Download Ideal Amplifiers (Op-Amps) and Instrumentation Amplifiers

Ideal Amplifiers (Op-Amps) and Instrumentation Amplifiers
Operational Amplifiers (Op-Amps) are the building blocks for analogue signal
conditioning circuits, and, in particular, instrumentation amplifiers. Conventional opamps are easy to use. They amplify electrical signals such as the small voltages coming
from instrumentation sensors. The amount they amplify (the Gain) is controlled by
external components, provided the amplifiers are operated within reasonable boundaries.
Thus they are easy to configure for many applications and they are cheap and reliable.
The op-amp is a differential amplifier. That is, it will amplify the difference between its
two inputs by its open loop gain. Op-amps allow you to not only amplify very small
sensor signals but also to add or subtract offset voltages and to electrically isolate (buffer)
sensors from the rest of system.
The analysis in this note will be based largely on ideal amplifiers. An ideal op-amp has
infinite (open-loop) gain, infinite input impedance and zero output impedance. External
components, such as resistors, are used to feed the output back to the input and thus to
reduce the infinite gain to any desired gain.
This can be easily shown.
Let the input be In the output be Out and the open loop gain be A. Let a portion (β) of the
output be fed back (subtracted) from the input, then
Out  ( In   .Out ). A
Out   .Out . A  In. A
Out
A
Gain 

In 1   . A
1
Gain 
1 
A
If A is infinite this becomes Out/In = 1/β
Thus the fraction of the out put which we feed back controls the overall gain on the
closed loop amplifier. β is selected by simply choosing appropriate resistor values.
Most circuits containing op-amps can be analyzed using a few simple rules. Practical
amplifiers can be built using these simple rules provided, as mentioned before, the
amplifier is operated within reasonable limits.
Ideal op-amp analysis rules:
0.
There must be a D.C. connection between Vout and I- (necessary pre-condition)
1.
2.
The output will change so there is 0v between I+ and INo current flows into the Op-Amp
A. Inverting Amplifier
The inverting amplifier converts positive voltages on the inputs to a negative amplified
voltages on the output and vice-versa.
The inverting amplifier is the simplest configuration for an op-amp.
Ri
II+
Vin
I   I   I in 
Vout  iin R f

