Linear Models for Operational Amplifiers: Including Dependent Sources, Slides of Electrical Circuit Analysis

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Chp 14-

Op Amp Circuits

Ckts W/ Operational Amplifiers

• OpAmp Utility

1. OpAmps Are Very

Useful Electronic

Components

2. We Have Already

Developed The

Tools To Analyze Practical OpAmp Circuits

3. The Linear Models for OpAmps

Include Dependent Sources

• A PRACTICAL Application of Dependent Srcs

Apex PA HiPwr OpAmp

 Notice OutPut Rating

• 30A @75 V

 PwrOut → 30A•75V

→ 2.25 kW!

OpAmp Symbol & Model

• The Circuit Symbol Is a Version of the Amplifier TRIANGLE

 The Linear Model

: 1 MHz

: 10 10

: 1 50

: 10 10

5 7

5 12

BW

A

R

R O

i

−

Ω − Ω

Ω − Ω

• Typical Values

OUTPUT RESISTANCE

INPUT RESISTANCE

GAIN

OpAmp Power Connections

 BiPolar Power

Supplies

 UniPolar Supply

 For Signal I/O Analysis the Supplies

Need NOT be shown explicitly

• But they MUST physically be there to actually Power the Operational Amplifier

OpAmp Circuit Model

DRIVING CIRCUIT

LOAD OP-AMP

Unity Gain Buffer (FeedBack)

 Controlling Variable = Vin^ = RiI  Solve For Buffer Gain ( I = V in/ R ) → ∞

= (^) O

O O i

s i

out (^) A

R A R

V R

V (^) recall

1

(^1)  Thus The Amplification

→∞⇒ → 1 S

out O (^) V

V

A

Op-Amp BUFFER GAIN LM324 0. LMC6492 0. MAX4240 0. KVL: − Vs + RiI + ROI + AOVin = 0 KVL: -Vout+ RO I + AOVin = 0

FeedBack Loop

The Ideal OpAmp

• The IDEAL Characteristics
  • Ro = 0
  • R (^) i = ∞
  • A = ∞ (open loop gain)
  • BW = ∞
• The Consequences

of Ideality

@ V 3 : V 3 = VS 1 = 12 [ V ]

i + i −

A = ∞ ⇒ v + = v −

Ri = ∞⇒ i + = i − = 0

Ro = 0 ⇒ vo = A ( v (^) + − v −)

Analyzing Ideal OpAmp Ckts

1. Verify the presence of NEGATIVE FeedBack
2. Assume the Summing Point Constraint

Applies in this fashion:

• i+ = i−= 0 (based on R i = ∞)
• v+ − v− = 0 (based on A O = ∞)

3. Use KVL, KCL, Ohm’s Law, and other linear ckt

analysis techniques to determine quantities of interest

Voltage Follower

• The Voltage Follower
  • Also Called Unity Gain Buffer (UGB) from Before

Connection w/o Buffer Buffered Connection

v (^) + = v s

v − = v + v (^) O = v −

vO = v S

 The SOURCE Supplies The Power

 The Source Supplies NO Power (the OpAmp does it)

 Usefulness of UGB

vO = vS − iRs vO = v S

Replace OpAmp w/ Linear Model

• Consider Again the

Inverting OpAmp

Circuit

 Draw the

Linear Model

1. Identify the Op

Amp Nodes

v −

v +

v o

Drawing the OpAmp Linear Model

2. Redraw the circuit

cutting out the

Op Amp

3. Draw components

of linear OpAmp

(on the circuit of

step-2)

v −

v +

v o

v −

v +

v o

R O

− A v (^^ +^ − v − )

R i

NonIdeal Inverting Amp

• Replace the OpAmp with the LINEAR Model - Label Nodes for Tracking

 Draw The Linear Equivalent For Op-amp

 Note the External Component Branches

b - a

b - d

NonIdeal Inverting Amp cont.

• On The LINEAR Model Connect The External Components

 ReDraw Ckt for Increased Clarity

 Now Must Sweat the Details

R 2

ve = v + − v −