Operational AmplifiersOperational Amplifiers

What is an Op Amp?What is an Op Amp?High voltage gain IC with High voltage gain IC with differential inputsdifferential inputs– Designed to have Designed to have

characteristics near idealcharacteristics near ideal

Inexpensive, widely used ICInexpensive, widely used IC

Available in wide range of Available in wide range of packagespackages

Typically require a positive Typically require a positive and a negative power supplyand a negative power supply

Uses: amplifier, buffer, summer, differentiator, Uses: amplifier, buffer, summer, differentiator, integrator, comparator, instrumentation amp, integrator, comparator, instrumentation amp, Schmitt trigger, negative impedance, super Schmitt trigger, negative impedance, super diode, logarithmic/exponential output, simulated diode, logarithmic/exponential output, simulated inductorinductor

History of Op AmpsHistory of Op AmpsOriginally designed for analog computers using vacuum Originally designed for analog computers using vacuum tubestubes– Output voltage is a function of input voltage (addition, subtraction, Output voltage is a function of input voltage (addition, subtraction,

integration, differentiation, exponential, logarithm…)integration, differentiation, exponential, logarithm…)

K2-W: first mass produced op amp (1952)K2-W: first mass produced op amp (1952)– Invented by George PhilbrickInvented by George Philbrick– $22. Gain ≈ 20,000. Gain-bandwidth ≈ 1MHz. $22. Gain ≈ 20,000. Gain-bandwidth ≈ 1MHz.

Input impedance ≈ 50kInput impedance ≈ 50kΩΩ– See picture (K2-W with and without shell)See picture (K2-W with and without shell)

History of Op AmpsHistory of Op Amps

First transistor op amp (μA702) used 12 BJTsFirst transistor op amp (μA702) used 12 BJTs– Invented in 1964 by Bob WidlarInvented in 1964 by Bob Widlar– Sold for $300Sold for $300– Prone to short circuitsProne to short circuits

μA709 improved on μA702 (used 14 transistors)μA709 improved on μA702 (used 14 transistors)– Invented in 1965 also by Bob WidlarInvented in 1965 also by Bob Widlar– Higher gain, more bandwidth, cheaper, more robustHigher gain, more bandwidth, cheaper, more robust– Sold for $70 to start, then $2 within a few yearsSold for $70 to start, then $2 within a few years

741 Op Amp741 Op AmpIntroduced in 1968, and versions still Introduced in 1968, and versions still available and in use todayavailable and in use today

μA741 Op AmpμA741 Op Amp

Op Amp FlavoursOp Amp Flavours

High output powerHigh output powerHigh speedHigh speedlarge bandwidthlarge bandwidthLow noiseLow noiseLow power Low power Low voltageLow voltagePrecisionPrecisionRail-to-RailRail-to-RailSmall packageSmall package>1 Op Amp per package>1 Op Amp per package

Ideal Op AmpIdeal Op Amp• Input resistance is infinite

• Output resistance is zero

• Bandwidth is infinite

• Input current is zero

• Open loop gain is infinite

• Output voltage is zero when input voltages are zero

AV

V V

V

VOU T OU T

IN

ROU T 0

I 0

R IN

I 0

Ideal Op Amp GainIdeal Op Amp Gain

If open loop gain of ideal op amp → ∞, what’s If open loop gain of ideal op amp → ∞, what’s the use?the use?– Any input will result in + or – saturationAny input will result in + or – saturation

Even non-ideal op amps not useful with open Even non-ideal op amps not useful with open looploop– Only small input voltages before + or - saturationOnly small input voltages before + or - saturation

Op amps almost never use open loop.Op amps almost never use open loop.– Use feedback to control the actual gainUse feedback to control the actual gain

Feedback!Feedback!

