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Differential amplifier (Difference Amplifier)

Earlier we have seen that the 741 and other op amp ICs can not be used to amplify

signals without adding external components to reduce their voltage gain as they

possess extremely high gains. Under this situation, even the very small noise signals

associated with input can drive the op amp output into saturation. Because of this

drawback, op amps can not be used as differential amplifiers in applications though

they are excellent differential amplifiers. The following circuit shows how an op amp

can be employed to construct a differential amplifier with reduced voltage gain.

Since the circuit is a linear network, the principle of superposition can be applied to

find an expression for its voltage gain.

To apply superposition, first reduce v2 to zero and then find corresponding outpuvoltage 0v due to v1 [See circuit (a)]. Next, reduce v1 to zero and evaluate the

corresponding output voltage 0v[See circuit (b)]. Then the output voltage when both

voltages are applied simultaneously is given by 0 0 0v v v = + .

+

_

R1

R2

R1

R2

v1

v2

v0

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(a) can be recognized as a non inverting configuration with a potential divider at the

input, and (b) is an inverting configuration with grounded non-inverting input thro

two resistors.

Consider circuit (a)

21

1 2

Rv v v

R R+ = =

+

But1

0

1 2

Rv v

R R

=+

20 1

1

Rv v

R =

Now consider circuit (b)

+

_

R1

R2

R1

R2

v1

0v

(a)

v2

+

_

R1 R2

R1

R2

0v

(b)

v+

v

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20 2

1

Rv v

R = (Note that the parallel combination of two resistors attached to the

non inverting input reduces the output offset voltage due to input leakage current).

Therefore when both input appear at their respective inputs,

( )20 1 21

Rv v v

R=

i.e. it is a differential amplifier with a gain of

2

1

R

R .

This simple amplifier circuit has several drawbacks. (1) It is not easy to find two

identical resistors each for R1 andR2. (2) In order to change the gain of the amplifier

the values of two resistors, both resistors of eitherR1 or R2, have to be changed by the

same magnitudes, which is also difficult. (3) The two input terminals represents two

different amplifier configurations (non-inverting and inverting amplifiers) presenting

two different input impedances to input signals. The inverting configuration offers

relatively very low input impedance compared to the non inverting input. This

situation is aggravated if the amplifier is required to have a large differential gain

thenR1has to be small and therefore input impedance of the inverting input becomes

very small. A much superior circuit which provides solutions to above problems is

shown below. It is called the instrumentation amplifier.

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Instrumentation amplifier

Potential difference acrossR1 = 1 2v v

Current throughR1 =

1 2

1

v v

R

and

Voltage1 2

1 2

1

x

v vv v R

R

= +

Similarly, voltage1 2

2 2

1

y

v vv v R

R

=

But ( )403

y xRv v vR

=

From the above equations

+

_

+

_

+

_

R1

R2

R2

R3

R3

R4

R4

v0

1v

2v

2v

1v

xv

yv

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( ) ( )

( )

22 1 1 2

1

2

2 11

2

21

y x

Rv v v v v v

R

Rv v

R

=

= +

( )4 20 2 13 1

21

R Rv v v

R R

= +

Thus the instrumentation amplifier has a differential voltage gain

0 4 2

2 1 3 1

21

d

v R RA

v v R R

= = +

It can be seen from the gain expression that the voltage gain of the amplifier can be

varied by varying the single resistor 1R . Since both of the inputs are connected in the

noninverting configuration, the input impedance seen by 1vand 2v are extremely large.

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Comparators

Operational amplifiers can be used to compare the magnitudes of two voltages or one

voltage with reference to another. Consider the following circuit.

In figure (a), the voltageEiat the non inverting input is compared with the reference

voltage Vref (Vref= 0 in this case) applied to the inverting input. When Ei is above

Vref, Vo equals Vsat, and when it is below Vref, Vo becomes Vsat. The polarity of Vo

tells ifEi is above or below Vref.

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In addition it indicates the time at which Ei crosses zero voltage level. The circuit

shown in figure (a) is therefore called a noninverting zero-crossing detector. The

circuit shown in figure (b) is called inverting zero-crossing detector.

Positive and negative voltage level detectors

In positive voltage level detectors a positive reference voltage applied to one of the

op amp inputs. This means that the op amp is set up as a comparator to detect a

positive voltage. If the signal is applied to the (+) input, the circuit action is

noninverting. If it is applied to (-) input, the circuit action is inverting.

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Negative voltage level detector

This circuit detects when an input signal crosses a negative voltage Vref.

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Some practical application of voltage level detectors

Sound activated switch

An adjustable reference voltage is realized with a potential divider having a 10 k po

and a 5 k connected to +15 V supply. It provides a large adjustable voltage range of 0

to 10 V. The 100:1 voltage divider will provide an adjustment down to a desired

reference voltage level of 0 100 mV. (Pick a 100 k (large) resistor to avoid loading

of the main divider)

Procedure

(1) Open the reset switch to turn off both SCR and the alarm.(2) In a quiet environment, adjust the sensitivity control until Vo just swings to

-Vsat.

