710 Chapter 20

ating conditions of the active devices. Negative feed-
back loops lose control under clipping conditions and
recovery from such conditions may be poorer with
negative feedback than without it.

20.2.3 Operational Amplifiers

Operational amplifiers derive the name as a result of
their first employment in analog computing systems. In
this role, with suitable feedback, they were employed to
accomplish the mathematical operations of addition,
subtraction, integration, and differentiation. In their
current form of integrated circuits, operational ampli-
fiers have become the fundamental building blocks of
electronic analog circuits with notable uses in power
supply regulation, voltage and current amplification, and
active filters, as well as other forms of signal processors.

Operational amplifiers are dc-coupled voltage ampli-

fiers possessing, under open loop conditions, very high

gain, wide bandwidth, high input impedance, low

output impedance, balanced or difference inputs accom-

panied usually by a single-ended output, and provisions

for accomplishing a dc voltage balance at the output.

Fig. 20-11 displays the configurations commonly

employed for operational amplifiers where signal inver-

sion (polarity change) is required or desirable. In each

instance the open loop transfer function, A, is negative

and real at low frequencies.

In Fig. 20-11A through 20-11D expressions are

given for the respective closed loop transfer functions

Ac. These expressions are valid without correction

provided that the input impedance of the operational

amplifier under open loop conditions is much larger

than the impedances used in structuring the loop and

that the output impedance of the operational amplifier

Figure 20-11. Inverting operational amplifier circuits.

++

+

+

+

+

+

+

+

+ + +

• 
  
  
  
  • 
    
    
    
    • 
      
      
      
      • 
        
        
        
        • 
          
        
        
        
        
      
      
      
      
    
    
    
    
  
  
  
  


• 
  


• 
  


• 
  
  
  
  • 
    

    ––

    
    
  
  
  
  

Z 2

R 1

R 2

R 1

R 1

R 2

R 2

Z 1

Z 2

Z 1

Z 1

Z 2

R 1 R 2 R 3

R

V 1

V 1

V 1

V 1

V 1

V 0

V 0

V 0

V 0

V 0

A

A

A

A

A

A. Unbalanced input. B. Balanced input.

C. Unbalanced but more versatile than A. D. Balanced but more versatile than B.

E. Combining amplifier.

V 0

V 1

V 0

V 1

R 2

R 1

V 0

V 1

V 0

V 1

Z 2

Z 1

V 1

R 1

V 2

R 2

V 3

R 3

V 0

V 1

V 0

V 1

V 0

V 1

V 0

V 1

R 2

R 1

• Z 2
  Z 1

R 2

R 1 + R 2

()A –R 1

A' =

A' = A' =

A' =

R 2

R 1 + R 2

A –

()R 1

Z 2

Z 1 + Z 2

A –

()Z 1

Z 2

Z 1 + Z 2

()A –Z 1

=–

=

• =

=

=

=

=–R[ (^) ]

• 
  

RIN = R 1

ROUT = 0

ZIN ¾ Z 1

ZOUT =¾ 0

RIN = 2R 1

ROUT = 0

ZIN = 2Z 1

ROUT = 0

V 2 V 3

=

=