Bel 08 Operational Amplifiers

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Operational Amplifier

The term Operational Amplifier ( Op Amp ) was originally

the name of a circuit used for carrying out mathematical

operations, such as summation, integration etc. More

recently it is used for many functions besides mathematical

operations. An essential feature of Op Amp is that it is adirect coupled amplifier with high voltage gain.

The integrated Op Amp has gained wide acceptance as a

versatile predictable and economic system building block.

It offers all the advantages of monolithic ICs: small size,high reliability, reduced cost and temperature tracking.

S. Kal, IIT-Kharagpur


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Op Amp Architecture

A majority of commercially available Op Amps employ four-stage

structure as shown below:

The first stage is a differential amplifier with a double-endedoutput : this provides high input resistance, high gain fordifference signals, and rejection of signals common to bothterminals.



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Op Amp Architecture

The second stage is single output differential amplifier that

provides more gain.

The third stage is an emitter follower, a buffer to provide low

output resistance and isolation of the amplifier from the load.

The last stage is combination of level shifter and a driver

stage. The level shifting corrects for any dc offsets that have

been introduced by the bias network. The driver is a power

amplifier to provide larger output current with a low output

resistance.



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Differential Amplifier ( Diff Amp )

A differential amplifier amplifies the difference of two input

signals, vi1 and vi2 .

For an ideal DIFF AMP.,

v0 = Ad ( vi1 vi2), where

Ad is the voltage gain ofthe DIFF. AMP.

However, for a practical DIFF. AMP. v0 = Ad vd + Ac vc

where vd = ( vi1 vi2 ) = difference signal, and vc = (vi1 + vi2) / 2= average or common mode signal,

Ad = difference mode gain and Ac = common mode gainS. Kal, IIT-Kharagpur


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General Features of an Ideal Op Amp

An Op Amp has two input terminals and one output terminal and

a gain of at least 105.

V0 = - Av ( Vn Vp ) = - Av Vi ; Vi = Vn - VpS. Kal, IIT-Kharagpur


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Pin configuration of 8 pin IC 741 Op Amp

Vn p inverting input, [ Pin no. 2 ]Vp p non-inverting input, [ Pin no. 3 ]Vo p Output [ Pin no. 6 ]+ VCC p + ve supply voltage [ Pin no. 7 ] VCC p - ve supply voltage [ Pin no. 4 ]

Pin nos. 1, 5 [ offset null ], Pin no.-8 [ no connection ]

Characteristics of an ideal Op Amp

i. Input resistance, Ri = wii. Output resistance, R0 = 0

iii. Open loop voltage gain, Av

= wiv. Bandwidth, B.W = wv. CMRR, V = wvi. Perfect balance, i.e. V0 = 0, if Vn = Vpvii.Characteristics are stable against temperature variations



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A practical Op Amp has very high differential gain ( say 80 dB ),very high input impedance ( ~ 2 M;), very low output resistance ( ~

10 ;), very wide bandwidth ( 0 100 kHz, say ) and large CMRR ( ~80 dB ).

Op Amp integrated circuit (IC) chips of different capabilities areavailable. The IC Q741 is most inexpensive, widely used Op Ampchip. Number of components packed in a silicon chip ( ~ 1 mm x 1

mm) transistors ~ 15, resistors ~ 15 and diodes ~ 6.



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SLEW RATE

The slew rate is the maximum rate of change of output voltage (

dv0 /dt ) of an Op Amp, when the input voltage level isinstantaneously changed from a large value to a small value.

The higher the slew rate, the faster the Op Amp. The slew rate ofQ741 Op Amp is 0.5 V/Qsec at unity gain. A high speed Op Ampmay have slew rate as high as 1500 V / Qsec.

Common Mode Rejection Ration ( CMRR )

CMRR is defined as: CMRR = V = Ad /Ac , IfV >> 1, v0 } Ad vd

A good Op Amp should have a large value of CMRR ( say,> 60 dB )S. Kal, IIT-Kharagpur


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Virtual Ground Concept of an Ideal Op Amp

The infinite gain property will mean that for a finite V0, the input

voltage between the positive and negative terminals is zero.

Infinite input resistance ( Ri )will mean that none of the

input terminals draw anycurrent, i.e In=0 and Ip=0.

Zero output resistance willmean that any current can betaken from the output without

disturbing V0.



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The equivalent circuit shows the condition that Vi=0. Thesimultaneous requirement that the Op amp does not draw anycurrent at any of its input ports is indicated by stipulating Ii = 0.

