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Analogue Electronic 2
EMT 212
Chapter 2
Op-Amp Applications and
Frequency Response
By
En. Tulus Ikhsan Nasution
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Introduction
Op-amps are used in many different applications.
We will discuss the operation of the fundamental
op-amp applications. Keep in mind that the basic
operation and characteristics of the op-amps do not
change — the only thing that changes is how we
use them.
1. Constant-Gain Multiplier
One of the most common op-amp circuit is an inverting
constant-gain multiplier (Fig. 2-1 (a)) or a non-inverting
constant-gain multiplier (Figure 2-1 (b)), which provides
a precise gain or amplification.
(a)
(b)
V
Fig. 2-1: Fixed-gain amplifier.
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Multiple-Stage Gains
When a number of stages are connected in series, the
overall gain is the product of the individual stage gains.
Fig. 2-2: Constant-gain connection with multiple stages.
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The first stage provides non-inverting gain and
the next two stages provides an inverting gain.
The overall circuit gain is then non-inverting and
is calculated by
A  A1A 2 A3
(2-1)
where A1 = 1 + Rf/R1, A2 = -Rf/R2 and A3 = -Rf/R3.
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2. Voltage Subtraction
Two signals can be subtracted from one another in a
number of ways. Figure 2-3 shows two op-amp stages
used to provide subtraction of input signals.
Fig. 2-3: Circuit for subtracting two signals.
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The resulting output is given by
 Rf

R
Vo   V2 
V1 
R

R
R
1 3
 2

2
f
(2-2)
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Another connection to provide subtraction of two signals
is shown in Figure 2-4. This connection uses only one
op-amp stage to provide subtracting two input signals.
Using superposition, we can
show the output to be
R3 R2  R4
R4
Vo 
V1  V2
R1  R3 R2
R2
(2-3)
Fig. 2-4: Subtraction circuit.
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3. Voltage Follower/Buffer

This “buffer” is used to isolate an input signal from a
load by using a stage having unity voltage gain (Av
= 1).

The input impedance to the buffer is very high and its output
impedance is low.
The output voltage is
determined by
Vo  V1
Fig. 2-5: Unity-gain (buffer) amplifier.
(2-4)
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Figure 2-6 shows how an input signal can be provided
to two separate outputs.
Fig. 2-6 : Use of buffer amplifier
to provide output signals.
The advantage of this
connection is:
The load connected across
one output has no (or
little) effect on the other
output because the
outputs are buffered or
isolated from each other.
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4. Comparators


The comparator is an op-amp circuit that compares two
input voltages and produces an output indicating the
relationship between them. The inputs can be two
signals (such as two sine waves) or a signal and a fixed
dc reference voltage.
Comparators are most commonly used in digital applications.
Digital circuits respond to rectangular or square waves, rather
than sine waves. These waveforms are made up of alternating
(high and low) dc levels and the transitions between them.
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Fig. 2-7: Digital waveform characteristics.
3.1. Zero Level Detection
An op-amp without negative feedback (or in the openloop configuration) is essentially a comparator.
Fig. 2-8: The op-amp as a zero-level detector.
Figure 2-8 (a) shows that a zero-level detector can be built by
applying the input signal voltage to the non-inverting (+) input
and the inverting (-) input is grounded to produce a zero level.
VV+
Figure 2-8 (b) shows the result of a sinusoidal input voltage
applied to the non-inverting (+) input of the zero-level detector.
When the sine wave is above the zero line (V+>V-) the output
reaches its maximum positive level. When the sine wave is
below the zero line (V->V+), the amplifier is driven to its
opposite state and the output reaches its maximum negative
level. As can be seen here, the zero-level detector can
produce a square wave from a sine wave.
3.2. Nonzero-Level Detection
The zero-level detector in Figure 2-8 (a) can be modified
in three different arrangements to set the reference
voltage, VREF by connecting a reference voltage to the
inverting (-) input.
Fig. 2-9: Nonzero-level detectors.
 Fig. 2-9 (a) shows an op-amp circuit uses a fixed
voltage source to set the reference voltage.
 The circuit in Fig. 2-9 (b) uses a voltage-divider
circuit to set the reference voltage.
 The circuit in Fig. 2-9 (c) uses a zener diode to set
the reference voltage.
Among them, the voltage-divider circuit is most often
used to set the reference voltage for a given level
detector and the reference voltage is expressed as
VREF
R2

