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Announcements

Assignment 3 due now, or by tomorrow

5pm in my mailbox

Assignment 4 posted, due next week

Thursday in class, or Friday 5pm in my

mailbox

mid-term: Thursday, October 27th

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Lecture 11 Overview

Amplifier impedance

The operational amplifier

Ideal op-amp Negative feedback

Applications

Amplifiers Summing/ subtracting circuits

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Attach an input - a source voltage VS plus source impedance RS

Impedances

RIN

ROUT

VINAV

IN

VOUT

Note the voltage divider RS + RIN.

VIN

=VS(R

IN/(R

IN+R

S)

We want VIN = VS regardless of source impedance

So want RIN to be large.

The ideal amplifier has an infinite input impedance

VS

RS

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Attach a load - an output circuit with a resistance RL

Impedances

Note the voltage divider ROUT + RL.

VOUT

=AVIN

(RL/(R

L+R

OUT))

Want VOUT=AVIN regardless of load

We want ROUT to be small.

The ideal amplifier has zero output impedance

RIN

ROUT

VINAV

IN

VOUTVS

RS

RL

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Operational Amplifier

An op amp is a high voltage gain, DC amplifier with high input

impedance, low output impedance, and differential inputs. Positive input at the non-inverting input produces positive output,

positive input at the inverting input produces negative output.

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Operational Amplifier

An op amp is a high voltage gain, DC amplifier with high input

impedance, low output impedance, and differential inputs. Positive input at the non-inverting input produces positive output,

positive input at the inverting input produces negative output.

Can model any amplifier as a "black-box" with a parallel input

impedance Rin, and a voltage source with gain Av in series with an

output impedance Rout.

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Ideal op-amp Place a source and a load on the model

Infinite internal resistance Rin(so vin=vs). Zero output resistance Rout(so vout=Avvin).

"A" very large

iin=0; no current flow into op-amp

-

+

vout

RL

RS

So the equivalent circuit of an

ideal op-amp looks like this:

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Many Applications e.g.

Amplifiers

Adders and subtractors

Integrators and differentiators

Clock generators

Active Filters

Digital-to-analog converters

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ApplicationsOriginally developed for use in analog computers:

http://www.youtube.com/watch?v=PBILL8UypHA

http://www.youtube.com/watch?v=PBILL8UypHAhttp://www.youtube.com/watch?v=PBILL8UypHAhttp://www.youtube.com/watch?v=PBILL8UypHAhttp://www.youtube.com/watch?v=PBILL8UypHA

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ApplicationsOriginally developed for use in analog computers:

http://www.youtube.com/watch?v=PBILL8UypHA

http://www.youtube.com/watch?v=PBILL8UypHAhttp://www.youtube.com/watch?v=PBILL8UypHAhttp://www.youtube.com/watch?v=PBILL8UypHAhttp://www.youtube.com/watch?v=PBILL8UypHA

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Using op-amps

Power the op-amp and apply a voltage

Works as an amplifier, but:

No flexibility (A~105-6

) Exact gain is unreliable (depends on chip, frequency and temp)

Saturates at very low input voltages (Max vout=power supply voltage)

To operate as an amp, v+-v-

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Noninverting Amplifier

21

2

)(

RR

RvvAv

vvAv

OINO

O

INOAv

RR

ARv

21

21

21

21RR

ARAvv IN

O

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When A is very large:

Take A=106, R1=9R, R2=R

10

10

1101

10

9101

10

6

6

6

6

INO

IN

O

IN

O

vv

vv

RRR

vv

2

21

21

2

21

21

R

RR

vv

RR

RA

Avv

RR

AR

Avv

INO

INO

IN

O

Gain now determined only by resistance ratio

Doesnt depend on A, (or temperature,

frequency, variations in fabrication)

>>1

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Negative feedback:

How did we get to stable operation in the linear

amplification region??? Feed a portion of the output signal back into the input

(feeding it back into the inverting input = negative feedback)

This cancels most of the input

Maintains (very) small differential signal at input

Reduces the gain, but if the open loop gain is ~, who

cares?

