ECEN 301Discussion #17 – Operational Amplifiers1 DateDayClass No. TitleChaptersHW Due date Lab Due...

ECEN 301Discussion #17 – Operational

Amplifiers1

Date Day ClassNo.

Title Chapters HWDue date

LabDue 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…


Amplifiers2

IncreaseHelaman 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.


Amplifiers3

Lecture 17 – Operational Amplifiers


Amplifiers4

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

0:21 CD


)()( tAvtv SL


Amplifiers5

Ideal AmplifiersSimplified 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 equivalent

NB: equivalent resistance

vS(t)+–

RS

+

vL

–

RLRin

+–

Rout

Avin+

vin

–


Amplifiers6

Ideal AmplifiersThe 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

SLout

L

inS

inL v

RR

R

RR

RAv

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


Amplifiers7

Ideal AmplifiersThe 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


Amplifiers8

Op-AmpsOperational 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


Amplifiers9

Op-Amps – Open-Loop ModeOpen-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


Amplifiers10



–

++

v+

–

+

v–

–

+

vo

–

io

i2

i1

–vin

+ Ideally i1 = i2 = 0(since Rin → ∞)

021 ii


Amplifiers11



What? No input current??In reality there is a small current021 ii


Amplifiers12

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


Amplifiers13



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

01 i


Amplifiers14



–

+ +

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


Amplifiers15



RF

–

+ +

vo

–

i1

RS

vS(t)+–

v+

v–

iF

iS

OLSFOLSFoS

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

//


Amplifiers16



OLSFOLSFoS ARRARR

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

vv

CLA

:Gain Loop-Closed


Amplifiers17



OL

out

A

vv

:Model Loop-Open FromRF

–

+ +

vo

–

i1

RS

vS(t)+–

v+

v–

iF

iSNB: as AOL → ∞ v– → 0

vv

AOL As


Amplifiers18



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


Amplifiers19


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


Amplifiers20



)cos(15.0

)cos(015.010

10

A

3

4

CL

t

t

vR

Rv

R

R

vv

SS

Fo

S

F

S

o

RF

–

+ +

vo

–

i1

RS

vS(t)+–

v+

v–

iF

iS

10

ACL

S

F

R

R


Amplifiers21



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)


Amplifiers22

Op-Amps – Closed-Loop ModeExample2: 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

05.91050

9500

Amax

minminCL

S

F

R

R

05.11950

10500

Amin

maxmaxCL

S

F

R

R

NB: nominal gain


Amplifiers23

Op-Amps – Closed-Loop ModeExample2: 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

%5.1010

11.0510100

A

AA100

:Error % Min

nomCL

maxCLnomCL


Amplifiers24


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


Amplifiers25



–

+ +

vo

–

RF

RS1

vS1(t)+–

v+

v– iF

i1

RS2

vS2(t)+–

i2

RSN

vSN(t) +–

iN

Node a

N , 2, 1, nRv

iSn

nSn

FN iiii 21

:a deNoat KCL

F

oF R

vi

NB: v– = v+ = 0


Amplifiers26



–

+ +

vo

–

RF

RS1

vS1(t)+–

v+

v– iF

i1

RS2

vS2(t)+–

i2

RSN

vSN(t) +–

iN

Node a

N

nsn

sn

Fo

F

oN

n sn

sn

vR

Rv

Rv

Rv

1

1


Amplifiers27


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

–

+ +

vo

–

i1

RF

RvS(t)

+–

v+

v–

iFRS

iS

i1


Amplifiers28



–

+ +

vo

–

i1

RF

RvS(t)

+–

v+

v–

iFRS

iS

i1

S

SS R

vi

FS

FS

ii

iii

0

:a deNoat KCL

1

F

oF R

vvi

01 i

Node a


Amplifiers29



–

+ +

vo

–

i1

RF

RvS(t)

+–

v+

v–

iFRS

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


Amplifiers30



–

+ +

vo

–

i1

RF

RvS(t)

+–

v+

v–

iFRS

iS

i1

Node a

S

F

S

o

R

R

vv

1

A

:Gain Loop-Closed

CL

NB: always positive and greater than or equal to 1


Amplifiers31


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

–

+ +

vo

–

i1

vS(t)+–

v+

v–

i1


Amplifiers32



svv

–

+ +

vo

–

i1

vS(t)+–

v+

v–

i1

NB: an ideal op-amp with negative feedback has the property

vv

ovv

So vv


Amplifiers33



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


Amplifiers34



–

+

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

ECEN 301Discussion #17 – Operational Amplifiers1 DateDayClass No. TitleChaptersHW Due date Lab Due...

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