(V )
R1  R2
(2-5)
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3.3. Effects of Input Noise on Comparator
Operation
In many practical situations, noise (unwanted voltage
fluctuations) appears on the input line. This noise voltage
becomes superimposed on the input voltage, as shown in
Fig. 2-10 for the case of a sine wave, and can cause a
comparator to erratically switch output states.
Figure 2-10:
Sine wave with
superimposed
noise.
Low-frequency
sinusoidal voltage
Fig. 2-11: Effect of noise on comparator circuit.
In order to understand the potential effects of noise
voltage, consider a low-frequency sinusoidal voltage
applied to the non-inverting (+) input of an op-amp
comparator used as a zero-level detector as shown in
Fig. 2-11 (a).
Fig. 2-11: Effects of noise on comparator circuit.
Reducing Noise Effects with Hysteresis
In order to make the comparator is less sensitive to
noise, a technique incorporating positive feedback,
called hysteresis, can be used.
Fig. 2-12: Comparator with positive feedback for hysteresis.
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Basically, hysteresis means that there is a
higher reference level when the input voltage
goes from a lower to higher value than when it
goes from a higher to a lower value.
The two reference levels are referred to as the
upper trigger point (UTP) and the lower trigger
point (LTP).
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The basic operation of the comparator with hysteresis
is illustrated in Fig. 2-13 .
(a)
(b)
Fig. 2-13: Operation of a comparator with hysteresis.
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(a)
When the input voltage Vin exceeds VUTP and the output is at
the maximum positive voltage, the output voltage drops to its
negative maximum, -Vout(max). The voltage fed back to the noninverting input is VLTP and is expressed as .
VLTP
R2

(Vout(max) )
R1  R2
(2-6)
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(b)
When the input goes below LTP and the output is at the
maximum negative voltage, the output switches back to the
maximum positive voltage. Now the voltage fed back to the
non-inverting input is VUTP and is expressed as
VUTP
R2

(Vout(max) )
R1  R2
(2-7)
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Fig. 2-14: Input and output signals for an
operation of a comparator with hysteresis.
This figure shows that the device triggers only once when
UTP or LTP is reached; thus, there is immunity to noise that
is riding on the input signal.
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3.4. Comparator Applications
Fig. 2-15: An over-temperature sensing circuit.
Thermistor is a temperature-sensing resistor with a negative
temperature coefficient (its resistance decreases as
temperature increases).
Fig. 2-16: An analog-todigital converter (ADC)
using op-amp as
comparators.
4. 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.
The types of controlled source are:
 Voltage-controlled voltage source
 Voltage-controlled current source
 Current-controlled voltage source
 Current-controlled current source
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4.1. Voltage-Controlled Voltage Source
A voltage source whose output Vo is controlled by an
input voltage V1 is shown in Figure 2-17.
Fig. 2-17: Ideal voltage-controlled voltage.
The output voltage is dependent on the input voltage
(times a scale factor k).
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The type of circuit in Figure 2-17 can be built using
an op-amp in two versions: one using the inverting
input and the other the non-inverting input as shown
in Figure 2-18.
Fig. 2-18: Practical voltage-controlled voltage source circuits
using (a) inverting input and (b) non-inverting input.
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4.2. Voltage-Controlled Current Source
Figure 2-19 shows an ideal circuit providing an output
current Io controlled by an input voltage.
Fig. 2-19: Ideal voltage-controlled current source.
The output current is dependent on the input voltage.
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A practical circuit can be built with the output current
through load resistor RL controlled by the input
voltage V1.
The current through RL
can be expressed as
V1
Io 
 kV1
R1
(2-8)
Fig. 2-20: Practical voltage-controlled
current source.
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4.3. Current-Controlled Voltage Source
A voltage source controlled by an input current is
shown in Fig. 2-21.
Fig. 2-21: Ideal current-controlled voltage source.
The output voltage is dependent on the input current.
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A practical circuit can be built using an op-amp as
shown in Figure 2-22.
Fig. 2-22: Practical current-controlled voltage source.
The output voltage is written as
Vo   I1RL  kI1
(2-9)
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4.4. Current-Controlled Current Source
Figure 2-23 shows an ideal circuit providing an output
current dependent on an input current.
Fig. 2-23: Ideal current-controlled current source.
The output current is dependent on the input current.
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A practical circuit can be built using an circuit
connection as follows,
The input current I1 can
result in the output
current Io so that
I o  I1  I 2
I1 R1
I o  I1 
R2
Fig. 2-24: Practical current-controlled
current source.