Good discussion of negative feedback here:

http://www.allaboutcircuits.com/vol_3/chpt_8/4.html

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Why use Negative feedback?:

Helps to overcome distortion and non-linearity

Improves the frequency response

Makes properties predictable - independent of

temperature, manufacturing differences or other

properties of the opamp

Circuit properties only depend upon the

external feedback network and so can be easily

controlled

Simplifies circuit design - can concentrate on

circuit function (as opposed to details of

operating points, biasing etc.)

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More insight

Under negative feedback:

vv

A

vR

RR

A

vvv

IN

O 01

21

We also know

i+ 0

i- 0 Helpful for analysis (under negative feedback)

Two "Golden Rules"

1) No current flows into the op-amp

2) v+ v-

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More insight

Allows us to label almost every point in circuit terms of vIN!

1) No current flows into the op-amp

2) v+ v-

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Op amp circuit 1: Voltage follower

So vO=vIN

or, using equations

2

21

R

RRvvINO

2

10

R

R

What's the gain of this circuit?

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Op amp circuit 1: Voltage follower

So vO=vIN

or, using equations

2

21

R

RRvvINO

2

10

R

R

What's the application of this circuit?

Buffer

voltage gain = 1

input impedance=

output impedance=0

Useful interface between different circuits:

Has minimum effect on previous and next

circuit in signal chain

RIN

ROUT

VINAVIN VOUTVS

RS

RL

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Op amp circuit 2: Inverting Amplifier

S

S

F

out

F

out

S

S

F

out

S

S

FS

inFS

vR

Rv

R

v

R

v

R

vv

R

vv

ii

iii

00

0

Signal and feedback resistor,

connected to inverting (-) input.

v+=v- connected to ground

S

F

S

out

R

R

v

vGain

0 vvv+ grounded, so:

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Op amp circuit 3: Summing Amplifier

SN

SN

F

S

S

F

S

S

F

out

F

out

SN

SN

S

S

S

S

FN

vR

Rv

R

Rv

R

Rv

R

v

R

v

R

v

R

v

iiii

.....

.....

.....

2

2

1

1

2

2

1

1

21

Same as previous, but add more

voltage sources

)...(21 SNSS

S

F

outvvv

R

Rv

SSNSSRRRR

...If21

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Summing Amplifier Applications

Applications - audio mixer

Adds signals from a number of waveforms

http://wiredworld.tripod.com/tronics/mixer.html

Can use unequal resistors to get a weighted sum

For example - could make a 4 bit binary - decimal converter

4 inputs, each of which is +1V or zero

Using input resistors of 10k (ones), 5k (twos), 2.5k (fours) and 1.25k (eights)

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Op amp circuit 4: Another non-inverting amplifier

Feedback resistor still to inverting input,

but no voltage source on inverting input

(note change of current flow) Input voltage to non-inverting input

vv FS ii

S

in

vvv

i

and0since F

out

S R

vv

R

v

0

S

F

S

out

S

S

F

out

S

F

out

R

R

v

v

vR

Rv

vR

Rv

1Gain

1

1

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Op amp circuit 5: Differential Amplifier (subtractor)

021 ii

)(12

1

2

2

21

2

21

1

vvR

Rv

vvRR

Rv

vv

R

vv

R

vv

out

out

Useful terms:

if both inputs change together, this is a common-modeinput change

if they change independently, this is a normal-modechange

A good differential amp has a high common-mode rejection ratio (CMMR)

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Differential Amplifier applications Very useful if you have two inputs corrupted with the same noise

Subtract one from the other to remove noise, remainder is signal

Many Applications : e.g. an electrocardiagram measures the

potential difference between two points on the body

The AD624AD is an instrumentationamplifier - this is a high gain, dc

coupled differential amplifier with a high input impedance and high CMRR

(the chip actually contains a few opamps)

http://www.picotech.com/applications/ecg.html

http://www.picotech.com/applications/graphics/ecg_circuit_big.gif