Module: Electronics I
Module Number: 610/650221-222
Electronic Devices and Circuit Theory, 9th ed., Boylestad and Nashelsky
Philadelphia University
Faculty of Engineering
Communication and Electronics Engineering
Operational Amplifiers (Op-Amps)
Basics
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Operational amplifier or op-amp is
 a very high gain differential amplifier with a high input impedance
(typically a few meg-Ohms) and
 low output impedance (less than 100 W). Note the op-amp has two inputs
and one output.
Typical uses of the operational amplifier are to provide voltage amplitude
changes (amplitude and polarity), oscillators, filter circuits, and many types of
instrumentation circuits.
An op-amp contains a number of
differential amplifier stages to achieve a
very high voltage gain.
The given figure shows a basic op-amp
with two inputs and one output as would
result using a differential amplifier input
stage. Recall from Parts II and III that each
input results in either the same or an
opposite polarity (or phase) output,
depending on the amplifier type itself.
According to this, the signal could be applied to the plus (+) or the minus (-)
input to give a phase shift or not, simultaneously.
Op-amp gain
Op-Amps have a very high gain. They can be connected open- or closed-loop.
a. Open-loop refers to a configuration where there is no feedback from output
back to the input. In the open-loop configuration the gain can exceed
10,000.
b. Closed-loop configuration reduces the gain. In order to control the gain of
an op-amp it must have feedback. This feedback is a negative feedback. A
negative feedback reduces the gain and improves many characteristics of the
op-amp.
Lecturer: Dr. Omar Daoud
١
Module: Electronics I
Module Number: 610/650221-222
Electronic Devices and Circuit Theory, 9th ed., Boylestad and Nashelsky
Basic Operation
The basic circuit connection using an op-amp is shown in Fig. 14.12. The circuit shown
provides operation as a constant-gain multiplier.
 An input signal, V1, is applied through resistor R1 to the minus input.
 The output is then connected back to the same minus input through resistor Rf.
 The plus input is connected to ground.
Since the signal V1 is essentially applied to the minus input, the resulting output is
opposite in phase to the input signal.
Operation of op-amp as constant-gain multiplier: (a) op-amp ac equivalent circuit; (b) ideal op-amp
equivalent circuit; (c) redrawn equivalent circuit.
 The Op-Amps AC equivalent circuit
Where: Vd is the differential voltage (equals Vi1-Vi2)
Ri is the input resistance
Ad is the differential gain
Ro is the output resistance
Ac is common mode gain
Lecturer: Dr. Omar Daoud
٢
Module: Electronics I
Module Number: 610/650221-222
Electronic Devices and Circuit Theory, 9th ed., Boylestad and Nashelsky
 Differential Inputs
When separate inputs are applied to the op-amp, the resulting difference signal is
the difference between the two inputs (Vd = Vi1- Vi2 )
 Common Inputs
When both input signals are the same, a common signal element due to the two
inputs can be defined as the average of the sum of the two signals (Vc= 0.5(Vi1 Vi2))
 Output Voltage
Since any signals applied to an op-amp in general have both in-phase and out-of
phase components, the resulting output can be expressed as Vo=AdVd-AcVc.
 The common-mode rejection ratio (CMRR) could be defined as
Example:
Calculate the CMRR for the circuit measurements shown in the given Fig. below
Lecturer: Dr. Omar Daoud
٣
Module: Electronics I
Module Number: 610/650221-222
Electronic Devices and Circuit Theory, 9th ed., Boylestad and Nashelsky
Inverting Op-Amp
The signal input is applied to the inverting (–) input. The non-inverting input (+) is
grounded. The resistor Rf is the feedback resistor. It is connected from the output to the
negative (inverting) input. This is negative feedback.
Apply kvl to the input loop
V1  I i  R1      (1)
But, I i   I f      (2)
Apply kvl to the output loop
Vo  I f  R f      (3)
substitute 1 and 2 in 3
Rf
Rf
Vo  
Vi  Av  
Ri
Ri
Noninverting Op-Amps
Summing Op-Amps
Because the op-amp has high input impedance, the multiple inputs are treated as separate
inputs.
Lecturer: Dr. Omar Daoud
٤
Module: Electronics I
Module Number: 610/650221-222
Electronic Devices and Circuit Theory, 9th ed., Boylestad and Nashelsky
Integrator Op-Amps
The output is the integral of the input. Integration is the operation of summing the area
under a waveform or curve over a period of time. This circuit is useful in low-pass filter
circuits and sensor conditioning circuits.
Differentiator Op-Amps
The differentiator takes the derivative of the input. This circuit is useful in high-pass filter
circuits.
Lecturer: Dr. Omar Daoud
٥
Module: Electronics I
Module Number: 610/650221-222
Electronic Devices and Circuit Theory, 9th ed., Boylestad and Nashelsky
Example 1:
Calculate the output voltages V2 and V3 in the given circuit below.
Solution:
Lecturer: Dr. Omar Daoud
٦
Module: Electronics I
Module Number: 610/650221-222
Electronic Devices and Circuit Theory, 9th ed., Boylestad and Nashelsky
Example 2:
What range of output voltage is developed in the given circuit below.
Solution:
Lecturer: Dr. Omar Daoud
٧