Operational Amplifiers

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Operational Amplifiers
ME 6405 Introduction to Mechatronics September
26, 2002 Kevin Socha Jiann Su Stathis Velenis
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Outline
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Background Ideal Op Amp Characteristics Feed
back Virtual Short Circuit Basic Op Amp
Circuits Inverting Type (Derivation) Non-Inverti
ng Type (Derivation) Integrating
Type Differential Type Summing Type
Applications Summary
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The Amplifier
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Q. Why do we want to amplify signals? A. Increase
the level of the signal
We use amplifiers to increase the voltage,
current, or power level of a circuit
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The Amplifier
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The amplifier transfer characteristic the
relationship between the input and the output
signals.
The level of signal amplification is called the
gain, Av, and is the slope of the amp transfer
characteristic.
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Background
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Operational Amplifier (Op Amp) Definition a
high gain electronic amplifying circuit
element in a feedback amplifier, that
accomplishes many functions or mathematical
operations in analog circuits.
The op amp is a differential amplifier it
amplifies the difference between the two input
signal voltages by a factor Aol the open loop
gain. Op amps are voltage amplifiers
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History
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1940s Analogue computers performed numerical
operations, such as addition and
multiplication, hence the name op amp. -
vacuum tubes
mid 1960s First commercial integrated (ic) op
amps produced by Fairchild (uA702 the uA709 and
the uA741 still widely used today)
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Op Amp
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The op amp has a minimum of five terminals
2 signal input terminals, V and V- 1 signal
output terminal Vo 2 DC power supply input
terminals, V and -V
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Op Amp
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Single device 8 pin computer chip
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Internal Structure of an Op Amp
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Inside the black box transistors, diodes,
capacitors, resistors, etc.
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The Op Amp Transfer Characteristic
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Transfer Characteristic saturation (Vo
Vcc) - saturation (Vo - Vcc) linear region
(Vo A(V - V-))
We design the op amps to operate in the linear
region, therefore the difference voltage at the
input terminals must lie within the range.
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The Ideal Op Amp
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Characteristics 1. The open loop gain is
infinite over all frequencies 2. The input
terminals have infinite input impedance - No
current flows through 3. The differential input
voltage is zero - Tries to make both inputs
equal 4. The output resistance is zero 5. The op
amp generates no noise
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Ideal Op Amp Circuit Model
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Also called dependant source model.
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Op Amp Circuit Model - Discussed
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Input Resistance Accounts for the fact that the
op amp will draw a finite amount of input current
from the signal source,
Output Resistance Accounts for the fact that
there will be a change in the output voltage as
the op amp is called upon to supply more current
to the load,
High input resistance to draw little current
from the source Low output resistance so the
output voltage is independent of the current
required by the load, and Infinite open loop gain
control this with closed loop gain
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Controlling the Infinite Gain
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The op amp has a large open loop gain, as a
result we can only amplify signals with a
limited input signal range for operation in the
linear region.
How can we use the op amp? Use feedback to
control the gain of the op amp and maintain
operation in the linear region.
Therefore we take a sample of the output signal
and feed it back into the input of the op amp.
This is called negative feedback.
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Concept of Negative Feedback
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Advantage of Negative Feedback The gain of the
circuit is independent of the active device (the
amplifier in this case) and is defined entirely
by the properties of the feedback circuit applied
around the amplifier.
Feedback Network Can be implemented using simple
passive devices, resistors, capacitors, etc.
Application to Op Amp circuits Negative feedback
is essential in op-amps for two main reasons 1.
To provide a method for controlling the gain of
an op amp 2. To ensure the differential input
voltage is zero hence, operation in the linear
mode.
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Infinite Open Loop Gain
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What if the feedback was added to the input? i.e.
positive feedback
Positive feedback results in an unstable circuit.
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Virtual Short Circuit
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What we know For operation in the linear mode,
the differential input signal to the op amp must
be very small, 0V for the infinite open loop
gain. (Feedback permits this)
What we can assume Since the difference between
the input signals is 0V, then the signal voltages
at the two inputs must always be the same. We
call this concept the virtual short circuit.
Keeping in mind the two main assumptions of an
ideal op amp 1) No current flows through the op
amp, and 2) the virtual short between the
inputs, we will now derive the transfer functions
for the gain for the inverting and the
non-inverting types.
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Basic Circuits of Operational Amplifiers
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• Kirchoffs Voltage Law
• Sum of voltages in a closed loop 0
• Kirchoffs Current Law
• Sum of currents into a node sum of voltages out
  of a node
• Ohms Law
• Voltage Current Resistance

