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Dr. Inderbir Kaur Operational Amplifier and Applications Covid 19 Week -5(13-19April2020) Reference study material
UNIT 3
COMPARATORS
A comparator compares a signal voltage on one input of an opamp
with a known reference voltage on the other input. We can say A
comparator has two inputs one is usually a constant reference
voltage VR and other is a time varying signal Vi and one output VO.
We know that in an op-amp with an open loop configuration with a
differential or single input signal has a value greater than 0, the
high gain which goes to infinity drives the output of the op-amp into
saturation. Thus, an op-amp operating in open loop
configuration will have an output that goes to positive
saturation or negative saturation level or switch between
positive and negative saturation levels. This principle is used in
a comparator circuit with two inputs and an output.
BASIC COMPARATOR
When the non inverting voltage is larger than the inverting voltage
the comparator produces a high output voltage (+Vsat). When the
non-inverting output is less than the inverting input the output is
low (-Vsat). Figure below shows the output of a comparator for a
sinusoidal input.
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We can infer that vO = -Vsat if Vi > VR
= + Vsat if Vi < VR
NON INVERTING COMPARATOR
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EXPLANATION
It is called a non-inverting comparator circuit as the
sinusoidal input signal Vin is applied to the non-inverting
terminal. The fixed reference voltage Vref is connected to the
inverting terminal of the op-amp.
When the value of the input voltage Vin is greater than the
reference voltage Vref the output voltage Vo goes to positive
saturation. This is because the voltage at the non-inverting
input is greater than the voltage at the inverting input.
When the value of the input voltage Vin is lesser than the
reference voltage Vref, the output voltage Vo goes to
Dr. Inderbir Kaur Operational Amplifier and Applications Covid 19 Week -5(13-19April2020) Reference study material
negative saturation. This is because the voltage at the non-
inverting input is smaller than the voltage at the inverting
input. Thus, output voltage Vo changes from positive
saturation point to negative saturation point whenever the
difference between Vin and Vref changes.
The comparator can be called a voltage level detector, as for
a fixed value of Vref, the voltage level of Vin can be
detected.
The circuit diagram shows the diodes D1and D2. These two diodes
are used to protect the op-amp from damage due to increase in input
voltage. These diodes are called clamp diodes as they clamp the
differential input voltages to either 0.7V or -0.7V. Most op-amps do not
need clamp diodes as most of them already have built in protection.
Resistance R1 is connected in series with input voltage Vin and R is
connected between the inverting input and reference voltage Vref. R1
limits the current through the clamp diodes and R reduces the offset
problem.
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741 IC Op-Amp Non-Inverting Comparator Waveform
Similarly we can design an Inverting comparator
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It is called a inverting comparator circuit as the sinusoidal input
signal Vin is applied to the inverting terminal.
The fixed reference voltage Vref is given to the non-inverting
terminal (+) of the op-amp. A potentiometer is used as a voltage
divider circuit to obtain the reference voltage in the non-inverting
input terminal.
Both ends of the Potentiometer are connected to the dc supply
voltage +VCC and -VEE. The wiper is connected to the non-
inverting input terminal.
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When the wiper is moved to a value near +VCC, Vref becomes
more positive, and when the wiper is moved towards -VEE, the
value of Vref becomes more negative. The waveforms are shown
below.
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ZERO CROSSING DETECTOR
If in the above circuits , we take VRef to zero, the circuit becomes
that of zero crossing detector, If VR = 0, then slightest input voltage
(in mV) is enough to saturate the OPAMP and the circuit acts as
zero crossing detector as shown in waveforms below
It can be seen in the above waveform that whenever the sine wave
crosses zero, the output of the Op-amp will shift either from negative to
positive or from positive to negative. It shifts negative to positive when
sine wave crosses positive to negative and vice versa. This is how a
Zero Crossing Detector detects when the waveform is crossing zero
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every time. As you can observe that the output waveform is a square
wave, so a Zero Crossing Detector is also called a Square wave
Generator Circuit.
Limitations
If the input to a comparator contains noise, the output may show
error when Vin is near a trip point.
For instance, with a zero crossing, the output is low when vin is
positive and high when vin is negative. If the input contains a noise
voltage with a peak of 1mV or more, then the comparator will
detect the zero crossing produced by the noise. Figure below,
shows the output of zero crossing detector if the input
contains noise.
This can be avoided by using a Schmitt trigger, circuit
which is basically a comparator with positive feedback.
