Schedule Date Day Class Title Chapters HW Lab Exam No. Due - - PowerPoint PPT Presentation

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…

ECEN 301 Discussion #17 – Operational Amplifiers 2

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

• f 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.

ECEN 301 Discussion #17 – Operational Amplifiers 3

Lecture 17 – Operational Amplifiers

ECEN 301 Discussion #17 – Operational Amplifiers 4

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

Source Amplifier Load

) ( ) ( t Av t v

S L

ECEN 301 Discussion #17 – Operational Amplifiers 5

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

Source Amplifier Load NB: Thévenin equivalent NB: equivalent resistance

vS(t)

+ – RS + vL – RL Rin +

–

Rout Avin + vin –

ECEN 301 Discussion #17 – Operational Amplifiers 6

Ideal Amplifiers

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

L

• ut

L in L

R R R Av v

vS(t)

+ – RS + vL – RL Rin +

–

Rout Avin + vin –

in S in S in

R R R v v

S L

• ut

L in S in L

v R R R R R R A v

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

ECEN 301 Discussion #17 – Operational Amplifiers 7

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 L

• ut

L in L

Av R R R Av v R if

• ut

vS(t)

+ – RS + vL – RL Rin +

–

Rout Avin + vin –

S in S in S in

v R R R v v : R if

in

S L

Av v

NB: it is desirable for an amplifier to have:

• a very large input impedance
• a very small output impedance

ECEN 301 Discussion #17 – Operational Amplifiers 8

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

ECEN 301 Discussion #17 – Operational Amplifiers 9

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 +

– +

+

–

Rout Rin i1 AOLvin + vo – – vin + v– v+ NB: op-amps have near-infinite input resistance (Rin) and very small output resistance (Rout)

) ( v v A v A v

OL in OL

• AOL – open-loop voltage gain

i2

ECEN 301 Discussion #17 – Operational Amplifiers 10

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 +

Ideally i1 = i2 = 0 (since Rin → ∞)

2 1

i i

ECEN 301 Discussion #17 – Operational Amplifiers 11

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)

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

2 1

i i

ECEN 301 Discussion #17 – Operational Amplifiers 12

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

ECEN 301 Discussion #17 – Operational Amplifiers 13

Op-Amps – Closed-Loop Mode

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

S S S

R v v i

– + + 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

F S F S

i i i i i : a de No at KCL

1

F

• F

R v v i

1

i

ECEN 301 Discussion #17 – Operational Amplifiers 14

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

OL

• OL

OL OL

• A

v v v A v A v v A v ) ( ) ( : Model Loop

• Open

From

ECEN 301 Discussion #17 – Operational Amplifiers 15

Op-Amps – Closed-Loop Mode

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

RF

– + + vo – i1

RS

vS(t)

+ –

v+ v– iF iS

OL S F OL S F

• S

S OL

• F

OL

• S

S S S F OL

• F
• S

OL

• S

S F

• S

S F S

A R R A R R v v R A v R A v R v R v R A v R v R A v R v R v v R v v i i 1 / 1 / 1 / /

ECEN 301 Discussion #17 – Operational Amplifiers 16

Op-Amps – Closed-Loop Mode

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

OL S F OL S F

• S

A R R A R R v v 1 / 1 / 1

RF

– + + vo – i1

RS

vS(t)

+ –

v+ v– iF iS

NB: if AOL is very large these terms → 0

S F S

• R

R v v

CL

A : Gain Loop

• Closed

ECEN 301 Discussion #17 – Operational Amplifiers 17

Op-Amps – Closed-Loop Mode

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

OL

• ut

A v v : Model Loop

• Open

From

RF

– + + vo – i1

RS

vS(t)

+ –

v+ v– iF iS

NB: as AOL → ∞ v– → 0

v v AOL As

ECEN 301 Discussion #17 – Operational Amplifiers 18

Op-Amps – Closed-Loop Mode

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

v v i i

2 1

RF

– + + vo – i1

RS

vS(t)

