BENE 2133 Analog Electronics
CHAPTER 5:
OPERATIONAL AMPFLIFIER (OPAMP) & APPLICATIONS
Part 2:
DC-Offset Parameters, Frequency Parameters,
Common Op-Amp Applications, Instrumentation
Circuits, Active Filters
1
Learning Outcomes
• Learn the basics of an operational amplifier
• Develop an understanding of what common mode operation is
• Describe double-ended input operation
• Learn about constant gain, summing, and buffering amplifiers
• Understand how an active filter works
• Describe different types of controlled sources
DC-Offset Parameters
Even when the input voltage is zero, an op-amp can have an
output offset. The following can cause this offset:
Input offset voltage
Input offset current
Input offset voltage and input offset current
Input bias current
Input Offset Voltage (VIO)
The specification sheet for an op-amp indicates
an input offset voltage (VIO).
The effect of this input offset voltage on the
output can be calculated with
Vo(offset) = VIO
R1 + Rf
R1
Input Offset Current (IIO)
If there is a difference between the dc bias currents generated by
the same applied input, this also causes an output offset voltage:
The input offset current (IIO) is specified in the specifications for
an op-amp.
The effect of IIO on the output offset voltage can be calculated
using:
V o( offset ) = Vo ( offset due to VIO ) + Vo ( offset due to IIO )
Total Offset Due to VIO and IIO
Op-amps may have an output offset voltage due to VIO
and IIO. The total output offset voltage equals the sum of
the effects of both:
Vo (offset ) = Vo (offset due to VIO ) + Vo (offset due to I IO )
Input Bias Current (IIB)
A parameter that is related to input offset current (IIO) is called
input bias current (IIB)
The input bias currents are calculated using:
IIB− = I IB −
IIO
2
IIB+ = IIB +
The total input bias current is the average of the
two:
IIB− + IIB+
IIB =
2
IIO
2
Frequency Parameters
An op-amp is a wide-bandwidth amplifier. The
following factors affect the bandwidth of the opamp:
Gain
Slew rate
Gain and Bandwidth
The op-amp’s high frequency response is limited by
its internal circuitry. The plot shown is for an open loop
gain (AOL or AVD). This means that the op-amp is
operating at the highest possible gain with no
feedback resistor.
In fact, the unity-gain frequency and cutoff frequency
are related by
In the open loop mode, an op-amp has a narrow bandwidth. The
bandwidth widens in closed-loop mode, but the gain is lower.
Example Gain and Bandwidth
Slew Rate (SR)
Slew rate (SR): The maximum rate at which an
op-amp can change output without distortion.
ΔVo
SR =
Δt
(in V/s)
The SR rating is listed in the specification sheets
as the V/s rating.
Example Slew Rate
• For an op-amp having a slew rate of SR = 2 V/s, what is the maximum
closed-loop voltage gain that can be used when the input signal varies by 0.5
V in 10 s?
ΔVo
SR =
(in V/s)
Solution:
Δt
VO = ACLVi
VO
Vi
= ACL
t
t
ACL
VO / t
2 V / s
SR
=
=
=
= 40
Vi / t Vi / t 0.5V / 10s
Maximum Signal Frequency
The slew rate determines the highest
frequency of the op-amp without distortion.
f 
SR
2πVp
where VP is the peak voltage
General Op-Amp Specifications
Other op-amp ratings found on specification
sheets are:
Absolute Ratings
Electrical Characteristics
Performance
Absolute Ratings
These are
common
maximum ratings
for the op-amp.
Electrical Characteristics
Note: These ratings are for specific circuit conditions, and they often
include minimum, maximum and typical values.
CMRR
One rating that is unique to op-amps is CMRR or common-mode
rejection ratio.
Because the op-amp has two inputs that are opposite in phase
(inverting input and the non-inverting input) any signal that is
common to both inputs will be cancelled.
Op-amp CMRR is a measure of the ability to cancel out commonmode signals.
Op-Amp Performance
The specification sheets
will also include graphs
that indicate the
performance of the opamp over a wide range of
conditions.
Common Op-Amp Applications
Constant-gain amplifier
Voltage summing
Voltage buffer
Controlled sources
Instrumentation circuits
Active filters
Constant-gain Amplifier
Inverting amplifier
Noninverting amplifier
Multiple-Stage Gains
The total gain (3-stages) is given by:
or:
 Rf  Rf  Rf 

