EENG 2610: Circuits Analysis
Class 6: Operational Amplifiers (Op-Amp), 1/2
Oluwayomi Adamo
Department of Electrical Engineering
College of Engineering, University of North Texas
Operational Amplifier (Op-Amp)




Op-amp is the single most important integrated circuit (IC) for analog circuit
design; it has been extensively used in circuit design at all levels.
Op-amp is consisted of individual transistors and resistors interconnected
on a printed circuit board (PCB)
Op-amp was originally designed to perform mathematical operations such
as addition, subtraction, differentiation, and integration.
We have learned tools to analyze practical circuits using op-amps !
Op-Amp Models


Op-amp is just a really good voltage amplifier!
Example: LM324 from National Semiconductor

General purpose quad (four in a pack) op-amp.
unit: inch
In-Out Voltage Relation: V  A ( IN  IN )
0
0


Typically, A0 is between 10,000 and 1,000,000 !
Dual Inline Pack (DIP) style package
Four identical op-amps in the package
IN +: noninverting input
IN -: inverting input
OUT : output
VCC: positive voltage
VEE: negative voltage or ground
Power Supply and Ground
voltage source

Op-amp is modeled using a dependent voltage source and resistors
Ri : input resistor
Ro : output resistor
A : op - amp gain
In-Out Voltage Relation:
vo  A(v  v )
A simple model of op-amp
Effects of Power Supply
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Each op-amp has minimum and maximum supply ranges over which
the op-amp is guaranteed to function
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For proper operation, the input and output voltages are limited to no
more than the supply voltages (VCC, VEE).
Inputs and output are called rail-to-rail, if the inputs and output can
reach within a few dozen millivolts of the supplies.
An op-amp is said to be in saturation,

If an increase in the input voltage may not yield a corresponding
increase in the output voltage
Saturation and
Rail-to-Rail
In-Out Voltage Relation:
vo  A(v  v )
Rail-to-rail output voltage
PA03
Unity Gain Buffer Circuit
 Vs  Ri I  RO I  AO vin  0
 vout  RO I  AO vin  0
Voltage
Gain:
vin  IRi
Op-Amp BUFFER GAIN
LM324
0.99999
LMC6492
0.9998
PERFORMANCE OF REAL OP-AMPS
MAX4240
0.99995
vout

Vs 1 
1
Ri
RO  AO Ri
AO   
Vout
1
VS
That’s why it’s called Unity Gain Buffer,
or Voltage Follower.
Equivalent resistance
of voltage source
Op-amp Model
Equivalent load
resistance
What should be the values for
Ri , Ro , Ao ?
vo  Ri   RL 

 Ao 

VS  Ri  RTh1   Ro  RL 
Voltage Gain:
To achieve large overall gain independent of RTh1 , RL
ideally
A  , R  , R  0
o
i
o
(Commercial op-amps do have this tendency !)
Ideal Op-Amp Model
i
i
Ideal Model: RO  0, Ri  , A  
Ri  
A
vo  A(v  v )
v  v  0
i  i  0
v  v
Analyze unity gain buffer using ideal model
v
v
Ideal Model: RO  0, Ri  , A  
i  i  0
v  v
vo  v   v   v s
VCC
Where does the current i1 come from?
v
i  0
i1
v
i  0
RL
Why use unity gain buffer?
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Unity gain buffer is buffer amplifier
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Unity gain buffer isolates driving circuits from load circuits, which is
called buffering
The load current (or energy) comes from op-amp power supply, which
have plenty of current (or energy) output capacity, rather than the driving
circuit.
RS consume source energy
CONNECTION WITHOUT BUFFER
0
RS does not consume source energy
CONNECTION WITH BUFFER
load
0
VCC
vS
driving circuit
vo  v s  Rs i
driving circuit
vo  v s
load
Op-Amp Circuit Analysis
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General rule for op-amp circuit analysis
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Use the ideal op-amp model conditions
Write nodal equations at the op-amp input terminals
Ideal Model: RO  0, Ri  , A  
i  i  0
v  v
Example 4.2: Basic inverting op-amp configuration
Determine gain using both non-ideal model and ideal model
Equivalent
Note: the ground can all be connected to a single node.
Using non-ideal op-amp model:
1.
3.Draw components of linear op-amp
Identify op-amp nodes
v
v
vo
vo
Ri
v
RO
v


2. Redraw the circuit cutting out the op-amp
4. Redraw as needed
v
R2
v
vo
v
v
A(v  v )
v3
Typical values:
A  105 , Ri  108 , R0  10,
R1  1k, R2  5k
v2
vo
 4.9996994 5
vS
1
A v
 )( S )
R2 Ro R1
vo 
1 1
1 1
1
1 1
A
(   )(  )  ( )(  )
R1 Ri R2 R2 Ro
R2 R2 Ro
(
vo

vS

R2
R1
 1 1
1 1
1
1
1
A 
1  (   )(  ) ( ) (  )
R2 R2 Ro 
 R1 Ri R2 R2 Ro
lim
A 
 vo

 vS

R
   2  5
R1

Using ideal op-amp model:
v
vo
v  v  0
vS  0 vo  0

0
R1
R2

vo
R
 2
vs
R1
v

Ideal op-amp model:
i  i  0
v  v
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General rule for op-amp circuit analysis
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
Use the ideal op-amp model conditions
Write nodal equations at the op-amp input terminals
From now on, unless
otherwise stated, we will
use the ideal op-amp
model to analyze circuits
containing op-amp.