Operational Amplifiers
Spring 2008
Sean LynchLambros Samouris
Tom Groshans
Op Amps
Background
Ideal
Inverting
Non-Inverting
Integrating
Differential
Summing
Applications
History of Op Amps
• Named for their originally intended functions: performing mathematical operations and amplification– Addition– Subtraction– Integration– Differentiation
Op Amps
Background
Ideal
Inverting
Non-Inverting
Integrating
Differential
Summing
Applications
History of Op Amps
• Op Amps were initially developed in the vacuum tube era, but later were made into IC’s (Integrated Circuits)
• First integrated Op Amp to become widely available was the bipolar Fairchild µA709– Quickly superseded by the 741, a name
that has stuck with Op Amps since
Op Amps
Background
Ideal
Inverting
Non-Inverting
Integrating
Differential
Summing
Applications
History of Op Amps• The most common and most famous op-
amp is the mA741C or just 741, which is packaged in an 8-pin mini-DIP. – The integrated circuit contains 20 transistors and
11 resistors– Introduced by Fairchild in 1968, the 741 and
subsequent IC op-amps including FET-input op-amps have become the standard tool for achieving amplification and a host of other tasks. Though it has some practical limitations, the 741 is an electronic bargain at less than a dollar.
Op Amps
Background
Ideal
Inverting
Non-Inverting
Integrating
Differential
Summing
Applications
Op Amp Features
• Op Amps have two different inputs, inverting, V-, and non-inverting, V+
• Vs+ and Vs- are the positive and negative power supplies
• Vout is the output
Op Amps
Background
Ideal
Inverting
Non-Inverting
Integrating
Differential
Summing
Applications
Diagram of the 741
• Showed below is the 8-pin version of the 741 op amp
Op Amps
Background
Ideal
Inverting
Non-Inverting
Integrating
Differential
Summing
Applications
Ideal Op Amps
• Infinite open-loop gain• Obtained when no feedback is used in the circuit• On differential signal• Applying feedback limits the gain to a usable
range• Zero gain for common mode input signal
• Infinite input impedance• Thévenin equivalent of the IC looking into its
input• Current into the Op Amp is zero
Op Amps
Background
Ideal
Inverting
Non-Inverting
Integrating
Differential
Summing
Applications
Ideal Op Amps
• Infinite bandwidth• Usable frequency range & Gain• Infinite slew rate
• Zero output impedance• The Thévenin equivalent impedance looking
back into the output terminals • Op amp can supply any current / voltage
combination• Zero noise
Op Amps
Background
Ideal
Inverting
Non-Inverting
Integrating
Differential
Summing
Applications
Real Op-AmpsIdeal Op-Amp Typical Op-Amp
Input Resistance
infinity 106 Ω (bipolar)109 Ω - 1012 Ω (FET)
Input Current 0 10-12 – 10-8 A
Output Resistance
0 100 – 1000 Ω
Operational Gain
infinity 105 - 109
Common Mode Gain
0 10-5
Bandwidth infinity Attenuates and phases at high frequencies
(depends on slew rate)
Temperature independent Bandwidth and gain
9http://hyperphysics.phy-astr.gsu.edu/hbase/electronic/opampcon.html#c1
Op Amps
Background
Ideal
Inverting
Non-Inverting
Integrating
Differential
Summing
Applications
Real Op Amps
• Open Loop• Supply Limits (Rails), Saturation
• Feedback• Reduces Gain
• Bandwidth – Gain Product• 1 MHz gain-bandwidth product would have a
gain of 5 at 200 kHz, and a gain of 1 at 1 MHz
• Analysis• Feedback, positive, negative• 0 Current, 0 Voltage
Op Amps
Background
Ideal
Inverting
Non-Inverting
Integrating
Differential
Summing
Applications
Inverting Amplifier
• For an ideal op-amp, the inverting amplifier gain is given by:
The circuit that yields this equation is given on the diagram on the right
Op Amps
Background
Ideal
Inverting
Non-Inverting
Integrating
Differential
Summing
Applications
Inverting Amplifier
• For equal resistors, it has a gain of -1, and is used in digital circuits as an inverting buffer, or simply an inverter
Op Amps
Background
Ideal
Inverting
Non-Inverting
Integrating
Differential
Summing
Applications
Non-Inverting Amplifier
• For an ideal op-amp, the non-inverting amplifier gain is given by
A diagram of thecircuit that yields theabove equation isgiven on the right
Op Amps
Background
Ideal
Inverting
Non-Inverting
Integrating
Differential
Summing
Applications
Non-Inverting Amplifier• For an non-inverting amplifier, the current rule tries
to drive the current to zero at point A and the voltage rule makes the voltage at A equal to the input voltage.
