Download Nonideal Op Amps

NONIDEAL OP AMP
CIRCUITS
Objective of Lecture
• Describe the impact of real operational amplifiers on the
models used in simulation and on the design approaches
that have to be used.
• The output voltage of the amplifier is limited by the values of the
•
•
•
•
power supplies.
Rin   and current does enter the two input terminals
The open-loop gain, AOL, of an op amp is not infinite.
The gain of an op amp is dependent on the frequency of the signal.
The slew rate of the op amp can cause oscillations rather than
amplification, particularly when the amplifier gain is high.
Inverting Amplifier: Voltage Supplies
if
is
i2 = 0
i1 = 0
V+ = 15V
V– = -10V
i
Example #1 (con’t)
if
is
i2 = 0
i
i1 = 0
V+ = 15V
V– = -10V
Example #1 (con’t)
is  i f  i2  i f
i2  i1  0mA
is  VS / R1
if
i f  Vo / R f
is
Av  Vo Vs   R f R1
i1 = 0
i
i2 = 0
R f  10k
R1  1k
Av  10
Example #1 (con’t)
• SinceAv
= -10
• If VS = 0V, then Vo = -10(0V) = 0V
• If VS = 0.5V, then Vo = -10(0.5V) = -5V
• If VS = 1V, then Vo = -10(1V) = -10V
• If VS = 1.1V, then Vo = -10(1.1V) < V–, Vo = -10V
• If VS = -1.2V, then Vo = -10(-1.2V) = +12V
• If VS = -1.51V, then Vo = -10(-1.51V) > V+, Vo = +15V
Example #1 (con’t)
• Voltage transfer characteristic
Slope of the voltage transfer
characteristic in the linear
region is equal to AV.
Rails
• Rails is another turn for the voltage supplies that power
the operational amplifier.
• Rail-to-rail operation means that the output voltage can equal V+
and V– at some points during its operation.
• 15 mV away from the voltage supplies is close enough to be called rail-
to-rail.
LM 741 Operational Amplifier
http://www.ti.com/lit/ds/symlink/lm741.pdf
Non-symmetrical Swing
• LM324 operational amplifier where VCCmax = 32 V
Inverting Amplifier: Finite Rin
if
is
i2
0
i
i1
0
Example #2 (con’t)
if
is
i2
0
i
i1
0
Rin
∞
Example #2
if
iS  i2  i f
i2  i1
if  i
is
VS  V2 V2 V2  VO


R1
Rin
Rf
 R  Rin 
VS  1  1
R f V2
R1
R1Rin


VO  AOL vd  AOL V1  V2    AOLV2
VO  
Rf
i2
i1
i
_
vd
+
AOLvd
 R  Rin  VO
VS  1  1
Rf 
R1
R
R
1 in

 AOL








Rf 
Rf 
AOL
AOL


VO   VS 


V


S
R1 
R1 
 R1  Rin  
 R1  Rin R f  
A  1
Rf 
AOL  1 

 OL 


R1Rin
R
R
in
1




VO  
Rf
Gain
• The gain of the amplifier is a function of R1, Rf, and Rin.
VO
G  ACL 
VS




Rf 
AOL

ACL  


R
R1 
 R1  Rin f  
AOL  1 


R
R
1 
in

Rf
If Rin  , ACL  
R1
Differential Voltage (vd )
∞, then i1 and i2 are not equal to zero.
• That means that the voltages at the input terminals of the
op amp are not equal
• Since Rin
• V1
V2
• vd 0 V
• Because of nonideal operation of the transistors inside the operational
amplifier, vd 0 V even when VO = 0 V.
• Thus, there is an input offset voltage V1 – V2
0V.
• Some transistors have a pin that allow you to counterbalance this
offset voltage.
Gain
• As the open-loop gain,
AOL, of the op amp is
finite, the closed-loop
gain is a function R1, Rf,
Rin, and AOL.
VO
G  ACL 
VS




Rf 
AOL

ACL  


R
R1 
 R  Rin f  
AOL  1  1


R
R
in
1 

Rf
R  Rin
Let G  
and   1
R1
Rin




1


ACL  G 



1


G
1 

  AOL  
Gain-Bandwidth Product
• Over a certain range of frequencies:
f unity
f max
 ACL  1
If ACL  1,
f max 
f unity
f max
 ACL
f unity
ACL
f unity LM 741  1MHz
 10k
 10
1k
f
 unity  100kHz
ACL
ACL 
f max
Note ACL dB  20 log ACL 
Slew Rate
• The speed at which the output voltage changes after a change in the
input voltage.
• When the closed-loop gain is very large and the operating frequency is
high, there is a chance that the output voltage will not follow the input
voltage because it didn’t have time to reach the desired value before the
input voltage changed.
• When this happens, it is possible for the op amp circuit to start oscillating.
Electronic Design Project
• The time-varying signal will be very small.
• To maximize the range of the mbed ADC that will be used to
digitize the analogue signal, the amplifier will have to have a large
gain.
• Because there will be significant noise on the signal that
you want to detect, a bandpass filter will have to be
designed that removes dc and very low frequency ac
signals and removes high frequency noise.
• Given the frequency range that the bandpass filter must operate
and that we would like the pulse meter to be powered by a battery,
the resistors used in the filters will be large.
Op Amp Circuits to Consider
• Buffers (Voltage Followers)
• Isolate one subsystem from another
• Used in impedance matching
• Cascade Amplifiers
• Several amplifiers in series where the overall gain is the
multiplication of the gain of each amplifier in series
• Active Filter
• An op amp with a combination of resistors and capacitors at the
input termal and/or in the feedback loop.
• This is considered to be a filter (low, high, or bandpass) with gain.
• Passive filters (RC networks) are always lossy
• VO never is exactly equal to Vin
Op Amp Circuits to Consider (con’t)
• Because there is only +9V, +5V, +3.3V, and ground
available (the battery, the voltage regulator output, and
the logical high voltage on the mbed), inverting amplifiers
should not be used because at least half of the signal will
be lost.
• Consider non-inverting amplifiers and difference amplifiers.