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Dr. Inderbir Kaur Operational Amplifier and Applications Covid 19 Week -5(13-19April2020) Reference study material
SCHMITT TRIGGER
A Schmitt trigger circuit is also called a regenerative
comparator circuit.
The circuit is designed with a positive feedback and hence
will have a regenerative action which will make the output
switch levels. Also, the use of positive voltage feedback
instead of a negative feedback, aids the feedback voltage to
the input voltage, instead of opposing it.
The use of a regenerative circuit is to remove the difficulties
in a zero-crossing detector circuit due to low frequency
signals and input noise voltages.
The purpose of the Schmitt trigger is to convert any regular
or irregular shaped input waveform into a square wave
output voltage or pulse. Thus, it can also be called a
squaring circuit.
Circuit: inverting comparator as Schmitt trigger circuit using OPAMP
VREF
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Explanation
We can see in the circuit above that because of the voltage divider
circuit, there is a positive feedback voltage. When OPAMP is positively
saturated, a positive voltage is feedback to the non-inverting input, this
positive voltage holds the output in high stage. (vin< vf). When the output
voltage is negatively saturated, a negative voltage feedback to the
inverting input, holding the output in low state.
When the output is +Vsat then reference voltage Vref is given by
Vref = [R2 /( R1 + R2 ) ] (+Vsat) = +β Vsat
If Vin is less than Vref output will remain +Vsat.
When input vin exceeds Vref = +Vsat the output switches from +Vsat to
–Vsat.
Now the reference voltage is given by
Because voltage being feedback is –Vsat
The output will remain –Vsat as long as Vin > Vref
If Vin < Vref i.e. Vin becomes more negative than –Vsat then again output
switches to +Vsat and so on. Input and output waveforms of Schmitt
Trigger are given below.
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Positive feedback has an unusual effect on the circuit. It forces the
reference voltage to have the same polarity as the output voltage, The
reference. voltage is positive when the output voltage is high (+Vsat) and
negative when the output is low (–Vsat).
In a Schmitt trigger, the voltages at which the output switches from
+Vsat to –Vsat or vice versa are called upper threshold voltage (VUT) or
Upper threshold point, UTP and lower threshold voltage (VLT) or lower
threshold point, LTP. The difference between the two threshold voltages
is called hysteresis, a dead band condition
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VO versus Vin plot of the Hysterisis voltage
Thus if the threshold voltages VUT and VLT are made larger than
input noise voltages, the positive feedback will eliminate false
output transitions.
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CHARACTERISTICS OF COMPARATOR
1. Operation Speed – According to change of conditions in the input, a
comparator circuit switches at a good speed beween the saturation
levels and the response is instantaneous.
2. Accuracy – Accuracy of the comparator circuit depends on the
following characteristics:-
(a) High Voltage Gain – The comparator circuit is said to have a high
voltage gain characteristic that results in the requirement of smaller
hysteresis voltage. As a result the comparator output voltage switches
between the upper and lower saturation levels.
(b) High Common Mode Rejection Ratio (CMRR) – helps to reject The
common mode input voltages such a noise at the input terminals
(c) Very Small Input Offset Current and Input Offset Voltage – A
negligible amount of Input Offset Current and Input Offset Voltage
causes a lesser amount of offset problems..
3 Compatibility of Output : since the comparator is a form of analog to
digital converter, its output must swing between two logic levels suitable
for a certain logic family such as TTL.
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Limitations of Opamp as Comparators
An op-amp is usually used as a comparator in cases where its
speed and accuracy are not critical.
As explained above, the switching speed of the op-amp
comparator can be improved and noise can also be eliminated.
The offset problems can also be reduced by adding a voltage
compensating network and a offset reducing resistor.
Since the op-amp’s output voltage swing is generally large
because it is originally designed to act as an amplifier. Or we can
say its output will not be compatible with logic families like TTL. A
TTL requires input voltages which range between (0-5) volts. Thus,
to keep the op-amp’s output voltage swing between these ranges,
other components like zener diodes and diodes are added onto the
circuit. Such circuits with specified output swing are called voltage
limiters.
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Voltage Limiters
(1) Two zener diodes connected in the feedback path.
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Explanation
As shown in the waveform, as the voltage Vin increases from 0 to
positive voltage, the value of V0 increases in the opposite direction
(negative). This goes on until the diode D1 becomes forward
biased and D2 goes into avalanche breakdown.
At this condition, V0 = VZ + VD1
VZ – Zener Voltage
VD1 – Voltage drop across D1 = 0.7V
If Vo increases from 0 to negative voltage, Vo increases positively
until diode D2 is forward biased and D1 goes into avalanche
condition.
