• What is an Op Amp?

• Ideal Op Amps

• Applications

• Examples

Lecture 9. Op Amps I

1

2

What is an Op Amp?

• Op Amp is short for operational amplifier.• An operational amplifier is modeled as a voltage

controlled voltage source.• An operational amplifier has a very high input impedance

and a very high gain.• It has usually differential inputs and a single output.

3

Use of Op Amps

• Op amps can be configured in many different ways using resistors and other components.

• Amplifiers provide gains in voltage or current.• Op amps can convert current to voltage.• Op amps can provide a buffer between two circuits.• Op amps can be used to implement integrators and

differentiators.• Lowpass and bandpass filters.

4

Applications of Op Amps

• Amplifiers provide gains in voltage or current.• Op amps can convert current to voltage.• Op amps can provide a buffer between two circuits.• Op amps can be used to implement integrators and

differentiators.

5

The Op Amp Symbol

+

-

Non-inverting input

Inverting input

Ground

High Supply

Low Supply

Output

6

The Op Amp Model – Voltage Dependent Source

+

-Inverting input

Non-inverting input

Rin

v+

v-

+

-A(v+ -v- )

vo

7

Typical Op Amp

• The input resistance Rin is very large (practically infinite).

• The voltage gain A is very large (practically infinite).

+

-Inverting input

Non-inverting input

Rin

v+

v-

+

-A(v+ -v- )

vo

8

“Ideal” Op Amp

• The input resistance is infinite.• The gain is infinite.• The op amp is in a negative feedback configuration. • Infinite input resistance means the current into the

inverting input is zero:

i- = 0

• Infinite gain means the difference between v+ and v- is zero:

v+ - v- = 0

9

The Basic Inverting Amplifier

-

+Vin

+

-

+

-Vout

R1

R2

10

Solving the Amplifier Circuit

Nodal Analysis:

i1 + i2 + i-=0

-R1

R2

i1 i-

i2

11

0i

111 R

v

R

vvi inin

222 R

v

R

vvi outout

Solving the Amplifier Circuit

021

R

v

R

v outini1 + i2 + i-=0

12

Amplifier gain:

inout vR

Rv

2

1

1

2

R

R

v

vG

in

out

Solve for vout

Solving the Amplifier Circuit

13

How to solve Op Amp Circuit?

• Nodal analysis or other methods to solve for the output voltage in terms of the input(s).

• Keep in mind that the ideal op amp model leads to the following conditions:

i- = 0

v+ = v-

14

Where is the Feedback?

-

+Vin

+

-

+

-Vout

R1

R2

15

The Non-Inverting Amplifier

+

-

vin

+

-

+

-

vout

R1

R2

16

Nodal Analysis: Finding the nodes

+

-

vin

+

-

+

-

vout

R1

R2

i-

i1 i2

17

0i

111 R

v

R

vi in

222 R

vv

R

vvi inoutout

Nodal Analysis: Apply KCL

18

Nodal Analysis: Solve for Vout

021

R

vv

R

v inoutin

1

21R

Rvv inout

19

A Mixer Circuit

-

+v2

+

-

+

-vout

R2

RfR1

v1

+

-

20

Nodal Analysis: Finding the nodes

-

+v2

+

-

+

-vout

R2

RfR1

v1

+

-

i1

i2

if

i-

21

Nodal Analysis: Apply KCL

1

1

1

11 R

v

R

vvi

2

2

2

22 R

v

R

vvi

0i

f

out

f

outf R

v

R

vvi

22

Nodal Analysis: Solve for Vout

02

2

1

1 f

out

R

v

R

v

R

v

22

11

vR

Rv

R

Rv ff

out

23

Class Examples

• Seeing atoms with STM

1 nA

24

Class Examples

• Solar cell

1 nA

A circuit constructed for measuring current from the solar cell.  The first Op Amp is the current-to-voltage converter and the second op Amp inverts the voltage.