Operational Amplifiers

Brandon Borm

Shelley Nation

Chloe Milion

Outline

Introduction Background Fundamentals of Op-Amps Real vs. Ideal Applications

What is an Op-Amp

Low cost integrating circuit consisting of transistorsresistorscapacitors

Op-amps amplify an input signal using an external power supply

Uses for Op-Amps Op-Amps are commonly used for both linear and

nonlinear applications Linear

Amplifiers Summers Integrators Differentiators Filters (High, Low, and Band Pass)

Non-linear Comparators A/D converters

Vacuum Tube Op-Amps First op amps built in 1930’s-

1940’s Technically feedback amplifiers

due to only having one useable input

Used in WWII to help how to strike military targets Buffers, summers, differentiators,

inverters

Took ±300V to ± 100V to power

http://en.wikipedia.org/wiki/Image:K2-w_vaccuum_tube_op-amp.jpg1

Solid State Discrete Op-Amps Solid state op amps invented in

1960’sPossible due to invention of

silicon transistors and the IC Chip and discrete parts

Reduced power input to ±15V to ±10V

Packaging in small black boxes allowed for integration with a circuit

Monolithic Integrated Circuit Op-Amp First created in 1963

μA702 by Fairchild Semiconductor

μA741 created in 1968 Became widely used due to its ease

of use 8 pin, dual in-line package (DIP)

Further advancements include use of field effects transistors (FET), greater precision, faster response, and smaller packaging

Features of Op-Amps +Vin: non-inverting input

-Vin: inverting input

+Vs: positive source

-Vs: negative source

Vout: output voltage ON: Offset Null NC: Not Connected

Vout

+Vs

-Vs

+Vin

-Vin

+

-

ON

-Vin

+Vin

-Vs ON

Vout

+Vs

NC

Characteristics of Op-AmpsIdeal Op-Amp

Infinite open loop gain (GOL): Zero common mode gain

Infinite bandwidth: Range of frequencies

with non-zero gain

Real Op-Amp

Limited open loop gain: Decreases with increase

in frequency Non-zero common mode

gain

Limited Bandwidth: Gain becomes zero at

high frequencies

Characteristics of Op-AmpsIdeal Op-Amp

Infinite slew rate

Infinite input impedance No input current

Zero output impedance Infinite output current

Real Op-Amp

Finite slew rate

Large input impedance Small input current

Non-zero output impedance Limited output current

Summary of Characteristics

Parameter Ideal Op-Amp Typical Op-Amp

GOL ∞ 105 - 109

Common Mode Gain

0 10-5

Bandwidth ∞ 1-20 MHz

Input Impedance

∞ 106 Ω (bipolar)

109-1012 Ω (FET)

Output Impedance

0 100-1000 Ω

Ideal Op-Amp

Active device Infinite open loop gain Infinite input impedance Zero output impedance

+

-

+Vs

-Vs

Vdiff

iin = 0A

Vout = Vdiff x Gopenloop

Negative Feedback

Vout is a linear function of the input voltage

Zin = infinity Iin=0A Vdiff=0V

Modelisation of basic mathematical operation

Non Inverting Circuit

+

-

R1 R2

+Vs

-Vs

iin = 0A

Vdiff = 0VVin

Vout

0A

V- V- - Vout

i

(1) V- - Vout = R2 x i

(2) V- = - R1 x i

V- = V+ = Vin

(2) i = -Vin/R1

(1) Vin – Vout = -Vin x R1/R2

Vout = (1 + R1/R2) x Vin

Inverting Circuit

+

-

R1 R2

+Vs

-Vs

Vdiff = 0V

Vin

Vout

iin = 0A

i

V- - VoutVin – V-

(1) V- - Vout = R2 x i

(2) Vin - V- = R1 x i

V- = V+ = 0(1) i = Vin / R1

Vout = - R2/R1 x Vin

Follower Circuit

Vin Vout

+ Vs

- Vs

Summing Op-Amp• Adds analog signals

f

out

R

VV

R

VV

R

VV

R

VV

3

3

2

2

1

1

3

3

2

2

1

1

R

V

R

V

R

VRV foutSolving for Vout:

Ohm’s Law:

Summing Op-Amp

Difference Op-Amps• Subtracts analog signals

1

1

32

124

413

)(V

R

RV

RRR

RRRVout

• Output voltage is proportional to difference between input voltages:

Difference Op-Amp

Integrator Op-Amps•Similar layout to inverting op-amp, but replace feedback resistor with a capacitor

•A constant input signal generates a certain rate of change in output voltage

• Smoothes signals over time

t

ininitialoutfinalout dtVRC

VV0

,,

1

•Output voltage is proportional to the integral of the input voltage:

Integrator Op-Amp

Differentiating Op-Amp•Similar to inverting op-amp, but input resistor is replaced with a capacitor

•Accentuates noise over time

dt

dVRCV in

out • Output signal is scaled derivative of input signal:

Differentiating Op-Amp

Active Filters

Different types of active filters:Low Pass

Filters out frequencies above a cutoff frequency

High Pass Filters out frequencies below a cutoff frequency

Band Pass Passes a range of frequencies between two cutoff

frequencies

Active Low-Pass Filter

Cutoff frequency:CRc2

1

Active High-Pass Filter

Switch positioning of capacitors and resistors from low-pass filter locations to create high-pass filter.

Active Band-Pass Filter

Created by connecting output of a high-pass filter to the input of a low-pass filter or vice versa.

Also can create using only 1 op-amp with feedback and input capacitors

No negative feedback

Vout is a non-linear function of the differential input voltage V+ - V-

V+ - V- = Vdiff

Vout = sign(Vdiff) x Vs

Binary logic and oscillator

Comparator

+

-

+Vs

-Vs

iin = 0A

Vdiff

V+

V-

Vout

0V

+ Vs

Vout ( volts )

Vdiff

- Vs

Comparator

Questions?

References

“Operational Amplifiers.” http://en.wikipedia.org/wiki/Op_amp

“Real vs. Ideal Op Amp.” http://hyperphysics.phy-astr.gsu.edu/hbase/electronic/opamp.html#c4

“741 Op Amp Tutorial.” http://www.uoguelph.ca/~antoon/gadgets/741/741.html

“Op Amp History.” Analog Devices. http://www.analog.com/library/analogDialogue/archives/39-05/Web_ChH_final.pdf