Basic Block Diagram of Op-Amp
An Op-Amp can be conveniently divided in to four main blocks
1.
An Input Stage or Input Diff. Amp.
2.
The Gain Stage
3.
The Level Translator
4.
An Out put Stage
Note: It can be used to perform various mathematical operations such
as Addition, Subtraction, Integration, Differentiation, log etc.
V1
I/ P
V2
Input Stage
(Diff. Amp.)
Gain Stage
(C E Amp.)
Level
Shifter
Out put
Stage
(Buffer)
Op-Amp IC
VO
An IDEAL OP AMP
An ideal op amp has the following characteristics:
1.
2.
3.
4.
5.
6.
7.
Infinite open-loop voltage gain, AV ≈ ∞.
Infinite input resistance, Ri ≈ ∞.
Zero output resistance, Ro ≈ 0.
Infinite CMRR, ρ =∞
The output voltage Vo=0; when Vd = V2-V1 = 0
Change of output with respect to input, slew rate = ∞
Change in out put voltage with Temp., ∂Vo/∂Vi=0
An Electrical Representation of Op Amp.
The Operational Amplifier
+VS
Inverting
_
i(-)
RO
vid
Noninverting
i(+)
Ri
Output
vO = AdVid
A
+
-VS
• i(+), i(-) : Currents into the amplifier on the inverting and non-inverting lines
respectively
• vid : The input voltage from inverting to non-inverting inputs
• +VS , -VS : DC source voltages, usually +15V and –15V
• Ri : The input resistance, ideally infinity
• A : The gain of the amplifier. Ideally very high, in the 1x1010 range.
• RO: The output resistance, ideally zero
• vO: The output voltage; vO = AOLvid where AOL is the open-loop voltage gain
Operational Amplifier Model
•
An operational amplifier circuit is designed so that
1) Vout = Av (V1-V2) (Av is a very large gain)
2) Input resistance (Rin) is very large
3) Output resistance (Rout) is very low
V1
Rout
Rin
V2
+
-
Av(V1- V2)
Vout
Practical Op-Amp Circuits
These Op-amp circuits are commonly used:
– Inverting Amplifier
– Noninverting Amplifier
– Unity Follower
– Summing Amplifier
– Integrator
– Differentiator
Inverting Op-Amp
Slide 7
 Rf
Vo 
V1
R1
Noninverting Amplifier
Rf
Vo  (1 
) V1
R1
Notice the output formula is similar to Inverting Amplifier, but they are not the same.
Summing Amplifier
Because the op-amp has a high input impedance the multiple inputs are treated as separate inputs.
Rf
Rf 
 Rf
Vo   V1 
V2 
V3 
R2
R3 
 R1
Summing Amplifier
Inverting Amplifier: Input and
Output Resistances
Rout is found by applying a test current
(or voltage) source to the amplifier
output and determining the voltage (or
current) after turning off all
independent sources. Hence, vs = 0
vo  i R  i R
2 2 11
But i1=i2
vo  i (R  R )
1 2 1
vs
R   R since v  0
in i
1
s

Since v- = 0, i1=0. Therefore vo
= 0 irrespective of the value of io
.
Rout  0
Differential Amplifier Using Op Amp
R2
I/P Current to op amp is zero
v  v
v1  v
i1 
R1
v1
v2
R1
v
v
+
R1
R2
v  v0
i1 
R2
R2
v 
v2
R1  R2
i1
i1
v1  v v  v0

R1
R2
v1 
R2
R2
v2
v2  v0
R1  R2
R  R2
 1
R1
R2
vo
Differential Amplifier Using Op Amp
R2
R2
v1 
v2
v2  v0
R1  R2
R1  R2

R1
R2
R2
v1
v2
R2
R2
R22
v0   v1 
v2 
v2
R1
R1  R2
R1  R1  R2 
R2
R2  R2 
v0   v1 
1   v2
R1
R1  R2  R1 
R2
v0 
 v2  v1 
R1
i1
R1
v
v
+
R1
R2
i1
vo
The Unity-Gain Amplifier or “Buffer”
•
•
•
•
This is a special case of the non-inverting amplifier, which is also
called a voltage follower, with infinite R1 and zero R2.
Hence Av = 1.
It provides an excellent electrical isolation while maintaining the
signal voltage level.
The “ideal” buffer requires no input current and can drive any
desired load resistance without loss of signal voltage.
Such a buffer is used in many sensor and data acquisition system
applications.
Unity-Gain Buffer
vi
v
v
Closed-loop voltage gain
+
-
vo
vo
AF 
vi
vi  v  v  vo
vi  v  v  vo
v
AF  o  1
vi
Used as a "line driver" that transforms a high input impedance (resistance) to
a low output impedance. Can provide substantial current gain.
Op-Amp Integrator
Op-Amp Integrator Cont…
Since the inverting input is at virtual ground
v in
i1 
R
dv
i2  C o
dt
Applying KCL at the inverting input
i1+i2 = 0
dv o v in

0
dt
R
1
 vo  
v in dt  v o (initial )

RC
 C
Op-Amp Differentiator Circuit
Op-Amp Differentiator Cont…
Since the inverting input is at virtual ground
dv in
i1  C
dt
vo
i2 
R
Applying KCL at the inverting input
i1+i2 = 0
dv in v o
 C

0
dt
R
dv in
 v o   RC
dt
Differentiators are avoided in practice as they amplify noise
Instrumentation Amplifier
R
vo   4 (va  v )
b
R
3
va  iR  i(2R )  iR  v
2
1
2 b
NOTE
Combines 2 non-inverting amplifiers
with the difference amplifier to provide
higher gain and higher input
resistance.
Gain can be varied by varying single
resistor R1
v v
i 1 2
2R
1
R  R 
vo   4 1 2 (v  v )
R  R  1 2
3
1
Ideal input resistance is infinite
because input current to both op
amps is zero. The CMRR is
determined only by Op Amp 3.
Finite Open-loop Gain and Gain Error
vo  Av  A(vs  v )  A(vs  vo)
1
id
vo
A
Av  
vs 1 A
R
Av  1 2

R
1
This is the “ideal” voltage gain
of the amplifier. If A is not
>>1, there will be “Gain Error”.
1
R
1 v  v
v 
o
1 R R o
1 2
R
1

is called the
R R
feedback factor.
1 2

• Gain Error is given by
GE = (ideal gain) - (actual gain)
For the non-inverting amplifier,
GE 
1
A
1

 1 A  (1 A )

• Gain error is also expressed as a
fractional or percentage error.
A
1
1
FGE   1 A 

1
1 A A
1


PGE 
1
100%
A
Output Voltage and Current Limits
Practical op amps have limited
output voltage and current ranges.
Voltage: Usually limited to a few
volts less than power supply span.
Current: Limited by additional circuits
(to limit power dissipation or protect
against accidental short circuits).
The current limit is frequently
specified in terms of the minimum
load resistance that the amplifier can
drive with a given output voltage
swing. Eg:
5V
io 
10mA
500
io  i  i 
L F
vo

vo

vo
R
R R R
L
2 1
EQ
R  R (R  R )
EQ L 1 2
For the inverting amplifier,
R
R R
EQ L 2
Bistable