+ –

v+ v– iF iS

NB: two important results for an ideal

• p-amp with negative feedback

i2

ECEN 301 Discussion #17 – Operational Amplifiers 19

Op-Amps – Closed-Loop Mode

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

ECEN 301 Discussion #17 – Operational Amplifiers 20

Op-Amps – Closed-Loop Mode

Example1: determine AOL and vo

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

) cos( 15 . ) cos( 015 . 10 10 A

3 4 CL

t t v R R v R R v v

S S F

• S

F S

• RF

– + + vo – i1

RS

vS(t)

+ –

v+ v– iF iS

10 ACL

S F

R R

ECEN 301 Discussion #17 – Operational Amplifiers 21

Op-Amps – Closed-Loop Mode

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

• 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) Voltage (V) vs(t) vo(t)

ECEN 301 Discussion #17 – Operational Amplifiers 22

Op-Amps – Closed-Loop Mode

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

10 A

nom CL

RF

– + + vo – i1

RS

vS(t)

+ –

v+ v– iF iS

05 . 9 1050 9500 A

max min min CL S F

R R 05 . 11 950 10500 A

min max max CL S F

R R

NB: nominal gain

ECEN 301 Discussion #17 – Operational Amplifiers 23

Op-Amps – Closed-Loop Mode

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

RF

– + + vo – i1

RS

vS(t)

+ –

v+ v– iF iS

% 5 . 9 10 9.05 10 100 A A A 100 : Error % Max

nom CL min CL nom CL

% 5 . 10 10 11.05 10 100 A A A 100 : Error % Min

nom CL max CL nom CL

ECEN 301 Discussion #17 – Operational Amplifiers 24

Op-Amps – Closed-Loop Mode

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

ECEN 301 Discussion #17 – Operational Amplifiers 25

Op-Amps – Closed-Loop Mode

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 Node a

N , 2, 1,  n R v i

Sn n S n

F N

i i i i 

2 1

: a de No at KCL

F

• F

R v i

NB: v– = v+ = 0

ECEN 301 Discussion #17 – Operational Amplifiers 26

Op-Amps – Closed-Loop Mode

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 Node a

N n sn sn F

• F
• N

n sn sn

v R R v R v R v

1 1

ECEN 301 Discussion #17 – Operational Amplifiers 27

Op-Amps – Closed-Loop Mode

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

ECEN 301 Discussion #17 – Operational Amplifiers 28

Op-Amps – Closed-Loop Mode

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

S S S

R v i

F S F S

i i i i i : a de No at KCL

1

F

• F

R v v i

1

i

Node a

ECEN 301 Discussion #17 – Operational Amplifiers 29

Op-Amps – Closed-Loop Mode

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

v v v R i

S

drop) voltage no rough current th no (i.e. : Since

1

S F S

• S

S F S

• S

F

R R v v R v R v v i i 1

Node a

ECEN 301 Discussion #17 – Operational Amplifiers 30

Op-Amps – Closed-Loop Mode

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 Node a

S F S

• R

R v v 1 A : Gain Loop

• Closed

CL

NB: always positive and greater than or equal to 1

ECEN 301 Discussion #17 – Operational Amplifiers 31

Op-Amps – Closed-Loop Mode

Voltage Follower: the voltage on the output of the

• p-amp is equal to the source voltage

– + + vo – i1

vS(t)

+ –

v+ v– i1

ECEN 301 Discussion #17 – Operational Amplifiers 32

Op-Amps – Closed-Loop Mode

Voltage Follower: the voltage on the output of the

• p-amp is equal to the source voltage

s

v v

– + + vo – i1

vS(t)

+ –

v+ v– i1

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

v v

• v

v

S

• v

v

ECEN 301 Discussion #17 – Operational Amplifiers 33

Op-Amps – Closed-Loop Mode

Voltage Follower: the voltage on the output of the

• p-amp is equal to the source voltage

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

ECEN 301 Discussion #17 – Operational Amplifiers 34

Op-Amps – Closed-Loop Mode

Voltage Follower: the voltage on the output of the

• p-amp is equal to the source voltage

– +

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