Microelectronic Circuits I Ch 2: Operational Amplifiers

Microelectronic Circuits I

Ch 2: Operational Amplifiers

2.1 The Ideal OP Amp

2.2 Inverting Configuration

2.3 Noninverting Configuration

2-2

Operational-Amplifier (Op-Amp) Terminals

IC op amp require two dc power supplies

Reference grounding point is just the common terminal of the two power supplies

2 input terminals output terminal

OP-Amp : Ideal circuit building block

Terminal characteristics & application What is inside the op-amp package?

Ideal Op Amp

•R_in = ∞ à i₁ = i₂ = 0

•R_out = 0 (v₃ is ideal voltage source)

•v_O = A (v₂-v₁) (proportional to differential input)

•v_O = 0 when v₁ = v₂ (common-mode rejection)

•A: differential open-loop gain (~∞)

•Infinite input impedance

•Zero output impedance

•Zero common mode gain

•Infinite open-loop gain A

•Infinite bandwidth

v₃ = A (v₂-v₁)

2-4

2 2

2 1

Id Icm

Id Icm

v v v

v v v

+

=

-

=

Differential and Common-mode Signals

Differential input signal v_Id : difference between the two input signals v₁ and v₂

1

2 v

v v_Id = -

Common-mode input signal v_Icm : average of the two input signals v₁ and v₂ )

2( 1

1

2 v

v v_Icm = +

Representation of the signal sources v₁ and v₂ in terms of their differential and common-mode components

Inverting Closed-Loop Configuration

passive components in a feedback à closed loop

Closed loop gain

I O

v G º v

•Terminal 1 is a virtual ground - having zero voltage but not physically connected to ground because v₂=0, then v₁=0

1

0

2

- = »

A v v

v

v »

v

•Virtual short circuit means that whatever voltage is at 2 will appear at 1 because of A=∞ : two input terminals “tracks each other in potential”

R₂ : output terminal back to inverting or negative input terminal à negative feedback

2-6

Inverting Closed-Loop Configuration

1 2

2 1 2

1 1

1 1

1 1

0

R R v

v

R R R v

i v v

R v R

v i v

I O

I O

I I

-

=

-

= -

= - »

=

Closed-loop Open-loop

A -R₂ / R₁

Poor Good

Gain Accuracy

By virtual ground, v₂ = 0 & v₁ = 0

• Closed loop gain is smaller but stable & predictable

• Trade gain for accuracy

Closed loop gain depends on external components with appropriate accuracy and is independent of the op-amp gain

Phase shifted 180’ with respect to input signal Gain is negative

Effect of Finite Open-Loop Gain (A≠∞)

1 1

1

) (

R A v v R

A v

i v^{I O I} + ^O

- =

= -

Since input impedance is ¥

2 2

1

2 1 1 2 1 1 1 2

1

) (

) (

R R A v v A v

R A i

v

R i v R i R i v v

i i

O I O

O I O

- + -

=

- -

=

-

= -

-

=

=

A R R

R R v

G v

I O

) 1

(

1 _{2 1}

1 2

+ +

= - º

For virtual ground assumption, A is ¥

1 2

R G = - R

or R A R <<

+

1

1 2

\

2-8

Input & output resistances of closed loop inverting amp.

+

-

+ -

R1

R_i = vI

0

O = R

vI

R R

1

- 2 -

I +

v

R1

R2

A +

v0 - 1

2

3

0

/

1

=

=

= º

o

I I I

i

R

R R v

v i

R v i

Equivalent circuit

(relatively low)

By the infinite open-loop gain, the input resistance of the inverter is

The reduced input impedance causes the loss of input signal strength

Ex 2.2 Modified inverting configuration for higher R

÷ ÷ ø ö ç ç

è

æ + + -

=

=

3 4 2

4 1

2

1

R R R

R R

R v

G v

I O

For G = 100 and R_i = 1 MW

R₁ = 1 MW, R₂ = R₄ = 1 MW, R₃ = 10.2 kW

Compared to R₁ = 1 MW, and R₂ = 100 MW for the conventional case

2-10

Weighted Summer

÷÷ ø ö çç

è

æ + + +

-

=

-

= -

=

+ + +

=

=

=

=

n n f f

f O

f f

O

n n

n

R v v R

R v R

R v R

iR iR

v

i i

i R i

i v R

i v R i v

...

0

...

..., , ,

2 2 1

1

2 1 1

2 2 2

1 1 1

Weighted Summer

÷÷ø ö ççè - æ

÷÷ ø ö çç è - æ

÷÷ ø ö çç è æ

÷÷ø ö ççè + æ

÷÷ ø ö çç è æ

÷÷ø ö ççè

= æ

4 4 3

3 2

2 1

1 R

v R R

v R R

R R

v R R

R R

v R

v ^{c c}

b c a

b c a

O

A weighted summer capable of implementing summing coefficients of both signs

2-12

Non-inverting Configuration

1 2

2 1 1

2

1

0

R R v

v

R R v v

v

A A for

v v v

I O

I I

O

O

+

=

÷÷ø ö ççè +æ

=

¥

=

=

= -

Voltage divider & virtual short

Degenerative feedback

v_I↑, v_Id (=v₂ -v₁) ↑, v_O ↑ à a fraction of increase in v_O is fed back to v₁ through R₁

& R₂ voltage divider à counter act the increase in v_Id, driving v_Id back to zero

÷÷ø ö ççè

æ

= +

2 1

1

R R

v R v_{I O}

Gain is positive

Non-inverting Configuration

The output of non-inverting amplifier is taken at the

terminal of the ideal voltage source A(v₂-v₁) è R_o = 0

l Equivalent circuit model

l Input/ output resistance of non- inverting amplifier

v

0

O

= R

vI

R R

÷÷ø ö ççè

æ +

1

1 2

¥

i

= R

-

+

-

1 2

3

2-14

+ -

+ -

R₁

R₂

v₁

v₂ -

+ v_I

A(v₂ –v₁ )

v_O

0 0

) (

) (

2 1

1 1 1 1 2

+ = - -

= - -

= -

= -

O O

I

O I

O I

O

R v R

R A

v v

A v v v

v v

v A

v v

v A

For finite open loop gain A

A R

R

R R

v G v

I O

/ ) / 1

( 1

/ 1

1 2

1 2

+ +

= +

=

\

Non-inverting Configuration

1

1 2

R G = + R R A

R <<

+

1

1 2

1 2

3

The Voltage Follower, unity-gain amplifier (Buffer, Impedance Transformer)

Non-inverting configuration

R₂=0, R₁= ¥

Voltage follower : Output follows input

Ideal voltage follower

R_in = ¥ R_out = 0 v_O = v_I

Ideal voltage follower

R_in = ¥ R_out = 0 v_O = v_I