Operational Amplifiers (Op Amps)

Discussion D3.1

Operational Amplifiers (Op Amps)

• Ideal Op Amp

• Non-inverting Amplifier

• Unity-Gain Buffer

• Inverting Amplifier

• Differential Amplifier

• Current-to-Voltage Converter

• Non-ideal Op Amp

Ideal Op Amp

1) 0 vv A v v

The open-loop gain, Av, is very large, approaching infinity.

2) 0i i The current into the inputs are zero.

+

-

i

ov

v

vi

DDV

SSV

0SS DDV v V

Ideal Op Amp with Negative Feedback+

-ov

v

v

Network

Golden Rules of Op Amps:

1. The output attempts to do whatever is necessary to make the voltage difference between the inputs zero.

2. The inputs draw no current.

Operational Amplifiers (Op Amps)

• Ideal Op Amp

• Non-inverting Amplifier

• Unity-Gain Buffer

• Inverting Amplifier

• Differential Amplifier

• Current-to-Voltage Converter

• Non-ideal Op Amp

Non-inverting Amplifier

+

-

1R2R

iv ovv

v oF

i

vA

v

2

1

1oF

i

v RA

v R

1

1 2i o

Rv v v v

R R

Closed-loop voltage gain

Operational Amplifiers (Op Amps)

• Ideal Op Amp

• Non-inverting Amplifier

• Unity-Gain Buffer

• Inverting Amplifier

• Differential Amplifier

• Current-to-Voltage Converter

• Non-ideal Op Amp

Unity-Gain Buffer

+

-ov

v

viv

oF

i

vA

v

1oF

i

vA

v

i ov v v v

Closed-loop voltage gain

Used as a "line driver" that transforms a high input impedance (resistance) to a low output impedance. Can provide substantial current gain.

Operational Amplifiers (Op Amps)

• Ideal Op Amp

• Non-inverting Amplifier

• Unity-Gain Buffer

• Inverting Amplifier

• Differential Amplifier

• Current-to-Voltage Converter

• Non-ideal Op Amp

Inverting Amplifier

0v v

1 1

0i ii

v vi

R R

Current into op amp is zero

+

-

1R

2R

iv ovv

vii ii

0 0

2 2

0i

v vi

R R

2

1

oF

i

v RA

v R

0

1 2

iv v

R R

Operational Amplifiers (Op Amps)

• Ideal Op Amp

• Non-inverting Amplifier

• Unity-Gain Buffer

• Inverting Amplifier

• Differential Amplifier

• Current-to-Voltage Converter

• Non-ideal Op Amp

Differential Amplifier

v v

11

1

v vi

R

Current into op amp is zero

01

2

v vi

R

+

-1R

2R

1vovv

v1i

1i

2v1R

2R

22

1 2

Rv v

R R

01

1 2

v vv v

R R

2 21 2 2 0

1 2 1 2

1 2

R Rv v v v

R R R R

R R

Differential Amplifier

+

-1R

2R

1vovv

v1i

1i

2v1R

2R

2 21 2 2 0

1 2 1 2

1 2

R Rv v v v

R R R R

R R

2

2 2 20 1 2 2

1 1 2 1 1 2

R R Rv v v v

R R R R R R

2 2 20 1 2

1 1 2 1

1R R R

v v vR R R R

20 2 1

1

Rv v v

R

Operational Amplifiers (Op Amps)

• Ideal Op Amp

• Non-inverting Amplifier

• Unity-Gain Buffer

• Inverting Amplifier

• Differential Amplifier

• Current-to-Voltage Converter

• Non-ideal Op Amp

Current-to-Voltage Converter

i fi i

0v v

00 f Fv i R

0 i Fv i R

0Transresistance i Fv i R

+

-ov

v

vii

FR fi

Photodiode Circuit25 A per milliwatt of incident radiationii

650 25 10 1.25mAii

Assume 3.2kFR

3 30 1.25 10 3.2 10 4Vi Fv i R

+

-ov

v

vii

FR fi

h At 50 mW

Operational Amplifiers (Op Amps)

• Ideal Op Amp

• Non-inverting Amplifier

• Unity-Gain Buffer

• Inverting Amplifier

• Differential Amplifier

• Current-to-Voltage Converter

• Non-ideal Op Amp

Non-ideal Op Amp• Output voltage is limited by supply voltage(s)• Finite gain (~105)• Limited frequency response• Finite input resistance (not infinite)• Finite output resistance (not zero)• Finite slew rate• Input bias currents• Input bias current offset• Input offset voltage• Finite common mode rejection ratio (CMRR)

0slew rate ( ) MAXdv t dt