Student Lecture #1: Operational Amplifiers

Report
James Kelly
Nathan Knight
Gustavo Lee

Introduction

Characteristics of Ideal and Real Op-Amps

Basic Circuits of Op-Amps

Applications

Exercise



An Operational Amplifier (known as an “Op-Amp”) is an
integrated circuit that sets an output voltage based on the
input voltages provided.
In a circuit, it is used to perform an operation and an
amplification where the operation may be add, subtract,
filter, integrate, differentiate, etc.
Op-Amps are composed of transistors, resistors,
capacitors, and diodes.

1941: Karl Swartzel of Bell Labs developed the first Op-Amp.
 Used 3 vacuum tubes, only one input (inverting), and operated
on + 350 V to achieve 90 dB gain.

1947: Loebe Julie developed the Op-Amp as it is known today, with
two inputs – inverting and non-inverting.
 The differential input made a whole range of new functionality
possible.

1953: First commercially available Op-Amp.
 George A. Philbrick Researches (GAP-R). GAP-R pioneered the
first reasonable-cost, mass-produced operational amplifier

1961: Advent of solid-state, discrete Op-Amps.
 Made possible by the invention of the silicon transistor, which
led to the concept of Integrated Circuits (IC)
 Reduced power input to ±15V to ±10V

1962: Op-Amp in a potted module.
 Packaging in small black boxes allowed for integration with a
circuit

1963: First monolithic IC Op-Amp, the
μA702, designed by Bob Widlar at Fairchild
Semiconductor.


Monolithic ICs consist of a single chip
1968: Release of the μA741

The μA741 became the canonical Op-Amp, from
which many modern op-amps base their pinout
from, and is still in production today.
Parameter
Range
Frequency Spectrum
5-kHz to beyond 1-GHz GBW
Supply Voltage
0.9 V to a maximum 1000 V
Input Offsets
Approximately Zero

Introduction

Characteristics of Ideal and Real Op-Amps

Basic Circuits of Op-Amps

Applications

Exercise

+ : positive power supply

− : negative power supply

+ : non-inverting input terminal

− : inverting input terminal

 : output terminal
 + , − ,  are all referenced to ground
Parameter Name
Symbol
Value
Input impedance

∞
Output impedance

0
Open-loop gain

∞
Bandwidth

∞

Temperature-independent.
 =  + − − =  ∙ 

The maximum output voltage value is the supply voltage (saturation):
 − ≤  ≤ +

What this means:
 Current flow into the op-amp from either input terminal is zero.
▪ − = + = 0
 Differential voltage between the two input terminals is zero.
▪ + − − = 0
Parameter Name
Symbol
Value
Input impedance

106 Ω
Output impedance

102 Ω
Open-loop gain

104 ~107
Bandwidth

103 ~109 Hz

Operating temperature range:
 Commercial: 0℃~70℃
 Industrial: −25℃~85℃
 Military: −55℃~125℃
 =  + − − =  ∙ 
Vout
Saturation results when the output
voltage is equal to the power supply’s
voltage
 In typical op-amps, the saturation level is
about 80% of the supply voltage.

Vsat+
Slope = G
Vin
Vsat-
Saturation
Cutoff Points

Positive Saturation Cutoff:
  = + ≈ +

Linear Mode:
  =  + − −

Negative Saturation Cutoff:
  = − ≈ −

Introduction

Characteristics of Ideal and Real Op-Amps

Basic Circuits of Op-Amps

Applications

Exercise

A closed-loop op-amp has feedback from the
output back to one of the inputs, whereas an
open-loop op-amp does not.
Open-Loop
Closed-Loop

Negative feedback connects the output to the inverting
input (-), whereas positive feedback connects the output to
the non-inverting input (+).
Negative Feedback
Positive Feedback


Negative feedback op-amps can produce any voltage in the
supply power range.
Positive feedback op-amps can only produce the maximum
and minimum voltages of the range.
Vout
Vout
Vsat+
Vsat+
Vin
VsatNegative Feedback
Vin
VsatPositive Feedback

Functionality: to amplify the input voltage to output
voltage with a negative gain.
+ = 0 
  = − =  ∙ 
  =  ∙ −





=
−∙
∙
 = −


∙ 


Functionality: to amplify the input voltage to output
voltage with a positive gain.



