Operational Amplifier
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Introduction
Brief of History
Fundamentals of Op-Amps
Applications
Introduction
• Operational Amplifier (Op-Amp) is an active
circuit element design to perform mathematic
operations.
• Op-Amp is a low cost integrating circuit
consisting of transistors, resistors and
capacitors.
• Op-Amp amplify an input signal produces an
output voltage equal to the difference between
the two input terminals multiplied by the gain A
Op-Amps are commonly used for both linear
and nonlinear applications:
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Inverting/Non-inverting Amplifiers
Variable Gains Amplifiers
Summers
Integrators/Differentiators
Filters (High, Low, Band Pass and Notch Filters)
Schmitt trigger
Comparators
A/D converters
Brief History
• Vacuum Tubes Op-Amp (use ±300 to ±100V) built in
1930’s-1940’s
• Solid State Discrete Op-Amps (use ±15 to ±10V) 1960’s
• Integrated Circuit Op-Amp (µA702 in 1963 and µA741 in
1968)
The Equivalent Circuit of the Op-Amp
v d = v2 - v 1
vo = Avd = A(v2 – v1)
Parameters of Typical Range vs Ideal Values of the Op Amp
The Ideal Op-Amp
1) The input impedance Ri is infinite - i.e. no current flows into either
input.
2) The output impedance Ro is zero - i.e. the op-amp can drive any
load impedance to any voltage.
3) The open-loop gain (A) is infinite.
4) The bandwidth is infinite.
5) The output voltage is zero when the input voltage difference is zero.
Op-Amp Gain
Open loop gain:
This form of gain is measured when no feedback is applied
to the op amp.
Figures are often quoted in the op amp datasheets in terms of
volts per millivolt, V/mV.
Closed loop gain:
This form of gain is measured when the feedback loop is
operation, i.e. a closed loop.
Slew Rate
The slew rate of an op amp or any amplifier circuit is the rate of
change in the output voltage caused by a step change on the input.
Op amp bandwidth basics
The frequency response of a typical op amp chip will often
start to fall at a very low frequency when operated in its
open loop mode.
Feedback vs bandwidth
In view of the very high gain of the operational amplifier it is
possible to, in effect, exchange some of the open loop gain
for bandwidth. For a circuit like this, applying feedback will
reduce the gain but increase the bandwidth.
Slew rate calculation & formula
Where
slew rate is measured in volts / second, although actual
measurements are often given in v/µs
f = the highest signal frequency, Hz
V = the maximum peak voltage of the signal.
As an example, take the scenario where an op amp is required to
amplify a signal with a peak amplitude of 5 volts at a frequency of
25kHz. An op amp with a slew rate of at least 2 π x 25 000 x 5 =
0.785V/µs would be required
Op Amp Offset Null
The offset null capability is used to reduce small DC
offsets that can be amplified. These can be important in
DC amplifiers where these small voltages can then
become significant where large gains are required.
This input offset voltage is small and arises from
mismatches in the differential input stage of the op amp
chip. These small offsets are caused by a variety of
unavoidable issues within the manufacture of the op
amp. They include aspects including mismatched
transistor pairs, collector currents, current-gain betas
(β), collector or emitter resistors, etc..
To remove or null the offset, many op-amp chips provide
two pins that enable this to be done. Using the offset null
adjustment requires a potentiometer with its wiper
connected to the negative supply with some op amps or to
0 V with othersVR1 is typical 10 KΩ to 100 KΩ.
The Voltage Follower
VOUT = V-
VOUT = A(V+ - V-)
V+
VOUT = A/(A+1) V+
V-
VOUT = V+= VIN
VOUT = VIN
Voltage followers are used to buffer or isolate a low impedance load
from a voltage source.
The Inverting Op Amp
The V- terminal is referred
to as a "virtual ground“
due to negative feedback.
VOUT = A(0-V-) thus
Apply KCL at node A: i1 = i2  (vin – v-)/R1= (v- – vOUT)/R2
Since v-= v+ = 0, vi /R1 = - vOUT/R2 or
vOUT = - (R2 /R1)vin
The Non-Inverting Amp
v- = v+ = vi n  vi n = R1 i1
Since no current flows into either of the Op-Amp inputs i1 = i2
 Vout = R1 i1 + R2 i2 = Vin + R2 Vin/R1
vout= (1 + R2 /R1)vin
The Summing Amp
i = i 1 + i 2 + i3
i1 = (v1 – va)/R1 i2 = (v2 – va)/R2
i3 = (v3 – va)/R3 i = (va – vo)/Rf
Since va= 0
The Difference Amp
Apply KCL at node a
(v1 – va)/R1 = (va – vo)/R2 or
vo = (R2/R1+ 1)va- (R2/R1)v2
Apply KCL at node b
(v2 – vb)/R3 = (vb – 0)/R4 or
vb = {R4/(R3+R4)}v2
Since va = vb
If R1/R2 = R3/R4 then
vo = R2/R1 (v2 - v1)
or
Comparator
A typical comparator circuit will have one of the inputs
held at a given voltage. This may often be a potential
divider from a supply or reference source. The other
input is taken to the point to be sensed.
Example: Uses a 301 op amp as a comparator.
When vI < VT  vO = - Vsat and vI > VT  vO = + Vsat
If VT ≠ 0V, the circuit is aptly called a threshold detector.
If VT = 0 V, the circuit is referred to as a zero-crossing
detector.
Inverting Schmitt Trigger
Use a voltage divider to provide positive dc feedback for a 301 op
amp. The circuit can be viewed as an inverting- type threshold
detector whose threshold is controlled by the output. Since the
output has two stable states, this threshold has two possible values,
namely,
Reference:
• Fundamental of Electric Circuit by Charles K. Alexander
and Matthew N.O. Sadiku
• Lecture EE122, Stanford University, Prof. Greg Kovacs
• “Op Amp History.” Analog Devices.
http://www.analog.com/library/analogDialogue/archives/
39-05/Web_ChH_final.pdf
• www.learningaboutelectronics.com/Articles/
• http://www.radioelectronics.com/info/circuits/opamp_basics/operationalamplifier-slew-rate.php
• Design With Operational Amplifiers And Analog
Integrated Circuits, 4th Edition by Sergio Franco