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Electronic Instrumentation
Experiment 4
* Operational Amplifiers
* Op-Amp Circuits
* Op-Amp Analysis
Operational Amplifiers

Op-Amps are possibly the most versatile linear
integrated circuits used in analog electronics.
 The Op-Amp is not strictly an element; it contains
elements, such as resistors and transistors.
 However, it is a basic building block, just like R,
L, and C.
 We treat this complex circuit as a black box!
• Do we know all about the internal details? No!
• Do we know how to use it and interface it with other
electronic components? Yes, we must!
Op-Amp Circuits perform Operations

Op-Amps circuits can perform mathematical
operations on input signals:
• addition and subtraction
• multiplication and division
• differentiation and integration

Other common uses include:
•
•
•
•
Impedance buffering
Active filters
Active controllers
Analog-digital interfacing
The Op-Amp Chip

The op-amp is a chip, a small black box with 8
connectors or pins (only 5 are usually used).
 The pins in any chip are numbered from 1
(starting at the upper left of the indent or dot)
around in a U to the highest pin (in this case 8).
741 Op Amp
Op-Amp Input and Output

The op-amp has two inputs, an inverting input (-)
and a non-inverting input (+), and one output.
 The output goes positive when the non-inverting
input (+) goes more positive than the inverting (-)
input, and vice versa.
 The symbols + and – do not mean that that you
have to keep one positive with respect to the other;
they tell you the relative phase of the output.
(Vin=V1-V2)
A fraction of a millivolt
between the input
terminals will swing
the output over its full
range.
Powering the Op-Amp

Since op-amps are used as amplifiers, they need
an external source of power.
 The op-amp must be connected to an external
constant DC source in order to function.
 Typically, this source will supply +15V at +V and
-15V at -V. The op-amp will output a voltage
range of of somewhat less because of internal
losses.
The power inputs
determine the output range
of the op-amp. It can
never output more than
you put in. Here the
maximum range is about
28 volts.
Op-Amp Intrinsic Gain

Amplifiers increase the magnitude of a signal by
multiplier called a gain -- “A”.
 The internal gain of an op-amp is very high (105106).
 The exact gain is often unpredictable.
 We call this gain the open-loop gain or intrinsic
gain.
Vout
5
6
 A open loop  10  10
Vin
Op-Amp Saturation



Note that in spite of the huge gain, the maximum or
minimum output is still limited by the input power.
When the op-amp is at the maximum or minimum
extreme, it is said to be saturated.
Ideally, the saturation points for an op-amp are
equal to the power voltages, in reality they are
1-2 volts less.
 V  Vout  V
Vout  V
positive saturation
Vout  V
negative saturation
Internal Model of a Real Op-amp
+V
V2
Zin
Vin = V1 - V2
V1
Zout
+
AolVin
Vout
+
-
-V
• Zin is the input impedance (very large ≈ 2 MΩ)
• Zout is the output impedance (very small ≈ 75 Ω)
• Aol is the open-loop gain
Real Op-Amp Characteristics





dc-coupled: the op amp can be used with ac and dc
input voltages
differential voltage amplifier: the op amp has two
inputs (inverting and non-inverting)
single-ended low-resistance output: the op amp has
one output whose voltage is measured with respect
to ground. The output looks like a voltage source.
very high input resistance: the op-amp input looks
like a load circuit to any circuit connected to its
input (ideally 0 current; actually < 1nA)
very high voltage gain: the op-amp will saturate
either positive or negative depending on the inputs
Problems using op-amps directly as amplifiers

The op-amp intrinsic gain, Aol, can be relied upon to
be very large (1 to 5 million V/V ) but cannot be relied
upon to be an accurate stable value.
 Using op-amps, we can construct circuits whose
performance depends mainly on passive components
selected to have accurate and stable values.
 As long as Aol is large enough, the behavior of our
circuits will depend upon the values of the stable
components rather than Aol
 Feedback is the process of coupling the op-amp output
back into one of the inputs. Understanding feedback
is fundamental to understanding op-amp circuits.
Types of Feedback

Negative Feedback
• As information is fed back, the output becomes more
stable. Output tends to stay in the desired range.
• Examples: cruise control, heating/cooling systems

Positive Feedback
• As information is fed back, the output destabilizes. The op
amp will saturate.
• Examples: Guitar feedback, stock market crash
Op-Amp Circuits use Negative Feedback

