Operational Amplifiers

1
Operational Amplifiers
Homework Barnaal 2, 3, 4 (pg.229/230) Lab
Operational Amplifier I Read Chapter A5 and A6
2
The power of feedback
Purpose Make a standard component that could be
used to construct amplifiers with stable and
controllable gain (current or voltage) without
needing to go back to the level of
transistors. This is made possible by design of
circuits that have near ideal properties that we
can alter by adding a few external components.
These must change the relationship between the
output and input signals, which requires
feedback. Positive Feedback - couple output to
input in such a manner as to accentuate or
magnify the input. Used for oscillators. Negative
Feedback - couple input to output in manner that
some of the input is cancelled. Basis of almost
all operational amplifier circuits.
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Introduction to operational amplifiers
Inverting input, V-
1
8
-
Output, Vout
NC
A
Invert
V
Noninvert
Output

V-
Noninverting input, V
Symbol
Typical Package

• Op-amps are linear IC devices with two input
  terminals, and one output terminal. One input is
  inverting (-), and the other noninverting ().
• Standard symbol usually does not show dc supply
  terminals.

4
Introduction to operational amplifiers
  mid 1960s first op amp (µA 709) based on
integrated circuits, before then vacuum tube
technology   large of transistors and
resistors on the same silicon chip (shown for
LT1028)

• basic building block
• designer often doesnt care about the inside
  only the terminal characteristics
• Available in hundreds of types, fairly inexpensive

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Introduction to operational amplifiers

• Enormous gain, never used without feedback
• Feedback network determines characteristics of
  your circuit
• Very versatile one can do almost anything with
  opamps
• For instance
• Summing amplifier, Integrator, Differentiator,
  Logarithmic amplifier, Difference amplifier, math
  functions in analog computation, Inverting
  amplifier, Noninverting amplifier, Follower,
  Buffer, Comparator, Current sink and source
  circuits, DC/AC Voltmeter, Limiting circuits,
  Peak detectors, Switching circuits, Crossing
  detectors, Multivibrator, Wave generator, Active
  filters, DC voltage regulator, many more .

This is what caused the terminology operational
amplifier
6
Remember voltage amplifier
Microphone
Speaker
Zout
Zin
RS
Rload
Vin
VS
AV Vin
Vout
Amplifier
Source
Load
All electrical signals have a source resistance,
the Norton or Thevenin resistance. Also all
output transducers like speakers have a load
impedance. An amplifier serves to couple and
perhaps amplify a signal and a output device.
The diagram above schematically shows how to
think of a voltage amplifier. Like the other
measuring devices it has a finite input impedance
Zin (the oscilloscope had a 1M? resistance), and
like all voltage sources it has an output
impedance Zout. It increases the voltage Vin
that it sees across its inputs by a voltage gain
or amplification of AV. An ideal amplifier would
have Zin ? and Zout 0.
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Ideal op amp
Zout
Zin
RS
Rload
Vin
VS
Vout
AV Vin
Amplifier

• Our basic picture of an amplifier includes three
  parameters
• the voltage gain
• the input impedance Zin
• the output impedance Zout.
• The ideal op-amp has

1) Av ?, 2) Zin ?, 3) Zout 0.
8
Ideal versus practical op-amp
Ideal op-amp characteristics Zin ? Av
? bandwidth ? Zout 0
-
Zin
Vout
Vin
AvVin
Zo
Practical op-amp characteristics Zin very high
(MW) Av very high (100,000) Zout very low
(lt100 W) bandwidth few MHz range Vout and Iout
have limitations

Op-amp representation
9
Example the 741
A common op-amp is the 741, which is available in
a 8 pin DIP This has power supply connections V
and V- that are typically 12 or 15 V There are
two inputs because this is a differential
amplifier, meaning
The input impedance is 2 MW, large but not huge.
This is because it is based on BPJ transistors as
an input stage. The 411 has JFET inputs with Zin
1012 W.
We will not use the offset null connections until
next week.
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Example - 741 packaging
The reason it is called a DIP is that it is a
Dual Inline Package, typically made of ceramic or
plastic on the outside. The actual integrated
circuit IC is only about 1 mm2. The pins are
located 0.1 apart so that they fit in our
breadboards.
Pin 1 always is uniquely identified
11
Negative feedback
Vin
Vout
A
B
G closed loop gain A open loop gain AB loop
gain
12
Negative feedback

• Since the open-loop gain of the op-amp is very
  high, an extremely small input voltage would
  drive the op-amp into saturation.
• By feeding a portion of the output voltage to the
  inverting input of the op-amp (negative
  feedback), the closed-loop voltage gain (Acl) can
  be reduced and controlled (i.e. stable) for
  linear operations.
• Negative feedback also provides for control of
  Zin, Zout, and the amplifiers bandwidth.

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Golden rules for op amps
We can analyze op amp circuits with the following
rules (from Horowitz/Hill) assuming that there is
negative feedback, and that the output is within
the range of voltages and currents provided by
the power supplies (always remember that there
must be power connected). Golden Rule I The
output attempts to do whatever is necessary to
make the voltage difference between the inputs
zero (this is required if Av ?,
and Vout is finite). Golden Rule II The inputs
draw no current ( this follows from Zin ? ).
It is easiest to see how this works by just
applying the rules.
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Inverting amplifier
From the golden rules we know that since there is
negative feedback (there is a connection between
the output pin and the inverting input) that the
inputs should have the same voltage, V 0. On
the non-inverting this is because it is connected
to ground. For the inverting pin it is called a
virtual ground, because feedback makes it zero
(or almost).
We also note that since there is no current into
the inputs Iin If. Then we find
Iout can be any value, depending on what the load
is. It is provided primarily by the op-amp
itself.
Minus sign ? 180o phaseshift ? inverting
amplifier
15
Summing amplifier
The point called the summing node is where we add
currents, according to Kirchhoff's laws. Because
we are feeding them through resistors first we
are effectively adding voltages.
By changing the value of Ri we can make this a
weighted sum, that is for a smaller input
resistor the current is higher meaning it
contributes a higher weight to the summed current.
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Non-inverting amplifier
One feature of the last two circuits was that if
we input a positive voltage the output was
negative. Here is a different circuit that I
claim does not invert. Another thing to note is
that it draws no current from the source, meaning
it has Zin ?. This was not true of the
previous circuits, which did draw current.
I1
Rf
Vout
R1
Vin
Iout
Analysis relies on the two resistors acting like
a voltage divider, with the middle point equal to
Vin , because of feedback. Then
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Summary inverting/non-inverting amplifier
18
Follower - special case of the non-inverting
amplifier

• Ideal as a buffer amplifier.

In the non-inverting amplifier we can let Rf 0
and R1 ?. Then the gain equals unity. This is
called a follower. What good is a gain of 1 you
might ask. Remember that Zin ? for this
circuit, but Zout 0. This is perfect! We will
not load any signal source, because we draw no
current when we attach the follower (it is like
it is not even there).
This circuit is common enough that there are ICs
that have the output and inverting input
connected internally.