 −
 −
A = 1 +
 R1  R2  R3 
A = A1A2 A3
Solution:
Design each stage of Op-Amp
LM124 Pin Layout
Therefore, the output voltage is
11
Gain +ve
Non-Inverting Op-Amp
Gain -ve
Non-Inverting Op-Amp
Gain -ve
Non-Inverting Op-Amp
Voltage Summing
The output is the sum
of individual signals
times the gain:
R

R
R
Vo = − f V1 + f V2 + f V3 
R2
R3 
 R1
Voltage Buffer
Any amplifier with no gain or loss is called a unity gain
amplifier.
The advantages of using a unity gain amplifier:
• Very high input impedance
• Very low output impedance
The unity gain amplifier shown
is commonly referred to as a
voltage buffer or a voltage
follower.
Controlled Sources
• Operational amplifiers can be used to form various types of controlled sources.
• An input voltage can be used to control an output voltage or current, or an input current can be
used to control an output voltage or current.
• These types of connections are suitable for use in various instrumentation circuits.
• A form of each type of controlled source is provided next.
Voltage-controlled voltage source
Voltage-controlled current source
Current-controlled voltage source
Current-controlled current source
Voltage-Controlled Voltage Source
Noninverting Amplifier Version
• non-inverting Op-Amp
 R 
VO = 1 + f V1 = kV1
R1 

Inverting Amplifier Version
• Inverting Op-Amp
VO = −
Rf
R1
V1 = kV1
Voltage-Controlled Current Source
The output current
is:
Io =
V1
= kV1
R1
Current-Controlled Voltage Source
This is simply another way of applying the op-amp operation.
Whether the input is a current determined by Vin/R1 or as I1:
Vout
or
− Rf
=
Vin
R1
Vout = −I1RL
Current-Controlled Current Source
This circuit may appear more complicated than the others but it is
really the same thing.
R 
Vout = − f Vin
 Rin 
Vout
V
= − in
Rf
R1||R 2
Vout
V
= − in
Rf
Rin
Io = −
Vin
R1||R 2
 R + R2 

Io = −Vin  1
R

R
2 
 1
V  R + R2 

Io = − in  1
R1  R2 

R 
Io = −I 1 + 1  = kI
 R2 
Instrumentation Circuits
Some examples of instrumentation circuits using op-amps:
Display driver
Instrumentation amplifier
Display Driver
When the noninverting input to the circuit in Fig. 11.27 a
goes above the inverting input, the output at terminal 1 goes
to the positive saturation level (near 5 V in this example)
and the lamp is driven “on” when transistor Q 1 conducts.
As shown in the circuit, the output of the op-amp provides
30 mA of current to the base of transistor Q 1 , which then
drives 600 mA through a suitably selected transistor (with
𝛽 > 20) capable of handling that amount of current.
Figure 11.27 b shows an op-amp circuit that can
supply 20 mA to drive an LED display when
the noninverting input goes positive compared
to the inverting input.
Instrumentation Amplifier
For all resistors at the same
value (except Rp):
 2R 
(V1 − V2 ) = k (V1 − V2 )
Vo = 1 +
RP 

Active Filters
• Adding capacitors to op-amp circuits provides external control of the cutoff
frequencies. The op-amp active filter has controllable cutoff frequencies and
controllable gain.
Low-pass filter
High-pass filter
Bandpass filter
Low-Pass Filter, First-Order
The upper cutoff frequency and
voltage gain are given by:
fOH =
1
2πR1C1
Av = 1 +
Rf
R1
Low-Pass Filter, Second-Order
The roll-off can be made steeper by adding more RC networks.
High-Pass Filter
The cutoff frequency is determined by:
fOL =
1
2πR1C1
Bandpass Filter
There are two cutoff
frequencies: upper and
lower. They can be
calculated using the same
low-pass cutoff and highpass cutoff frequency
formulas
in
the
appropriate sections.