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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.


We can infer that vO = -Vsat if Vi > VR

= + Vsat if Vi < VR

NON INVERTING COMPARATOR


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


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.


741 IC Op-Amp Non-Inverting Comparator Waveform

Similarly we can design an Inverting comparator


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.


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.


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


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.


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

http://www.circuitstoday.com/zero-crossing-detector


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.


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


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.


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.


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.


Voltage Limiters

(1) Two zener diodes connected in the feedback path.


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)].


(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)


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


(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.


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.


UNIT 3 Signal Generators

Link to oscillators : Lecture27

https://nptel.ac.in/courses/108/108/108108111/

Link to phase shift oscillators : lecture 28


Link to wein bridge oscillators : Lecture 29


1 Oscillators

An oscillator may be described as a source of alternating voltage. It is

different than amplifier





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.


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


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


Figure 1Circuit of Phase Shift Oscillator

Figure 2 Output waveform generated shown below


Explanation for the frequency and gain expressions


(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


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,


Vf (S) = (ZP(S) VO(S)) /( ZP (S) + ZS (S) )


Q Design a wein Bridge Oscillator so that fO is 1 KHz.


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


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


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


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.


(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.


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.


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)


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.

http://www.eeeonline.org/


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


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 )


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 .

https://www.eeeguide.com/wp-content/uploads/2016/09/Triangular-Wave-Generator-Using-Op-amp-9.jpg




(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


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.




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

intended. This is only for the emergent situation of Covid period only where students don’t have

access to other reading material.

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.

https://www.elprocus.com/op-amp-as-comparator-circuit-and-working/

https://www.elprocus.com/op-amp-as-comparator-circuit-and-working/


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