Discussion #17 - Operational Amplifiersbmazzeo/ECEn_301_F08/Fall2008/slides...ECEN 301 Discussion #17 –Operational Amplifiers 1 Date Day Class No. Title Chapters HW Due date Lab

ECEN 301 Discussion #17 – Operational Amplifiers 1

Date Day Class

No.

Title Chapters HW

Due date

Lab

Due date

Exam

29 Oct Wed 17 Operational Amplifiers 8.1 – 8.2

30 Oct Thu

31 Oct Fri Recitation HW 7

1 Nov Sat

2 Nov Sun

3 Nov Mon 18 Operational Amplifiers 8.3 – 8.4

LAB 6

4 Nov Tue

5 Nov Wed 19 Binary Numbers 13.1 – 13.2

Schedule…


Increase

Helaman 12:2

2 Yea, and we may see at the very time when he doth prosper his people, yea, in the increase of their fields, their flocks and their herds, and in gold, and in silver, and in all manner of precious things of every kind and art; sparing their lives, and delivering them out of the hands of their enemies; softening the hearts of their enemies that they should not declare wars against them; yea, and in fine, doing all things for the welfare and happiness of his people; yea, then is the time that they do harden their hearts, and do forget the Lord their God, and do trample under their feet the Holy One—yea, and this because of their ease, and their exceedingly great prosperity.


Lecture 17 – Operational Amplifiers


Ideal Amplifiers

Amplifier: a device for increasing the power of a signal.

Power increase is called gain (A)

vS(t) +

–

RS

Gain A

+

vL

–

RL

Source Amplifier Load

0:21CD


)()( tAvtv SL


Ideal Amplifiers

Simplified Amplifier Model:The source ―sees‖ and equivalent load (Rin)

The load ―sees‖ and equivalent source (Avin)

vS(t) +

–

RS

Gain A

+

vL

–

RL


NB: Thévenin

equivalentNB: equivalent

resistance

vS(t) +

–

RS

+

vL

–

RLRin

+–

Rout

Avin

+

vin

–


Ideal Amplifiers

The gain is dependent on the source and load (i.e. is different for different sources and loads)

Lout

LinL

RR

RAvv

vS(t) +

–

RS

+

vL

–

RLRin

+–

Rout

Avin

+

vin

–

inS

inSin

RR

Rvv

S

Lout

L

inS

inL v

RR

R

RR

RAv

NB: expression for vL depends on the source (RS) and the load (RL)


Ideal Amplifiers

The gain can be made to be almost independent of the source (RS) and the load (RL)

Let Rin → ∞

Let Rout → 0

in

Lout

LinL

Av

RR

RAvv

0 R if out

vS(t) +

–

RS

+

vL

–

RLRin

+–

Rout

Avin

+

vin

– S

inS

inSin

v

RR

Rvv

: R if in

SL Avv

NB: it is desirable for an amplifier to have:

• a very large input impedance

• a very small output impedance


Op-Amps

Operational Amplifier: originally designed (late 1960’s) to perform mathematical operations (analog computer) Addition

Subtraction

Integration

differentiation

–

+

Positive power supply (usually +15V)

Negative power supply (usually –15V)

Output

Inverting Input

Noninverting Input

VS+

VS–

NB: the power supplies (VS+

and VS–) are often omitted in

drawings – they are implicit


Op-Amps – Open-Loop Mode

Open-Loop Model: an ideal op-amp acts like a difference amplifier (a device that amplifies the difference between two input voltages)

–

++

v+

–

+

v–

–

+

vo

–

io

i2

i1

–vin

+

–

+

+–

RoutRin

i1

AOLvin

+

vo

–

–

vin

+

v–

v+

NB: op-amps have near-infinite input resistance (Rin) and very small output resistance (Rout)

)( vvA

vAv

OL

inOLoAOL – open-loop voltage gain

i2




–

++

v+

–

+

v–

–

+

vo

–

io

i2

i1

–vin

+ Ideally i1 = i2 = 0

(since Rin → ∞)

021 ii




What? No input current??

In reality there is a small current021 ii


Op-Amps – Closed-Loop Mode

The Inverting Amplifier: the signal to be amplified is connected to the inverting terminal