Vin
Ri
Rf
Vout = - Rf Vin
Ri
( Rule 1)
( Rule 2)
 Vin R f
Ri
Rf
Vout

Vin
Ri
A variable gain amplifier can be created by replacing the feedback resistor, Rf, with a
variable resistor.
Advantages and Disadvantages
The major advantage of the inverting amplifier is that it is very easy to select a particular
gain and the gain will change linearly as we change Rf. There are two significant
disadvantages, input impedance is low and a dual power supply is required. The input
impedance of this circuit is approximately Ri. For normal components Ri is typically
chosen to be a few kilo-ohms. This is not very high and can easily cause a loading
problem for the sensor that is attached to it. The second problem is that this circuit also
inverts all inputs, positive voltages become negative amplified voltages and vice-versa.
In order to do this the amplifier must have a positive and negative voltage supply,
typically +12 to -12V. This is not convenient as most modern circuits are designned with
a single positive supply. For these reasons the inverting op-amp configuration is not used
very often in instrumentation applications. It is used in summing applications as will be
shown later.
B. Non-Inverting
Applications
Non-inverting amplifiers have very high input impedance and can be implemented with a
single 0 to 5V supply. The gain can be controlled by replacing Rf with a variable
resistor. Note that in this case the gain does not change linearly with changing Rf. A
commonly used variation of this amplifier,
called a follower, is as shown below.
Vin
I+
Vout
In this configuration Rf=0 and Rg=, so the
gain =1. The output of the amp simply
Ifollows the input, but the input impedance is
very high. This is a commonly used circuit
when you need to buffer the sensor from the
rest of the system.
This amplifier can be used as shown but is often used as the input stage of a differential
instrumentation amplifier.
C. Differential Input Amplifier
R2
V1
V2
R1
R1
II+
Vout =
R2
R1
V2 - V1
R2
This circuit can be analyzed by the ideal op-amp rules and the principle of superposition.
Set V2 = 0 and the circuit becomes the equivalent of the Inverting Amplifier. (No current
flows through I+ or the connected resistors so I+ is effectively at 0V.) (Rule 2)
 R2
.V1
R1
Set V1 = 0 (ground) and the circuit becomes equivalent to a non-inverting amplifier with
the voltage at I+ given by
R2
R  R2
R
V  V2 .
 1
R1  V2 . 2
R1  R2
R1
By superposition Vout = Vout1 + Vout2 = R2 / R1 (V2 - V1)
Vout1 
Note that matching pairs of resistors R1 and R2 are needed for this simple equation to
work. Vout can be calculated for other resistor values by adapting the above equations.
Applications of the differential amp
This circuit is the basis of the instrumentation amplifier. Non-inverting amplifiers are
attached to each of the inputs. This ensures that the input impedance is very high. It is
also possible to arrange these input stages so they share a common resistor Rg. This then
becomes the single resistor that controls the gain of the complete amplifier. All the other
resistors and amplifiers are built onto a single chip where matched resistance pairs are
easier to achieve and the entire amplifier gain is controlled from a single external resistor.
D. Summing Amplifier
The above configurations show how the gain of a signal can be controlled in various
ways. We frequently also wish to control zero offset. Zero offset can be adjusted by
adding a small positive or negative offset voltage to the signal. This can be done with a
summing amplifier.
Rofs
Vofs
Ri
Vin
II+
Vout = - Rf Vin - Rf Vofs
Rofs
Ri
Rf
Applications of the summing amp
This circuit can be used to shift a voltage level in a positive or negative direction. Since
it is based on an inverting amp it will also invert the signal. For example if a instrument
has an output signal in the range +0.5 volts to -3.2 volts then you can subtract an offset of
0.5 volts to shift the range to 0.0V to +3.7V, which can then be used with a standard 0 to
5 volt system. Notice that Rf can also be chosen to adjust the gain of the system. For
example if Rofs=Ri and Rf is chosen so that Rf /Ri =1.35 then if the input is +0.5 to -3.2 V
and Vofs is -0.5V the output will be 0.0 to 5.0 volts which is perfectly matched for a 0 to 5
volt instrumentation system.
If you do not wish to invert the signal this amplifier can be preceded by another inverting
amplifier with unity gain.
Since this amplifier needs to work with negative voltages it must obviously have both a
positive and negative supply voltage.
Arithmetic
Since amplifier can produce gains greater and less than one they can perform
multiplication and division functions. Since they can sum positive and negative values
they can perform addition and subtraction. Thus the basic arithmetic operations are
possible.
Instrumentation Amplifiers
It is very common for sensors to require some degree of amplification. This is the
commonest form of signal conditioning, to convert a low-level voltage or current into a
higher level in a standardized range such as 0 to 5 volts. For experimental purposes and
for short term needs this can usually be done through an op-amp (instrumentation amp).
Industrial sensors will often have the instrumentation amplifiers built into the sensor
module. They can also be purchased as separate modules and added to an existing
system.
Instrumentation amplifiers are op-amps which are DC coupled, configured for
differential high-impedance input, high common-mode-rejection-ratio (CMRR) and have
a single-ended output. They often also include offset trimming and single resistor gain
adjustment. Each of these features will be explained.
DC coupled: Most industrial instrumentation signals vary relatively slowly, typically
changing over minutes up to varying a few hundred times a second. These low
frequencies require a DC coupled amplifier. This means that there will be no capacitors
in series with the input since capacitors only pass AC currents.
Differential Input: The connection(s) between the sensor and the amplifier act as
antennas for any noise signals in the environment. There are usually many noise sources
in industrial applications. The noise can easily be a signal of significant size compared to
the sensor signal. This noise signal is induced into both the inverting and non-inverting
connections of the differential input and is therefore subtracted from itself by the op-amp.
This can be simply seen in the gain calculation. The gain for a differential op-amp is R2 /
R1 (V2 - V1). If we add the same noise, N, to both inputs this becomes
R2 / R1 ((V2 +N) - (V1 + N)) = R2 / R1 ((V2 - V1)+ (N - N)) = R2 / R1 (V2 - V1)
i.e. the noise cancels out.
CMRR: (Common Mode Rejection Ratio) Sometimes, for example in biomedical
applications, the common signal (noise) applied to both inputs will be larger than the
signal being measured. This common mode signal can overwhelm the amplifier. The
ability of the amplifier to ignore a large common signal and amplify the small difference
signal is called the common-mode rejection ratio. For example if there is a 2 volt signal
on both input leads and a 50 mV difference between them then the common mode ratio is
2/0.050 = 40 or 20 Log(40)=32 dB. Therefore the amplifier needs to have a CMRR > 32
dB to work with these conditions.
High Impedance input: Voltage signals such as those coming from piezo-electric sensors
or thermocouples, contain very little energy. The pressure or temperature information is
contained in the voltage fluctuation but we cannot treat this voltage as if it were a power
supply. The sensor cannot provide energy to the amplifier so the amplifier input must
have a very high input impedance to prevent it from overloading the sensor. Energy is
calculated from power = V2 / R. We can keep the power drawn from the sensor minimal
by making R very large. R in this case is the input impedance of the amplifier.
Single-ended output: A single-ended output always has the same polarity i.e. will never
go negative. This is desirable as it is relatively easy to match with the computer or
display that typically follows the amplifier. These are typically designed for 0-5 volt
input, so the output of the instrumentation amp is designed to match..
Offset trimming: A good instrumentation amplifier may include summing amplifier
capabilities to offset the voltage signal. A variable resistor can be attached to the
amplifier and used to zero out any offset signal present in the system. This allows us to
calibrate the sensor for zero output when there is zero input. Alternatively if we just wish
to operate the sensor over a small part of its range, for example a human-body
temperature sensor that operates from 80 to 120F, we can use the offset to ensure that
it is calibrated in this range. This allows us to partially correct for inherent non-linearities
in the sensor.
Single Resistor Gain Adjustment: It is possible to design a differential amplifier such
that all the matched resistors are on the integrated circuit and a single external resistor is
used to adjust the gain over a very wide range. This gain adjustment is not usually linear
but a formula is provided by the chip manufacturer to allow you to calculate any
particular gain needed.
By having external variable resistors to adjust gain and offset the instrumentation
amplifier can be used to calibrate the sensor, providing the sensor has a linear response in
the range of interest.
Reference
Horowitz, Paul and Hill, Winfield,, The Art of Electronics. . New York: Cambridge
University Press, 1990.