At this condition, V0 = VZ + VD2
VZ – Zener Voltage
VD1 – Voltage drop across D2 = 0.7V
Thus the limit of output voltage swing is between +(VZ + 0.7)
and –(VZ + 0.7).
In the circuit above, ROM is used to reduce the offset problems.
Vin will appear across resistor R [v1=v2=0V (virtual ground)].
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Dr. Inderbir Kaur Operational Amplifier and Applications Covid 19 Week -5(13-19April2020) Reference study material
(2) Combination of zener diode and rectifier diode in the
feedback path
Explanation
When Vin increases from 0 to positive voltage, D2 is reverse biased
and thus V0 = -Vsat. (Opamp will operate on open loop
configuration)
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When Vin increase from 0 to a negative voltage, D2 is forward
biased and D1 goes into avalanche condition. VO starts increasing
in the positive direction. Thus V0 = VZ + VD2
Dr. Inderbir Kaur Operational Amplifier and Applications Covid 19 Week -5(13-19April2020) Reference study material
(3) single zener diode in the feedback path of an op-amp
The output will be limited between +VZ and –VD.
VZ – Zener Voltage VD – Voltage drop across the forward biased zener.
Dr. Inderbir Kaur Operational Amplifier and Applications Covid 19 Week -5(13-19April2020) Reference study material
Q sketch the input and output waveform if positions of diodes are
interchanged in the circuit below:
Q Sketch the input output waveform if position direction of zener diode is
reversed in the circuit below.
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Dr. Inderbir Kaur Operational Amplifier and Applications Covid 19 Week -5(13-19April2020) Reference study material
UNIT 3 Signal Generators
Link to oscillators : Lecture27
https://nptel.ac.in/courses/108/108/108108111/
Link to phase shift oscillators : lecture 28
https://nptel.ac.in/courses/108/108/108108111/
Link to wein bridge oscillators : Lecture 29
https://nptel.ac.in/courses/108/108/108108111/
1 Oscillators
An oscillator may be described as a source of alternating voltage. It is
different than amplifier
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Oscillators may be classified in terms of their output waveform,
frequency range, components, or circuit configuration.
If the output waveform is sinusoidal, it is called harmonic oscillator
otherwise it is called relaxation oscillator, which include square,
triangular and saw tooth waveforms.
Oscillators employ both active and passive components. The active
components provide energy conversion mechanism. Typical active
devices are transistor, FET, Opamp, etc.
Passive components normally determine the frequency of oscillation.
They also influence stability, which is a measure of the change in output
frequency (drift) with time, temperature or other factors. Passive devices
may include resistors, inductors, capacitors, transformers, and resonant
crystals.
In this part we will be focussing on use of opamps as oscillators
capable of generating a variety of output waveforms
Oscillator Principles
An oscillator is a type of feedback amplifier in which part of the output is
fed back to the input via a feedback circuit.
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The amplifier is opamp inverting amplifier. The output is 180° out of
phase with input signal
vO= -A vin.
Now a feedback circuit is added. The output voltage is fed to the feed
back circuit. The output of the feedback circuit is again 180° phase
shifted. Thus the output from the feedback network is in phase with input
signal vin and it can also be made equal to input signal.
If this is so, Vf can be connected directly and externally applied signal
can be removed and the circuit will continue to generate an output
signal. The amplifier still has an input but the input is derived from the
output amplifier. The output essentially feeds on itself and is
continuously regenerated. This is positive feedback. The over all
amplification from vin to vf is 1 and the total phase shift is zero. Thus the
loop gain A β is equal to unity.
When this criterion is satisfied then the closed loop gain is infinite. i.e. an
output is produced without any external input.
vO = A verror
= A (v in + v f )
= A (vin + β vO)
or (1-A β )vO = A vin
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The criterion A β = 1 is satisfied only at one frequency. This is known
as Barkhausen Criterion.
1.1 Phase Shift Oscillator
Circuit below shows a phase shift oscillator which consist of an
opamp as the amplifying stage and three RC cascaded networks
as the feedback circuit
Opamp is used in the inverting mode.
An additional 180 degrees phase shift required for oscillation
is provided by the cascaded RC networks.