Thus, in spite of a short circuit at its input ports, the Op Amp

does not draw any current at the input.So at the input to the amplifier, there exists a virtual ground orshort circuit. The term virtual is used to imply that, though Vi =0, no current actually flows into this short circuit.

Virtual Ground Concept of an Ideal Op Amp



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Op Amp Applications

Op Amp is the basic building block of analog ( or linear) signalprocessing circuits, such as inverting and non-inverting amplifiers,voltage follower, summing and difference amplifiers, filters,differentiators, integrators, analog computers a circuit for solving3rd order differential equation.

1. Inverting Amplifier

Rfprovides a feedback path from output to inverting input (negative feedback ).



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Inverting Amplifier

Thus the two input terminals of an Op Amp offer a virtual short-circuit or ground. @ I = If= I

Across a practical or real short-circuit voltage is zero, but currentin the real short circuit can not be zero. Since across the inverting

and non-inverting input terminals of a good Op Amp (near ideal),voltage is zero as well as input current is zero, we may assume avirtual short circuit is present between the two input terminals.Hence from the equivalent circuit

Vs = I R1 and v0 = - I Rf @ AV = v0/vs = - Rf/R1

Note that I = If+ IdNow, v0 = - Av vdAs Av p E,@vd p 0Hence the inverting input

of Op Amp is practically

ground point.

Again, Id = vd /Ri = 0

( as Ri p E )



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2. Non-inverting Amplifier

The circuit diagram of a non-inverting amplifier shows that theresistance Rf is connected between the output and negative input

terminal and a resistance R1 is connected between ve input and

ground. Input signal vs is connected at the +ve terminal. RL is

load resistance.

From the equivalent circuit, vs = v1 and v1 = R1 v0 /(R1 + Rf)

@ Av = v0 /vs = (R1 + Rf) / R1 = 1 + Rf /R1S. Kal, IIT-Kharagpur


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Here, Av is +ve and this amplifier is known as non-invertingamplifier.

If Rf= 0, Av = 1, even if Rp E, This amplifier is known as voltagefollower/ unity gain amplifier.

3. Voltage Follower

2.Non-inverting Amplifier



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Av is governed by only two resistors R1 and Rf and isindependent of source resistance and load resistance. This isvalid so long as ideal Op Amp assumptions are valid.

The output impedance is zero and hence the output can beloaded independent of the gain.

Input and Output Impedances

For inverting amplifier, the input impedance as seen by thesource ( vs ) is Zi = R1

For non-inverting amplifierp Zi= E ( ideal Op Amp )

= very high ( for practical Op Amp)

3. Voltage Follower



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OpOp AmpAmp cancan bebe usedused toto addadd twotwo oror moremore signalssignals asas shownshown

belowbelow::

4. Summing Amplifier

Id = v1/R1 + v2/R2 +v3/R3 + v0/Rf= 0

Or, v0

= - Rf[v

1/R

1+ v

2/R

2+v

3/R

3]

Or, v0 = - Rf/R [v1 + v2 +v3 ] { if R1 = R2 = R3 = R }

Thus, v0 = [v1 + v2 +v3 ] { if Rf= R }This is summing operation.



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The difference of the two signals v1 and v2 is amplified. The

inverting gain ( Rf /R1) is less than the non-inverting gain ( 1+

Rf/R1)

For subtracting v1 and v2, it is essential, therefore, to make the

gains of the two inputs equal. The non-inverting input is thus

reduced in amplitude by the R2, R3 network.

Difference Amplifier



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Linear superposition theorem is used to calculate v0. Initially

v01 is calculated assuming only v1 is present and then v02 iscalculated assuming only v2 is present. Overall output v0 is

obtained by adding v01 and v02.

Considering v1 only, v01 = v1 ( - Rf/R1)

Considering v2 only, v02 = [v2R3/(R2 +R3)] ( 1 + Rf/R1)

Thus, v0 = v01+v02 = -v1Rf/R1 +[v2 R3/(R2+R3)] ( 1+ Rf/R1)

v0 = Rf/R1 [ -v1 + v2 ( 1 + R1/Rf) ( 1 + R2/R3)-1 ]

Now, if R1/Rf= R2/R3 then, v0 = Rf/R1 [ v2 v1 ]

Thus we obtain the difference ( v2 - v1 ) at the output multiplied

by a factor of Rf/R1. The source impedances of v1 and v2 are

included in R1 and R2 respectively.S. Kal, IIT-Kharagpur


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Differentiator

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Other Applications

Active filters L

P, HP, BP, BR Comparators

Current to voltage converter

Analog signal processing

Analog computers

Bridge Amplifier

Bel 08 Operational Amplifiers

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