Operational
Amplifiers
Brandon Borm
Shelley Nation
Chloe Milion
Outline
Introduction
 Background
 Fundamentals of Op-Amps
 Real vs. Ideal
 Applications

What is an Op-Amp

Low cost integrating circuit consisting of
 transistors
 resistors
 capacitors

Op-amps amplify an input signal using an
external power supply
Uses for Op-Amps


Op-Amps are commonly used for both linear and
nonlinear applications
Linear
 Amplifiers
 Summers
 Integrators
 Differentiators
 Filters

(High, Low, and Band Pass)
Non-linear
 Comparators
 A/D
converters
Vacuum Tube Op-Amps

First op amps built in 1930’s1940’s
 Technically
feedback amplifiers
due to only having one useable
input

Used in WWII to help how to
strike military targets
 Buffers,
summers, differentiators,
inverters

Took ±300V to ± 100V to power
http://en.wikipedia.org/wiki/Image:K2-w_vaccuum_tube_op-amp.jpg1
Solid State Discrete Op-Amps

Solid state op amps invented in
1960’s
 Possible
due to invention of
silicon transistors and the IC
 Chip and discrete parts
Reduced power input to ±15V
to ±10V
 Packaging in small black boxes
allowed for integration with a
circuit

Monolithic Integrated Circuit Op-Amp

First created in 1963
 μA702

by Fairchild Semiconductor
μA741 created in 1968
 Became
widely used due to its
ease of use
 8 pin, dual in-line package (DIP)

Further advancements include
use of field effects transistors
(FET), greater precision, faster
response, and smaller packaging
Features of Op-Amps







+Vin: non-inverting input
-Vin: inverting input
+Vs: positive source
-Vs: negative source
Vout: output voltage
ON: Offset Null
NC: Not Connected
+Vin
+Vs
+
Vout
-Vin
-
-Vs
ON
-Vin
NC
+Vs
+Vin
Vout
-Vs
ON
Characteristics of Op-Amps
Ideal Op-Amp

Infinite open loop gain
(GOL):
 Zero

Real Op-Amp

 Decreases
with increase
in frequency
 Non-zero common mode
gain
common mode gain
Infinite bandwidth:
 Range
of frequencies
with non-zero gain
Limited open loop gain:

Limited Bandwidth:
 Gain
becomes zero at
high frequencies
Characteristics of Op-Amps
Ideal Op-Amp
Real Op-Amp

Infinite slew rate

Finite slew rate

Infinite input impedance

Large input impedance
 No

 Small
input current
Zero output impedance
 Infinite
output current

input current
Non-zero output
impedance
 Limited
output current
Summary of Characteristics
Parameter
Ideal Op-Amp Typical Op-Amp
GOL
∞
105 - 109
Common Mode
Gain
0
10-5
Bandwidth
∞
1-20 MHz
Input
Impedance
∞
Output
Impedance
0
106 Ω (bipolar)
109-1012 Ω (FET)
100-1000 Ω
Ideal Op-Amp




Active device
Infinite open loop gain
Infinite input impedance
Zero output impedance
+Vs
iin = 0A
+
Vdiff
Vout = Vdiff x Gopenloop
-Vs
Negative Feedback

Vout is a linear function of the input voltage

Zin = infinity

Modelisation of basic mathematical
operation
Iin=0A
Vdiff=0V
Non Inverting Circuit
iin = 0A
Vin
+Vs
(1) V- - Vout = R2 x i
+
Vout
Vdiff = 0V
0A
R1
V- = V+ = Vin
-Vs
i
(2)
i = -Vin/R1
R2
(1)
V-
(2) V- = - R1 x i
Vin – Vout = -Vin x R1/R2
V- - Vout
Vout = (1 + R1/R2) x Vin
Inverting Circuit
+Vs
iin = 0A
(1) V- - Vout = R2 x i
+
Vout
Vdiff = 0V
(2) Vin - V- = R1 x i
-Vs
Vin
R1
Vin – V-
i
R2
V- - Vout
V- = V+ = 0
(1)
i = Vin / R1
Vout = - R2/R1 x Vin
Follower Circuit
+ Vs
Vin
Vout
- Vs
Summing Op-Amp
• Adds analog signals
Ohm’s Law:
Solving for Vout:
V1  V V2  V V3  V V  Vout



R1
R2
R3
Rf
Vout
 V1 V2 V3 
  R f  
 
 R1 R2 R3 
Summing Op-Amp
Difference Op-Amps
• Subtracts analog signals
• Output voltage is proportional to
difference between input voltages:
Vout

R3  R1 R4

V
R3
V1
2 
( R4  R2 ) R1
R1
Difference Op-Amp
Integrator Op-Amps
•Similar layout to inverting op-amp,
but replace feedback resistor with
a capacitor
•A constant input signal generates
a certain rate of change in output
voltage
• Smoothes signals over time
•Output voltage is proportional to
the integral of the input voltage:
t
1
Vout , final  Vout ,initial  
Vindt

RC 0
Integrator Op-Amp
Differentiating Op-Amp
•Similar to inverting op-amp, but
input resistor is replaced with a
capacitor
•Accentuates noise over time
• Output signal is scaled
derivative of input signal:
Vout
dVin
  RC
dt
Differentiating Op-Amp
Active Filters

Different types of active filters:
 Low

Pass
Filters out frequencies above a cutoff frequency
 High

Filters out frequencies below a cutoff frequency
 Band

Pass
Pass
Passes a range of frequencies between two cutoff
frequencies
Active Low-Pass Filter

Cutoff frequency:
1
c 
R2C
Active High-Pass Filter

Switch positioning of capacitors and resistors from lowpass filter locations to create high-pass filter.
Active Band-Pass Filter


Created by connecting output of a highpass filter to the input of a low-pass filter or
vice versa.
Also can create using only 1 op-amp with
feedback and input capacitors
No negative feedback

Vout is a non-linear function of the differential
input voltage V+ - V-

V+ - V- = Vdiff

Vout = sign(Vdiff) x Vs

Binary logic and oscillator
Comparator
Vout ( volts )
+Vs
iin = 0A
+
Vout
Vdiff
+ Vs
-
V+
Vdiff
0V
V-
-Vs
- Vs
Comparator
Questions?
References




“Operational Amplifiers.”
http://en.wikipedia.org/wiki/Op_amp
“Real vs. Ideal Op Amp.”
http://hyperphysics.phyastr.gsu.edu/hbase/electronic/opamp.html#c4
“741 Op Amp Tutorial.”
http://www.uoguelph.ca/~antoon/gadgets/741/74
1.html
“Op Amp History.” Analog Devices.
http://www.analog.com/library/analogDialogue/ar
chives/39-05/Web_ChH_final.pdf