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Operational Amplifiers

A Linear IC circuit

Operational Amplifier (op-amp)

• An op-amp is a high-gain amplifier that has highinput impedance and low output impedance.

• An ideal op-amp has infinite gain and inputimpedance and zero output impedance.

• An integrated circuit (IC) contains a number ofcomponents on a single piece of semiconductor.

• Most op-amps are IC chips.

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The 741 Operational Amplifier

Op-Amp Input/Output

• We consider the op-amp as a singlecomponent with inputand outputcharacteristics.

• Two signal inputs: Inverting Non-inverting

• Two dc power supplyleads (+ and −)

• One output lead

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Op-Amp Packages

The Operation of Op-amps

• The input stage of an op-amp is adifferential amplifier.

• The op-amp amplifies the differencebetween the two input terminal voltages.

−

+

V1

V2

Vdiff =V2 −V1

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Op-Amp Output

• The output of the amplifier is determined by

The gain of the amplifier. The polarity relationship between V1 and V2. The values of the supply voltages, +V and -V. The load resistance

Op-Amp Gain

• The maximum possible gain of an op-ampis called the open-loop gain AOL.

• Generally AOL is greater than 10,000.• Typical values are on the order of 200,000.• An ideal op-amp would have infinite gain.

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Input/Output Polarity

• The output polarity follows the sign of Vdiff.• If V2 – V1 > 0 the output polarity will be positive.• If V2 – V1 < 0 the output polarity will be negative.

−

+

V1

V2

Supply Voltages

• The supply voltages determine the limits of outputvoltage swing. No matter what the gain and inputvoltages the output value can not exceed +V or–V.

• In practice the maximum output voltage is slightlyless than the supply voltages. For resistive loads > 10kΩ the output voltages are

about 1V “less” than the supply voltages. For resistive loads > 2kΩ the output voltages are about

2V “less” than the supply voltages.

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Open Loop Op-amp Use

• As the open loop gain of most op-amps isextremely large the output of an open-loop circuitis either the maximum positive or negativevoltage.

−

+

V1

V2

+15 V

-15 V

12

12

V14

V14

VV

VVVout

<

>

!"#

$

+=

Feedback Circuits

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Feedback

• Most op-amp circuits are designed to usefeedback.

• Feedback is defined as taking a portion of theoutput of a circuit and coupling or feeding it backinto the input.

• If the output fed back is in phase with the inputthen the circuit has positive feedback.

• If the output fed back is out of phase with theinput then the circuit has negative feedback.

Negative Feedback

• Most amplifiers use negative feedback.• Disadvantages:

decreased gain.• Advantages:

increased circuit stability, increased input impedance, decreased output impedance, increased frequency bandwidth at constant

gain.

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Negative Voltage Feedback• A fraction B < 1 of the output voltage is subtracted from the

input voltage.

-B

AOLΣvin vout

v′

outinBvvv !="

Negative Voltage Feedback• The closed loop gain, Av, is defined as

• The closed loop gain can be calculated from two equations

-B

AOLΣvin vout

v′

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Negative Voltage Feedback• Solving for Av gives

• Usually the open-loop gain is so large that we can approximate:

-B

AOLΣvin vout

v′

Negative Feedback

• The gain of the amplifier circuitdepends only on B, the fractionof output voltage fed back.

• B can be made very constant sothat the amplifier has great gainstabilization.

• Example: B could be determinedby two resistors in a voltagedivider relationship.

R1

R2

vout

Bvout

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Negative Feedback Impedance

• The input and output impedance is alsochanged by the feedback.

Op-Amp Circuits With NegativeFeedback

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Non-Inverting Amplifier

• Using Kirchoff’s rule, Ohm’s Law, and our knowledge ofop-amps we can derive a closed loop-voltage gain for thenon-inverting amplifier circuit shown below.

vinvout

R2

R1

i1

i´

i2

v1

v2

Non-Inverting Amplifier

• As the input resistance of the op-amp is very large we canneglect i´.

• The output voltage is given by the voltage difference andthe open-loop gain.

vinvout

R2

R1

i1

i´

i2

v1

v2

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Non-Inverting Amplifier

• Combining the previous equations we find:

• If the open-loop gain is very large:

vinvout

R2

R1

i1

i´

i2

v1

v2

!

Av

=vout

vin

=AOL(R

1+ R

2)

(AOL

+1)R1+ R

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Inverting Amplifier

• Using Kirchoff’s rule, Ohm’s Law, and our knowledge ofop-amps we can derive a closed loop-voltage gain for theinverting amplifier circuit shown below

vin vout

R2

R1

i1

i´

i2

v1

v2

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Inverting Amplifier

• The output voltage is related to the voltage difference.

• Neglecting i´ and combining the equations gives

vin vout

R2

R1

i1

i´

i2

v1

v2

Inverting Amplifier

• For a very large open-loop gain

becomes

vin vout

R2

R1

i1

i´

i2

v1

v2

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The Two Golden Rules ofOp-Amp Circuits

• Notice in both derivations two approximations were made: (1)the input current i´ flowing into the op-amp was neglectedcompared to other currents; and (2) the open-loop op amp gainAOL was assumed to be very large compared to the gain withfeedback.

• These two approximations can be extended to form two “goldenrules” for analyzing an op-amp circuits with negative feedback.

• Op-Amp Current Rule (OACR): The current into or out of eachop-amp input terminal is approximately zero.

• Op-Amp Voltage Rule (OAVR): The voltage difference betweenthe two op-amp input terminals is approximately zero.

Op-Amp Current Rule

• The OACR basically says that the inputimpedance of the op-amp is much higherthan the external input impedance from theinput terminal to ground.

• For BJT op-amps input impedance is on theorder of 10MΩ.

• For FET op-amps input impedance is on theorder of 1012 Ω.

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Op-Amp Voltage Rule

• The OAVR is the equivalent of saying that the open-loopgain is infinite.

• The output of the op-amp can never be greater than thesupply voltage (~15V) which means that (v2-v1) must beless that 150 µV for a typical AOL or the output will besaturated. Therefore if the op-amp is not saturated then thedifference between the input terminals must be nearly zero.

• The rule says that in an actual op amp circuit the negativefeedback plus the high gain of the op-amp effectively zerosthe difference between the two inputs.

Non-inverting Amp

• OACR: i1 = i2OAVR: v1 = v2 = vin

vinvout

R2

R1

i1

i2

v1

v2

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Inverting Amp

• OACR: i1 = i2OAVR: v1 = v2 = 0

vin vout

R2

R1

i1

i2

v1

v2

Instrumentation Amplifier

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Peak Detection Amplifier

Positive Feedback

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Positive Feedback Circuits

• Rather than placing a portion of the outputback into the inverting input a portion of theoutput is sent back to the non-invertingterminal to produce positive feedback.

Positive Feedback Circuits

• Oscillators

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Positive Feedback Circuits

• Oscillators