This leads to:
and the amplificationequation
Op Amps
Background
Ideal
Inverting
Non-Inverting
Integrating
Differential
Summing
Applications
Integrating Amplifier
-Vin+R C
+ Vout
-
-
+
-Vin+R C
+ Vout
-
-
+
Op Amps
Background
Ideal
Inverting
Non-Inverting
Integrating
Differential
Summing
Applications
Integrating Amplifier
Op Amps
Background
Ideal
Inverting
Non-Inverting
Integrating
Differential
Summing
Applications
Integrating Amplifier
RVi in−
= dtdVCi =
-Vin+R C
+ Vout
-
)0(0
=+=
=
=
∫ −
−
−
tVdtV
C
t
RCV
out
RCV
dtdV
RV
dtdV
in
inout
inoutUse KCL to find current through each element and remember that the op-amp
uses ‘no’ current.
Op Amps
Background
Ideal
Inverting
Non-Inverting
Integrating
Differential
Summing
Applications
Integrating Amplifier
-Vin+R C
+ Vout
-
-
+
)0(0
=+= ∫ − tVdtVt
RCV
outin
Op Amps
Background
Ideal
Inverting
Non-Inverting
Integrating
Differential
Summing
Applications
Differential Amplifier
-Vin+RC
+ Vout
-
-
+dtdVRCV in
out −=
Similar to Integrator except R and C have switched locations.
Op Amps
Background
Ideal
Inverting
Non-Inverting
Integrating
Differential
Summing
Applications
Differential Amplifier
-V1+
-V2+
R1R1
R2R2
R4R4
R3R3
+ Vout
-
-
+
A more complex circuit. Can simplify using superposition of an inverting amplifier and a non-inverting amplifier.
-V1+R1R1 R3R3
+ Vout
-
-
+
Op Amps
Background
Ideal
Inverting
Non-Inverting
Integrating
Differential
Summing
Applications
Differential Amplifier
⎟⎟⎠
⎞⎜⎜⎝
⎛−=
1
31_ R
RVV invertingout
Op Amps
Background
Ideal
Inverting
Non-Inverting
Integrating
Differential
Summing
Applications
Differential Amplifier
-V1+
-V2+
R1R1
R2R2
R4R4
R3R3
+ Vout
-
-
+
Op Amps
Background
Ideal
Inverting
Non-Inverting
Integrating
Differential
Summing
Applications
Differential Amplifier
R1R1 R3R3
+ Vout
-
-
++
Vin-
⎟⎟⎠
⎞⎜⎜⎝
⎛+=−
1
3_ 1
RRVV ininvertingnonout
?=inV
-V1+
-V2+
R1R1
R2R2
R4R4
R3R3
+ Vout
-
-
+
Op Amps
Background
Ideal
Inverting
Non-Inverting
Integrating
Differential
Summing
Applications
Differential Amplifier
Op Amps
Background
Ideal
Inverting
Non-Inverting
Integrating
Differential
Summing
Applications
Differential Amplifier
-V2+R2R2
R4R4+
Vth-
RthRth
⎟⎟⎠
⎞⎜⎜⎝
⎛+
=42
42 RR
RVVth
Op Amps
Background
Ideal
Inverting
Non-Inverting
Integrating
Differential
Summing
Applications
Differential Amplifier
⎟⎟⎠
⎞⎜⎜⎝
⎛+⎟⎟
⎠
⎞⎜⎜⎝
⎛+
=−1
3
42
42_ 1
RR
RRRVV invertingnonout
R1R1 R3R3
+ Vout
-
-
++
Vin-
-V1+R1R1 R3R3
+ Vout
-
-
+
⎟⎟⎠
⎞⎜⎜⎝
⎛+=−
1
3_ 1
RRVV ininvertingnonout
invertingoutinvertingnonoutout VVV __ += −
⎟⎟⎠
⎞⎜⎜⎝
⎛−⎟⎟⎠
⎞⎜⎜⎝
⎛ +⎟⎟⎠
⎞⎜⎜⎝
⎛+
=1
31
1
31
42
42 R
RVR
RRRR
RVVout
⎟⎟⎠
⎞⎜⎜⎝
⎛−=
1
31_ R
RVV invertingout
Op Amps
Background
Ideal
Inverting
Non-Inverting
Integrating
Differential
Summing
Applications
Differential Amplifier-V1+
-V2+
R1R1
R2R2
R4R4
R3R3
+ Vout
-
-
+
⎟⎟⎠
⎞⎜⎜⎝
⎛−⎟⎟⎠
⎞⎜⎜⎝
⎛ +⎟⎟⎠
⎞⎜⎜⎝
⎛+
=1
31
1
31
42
42 R
RVR
RRRR
RVVout
( ) ⎟⎟⎠
⎞⎜⎜⎝
⎛−=
1
312 R
RVVVoutIf R2=R1 and R3=R4,
Op Amps
Background
Ideal
Inverting
Non-Inverting
Integrating
Differential
Summing
Applications
Summing Amplifier
-V1+
-V2+
-V3+
-Vn+
R1R1
R2R2
R3R3
RnRn
RfRf
+ Vout
-
-
+.
