Operational Amplifier

Ideal OP Amp

1. iin=0, no current flow into op amp.

2. V+=V-

• Typically one end of op amp is connected to ground, therefore, V+=V-= 0V, virtual ground. Often V+ is connected to ground to avoid stability problem.

Circuit model

Two golden rules to perform calculations on op amps with negative feedback:

Applications: building block for analog systems

• Amplifiers• Adders and Substractors• Integrators & Differentiators• Clock generators• Filters• Digital-to-analog converters

Using op-amps

No flexibility

Let’s build a circuit……noninverting amplifier

When A is very large

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

Gain: • determined by resistance ratio• insensitive to A, temperature, fab variation

Why did this happen? Negative feedback

e.g. vIN=5V

Suppose I perturb the circuit (e.g. force v0 momentarily to 12V somehowStable point is when v+v-

Key: negative feedback portion of output fed to –ve input.

e.g. Car antilock brakes small corrections

How to control a high-strung device

• Antilock brakes

More op amp insights:

• Observe, under negative feedback,

• We also know • i+ 0• i- 0

Yield an easier analysis method (under negative feedback)

Insightful analysis method: under negative feedback

Voltage follower

has minimum effects on previous and next circuit.

Why is this circuit useful?

Inverting Amplifier

0 inFs iii

F

out

S

S

Fs

R

v

R

v

ii

00

SS

Fout v

R

Rv

S

F

S

out

R

R

v

vGain

Feedback resistor, always to negative input

Summing Amplifier: Add Circuit

FN iiii .....21

F

out

SN

SN

S

S

S

S

R

v

R

v

R

v

R

v ...

2

2

1

1

SN

SN

FS

S

FS

S

Fout v

R

Rv

R

Rv

R

Rv ...2

21

1

SNSSS

Fout vvv

R

Rv ...21

If RS1=RS2=…=RSN=RS

Non-innverting Amplifier

S

in

vvv

i

vv

0 since

F

out

S

Fs

R

vv

R

v

ii

0

SS

F

S

Fout

vR

R

vR

Rv

1

1 _

S

F

S

out

R

R

v

vGain

Feedback resistor, always to negative input

Differential Amplifier: Substractor

221

2 vRR

Rv

vv

21

1

21 0

R

vv

R

vv

ii

out

121

2 vvR

Rvout

Very useful if both signals are corrupted with noise: Electrocardiogram (EKG)