Analog Devices AN-539 Application Notes

AN-539

a

APPLICATION NOTE

One Technology Way • P.O. Box 9106 • Norwood, MA 02062-9106 • 781/329-4700 • World Wide Web Site: http://www.analog.com

Errors and Error Budget Analysis in Instrumentation Amplifier Applications

by Eamon Nash

+V

S

V

NOISE

+

–

I

BIAS

I

BIAS

I

OFS

VOSIN

R

GAIN

AD623

VOSOUT

V

OUT

REFERENCE

350V

V

CM

350V350V

I

NOISE

I

NOISE

= +VS/2

Figure 1. Error Sources in a Typical Instrumentation Amplifier

INTRODUCTION

This application note describes a systematic approach
to calculating the overall error in an instrumentation
amplifier (in amp) application. We will begin by describ­ing the primary sources of error (e.g., offset voltage,
CMRR, etc.) in an in amp. Then, using data sheet specifi­cations and practical examples, we will compare the
accuracy of various in amp solutions (e.g., discrete vs.
integrated, three op amp integrated vs. two op amp
integrated).

Because instrumentation amplifiers are most often used
in low speed precision applications, we generally focus
on dc errors such as offset voltage, bias current and low
frequency noise (primarily at harmonics of the line fre­quency of either 50 Hz or 60 Hz). We must also estimate
the errors that will result from sizable changes in tem­perature due the rugged and noisy environment in
which many in amps find themselves.

It is also important to remember that the effect of par­ticular error sources will vary from application to appli­cation. In thermocouple applications, for example, the
source impedance of the sensor is very low (typically
not greater than a few ohms even when there is a long
cable between sensor and amplifier). As a result, errors
due to bias current and noise current can be neglected
when compared to input offset voltage errors.

RTO and RTI

Before we consider individual error sources, under­standing of what we mean by RTO and RTI is important.
In any device that can operate with a gain greater than
unity (e.g., any op amp or in amp), the absolute size of
an error will be greater at the output than at the input.
For example, the noise at the output will be the gain
times the specified input noise. We must, therefore,
specify whether an error is referred to the input (RTI) or
referred to the output (RTO). For example, if we wanted
to refer output offset voltage to the input, we would sim­ply divide the error by the gain, i.e.,

Output Offset Error (RTI) = VOSOUT/Gain

Referring all errors to the input, as is common practice,
allows easy comparison between error sizes and the size
of the input signal.

Parts per Million—PPM

Parts per million or ppm is a popular way of specifying
errors that are quite small. PPM is dimensionless so we
must make the error relative to something. In these
examples, it is appropriate to compare to the full-scale
input signal. For example, the input offset voltage,
expressed in ppm, is given by the equation:

Input Offset Error (ppm) = (VOS/V

IN FULL SCALE

) ×

10

6

AN-539

V

Gain V

CMRR

20

OUT

CM

–1

=

×











log

Error Sources in Discrete and Integrated Instrumentation
Amplifiers

Figure 1 shows the most common and prevalent error
sources in discrete and integrated in amps. These error
sources are detailed individually below

.

Offset Voltage

Offset voltage results from a mismatch between transis­tor V

s in an amplifier’s input stage. This voltage can be

BE

modeled as a small dc voltage in series with the input
signal, as shown in Figure 1. Like the input signal, it will
be amplified by the gain of the in amp. In the case of in
amps with more than one stage (e.g., the classic three
op amp in amp) the input transistors of the output stage
will also contribute an offset component. However, as
long as the output stage has gain of unity, as is generally
the practice, the in amp’s programmed gain will have no
effect on the absolute size of the output offset error.
However, for error computation, this error is usually
referred back to the input so that its effect can be com­pared to the size of the input signal. This yields the
equation:

Total Offset Error (RTI) = V

OS_IN

+ V

OS_OUT

/Gain

From this equation, it is clear that the effect of output
offset voltage will decrease as the in amp’s pro­grammed gain increases.

current times the source impedance. Because either of
the bias currents can be the greater, the offset current
can be of either polarity.

Common-Mode Rejection

An ideal in amp will amplify the differential voltage be­tween its inverting and noninverting inputs regardless
of any dc offsets appearing on both inputs. So any dc
offset appearing on both inputs (+V

/2 in Figure 1) will

S

be rejected by the in amp. This dc or common-mode
component is present in many applications. Indeed,
removing this common-mode component is often the
primary function of an instrumentation amplifier in an
application.

In practice, not all of the input common-mode signal
will be rejected and some will appear at the output.
Common-mode rejection ratio is a measure of how well
the instrumentation amplifier rejects common-mode
signals. It is defined by the formula:

CMRR (dB) 20

=×

log



Gain V



V



×

OUT

CM





We can rewrite this equation to allow calculation of
the output voltage that results from a particular input
common-mode voltage.

Offset and Bias Currents

Bias currents flow into or out of the in amp’s inputs.
These are usually the base currents of npn or pnp tran­sistors. These small currents will therefore have a de­fined polarity for a particular type of in amp.

Bias currents generate error voltages when they flow
through source impedances. The bias current times the
source impedance generates a small dc voltage which
appears in series with the input offset voltage. However
if both inputs of the in amp are looking at the same
source impedance, equal bias currents will generate a

small common-mode input voltage (typically in the µV

range) that will be well suppressed by any device which
has reasonable common-mode rejection. If the source
impedances of the in amp’s inverting and noninvert­ing inputs are not equal, the resulting error will be
greater by the bias current times the difference in the
impedances.

AC and DC Common-Mode Rejection

Poor common-mode rejection at dc will result in a dc off­set at the output. While this can be calibrated away (just
like offset voltage), poor common-mode rejection of ac
signals is much more troublesome. If, for example, the
input circuit picks up 50 Hz or 60 Hz interference from
the mains, an ac voltage will result at the output. Its
presence will reduce resolution. Filtering is a solution
only in very slow applications where the maximum fre­quency is much less than 50 Hz/60 Hz.

Table I shows the output voltages of two in amps, the
AD623 and the INA126, that result when a 60 Hz
common-mode voltage of 100 mV amplitude is picked
up by the input.

We must also consider the offset current, which is the
difference between the two bias currents. This differ­ence will generate an offset type error equal to the offset

Table I. Effect of CMRR on Output Voltage of AD623 and INA126 for a 60 Hz, 100 mV Amplitude Common-Mode Input

Gain VIN (cm) CMRR–INA126 CMRR–AD623 V

–INA126 V

OUT

10 100 mV @ 60 Hz 83 dB 100 dB 70.7 µV 10 µV
100 100 mV @ 60 Hz 83 dB 110 dB 707 µV 31.6 µV
1000 100 mV @ 60 Hz 83 dB 110 dB 7.07 mV 316 µV

–2–

–AD623

OUT