Download Lecture 09

Lecture 9
Op-Amp Circuits
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Characteristics of Ideal Op
Amps
 Infinite gain for the differential input signal
 Zero gain for the common-mode input signal
 Infinite input impedances
 Zero output impedance
 Infinite bandwidth
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Real Versus Ideal Op Amp
Parameter
Open-loop gain A
Input resistance, Ri
Output resistance, Ro
Typical Range
10^5-10^8
10^5 to 10^13W
10 to 100W
Ideal Values

W
0W
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
SUMMING-POINT
CONSTRAINT
Operational amplifiers are almost always
used with negative feedback, in which part of
the output signal is returned to the input in
opposition to the source signal.
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
In a negative feedback system, the ideal opamp output voltage attains the value needed
to force the differential input voltage and input
current to zero. We call this fact the
summing-point constraint.
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Ideal op-amp circuits are
analyzed by the following steps:
1. Verify that negative feedback is present.
2. Assume that the differential input voltage
and the input current of the op amp are
forced to zero. (This is the summing-point
constraint.)
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
3. Apply standard circuit-analysis principles,
such as Kirchhoff’s laws and Ohm’s law, to
solve for the quantities of interest.
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
The Basic Inverter
v x  0  vo  0  v x decreases
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Applying the Summing Point
Constraint
i2 
0  vo
v
 i1  in
R2
R1

vo vin

R2
R1

Av 
vo
R
 2
vin
R1
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Inverting Amplifier
vin
Z in 
 R1
iin
Vout
R2

vin
R1
 Z out  0
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Summing Amplifier
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Summing Amplifier
iA
vA
iA 
RA
RA
VA
iout
V=0
iB
iout
0  vout  vout


RF
RF
iout
 vout v A v B
 i A  iB 


RF
R A RB
vout
 v A vB 

  RF 

 R A RB 
Vout
Rf
VB
RB
vB
iB 
RB
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Exercise 14.3
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Positive Feedback
With positive
feedback, the op
amp’s input and
output voltages
increase in magnitude
until the output
voltage reaches one
of its extremes.
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Non-inverting Amplifier
vi  0  v1  vin
 R2 
R1  R2
vin
 vo 
vin  1 
R1
R1 

 R 
v
Av  o  1  2 
vin 
R1 
R1
v1 
vo
R1  R2
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Non-inverting Amplifier
0  vin
iin 
R1
iin
iout
Vin
0
R1
iout
Vout
R2
vin  vout

R2
iin  iout
 vin vin  vout


R1
R2
vout vin vin


R2
R1 R2
vout
 R2 

 vin 1 
R1 

ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
NONINVERTING
AMPLIFIERS
Under the ideal-opamp assumption, the
non- inverting
amplifier is an ideal
voltage amplifier
having infinite input
resistance and zero
output resistance.
vo
R2
Av
1
vin
R1
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Voltage Follower
vo
R2
0
A v
 1
 1  1
vin
R1

ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Exercise 14.4
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Voltage-to-Current Converter
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Design of Simple Amplifiers
Amplifier design using op amps mainly
consists of selecting a suitable circuit
configuration and values for the
feedback resistors.
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
If the resistances are too small, an
impractical amount of current and power
will be needed to operate the amplifier.
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Very large resistance may be unstable in
value and lead to stray coupling of undesired
signals.
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Example 14.3
Want the voltage gain to be -10  5 percent:
Varying
resistance
vout
R2

 10  5%
vs
RS  R1
Need R1>>RS so that variability in
RS is a small percentage change
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Example 14.3
Choose R1 = 100Rs = 50kW
R1+RS min = 50kW
R1+RS max = 50.5kW
Rmax  Rmin 50 .5kW  50 kW 0.5


 1%
R1
50 kW
50
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.
Example 14.3
To get the gain of 10, choose R2  10R1 = 500kW
Since R1, RS, R2 can all vary, use 1% tolerance resistors:
R1 = 49.9kW  499W
R2 = 499kW  4.99kW
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc.