Spring 2008 Sean Lynch Lambros Samouris Tom Groshans

Operational Amplifiers

Spring 2008

Sean LynchLambros Samouris

Tom Groshans

Op Amps

Background

Ideal

Inverting

Non-Inverting

Integrating

Differential

Summing

Applications

History of Op Amps

• Named for their originally intended functions: performing mathematical operations and amplification– Addition– Subtraction– Integration– Differentiation

Op Amps

Background

Ideal

Inverting

Non-Inverting

Integrating

Differential

Summing

Applications

History of Op Amps

• Op Amps were initially developed in the vacuum tube era, but later were made into IC’s (Integrated Circuits)

• First integrated Op Amp to become widely available was the bipolar Fairchild µA709– Quickly superseded by the 741, a name

that has stuck with Op Amps since

Op Amps

Background

Ideal

Inverting

Non-Inverting

Integrating

Differential

Summing

Applications

History of Op Amps• The most common and most famous op-

amp is the mA741C or just 741, which is packaged in an 8-pin mini-DIP. – The integrated circuit contains 20 transistors and

11 resistors– Introduced by Fairchild in 1968, the 741 and

subsequent IC op-amps including FET-input op-amps have become the standard tool for achieving amplification and a host of other tasks. Though it has some practical limitations, the 741 is an electronic bargain at less than a dollar.

Op Amps

Background

Ideal

Inverting

Non-Inverting

Integrating

Differential

Summing

Applications

Op Amp Features

• Op Amps have two different inputs, inverting, V-, and non-inverting, V+

• Vs+ and Vs- are the positive and negative power supplies

• Vout is the output

Op Amps

Background

Ideal

Inverting

Non-Inverting

Integrating

Differential

Summing

Applications

Diagram of the 741

• Showed below is the 8-pin version of the 741 op amp

Op Amps

Background

Ideal

Inverting

Non-Inverting

Integrating

Differential

Summing

Applications

Ideal Op Amps

• Infinite open-loop gain• Obtained when no feedback is used in the circuit• On differential signal• Applying feedback limits the gain to a usable

range• Zero gain for common mode input signal

• Infinite input impedance• Thévenin equivalent of the IC looking into its

input• Current into the Op Amp is zero

Op Amps

Background

Ideal

Inverting

Non-Inverting

Integrating

Differential

Summing

Applications

Ideal Op Amps

• Infinite bandwidth• Usable frequency range & Gain• Infinite slew rate

• Zero output impedance• The Thévenin equivalent impedance looking

back into the output terminals • Op amp can supply any current / voltage

combination• Zero noise

Op Amps

Background

Ideal

Inverting

Non-Inverting

Integrating

Differential

Summing

Applications

Real Op-AmpsIdeal Op-Amp Typical Op-Amp

Input Resistance

infinity 106 Ω (bipolar)109 Ω - 1012 Ω (FET)

Input Current 0 10-12 – 10-8 A

Output Resistance

0 100 – 1000 Ω

Operational Gain

infinity 105 - 109

Common Mode Gain

0 10-5

Bandwidth infinity Attenuates and phases at high frequencies

(depends on slew rate)

Temperature independent Bandwidth and gain

9http://hyperphysics.phy-astr.gsu.edu/hbase/electronic/opampcon.html#c1

Op Amps

Background

Ideal

Inverting

Non-Inverting

Integrating

Differential

Summing

Applications

Real Op Amps

• Open Loop• Supply Limits (Rails), Saturation

• Feedback• Reduces Gain

• Bandwidth – Gain Product• 1 MHz gain-bandwidth product would have a

gain of 5 at 200 kHz, and a gain of 1 at 1 MHz

• Analysis• Feedback, positive, negative• 0 Current, 0 Voltage

Op Amps

Background

Ideal

Inverting

Non-Inverting

Integrating

Differential

Summing

Applications

Inverting Amplifier

• For an ideal op-amp, the inverting amplifier gain is given by:

The circuit that yields this equation is given on the diagram on the right

Op Amps

Background

Ideal

Inverting

Non-Inverting

Integrating

Differential

Summing

Applications

Inverting Amplifier

• For equal resistors, it has a gain of -1, and is used in digital circuits as an inverting buffer, or simply an inverter

Op Amps

Background

Ideal

Inverting

Non-Inverting

Integrating

Differential

Summing

Applications

Non-Inverting Amplifier

• For an ideal op-amp, the non-inverting amplifier gain is given by

A diagram of thecircuit that yields theabove equation isgiven on the right

Op Amps

Background

Ideal

Inverting

Non-Inverting

Integrating

Differential

Summing

Applications

Non-Inverting Amplifier• For an non-inverting amplifier, the current rule tries

to drive the current to zero at point A and the voltage rule makes the voltage at A equal to the input voltage.

This leads to:

and the amplificationequation

Op Amps

Background

Ideal

Inverting

Non-Inverting

Integrating

Differential

Summing

Applications

Integrating Amplifier

-Vin+R C

+ Vout

-

-

+

-Vin+R C

+ Vout

-

-

+

Op Amps

Background

Ideal

Inverting

Non-Inverting

Integrating

Differential

Summing

Applications

Integrating Amplifier

Op Amps

Background

Ideal

Inverting

Non-Inverting

Integrating

Differential

Summing

Applications

Integrating Amplifier

RVi in−

= dtdVCi =

-Vin+R C

+ Vout

-

)0(0

=+=

=

=

∫ −

−

−

tVdtV

C

t

RCV

out

RCV

dtdV

RV

dtdV

in

inout

inoutUse KCL to find current through each element and remember that the op-amp

uses ‘no’ current.

Op Amps

Background

Ideal

Inverting

Non-Inverting

Integrating

Differential

Summing

Applications

Integrating Amplifier

-Vin+R C

+ Vout

-

-

+

)0(0

=+= ∫ − tVdtVt

RCV

outin

Op Amps

Background

Ideal

Inverting

Non-Inverting

Integrating

Differential

Summing

Applications

Differential Amplifier

-Vin+RC

+ Vout

-

-

+dtdVRCV in

out −=

Similar to Integrator except R and C have switched locations.

Op Amps

Background

Ideal

Inverting

Non-Inverting

Integrating

Differential

Summing

Applications

Differential Amplifier

-V1+

-V2+

R1R1

R2R2

R4R4

R3R3

+ Vout

-

-

+

A more complex circuit. Can simplify using superposition of an inverting amplifier and a non-inverting amplifier.

-V1+R1R1 R3R3

+ Vout

-

-

+

Op Amps

Background

Ideal

Inverting

Non-Inverting

Integrating

Differential

Summing

Applications

Differential Amplifier

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

1

31_ R

RVV invertingout

Op Amps

Background

Ideal

Inverting

Non-Inverting

Integrating

Differential

Summing

Applications

Differential Amplifier

-V1+

-V2+

R1R1

R2R2

R4R4

R3R3

+ Vout

-

-

+

Op Amps

Background

Ideal

Inverting

Non-Inverting

Integrating

Differential

Summing

Applications

Differential Amplifier

R1R1 R3R3

+ Vout

-

-

++

Vin-

⎟⎟⎠

⎞⎜⎜⎝

⎛+=−

1

3_ 1

RRVV ininvertingnonout

?=inV

-V1+

-V2+

R1R1

R2R2

R4R4

R3R3

+ Vout

-

-

+

Op Amps

Background

Ideal

Inverting

Non-Inverting

Integrating

Differential

Summing

Applications

Differential Amplifier

Op Amps

Background

Ideal

Inverting

Non-Inverting

Integrating

Differential

Summing

Applications

Differential Amplifier

-V2+R2R2

R4R4+

Vth-

RthRth

⎟⎟⎠

⎞⎜⎜⎝

⎛+

=42

42 RR

RVVth

Op Amps

Background

Ideal

Inverting

Non-Inverting

Integrating

Differential

Summing

Applications

Differential Amplifier

⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛+

=−1

3

42

42_ 1

RR

RRRVV invertingnonout

R1R1 R3R3

+ Vout

-

-

++

Vin-

-V1+R1R1 R3R3

+ Vout

-

-

+

⎟⎟⎠

⎞⎜⎜⎝

⎛+=−

1

3_ 1

RRVV ininvertingnonout

invertingoutinvertingnonoutout VVV __ += −

⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟⎟⎠

⎞⎜⎜⎝

⎛ +⎟⎟⎠

⎞⎜⎜⎝

⎛+

=1

31

1

31

42

42 R

RVR

RRRR

RVVout

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

1

31_ R

RVV invertingout

Op Amps

Background

Ideal

Inverting

Non-Inverting

Integrating

Differential

Summing

Applications

Differential Amplifier-V1+

-V2+

R1R1

R2R2

R4R4

R3R3

+ Vout

-

-

+

⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟⎟⎠

⎞⎜⎜⎝

⎛ +⎟⎟⎠

⎞⎜⎜⎝

⎛+

=1

31

1

31

42

42 R

RVR

RRRR

RVVout

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛−=

1

312 R

RVVVoutIf R2=R1 and R3=R4,

Op Amps

Background

Ideal

Inverting

Non-Inverting

Integrating

Differential

Summing

Applications

Summing Amplifier

-V1+

-V2+

-V3+

-Vn+

R1R1

R2R2

R3R3

RnRn

RfRf

+ Vout

-

-

+.

.

-V1+

-V2+

-V3+

-Vn+

R1

R2

R3

Rn

Rf

+ Vout

-

-

+.

.

Op Amps

Background

Ideal

Inverting

Non-Inverting

Integrating

Differential

Summing

Applications

Summing Amplifier

-V1+

-V2+

-V3+

-Vn+

R1

R2

R3

Rn

Rf

.

.

NODE

1i

2i

3i

ni

fi

Op Amps

Background

Ideal

Inverting

Non-Inverting

Integrating

Differential

Summing

Applications

Summing Amplifier

fRV

RV

RV

RV

fn

outin

i

iiiiiii

iKCL

RViiRV

n

n =+++

+=+++

=

=

==

∑∑∑

...

0...

0

,

3

3

2

2

1

1

321

Op Amps

Background

Ideal

Inverting

Non-Inverting

Integrating

Differential

Summing

Applications

Summing Amplifier

( )n

nRV

RV

RV

RV

f

ff

RVout

RiVout

...3

3

2

2

1

1 +++−=

−=

-V1+

-V2+

-V3+

-Vn+

R1R1

R2R2

R3R3

RnRn

RfRf

+ Vout

-

-

+.

.

Op Amps

Background

Ideal

Inverting

Non-Inverting

Integrating

Differential

Summing

Applications

Applications555 Timer Circuit, Open Loop, Logic

Op Amps

Background

Ideal

Inverting

Non-Inverting

Integrating

Differential

Summing

Applications

ApplicationsA/D converter, Open Loop, Logic

Op Amps

Background

Ideal

Inverting

Non-Inverting

Integrating

Differential

Summing

Applications

ApplicationsClosed Loop, Voltage Level

•Transducers• Microphones• Strain Gauges

• PID Controllers

• Filters• Low Pass• High Pass• Band Pass• Butterworth

Op Amps

Background

Ideal

Inverting

Non-Inverting

Integrating

Differential

Summing

Applications Frequency range is governed by: 222

1CR

f⋅⋅

=π

ApplicationsClosed Loop, Low Pass Filter, Voltage Level

Op Amps

Background

Ideal

Inverting

Non-Inverting

Integrating

Differential

Summing

Applications

Practical Tips

• Try to use single supply op-amps in order to minimize need for a 10V difference from power supply

• Good low resistance, twisted, and shielded wire should be used when a sensor is located far away from the op-amp circuit.

• Minimize current draw in sensor circuits to reduce thermal drift• Filter power into op-amp circuits using capacitors• Design op-amp circuits so output cannot be negative in order

to protect 68HC11 A/D port.• Isolate op-amp circuit output with unity gain op-amp if

connected to an actuator.• Make sure bandwidth of op-amp is adequate• Use trimmer potentiometers to balance resistors in differential

op-amp circuits• Samples of op-amps can be obtained from National

Semiconductor (http://www.national.com)• Use the ‘Net for circuit examples

References

• Wikipedia: http://en.wikipedia.org/wiki/Operational_amplifier• The Art of Electronics, Horowitz and Hill • Electrical Engineering, Hambley• Previous Presentations• Lab Notes• http://users.ece.gatech.edu/~alan/ECE3040/Lectures/Lecture28-

Operational%20Amplifier.pdf

Op Amps

Background

Ideal

Inverting

Non-Inverting

Integrating

Differential

Summing

Applications