FeedbackFeedback

Positive FeedbackPositive Feedback– Output feeds back to input, and increase Output feeds back to input, and increase

output leading to out of control systemoutput leading to out of control system– E.g., microphone picks up speaker output, E.g., microphone picks up speaker output,

driving speaker output higher which is picked driving speaker output higher which is picked up by microphone…up by microphone…

Negative FeedbackNegative Feedback– Output feeds back to input to allow system to Output feeds back to input to allow system to

adjust and keep output within a certain rangeadjust and keep output within a certain range– E.g., body controlling blood glucose levelsE.g., body controlling blood glucose levels

Feedback in Op AmpsFeedback in Op AmpsIf output is fed back to non-inverting input – If output is fed back to non-inverting input – positive feedback occurspositive feedback occurs– Not usefulNot useful

If output is fed back to inverting input – negative If output is fed back to inverting input – negative feedback occursfeedback occurs– Widely used configurationWidely used configuration

Golden Rules for Op-AmpsGolden Rules for Op-Amps

1. With negative feedback:1. With negative feedback:The op amp drives the output so that The op amp drives the output so that the two inputs are at equal voltagethe two inputs are at equal voltage

2. 2. Assume that the input current is zero.Assume that the input current is zero.

Buffer or Voltage FollowerBuffer or Voltage Follower

No voltage difference between the output and No voltage difference between the output and the inputthe input

Buffer draws no current, so it puts no load on the Buffer draws no current, so it puts no load on the source. Output current supplied by VCC.source. Output current supplied by VCC.

Used to isolate sources from loadsUsed to isolate sources from loads

Non-Inverting AmplifierNon-Inverting Amplifier

Non-Inverting AmplifierNon-Inverting Amplifier

AAVV = V = Voo/V/VII

VVII = V = V22 (i.e., V (i.e., Vin+in+ = V = Vin-in- ) … from “Golden Rules” ) … from “Golden Rules” No current flows into VNo current flows into Vin+in+ (Golden Rule) therefore: (Golden Rule) therefore: VVII = V = V2 2 = V= Vo o * R1/(R* R1/(R11 + R + R22) … voltage divider) … voltage divider

AAVV = V = Voo/V/VII = (R = (R11 + R + R22)/R)/R11 = 1 + (R = 1 + (R22 / R / R11))

V2

Non-Inverting AmplifierNon-Inverting AmplifierOther ConsiderationsOther Considerations

R2 can’t be too low since the Op Amp has R2 can’t be too low since the Op Amp has limited current capabilitylimited current capability

R1 should be much smaller than the input R1 should be much smaller than the input impedanceimpedance

Circuit voltage gain should be much less Circuit voltage gain should be much less than the open loop gain of the Op Ampthan the open loop gain of the Op Amp

The output voltage swing has to be less The output voltage swing has to be less than the supply voltagesthan the supply voltages

Non-Inverting Amplifier Non-Inverting Amplifier ExamplesExamples

(from course package)(from course package)

Inverting AmplifierInverting Amplifier

Inverting AmplifierInverting Amplifier

Current through RCurrent through R11 equals the current equals the current

through Rthrough Rff

No current into the inputsNo current into the inputs

The voltage at both op amp inputs is zeroThe voltage at both op amp inputs is zero

Inverting AmplifierInverting Amplifier

• Current through R1

• Current through Rf

IV

R

V

R11

1

1

1

0

IV

R

V

RO

f

O

f2

0

Inverting AmplifierInverting Amplifier

Why the minus sign for the current through Why the minus sign for the current through RRff??

– The convention for Ohm’s Law is that the The convention for Ohm’s Law is that the current flows from the high voltage to the low current flows from the high voltage to the low voltage for a resistorvoltage for a resistor

– Here the current flows from the low voltage Here the current flows from the low voltage (ground) to the high voltage (V(ground) to the high voltage (VOO))

Inverting AmplifierInverting Amplifier

• The current through R1 must equal the current through R2 since there is no current in the inputs.

• Combining the two equations for the currentsV V

R

ROUT INf 1

Inverting Amplifier ExamplesInverting Amplifier Examples

(from course package)(from course package)

Op Amp ApplicationsOp Amp Applications

ArithmeticArithmetic– Summing, differencingSumming, differencing

CalculusCalculus– Integration, differentiationIntegration, differentiation

Level detectorsLevel detectors– Comparators, Schmitt TriggersComparators, Schmitt Triggers