsen
CMR value because none of
the resistors are correlated to
one another; they are all correlated to an ideal resistor value.
Since none are correlated, the
worst-case is when all four resistors are mismatched, resulting in Equation 2.
Figure 3: Differential signals are composed of a differential-mode component and a common-mode component.
CMRR is the ratio of differential gain and common-mode gain.
data sheet. While they are easy
to use building blocks, there
are times when a monolithic
device is not tailored to meet
an application’s needs.
In such cases, designers
resort to designing their own
difference amplifier or instrumentation amplifier. They need
to know the relationship between the resistors they use and
the common-mode they can
achieve. Figure 2 and 3 highlight
the resistors that are relevant in
achieving high CMR.
Resistors can be purchased
individually or as part of an array.
Resistors arrays or networks have
better matching because they
are built on the same substrate;
their resistor to resistor match is
generally better, as is their temperature coefficient match, than
two individual resistors pulled
from a bin.
Common-mode error is determined, to a first order, by the
resistor’s ratio tolerance. This
specification dictates the toler-
ance of one resistor to another
on the same array. For example,
the specification describes the
mismatch of R2, R3 and R4 to
R1. However, it is the mismatch
between the ratios, R2/R1 to
R4/R3 that determines common-mode rejection, not the
mismatch of the resistors.
Fortunately, this mismatch
between ratios can be calculated using the resistor array’s
specified ratio tolerance, circled in Figure 4. At worst, the
mismatch between ratios is
three times the ratio tolerance
because three of the resistors
are referred to one on the
same network.
Thus, one resistor is used
as the reference. If the resistor
array specifies a 0.1% ratio tolerance on the data sheet, then
the mismatch between ratios
is 0.3%. Equation 1 delineates
the relationship between ratio
tolerance and CMR. This relationship is useful in calculating the maximum mismatch
Equation 1: Worst-case CMR for
a resistor array. TR, is the resistor
array’s ratio tolerance as specified
in a data sheet. Resistor network
vendors specify the tolerance of
one resistor to another on the same
array. G refers to the gain of the difference amplifier (set by the resistor
network, e.g. R2/R1).
allowed for a desired common-mode rejection. For example, an array of same value
resistors would need to have
0.1% ratio tolerance to obtain
56.5dB of CMR.
Notice that the worst-case
CMR equation assumes three resistor deviate from the reference
resistor. The worst-case should
be assumed because network
resistors only state the tolerance
of one resistor to another, as opposed to the tolerance of one
ratio to another.
Figure 4: Resistor Arrays list an absolute tolerance and a ratio tolerance. The ratio tolerance dictates the common-mode
rejection of a difference or instrumentation amplifier. Example taken from the Vishay ORN Resistor Array data sheet.
eetindia.com | July 2007 | EE Times-India
Equation 2: Worst-case CMR when
using 4 discrete resistors. TA, is
the resistor’s absolute tolerance.
Vendors of discrete resistor specify
tolerance of the resistor to an ideal
resistor value. G refers to the gain of
the difference amplifier (set by the
resistor network, e.g. R2/R1).
Monolithic difference amplifiers and instrumentation
amplifiers have the relevant
internal resistor ratios laser
trimmed to achieve CMR of
80dB and higher. While they
are easy to use, offer high common-mode rejection and gain
accuracy, they may not offer
the flexibility that some applications require.
Understanding how resistor matching affects CMR allows designers to make savvy
decisions when choosing
components, whether they
build their own instrumentation amplifiers from resistor
arrays and op amps or use a
monolithic solution.
Update: The equations listed
above assume a ratio tolerance
that spans both the positive and
negative direction. For example,
it assumes a 0.1% ratio tolerance
has a worst-case of +0.1% to
-0.1% from another resistor on
the network. When designing
with resistor arrays, contact the
resistor vendor to learn how they
specify their ratio tolerance.
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