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(3) Close the reset switch. The alarm should remain off.When there is no signal at the gate G, the SCRs Kathode K and the anode A

terminals act like an open switch. Noise signal picked up by the microphone wil

produce an ac signal. The first positive swing of Ei above Vref will drive Vo to +

Vsat. The diode now conducts a current pulse of about 1 mA into the gate G of

the SCR and makes it turns on, and the alarm will also be activated. Alarm stays

on until it is reset by opening the Reset switch. Alarm can be replaced with othe

devices such as cameras etc.

Smoke detector

If a continuous signal is needed, the SCR- Alarm circuit can be employed here.

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The lamp and photoresistor must be mounted in a lightproof box that admits smoke.

Effect of noise on comparator circuits

Simple comparator circuits discussed above can operate properly only if the noise

voltages present at either input are of common mode type. However, if the noise is

present only in one input it will not be cancelled and the variation of the noise

amplitude at the reference level may leads to oscillations at the output of the

comparator. Such a noise voltage is shown below. For simplicity the noise signal is

shown as a square wave which is superimposed on a triangular wave

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The wave shape of Vo vs. time shows clearly how the addition of noise causes false

output signals. Vo should indicate only the crossing ofEi, not the crossing ofEi plus

noise voltage. These false crossings can be eliminated by positive feedback.

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Application of positive feedback

Positive feedback is accomplished by taking a fraction of the output voltage and

applying it to the noninverting (+) input as shown below.

In figure (a) above, output voltage Vo divides between R1 and R2, and a fraction of

Vo which is equal to 21 2

o

RV

R R

+ is fed back to the (+) input. This voltage becomes the

reference voltage ,VRef, and it depends on Vo.

Upper threshold voltage

When Vo is equal to + Vsat, the feedback voltage (the reference voltage mentioned

above) is called the upper-threshold voltage,VUT.

VUT is expressed from the voltage divider as

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( )21 2

UT sat

RV V

R R= +

+

For Ei values below VUT, the voltage at the (+) input is above the voltage at the (-

input, and Vo is locked at +Vsat.

IfEi is made slightly more positive than VUT, the polarity ofEd, as shown reverses

and Vo begins to drop in value. Now the fraction of Vo fed back top the positive input

is smaller, so Ed becomes larger. Vo then drops even faster (regenerative action) and

is driven quickly to Vsat. The circuit is then stable at the condition shown in Fig. (b)

above.

Lower threshold voltage

When Vo is at Vsat, the voltage fed back to the (+) input is called lower-threshold

voltage, VLT and is given by

( )

2

1 2LT sat

RV V

R R=

+

VLT is negative with respect to ground. Vo will therefore stay at Vsat as long asEi is

positive, or positive with respect toVLT. Vo will switch back to +Vsat only ifEi goes

more negative than VLT. So if the threshold voltages are larger than the peak noise

voltages, positive feedback will eliminate false output transitions.

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Output-Input characteristic (Hysteresis)

The output (Vo)-Input (Ei ) voltage characteristic of the above circuits (a &b) are

shown below.

For Ei less thanVLT, Vo = +Vsat. The RHS vertical line shows Vo going from +Vsat to

Vsat as Ei becomes greater thanVUT . The LHS vertical line shows Vo going from -

Vsat to +Vsat when Ei becomes less thanVLT . Note that when the input voltage, Ei,is

increased from a negative value to a positive value, the variation of the output

voltage follows the path through the RHS vertical line, but when Ei is decreased

from a positive value to a negative value Vo will follow a different path (path

through the LHS vertical line). i.e. the positive feedback has introduced the property

of hysteresis to the circuit.Whenever a circuit changes from one state to a second state at some input signa

level and reverts from the second to the first state at a different input signal level , the

circuit is said to exhibit hysteresis

( )2

1 2

UT sat

RV V

R R

= ++

Ei

Vo

( )21 2

LT sat

RV V

R R=

+

+Vsat

-Vsat

0

VH,Hysteresis voltage

a

b

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For the positive feedback comparator, the difference in input signals is

H UT LTV V V= , and it is called the hysteresis voltage.

If the hysteresis voltage is designed to be greater than the peak-to-peak noise voltage

then there will be no false output crossings. Thus VH tells us how much peak to peak

noise the circuit can withstand.

Circuit with hysteresis as a memory element

IfEi has a value that lies betweenVLT andVUT, it is impossible to predict the value of

Vo unless we already know the value of Vo. For example, suppose that we substitute

ground for Eiin the figure (a) given above, and turn on the power. The op amp wil

go to either +Vsat or Vsat depending on the inevitable presence of noise. If the op

amp goes to + Vsat, Eimust then go above VUT in order to change the output. If Vo

had gone to Vsat, thenEiwould have to go belowVLT to change Vo.

Thus the comparator with hysteresis exhibits the property of memory. That is, ifE

lies betweenVUT andVLT (within hysteresis voltage), the op amp remembers whethe

the last switching value ofEi was aboveVUT or belowVLT.