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Basic Circuits of Operational Amplifiers
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• Characterized by near-infinite input resistance
  and low output resistance
• Input with positive () sign is called the
  non-inverting input
• Input with negative sign (-) called inverting
  input

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Basic Circuits of Operational Amplifiers

• One basic assumption is made
• Current flowing into the input circuit is zero
• The open loop gain, is quite large

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Basic Circuits of Operational Amplifiers

• Because of the large open-loop voltage gain, op
  amps can be used as nearly ideal voltage or
  current amplifiers

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Inverting Amplifier

• Input signal is connected to the inverting
  terminal
• Non-inverting terminal is grounded
• Gain is chosen by selection of two resistors

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Inverting Amplifier

• Kirchoffs current law requires that
• Where the source current

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Inverting Amplifier
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• Feedback current is
• And the input current is

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Inverting Amplifier

• The open-loop model requires that
• or

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Inverting Amplifier

• By setting the source current feedback current,
  the following relationship between the source
  voltage and the output voltage is obtained

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Inverting Amplifier

• If the open-loop gain is large, then the previous
  expression can be reduced to
• The above equation is the closed loop gain for an
  inverting amplifier.

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Non-Inverting Amplifier

• Non-inverting op amp avoids the negative gain
• Input signal is applied to the non-inverting
  terminal

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Non-Inverting Amplifier
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Non-Inverting Amplifier

• By applying Kirchoffs Current Law at the
  inverting node
• Where

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Non-Inverting Amplifier

• Because there is no voltage drop across the
  source resistance
• Substituting back into the previous equations
  yields

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Non-Inverting Amplifier

• The closed-loop gain for a non-inverting
  amplifier is

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Differential Amplifier
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Differential Amplifier

• Combination of the inverting and non-inverting
  amplifiers
• Frequently used where difference between signals
  needs to be amplified

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Differential Amplifier

• Based on the assumption that no current flows
  into the amplifier, the voltage at the
  non-inverting terminal is given by the following
  equation

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Differential Amplifier

• If the inverting-terminal voltage is assumed to
  be the same as the non-inverting terminal
  voltage, then currents i1 and i2 are as follows

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Differential Amplifier

• The closed loop gain for a differential amplifier
  is

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Integrating Amplifier
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Integrating Amplifier

• Circuit contains energy-storage elements
• Time-varying circuits

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Integrating Amplifier

• As in other amplifiers
• Where

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Integrating Amplifier

• Therefore
• The above equation shows that the output voltage
  is the integral of the input voltage

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Summing Amplifier
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Summing Amplifier

• Summing is based on the inverting amplifier
• Adds signal sources
• Sources with internal impedances do not interact
  with each other

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Summing Amplifier

• From Kirchoffs Current Law at the inverting
  node
• Each of the source currents is given by

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Summing Amplifier

• While the feedback current is
• Therefore, the output is given by

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Summing Amplifier

• The output consists of the weighted sum of input
  signal sources
• Weighting factor for each source is equal to the
  ratio of the feedback resistance to the source
  resistance

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Applications
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• Signal Amplification
• Arithmetic Operations
• Signal Processing
• Op-Amp Oscillators
• Voltage Follower Circuits
• Comparator Circuits
• AD, DA Converters
• Logic Operations

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Numerical Operations
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• Summing Amplifier

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Arithmetic Operations
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• Difference Amplifier

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Signal Processing
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• Integrator

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Signal Processing
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• Differentiator

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Signal Processing
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• Active Low Pass Filter

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Signal Processing
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• Active High Pass Filter

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Signal Processing
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• Active Band-Pass Filter

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Signal Processing
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• Active Notch Filter

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Op-Amp Oscillators
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• Square Wave Generator

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Op-Amp Oscillators
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• Triangle Wave Generator

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Voltage Follower Circuits
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• Inverting DC Voltage Follower

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Comparators
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• Positive-Negative Clamped Comparator

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Logic Operations
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• Logic AND Gate

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Summary
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The Operational Amplifier (Op Amp) Background
Ideal Characteristics Negative Feedback Gain
Control Linear Region of Operation Derived
Transfer Functions for Inverting Non-Invertin
g Integrating Summing Differential Applicat
ions of Op Amps
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References
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• Fredrick W. Hughes. Op-Amp Handbook.
• William D. Stanley. Operational Amplifiers with
• Linear Integrated Circuits.
• Joseph J. Carr. Electronic Circuit Guidebook,
• volume 3, Op Amps.
• Rizzoni, Giorgio. Principles and Applications
  of
• Electrical Engineering. 3rd Edition.