R1 
 I1
I o  1 
 R2 
I o  kI1
(2-10)
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5. Scaling Adder
V1
V2
V3
Vo
Vn
Fig. 2-25: Summing amplifier with n inputs.
A different weight can be assigned to each input of a
summing amplifier by simply adjusting the values of the input
resistors .
As you have known that the output voltage is,
Rf
Rf
Rf 
 Rf
Vo   V1  V2  V3  ...  Vn 
R2
R3
Rn 
 R1
(2-11)
The weight of a input is set by the ratio of Rf to the resistance,
Rx, for that input (Rx = R1, R2, R3,…Rn.
For example: - if weight of Vin = 1, then Rx = Rf
- if weight of Vin = 0.5, required Rx = 2Rf
The greater the Rx, the smaller the weight and vice versa.
6. Summing Amplifiers Applications
Fig. 2-26: A scaling adder as four-digit digital-to-analog converter.
A four-digit digital-to-analog converter (DAC) is called a
binary-weighted resistor DAC.
Switch symbols represent transistor switches for applying
each of the four binary digits to the input.
I1
Virtual
ground
If
I2
IT
I3
I4
I f = IT
= I1+I2+I3+I4
Ii=0
Short
circuit
Fig. 2-26: A scaling adder as four-digit digital-to-analog converter.
Since the inverting (-) input is at virtual ground, the output
voltage is proportional to the current through the feedback
resistor Rf (sum of input current).
Fig. 2-26: A scaling adder as four-digit digital-to-analog converter.
The lowest-value resistor R corresponds to the highest
weighted binary input (23).
All of the other resistors are multiples of R and corresponds
to the binary weights 22, 21, and 20.
Fig. 2-27: An R/2R ladder DAC.
R/2R ladder is more commonly used for D/A conversion
than the scaling adder.
It overcomes one of the disadvantages of the binary-weightinput DAC because it requires only two resistor values.
7. Op-Amp Frequency Response &
Compensation

The “frequency response” of any circuit is the magnitude of
the gain in decibels (dB) as a function of the frequency of the
input signal.

The decibel is a common unit of measurement for the relative
magnitude of two power levels. The expression for such a
ratio of power is
Power level in dB = 10log10(P1/P2)

(A decibel is one-tenth of a "Bel", a seldom-used unit named
for Alexander Graham Bell, inventor of the telephone.)
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7.1. Frequency Versus Gain
Fig. 2-28: Op-amp frequency-response curve.
The relationship between the frequency and gain is as follows:
Decreasing the voltage gain of an op-amp will increases its
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maximum operating frequency.
The unity-gain frequency (funity) is the maximum
operating frequency of an op-amp measured at ACL =
0 dB (unity).
Since bandwidth (BW = fC2 – fC1; fC = cutoff frequency)
increases as voltage gain decreases, we can make the
following statements:
 The higher the gain of an op-amp, the narrower its
bandwidth.
 The lower the gain of an op-amp, the wider its bandwidth.
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7.2. Gain-Bandwidth Product
The gain-bandwidth product of an amplifier is a
constant that always equals the unity-gain frequency
of its op-amp.
The product of ACL and bandwidth is always approximately
equal to this constant.
The relationship among ACL, fC, and funity for an amplifier is:
ACL f C  f unity
(2-12)
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