Negative feedback couples the output back in such a
way as to cancel some of the input.
 This lowers the amplifier’s gain, but improves:
• Freedom from distortion and nonlinearity
• Flatness of frequency response or conformity to some
desired frequency response
• Stability and Predictability
• Insensitivity to variation in Aol

Amplifiers with negative feedback depend less and
less on the open-loop gain and finally depend only
on the properties of the feedback network itself.
Op-Amp Circuits

Op-Amp circuits we will do now
• inverting amplifier (multiply signal by negative gain)
• non-inverting amplifier (multiply signal by positive gain)
• differential amplifier (multiply difference between two
signals by a positive gain)

Op-Amp circuits we will do in experiment 8
•
•
•
•
weighted adder
integrator
differentiator
buffer (voltage follower)
Inverting Amplifier
Vout  
Rf
Rin
Vin
A
Rf
Rin
Non-inverting Amplifier
 Rf
Vout  1 
 R
g

Rf
A  1
Rg

Vin


Differential (or Difference) Amplifier
Vout
 Rf 
 (V2  V1 )
 
 Rin 
A
Rf
Rin
PSpice circuit you will use in exp 4
Op-Amp Analysis

We assume we have an ideal op-amp:
•
•
•
•
infinite input impedance (no current at inputs)
zero output impedance (no internal voltage losses)
infinite intrinsic gain
instantaneous time response
Golden Rules of Op-Amp Analysis

Rule 1: VA = VB
• The output attempts to do whatever is necessary to
make the voltage difference between the inputs zero.
• The op-amp “looks” at its input terminals and swings
its output terminal around so that the external
feedback network brings the input differential to zero.

Rule 2: IA = IB = 0
• The inputs draw no current
• The inputs are connected to what is essentially an
open circuit
How to analyze a circuit with an op-amp
1)  :
:
2)  : i 
V Vin  VB VB  Vout


R
Rin
Rf
 : VA  0
3) VA  VB  0
Vin  Vout

Rin
Rf
Rf
Vout

Vin
Rin
1) Remove the op-amp from the circuit and draw two circuits (one
for the + and – input terminals of the op amp).
2) Write equations for the two circuits.
3) Simplify the equations using the rules for op amp analysis and
solve for Vout/Vin
Analysis of Non-inverting Amplifier
1)  :
:
2)  : VA  Vin
 : VB 
Note that step 2 uses a
voltage divider to find the
voltage at VB relative to
the output voltage.
Rg
R f  Rg
3) VA  VB Vin 
Rf
Vout
 1
Vin
Rg
Vout
Rg
R f  Rg
Vout
Vout R f  Rg

Vin
Rg
Analysis of Difference Amplifier(1)
1)  :
:
Analysis of Difference Amplifier(2)
2)  : i 
V1  VB VB  Vout

Rin
Rf
 : VA 
Rf
Rin  R f
Note that step 2(-) here is very much
like step 2(-) for the inverting amplifier
and step 2(+) uses a voltage divider.
V2
V1 Vout

Rin R f
3) solve for VB : VB 
1
1

Rin R f
VA  VB :
Rf
Rin  R f
Rf
Vout

V2  V1 Rin
V2 
Rf
R f  Rin
R f V1  RinVout
VB 
Rin R f
R f  Rin
VB 
Rf
R f  Rin
V1 
Rin R f
V1 
Rin
Vout
R f  Rin
R f V2  R f V1  RinVout
What would happen to this analysis if
the pairs of resistors were not equal?
Rin
Vout
R f  Rin
Op-Amp Cautions (1)
In all op-amp circuits, the “golden rules” will be
obeyed only if the op-amp is in the active region,
i.e., inputs and outputs are not saturated at one of
the supply voltages.
 Typically it can swing only to within 1-2V of the
supplies.
 There must always be negative feedback in the
op-amp circuit. Otherwise, the op-amp is
guaranteed to go into saturation.
 Do not not mix the inverting and non-inverting
inputs.

Op-Amp Cautions (2)

Many op-amps have a relatively small maximum
differential input voltage limit. The maximum
voltage difference between the inverting and noninverting inputs might be limited to as little as 5
volts in either polarity. Breaking this rule will
cause large currents to flow, with degradation and
destruction of the op-amp.
 Note that even though op-amps themselves have a
high input impedance and a low output impedance,
the input and output impedances of the op-amp
circuits you will design are not the same as that of
the op-amp.