 = − = +
− = 1 ∙ 
 = (1 + 2 ) ∙ 



∙(1 +2 )
=
∙1
2
  = 1 +
1
∙ 


Functionality: takes the summation of input voltages
over time and provides that as the output signal


+ = 0 
−  =  ∙ ()=  ()
 ()
   =


1
  = − ∙
()
0


1
  = −
∙ 0  ()

()

Functionality: takes the rate of change of the
inverted input voltage signal and provides that as
the output signal
+ = 0 
1
 −  =  () = ∙   

 ()

  =∙
  = − ∙ ()


 = − ∙

 ()


Functionality: takes the difference
between two signals and provides that
as the output
 =

If

1
=

2

1
 +2
:
 =

1 +

1
(2 −1 )
Moreover, if  = 1 :
 = 2 − 1
2 −


1 1

Functionality: takes the sum of two or more input
voltages and provides an output voltage
proportional to the negative of the algebraic sum
 = −

+
2
2
+⋯+


If 1 = 2 = ⋯ =  :
 = −

1
1

1
(1 +2 + ⋯ +  )
Moreover, if  = 1 = 2 = ⋯ =  :
 = −(1 +2 + ⋯ +  )

By setting

1
1

= , the summing op-amp can be
used as an averaging operator:
1

 = − (1 +2 + ⋯ +  )

Introduction

Characteristics of Ideal and Real Op-Amps

Basic Circuits of Op-Amps

Applications

Exercise

Active filters
 Signal processing
 Digital Image processing
Strain gauges
 Control circuits

 PID controllers for aircraft
 PI controllers for temperature measurement circuitry

And much more…


Attenuates frequencies above
the cutoff frequency.
Cutoff frequency (Hz):
  =



1
22 
Gain in the passband:
 =−
2
1
Attenuates frequencies below
the cutoff frequency.
Cutoff frequency (Hz):
  =

1
21 
Gain in the passband:
 =−
2
1
Strain gauges consist of a pattern
of resistive foil mounted on a
backing material.
 As the foil is subjected to stress,
the resistance of the foil changes in
a defined way.
 This results in an output signal
directly related to the stress value,
typically a few millivolts.
 Op-Amps are utilized to amplify
the output signal level to 5~10 V, a
suitable level for application to
data collection systems.


A proportional-integral-derivative (PID) controller is a generic feedback
mechanism widely used in industrial control systems.
 It calculates an “error” value as the difference between a measured process
variable and a desired setpoint.
 Using this error, it calculates a control input using tuning parameters  ,  ,
and  to drive the error to zero.


  =    + 
   +  ()

0

So where do op-amps come in?
 The error is calculated using a Summing Op-Amp.
 Using this error voltage:
▪ The derivative of the error is calculated using a Derivative Op-Amp.
▪ The integral of the error is calculated using an Inverting Op-Amp.
 The tuning parameters  ,  , and  can be selected by
appropriate selection of resistors and capacitors.


Comparators
Detectors
 Threshold detector
 Zero-level detector

Oscillators
 Wien bridge oscillator
 Relaxation oscillator

Level shifters

Introduction

Characteristics of Ideal and Real Op-Amps

Basic Circuits of Op-Amps

Applications

Exercise

Consider the circuit above running for 5 seconds. Find
 (5) when:
  0 = 0
  t = 3t
  = 5Ω,  = 5,  = 10Ω,  = 20Ω









Cetinkunt, Sabri. Mechatronics. Hoboken, NJ: John Wiley & Sons Inc., 2007.
Jung, Walter G. Op Amp Applications Handbook. Analog Devices, Inc., 2005.
“Operational Amplifier.” http://en.wikipedia.org/wiki/Operational_amplifier.
“Operational Amplifier Applications.”
http://en.wikipedia.org/wiki/Operational_amplifier_applications.
“The Strain Gauge.”
http://web.deu.edu.tr/mechatronics/TUR/strain_gauge.htm.
“The PID Controller.” http://en.wikipedia.org/wiki/PID_controller.
“Feedback in Electronic Circuits: An Introduction.”
http://ecee.colorado.edu/~ecen4827/lectures/dm_feedback1.pdf.
“Differentiator and Integrator Circuits”
http://www.allaboutcircuits.com/vol_3/chpt_8/11.html.
“Inverting Op-Amp” http://www.wiringdiagrams21.com/2009/12/17/basicinverting-op-amp-circuit-diagram/
 Questions?

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