.
-V1+
-V2+
-V3+
-Vn+
R1
R2
R3
Rn
Rf
+ Vout
-
-
+.
.
Op Amps
Background
Ideal
Inverting
Non-Inverting
Integrating
Differential
Summing
Applications
Summing Amplifier
-V1+
-V2+
-V3+
-Vn+
R1
R2
R3
Rn
Rf
.
.
NODE
1i
2i
3i
ni
fi
Op Amps
Background
Ideal
Inverting
Non-Inverting
Integrating
Differential
Summing
Applications
Summing Amplifier
fRV
RV
RV
RV
fn
outin
i
iiiiiii
iKCL
RViiRV
n
n =+++
+=+++
=
=
==
∑∑∑
...
0...
0
,
3
3
2
2
1
1
321
Op Amps
Background
Ideal
Inverting
Non-Inverting
Integrating
Differential
Summing
Applications
Summing Amplifier
( )n
nRV
RV
RV
RV
f
ff
RVout
RiVout
...3
3
2
2
1
1 +++−=
−=
-V1+
-V2+
-V3+
-Vn+
R1R1
R2R2
R3R3
RnRn
RfRf
+ Vout
-
-
+.
.
Op Amps
Background
Ideal
Inverting
Non-Inverting
Integrating
Differential
Summing
Applications
Applications555 Timer Circuit, Open Loop, Logic
Op Amps
Background
Ideal
Inverting
Non-Inverting
Integrating
Differential
Summing
Applications
ApplicationsA/D converter, Open Loop, Logic
Op Amps
Background
Ideal
Inverting
Non-Inverting
Integrating
Differential
Summing
Applications
ApplicationsClosed Loop, Voltage Level
•Transducers• Microphones• Strain Gauges
• PID Controllers
• Filters• Low Pass• High Pass• Band Pass• Butterworth
Op Amps
Background
Ideal
Inverting
Non-Inverting
Integrating
Differential
Summing
Applications Frequency range is governed by: 222
1CR
f⋅⋅
=π
ApplicationsClosed Loop, Low Pass Filter, Voltage Level
Op Amps
Background
Ideal
Inverting
Non-Inverting
Integrating
Differential
Summing
Applications
Practical Tips
• Try to use single supply op-amps in order to minimize need for a 10V difference from power supply
• Good low resistance, twisted, and shielded wire should be used when a sensor is located far away from the op-amp circuit.
• Minimize current draw in sensor circuits to reduce thermal drift• Filter power into op-amp circuits using capacitors• Design op-amp circuits so output cannot be negative in order
to protect 68HC11 A/D port.• Isolate op-amp circuit output with unity gain op-amp if
connected to an actuator.• Make sure bandwidth of op-amp is adequate• Use trimmer potentiometers to balance resistors in differential
op-amp circuits• Samples of op-amps can be obtained from National
Semiconductor (http://www.national.com)• Use the ‘Net for circuit examples
References
• Wikipedia: http://en.wikipedia.org/wiki/Operational_amplifier• The Art of Electronics, Horowitz and Hill • Electrical Engineering, Hambley• Previous Presentations• Lab Notes• http://users.ece.gatech.edu/~alan/ECE3040/Lectures/Lecture28-
Operational%20Amplifier.pdf
Op Amps
Background
Ideal
Inverting
Non-Inverting
Integrating
Differential
Summing
Applications