Operational Amplifiers

Outline

Introduction

Background

Fundamentals of Op-Amps

Real vs. Ideal

Applications

What is an Op-Amp

Low cost integrating circuit consisting of

Transistors

Diodes

resistors

capacitors

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’s

Possible 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-Amps Ideal 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-Amps Ideal 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

The open-loop gain of an operational amplifier is the gain

obtained when no feedback is used in the circuit. Open loop

gain is usually exceedingly high; in fact, an ideal operational

amplifier has infinite open-loop gain.

The slew rate of an electronic circuit is defined as the

maximum rate of change of the output voltage. Slew rate is

usually expressed in units of V/µs

An ideal op-amp is usually considered to have the following properties, and they are

considered to hold for all input voltages:

1. Infinite open-loop gain (when doing theoretical analysis, a limit may be taken as open

loop gain AOL goes to infinity).

2. Infinite voltage range available at the output () (in practice the voltages available from

the output are limited by the supply voltages and ). The power supply sources are

called rails.

3. Infinite bandwidth (i.e., the frequency magnitude response is considered to be flat

everywhere with zero phase shift).

4. Infinite input impedance (so, in the diagram, , and zero current flows from to ).

5. Zero input current (i.e., there is assumed to be no leakage or bias current into the

device).

6. Zero input offset voltage (i.e., when the input terminals are shorted so that , the output

is a virtual ground or ).

7. Infinite slew rate (i.e., the rate of change of the output voltage is unbounded) and

power bandwidth (full output voltage and current available at all frequencies).

8. Zero output impedance (i.e., , so that output voltage does not vary with output current).

9. Zero noise.

10. Infinite Common-mode rejection ratio (CMRR).

11. Infinite Power supply rejection ratio for both power supply rails.

These ideals can be summarized by the two "golden rules":

1. The output attempts to do whatever is necessary to make

the voltage difference between the inputs zero.

2. The inputs draw no current.

The first rule only applies in the usual case where the op-amp is

used in a closed-loop design (negative feedback, where there is a

signal path of some sort feeding back from the output to the

inverting input). These rules are commonly used as a good first

approximation for analyzing or designing op-amp circuits.

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 = 0V Vin

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- - Vout Vin – 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

- 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 fout

Solving 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:

CRc

2

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

Common-Mode Input Resistance (RINCM)

For op amps operating in the linear region, this term defines the input

common-mode voltage range divided by the change in input bias current

across that range.

2. DC Common-Mode Rejection (CMRDC)

This is a measure of the op amp's ability to reject DC signals present in

equal measure at both inputs.

CMRDC can be calculated using the common-mode voltage range (CMVR)

and the change in peak-topeak input offset voltage across that range.

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