Thus the total phase shift around the loop is 360 degrees (
or 0 degrees)
At some frequency when the phase shift of the cascaded
RC network is 180 degrees and the gain of the amplifier is
sufficiently large, the circuit will oscillate at that frequency
This frequency is called the frequency of oscillation, given
by
FO = 1/ (2Π (√6) RC)
= 0.065/RC
At this frequency the gain of the amplifier must be atleast
29, i.e.,
│Rf / R1 │= 29
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Figure 1Circuit of Phase Shift Oscillator
Figure 2 Output waveform generated shown below
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Explanation for the frequency and gain expressions
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(2) Wein Bridge oscillator
The Wien Bridge oscillator is a standard oscillator circuit for low to
moderate frequencies, in the range 5Hz to about 1MHz. It is mainly
used in audio frequency generators.
The Wien Bridge Oscillator is so called because the circuit is based
on a frequency-selective form of the Wheatstone bridge circuit.
The Wien Bridge Oscillator uses a feedback circuit consisting of a
series RC circuit connected with a parallel RC of the same
component values producing a phase delay or phase advance circuit
depending upon the frequency. At the resonant frequency fo the
phase shift is 0o.
The frequency of oscillation fo is exactly the resonant frequency of the
Balanced Wheatstone Bridge and is given by
fo = 1/ 2ΠRC
= 0.159 / RC
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Dr. Inderbir Kaur Operational Amplifier and Applications Covid 19 Week -5(13-19April2020) Reference study material
Assuming that the resistors are equal in value, and capacitors are also
equal in value. At this frequency, the gain required for sustained
oscillations is given by
Av = 1/B =3
Or 1 + Rf / R1 = 3
Or Rf = 2 R1
Explanation
First transform the feedback circuit into s domain as given below. Using
the voltage divider rule,
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Vf (S) = (ZP(S) VO(S)) /( ZP (S) + ZS (S) )
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Q Design a wein Bridge Oscillator so that fO is 1 KHz.
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Unit 3 Signal Generators Part 2
1) Square wave Generator
Square wave outputs generated when the opamp is forced to operate in
the saturation region.
Output of opamp swings repetitively between + VSAT and - VSAT (≈ ± VCC )
resulting in square wave output.
This square wave generator also calledfree running or Astable
Multivibrator
Circuit of Square wave generator circuit given below
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Explanation
Assume voltage across C is zero volts at the instant when the dc supply
voltages + VCC and - VEE are appllied.
Voltage at the inverting input terminal is zero initially.
Voltage at the non inverting input terminal is very small finite value that
is a function of output offset voltage VOOT and the value of R1 and R2
resistors.
Hence Vid = voltage at V1
This will drive opamp into satuation
Condition 1 Suppose VOOT is positive and therefore V1 is also
positive driving opamp to + VSAT.
Capacitor C starts charging towards + VSAT through resistor R.
As soon as voltage V2 across capacitor is slightly more positive than V1,
opamp switches to - VSAT..
Now the voltage at V1 = [ R1/ R1 + R2 ] (- VSAT)
So Vid = V1 – V2 = negative, which holds the output of opamp at - VSAT.
CONDITION 2 The ouput remains in negative saturation until the
capacitor C discharges and then recharges to a negative voltage slightly
higher than –V1 . in that case as soon as capacitor voltage V2 becomes
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more negative than – V1 , Vid becomes positive and opamp drives to
+VSAT .
With output Voltage at +VSAT , voltage V1 at the non inverting input is
V1 = [ R1/ R1 + R2 ] (+VSAT)
The generated output waveform is
The time period T of the output waveform is
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T = 2RC ln [ ( 2R1 + R2 ) / R2 )
Or Frequency of output waveform fO = 1 / {2RC ln [ ( 2R1 + R2 ) / R2 )}
Above equation indicates that the frequency of output waveform fO is not
only a function of RC time constant but also of the relationship between
R1 and R2 . For example if R2 = 1.16 R1
Then fO = 1/ 2RC
The above Equation shows that smaller the RC time constant , the
higher the output frequency fO.
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(2) Triangular wave Generator
A Triangular Wave Generator Using Op amp can be formed by
simply connecting an integrator to the square wave generator.
Triangular wave is generated by alternatively charging and
discharging a capacitor with a constant current. This is achieved
by connecting integrator circuit at the output of square wave
generator as shown in the figure above.
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Assume that V’ is high at +Vsat. This forces a constant current
(+Vsat/R3) through C (left to right) to drive Vo negative linearly.
When V’ is low at —Vsat, it forces a constant current (— Vsat /R3)
through C (right to left) to drive Vo positive, linearly. The frequency
of the triangular wave is same as that of square wave.
This is shown in figure below.
Although the amplitude of the square wave is constant (± Vsat), the
amplitude of the triangular wave decreases with an increase in its
frequency, and vice versa.
