Differential Amplifier using an Op Amp
A Differential amplifier is a special amplifier configuration using an Op Amp that is uniquely suited to be
used with a Wheatstone Bridge circuit in instrumentation applications. A Wheatstone Bridge circuit has
2 outputs terminals and a Differential amplifier has 2 input terminals.
The “Diff Amp” inputs are V1 and V2 and the input voltage to the amplifier is the difference between
these signals V2 – V1. There are design constraints for this amplifier which are:
R1 must be equal to R2 and RF must be equal to Rg for optimal performance: R1 = R2 and RF = Rg
Modes of Operation
This amplifier has two modes – differential mode and common mode.
Differential Mode
In this mode the amplifier amplifies the difference signal at the 2 inputs V2 and V1 . This is
represented as V2 – V1 . Desired signals can appear on only 1 input or with opposite polarities on both
inputs. Desired signals are seen as Differential Mode signals and are amplified and appear at the output.
Differential Mode Gain
The voltage gain in this mode is AV,DM = RF/R1. So VOUT = RF/R1 x (V2 – V1). Ideally the differential mode
voltage gain is large to amplify desired signals.
Examples
1. A Differential amplifier has R1 = R2 = 10 kΩ and RF = Rg = 100 kΩ If V1 = 0.1 V and V2 = 0.3 V
what is VOUT?
VOUT = AV,DM x VIN,diff = 100 kΩ /10 kΩ x (0.3 – 0.1) = 10 x 0.2 V = 2 V
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2. A Differential amplifier has R1 = R2 = 10 kΩ and RF = Rg = 100 kΩ If V1 = - 0.1 V and V2 = 0.3 V
what is VOUT?
VOUT = 100 kΩ /10 kΩ x (0.3 – (-0.1)) = 10 x 0.4 V = 4 V
3. A Differential amplifier has R1 = R2 = 10 kΩ and RF = Rg = 100 kΩ If V1 = -0.1 V and V2 = -0.3 V
what is VOUT?
VOUT = 100 kΩ /10 kΩ x (-0.3 –(-0.1)) = 10 x -0.2 V = -2 V
Common Mode Configuration
In this mode the input signals are the same - V2 = V1. Common mode is not a preferred mode of
operation. In the most common occurrence of this mode the input signals V2 and V1 are usually
electrical noise signals (undesired signals) seen as Common Mode signals and are present in equal
amounts at both inputs.
Common Mode Gain
In an ideal differential amplifier the common mode gain AV,CM = 0. A practical differential amplifier has a
very small common mode gain ( << 1). The size of this gain is affected by the Op Amp itself and how
well the external resistors are matched (R1 = R2 and RF = Rg). So in a well designed differential
amplifier noise signals that appear equally at both inputs are significantly reduced by the common mode
gain and are thus small nose voltages at the output. There is no simple expression to calculate the
common mode gain – it can only be derived as a measured value.
Common Mode Rejection Ratio
Large differential mode gain and small common mode gain gives large desired signals and small
undesired signals so a good measure of an Op Amps’ ability to reject unwanted signals is the ratio of
differential mode gain to common mode gain. This is expressed as a new parameter called Common
Mode Rejection Ratio.
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Common Mode Rejection Ratio - Linear Value
CMRR = AV,DM /AV,CM
This can also be expressed in decibels as
CMRR (dB) = 20 log (AV,DM /AV,CM )
The LM 741 Op Amp has a typical CMRR value of 90 dB found on a data sheet.
Examples
1. A differential amplifier has a differential mode gain = 20 and a common mode gain = 0.01.
What is the Common Mode Rejection Ratio of the amplifier?
CMRR = 20/0.01 = 2000
CMRR db = 20 log 2000 = 66 dB
The value of CMRR calculated is less than the 90 dB specification – mismatches in the external resistors
of the amplifier would account for this.
2. Repeat the calculation for a Common Mode gain of 0.002. This would represent a situation
where there is a better match for the external resistors.
CMRR = 20/0.002 = 10000
CMRR db = 20 log 10000 = 80 dB
Disadvantages of the Differential Amplifier
1. Low input resistance
RIN = R1 (or R2)
2. Difficult to make the voltage gain adjustable
Instrumentation Amplifier
An Instrumentation amplifier is used to address these two disadvantages. This amplifier has two stages
– an input stage consisting of 2 Non-Inverting Op Amp buffer amplifiers and an output stage consisting
of a differential amplifier. The 5 kΩ Gain resistor RG is often a potentiometer that allows for adjustable
voltage gain. The Instrumentation amplifier retains the desirable characteristics of the differential
amplifier but adds variable gain capability and a large input resistance. This amplifier has a much larger
voltage gain than a differential amplifier as it is a 2 stage amplifier where the total voltage gain (linear) is
AV,Total = AV,Stage1 x AV,Stage2
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Gain resistor - RG – often a
variable resistor
Instrumentation amplifiers are commonly found in Integrated Circuit form.
Integrated Circuit Instrumentation amplifier – AD 8236
This is an 8 pin device from Analog Devices can operate on voltages as low as 1.8 V with a 40 μA
maximum supply current makes it an excellent choice in battery-powered applications
Connect external
Resistor to set gain
Specifications
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Low power: 40 μA supply current (maximum)
Low input currents1 pA input bias current, 0.5 pA input offset current
High CMRR: 110 dB CMRR, G = 100
Space-saving MSOP
Zero input crossover distortion
Rail-to-rail input and output
Gain set with single resistor
Operates from 1.8 V to 5.5 V
Application Note
Written by David Lloyd
Computer Engineering Program
Humber College
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