CSCI 2980: Introduction to Circuits, CAD, and Instrumentation
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Transcript CSCI 2980: Introduction to Circuits, CAD, and Instrumentation
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
Each op-amp has minimum and maximum supply ranges over which
the op-amp is guaranteed to function
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?
Unity gain buffer is buffer amplifier
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
General rule for op-amp circuit analysis
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
General rule for op-amp circuit analysis
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.