This is because the reactance of capacitor decreases at high
frequencies and increases at low frequencies.
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In practical circuits, resistance R4 is connected across C to avoid the
saturation problem at low frequencies as in the case of practical
integrator as shown in the Figure below
To obtain stable triangular wave at the output, it is necessary to have
5R3 C2 > T/2, where T is the period of the square wave input.
To obtain a stable integrator R4 = 10 R3 ( we have seen this in integrator
design).
Triangular generator with fewer components (Figure 1)
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It consists of a comparator (A) and an integrator (B). The output of
comparator A is a square wave of amplitude ± Vsat and is applied to the
inverting (-) input terminal of the integrator B. The output of integrator is
a triangular wave and it is feedback as input to the comparator A through
a voltage divider R2 R3.
Explanation of Triangular wave generator with fewer components
To understand circuit operation, assume that the output of comparator A
is at + Vsat . This forces a constant current (+ Vsat / R1) through C to give
a negative going ramp at the output of the integrator, as shown in the
Fig. above. Therefore, one end of voltage divider is at a voltage
+Vsat and the other at the negative going ramp. When the negative going
ramp reaches a certain value -Vramp, the effective voltage at point p
becomes slightly below 0V.
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Waveform of Triangular wave generator (Fig. 2)
As a result, the output of comparator A switches from positive saturation
to negative saturation (-Vsat).
This forces a reverse constant current (right to left) through C to give a
positive going ramp at the output of the integrator, as shown in the Fig.
above.
When positive going ramp reaches + Vramp, the effective voltage at point
p becomes slightly above 0V. As a result, the output of comparator A
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switches from negative saturation to positive saturation (+Vsat). The
sequence then repeats to give triangular wave at the output of integrator
B.
Amplitude and Frequency Calculations:
The frequency and amplitude of the Triangular Wave Generator Using
Op amp wave can be determined as follows :
When comparator output is at +Vsat, the output of the integrator
decreases until it reaches – Vramp .
At this time the output of comparator switches from +Vsat to -Vsat .
Just before switching occurs, the voltage at point P is 0 V. This
means – Vramp is developed across R2 and +Vsat across R3 .
Or we can say that
– Vramp / R2 = +Vsat / R3
– Vramp = (+Vsat / R3 ) R2 (1)
Similarly
+Vramp = (-Vsat / R3 ) R2 (2)
Thus from (1) and (2)
The peak to peak amplitude of triangular wave is
VO (pp) = +Vramp – (-Vramp )
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VO (pp) = 2 ( R2 / R3 ) (Vsat ) (3)
Vsat = │ +Vsat │ = │-Vsat │
Equation 3 indicates that the amplitude of triangular wave decreases
with increase in R3.
The time taken by the output to swing from – Vramp to + Vramp (or
from + Vramp to – Vramp) is equal to half the time period T/2.( Refer
Fig. 2.). This time can be calculated from the integrator output
equation as follows :
Substituting value of Vo(pp) we get,
Therefore, the frequency of oscillation can be given as,
Above equation shows that the frequency of oscillation fo increases with
an increase in R3 .
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(3) Sawtooth Wave Generator
Difference between Triangular wave and Sawtooth is that rise
time of triangular is always equal to its fall time.
Sawtooth waveform has different rise and fall times
How this is acheived
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A variable DC voltage is injected into the non inverting terminal of the
integrator. This can be achieved by using a potentiometer.
A potentiometer is used when the wiper moves toward negative
voltage(-V); then the rise time becomes more than the fall time. When
the wiper moves towards positive voltage(+V), then the rise time
becomes less than the fall time.
When the comparator output goes negative saturation, a negative
voltage is added to the inverting terminal, thereby the wiper moves to a
negative supply. This causes a decrease in the potential difference
across R1 and hence current through the capacitor and resistor
decreases.
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Then the slope decreases and rise time also decrease. When the
comparator output is under positive saturation, the potential difference
across the R1 increases and current through the capacitor resistor also
increases. This is due to the presence of a negative voltage at the
inverting terminal. Then the slope increases and fall time decreases.
And the output is obtained as a sawtooth waveform.
DISCLAIMER: This study material is only for the reference of students. No copyright infringement is
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References : 1 Opamps and linear integrated circuits technology : Ramakatnt A. Gayakwad 2 linear integrated circuits by D. Roy Chaudhary and Shail Jain 3 https://nptel.ac.in/courses/117/107/117107094/ 4 www. Circuitstoday.com
5 https://www.electronics-tutorials.