–

+ +

vo

–

i1

RF

RS

vS(t) +

–

v+

v–

iF

iS

i2




S

SS

R

vvi

–

+ +

vo

–

i1

Feedback current: current from the output

is fed back into the input of the op-amp

RF

RS

vS(t) +

–

v+

v–

iF

iS

Node a

FS

FS

ii

iii 0

:a deNoat KCL

1

F

oF

R

vvi 01i




–

+ +

vo

–

i1

RF

RS

vS(t) +

–

v+

v–

iF

iS

OL

o

OL

OL

OLo

A

vv

vA

vA

vvAv

)0(

)(

:Model Loop-Open From




RF

–

+ +

vo

–

i1

RS

vS(t) +

–

v+

v–

iF

iS

OLSFOLSF

oS

SOL

o

FOL

o

S

S

S

S

F

OLo

F

o

S

OLo

S

S

F

o

S

S

FS

ARRARRvv

RA

v

RA

v

R

v

R

v

R

Av

R

v

R

Av

R

v

R

vv

R

vv

ii

1

/

1

/

1

//




OLSFOLSF

oSARRARR

vv1

/

1

/

1RF

–

+ +

vo

–

i1

RS

vS(t) +

–

v+

v–

iF

iSNB: if AOL is very large these terms → 0

S

F

S

o

R

R

v

vCLA

:Gain Loop-Closed




OL

out

A

vv

:Model Loop-Open FromRF

–

+ +

vo

–

i1

RS

vS(t) +

–

v+

v–

iF

iS

NB: as AOL → ∞ v– → 0

vv

AOL As




vv

ii 021

RF

–

+ +

vo

–

i1

RS

vS(t) +

–

v+

v–

iF

iS

NB: two important results for an ideal

op-amp with negative feedback

i2



Example1: determine AOL and vo

RS = 1kΩ, RF = 10kΩ, vs(t) = Acos(ωt), A=0.015, ω = 50 rads/s

RF

–

+ +

vo

–

i1

RS

vS(t) +

–

v+

v–

iF

iS





)cos(15.0

)cos(015.010

10

A

3

4

CL

t

t

vR

Rv

R

R

v

v

S

S

Fo

S

F

S

oRF

–

+ +

vo

–

i1

RS

vS(t) +

–

v+

v–

iF

iS

10

ACL

S

F

R

R





RF

–

+ +

vo

–

i1

RS

vS(t) +

–

v+

v–

iF

iS

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.0 0.2 0.4 0.6 0.8 1.0

time (s)

Vo

lta

ge

(V

)

vs(t)

vo(t)



Example2: What is the min/max gain, and gain uncertainty if 5% tolerance resistors are used? RS = 1kΩ, RF = 10kΩ, vs(t) = Acos(ωt), A=0.015, ω = 50 rads/s

10A nomCL

RF

–

+ +

vo

–

i1

RS

vS(t) +

–

v+

v–

iF

iS

05.9

1050

9500

Amax

min

minCL

S

F

R

R

05.11

950

10500

Amin

max

maxCL

S

F

R

R

NB: nominal gain



Example2: What is the min/max gain, and gain uncertainty if 5% tolerance resistors are used? RS = 1kΩ, RF = 10kΩ, vs(t) = Acos(ωt),

A=0.015, ω = 50 rads/sRF

–

+ +

vo

–

i1

RS

vS(t) +

–

v+

v–

iF

iS%5.9

10

9.0510100

A

AA100

:Error % Max

nomCL

minCLnomCL

%5.10

10

11.0510100

A

AA100

:Error % Min

nomCL

maxCLnomCL



The Summing Amplifier: sources are summed together

independently of load and source impedances

–

+ +

vo

–

RF

RS1

vS1(t)+

–v+

v– iF

i1

RS2

vS2(t)+

–i2

RSN

vSN(t) +

–iN





–

+ +

vo

–

RF

RS1

vS1(t)+

–v+

v– iF

i1

RS2

vS2(t)+

–i2

RSN

vSN(t) +

–iN

Node a

N , 2, 1, nR

vi

Sn

nSn

FN iiii 21

:a deNoat KCL

F

oF

R

vi

NB: v– = v+ = 0





–

+ +

vo

–

RF

RS1

vS1(t)+

–v+

v– iF

i1

RS2

vS2(t)+

–i2

RSN

vSN(t) +

–iN

Node a

N

n

sn

sn

Fo

F

oN

n sn

sn

vR

Rv

R

v

R

v

1

1



The Noninverting Amplifier: the signal to be amplified is connected to the noninverting terminal

–

+ +

vo

–

i1

RF

R

vS(t) +

–

v+

v–

iF

RS

iS

i1




–

+ +

vo

–

i1

RF

R

vS(t) +

–

v+

v–

iF

RS

iS

i1

S

SS

R

vi

FS

FS

ii

iii 0

:a deNoat KCL

1

F

oF

R

vvi 01i

Node a




–

+ +

vo

–

i1

RF

R

vS(t) +

–

v+

v–

iF

RS

iS

i1

vvv

R

i

S

drop) voltageno rough current th no (i.e.

: 0 Since 1

S

F

S

o

S

S

F

So

SF

R

R

v

v

R

v

R

vv

ii

1

Node a




–

+ +

vo

–

i1

RF

R

vS(t) +

–

v+

v–

iF

RS

iS

i1

Node a

S

F

S

o

R

R

v

v

1

A

:Gain Loop-Closed

CL

NB: always positive and greater than or equal to 1



Voltage Follower: the voltage on the output of the op-amp is equal to the source voltage

–

+ +

vo

–

i1

vS(t) +

–

v+

v–

i1




svv

–

+ +

vo

–

i1

vS(t) +

–

v+

v–

i1

NB: an ideal op-amp with negative

feedback has the property

vv

ovv

So vv




Circuit 1

Loading: changing the behaviour of one circuit by connecting another circuit to it

+

va

–

If va ≠ vb

ib is the load current

Circuit 1 Circuit 2

+

vb

–

ib




–

+

Circuit 1 Circuit 2

Voltage follower can be used to prevent loading

(ib = 0)

Loading: changing the behaviour of one circuit by connecting another circuit to it

Documents

Discussion #17 - Operational Amplifiersbmazzeo/ECEn_301_F08/Fall2008/slides...ECEN 301 Discussion #17 –Operational Amplifiers 1 Date Day Class No. Title Chapters HW Due date Lab