Lecture 6-2 Electrical Systems II

Lecture 6-2

Electrical Systems II

Operational Amplifiers

Golden Rules of OP Amp

e1

e2

eo

0

K (

2 1

)

e  e  e

5 6

K 10 ~ 10

K  

i)

ii) for ac 1 MHz ~ 50MHz iii) Ideal CP amps

-

- no current flow into the input terminals

- the output voltage is not affected by the load connected to the output terminal

for dc signals and ac of less than 10 Hz frequency.

K  1

Operational Amplifiers

e

o

e

i

R2

i

1

R1

i

2

e _



1 2

1 2

i) e

ⁱ

e e e

^o

i i

R R

 

 

 

1 2

1 2

i i)

_op

0, , e

ⁱ

e e e

^o

i i i

R R

 

 

  

2

1 2 1

(0 ), 1, 0

o

i o

o i

since e K e K K e

e e R

e e

R R R

 

      

    

iii)

Inverting Amplifier

2 1

G R

  R

e

i

e

0 R2

R1

e



2 1

o i i

e e e

i R R

  

2 1

o

1

i

e R e

R

 

    

 

Non-inverting Amplifier

( )

e   e

i

 K   i

2 1

1 R

G R

 

   

 

e

i

e

0

i

3

i

2

R

2



 C

i

1

1 e

R ^_

1 2 3

0,

e   i   i i

1

1 i

, i e

 R 1

₂

( )

c o

c o o

dv de

dt c i dt

v e e e

 

      

    

3

2 2

o o

e e e

i R R

    

ex)

2 1

1 1

o

o i

de e e

dt CR CR

   

1 2 2

1 1

i c o

o o

e dv de

C e C e

R dt R dt R

    

Example of Operational Amplifier Circuit

Laplace Transform :

2 1

1 1

( ) ( )

o i

E s s E s

CR CR

 

  

 

 

Step input response :

1 1 0

( ) , ( )

0 0

i i

E s e t t

t s

 

    

2

1 2

2 2

1 2 1 2

( ) 1 ( )

1

1 1 1 1

1 (1/ )

o i

E s R E s

R R Cs

R R

R R Cs s R s s R C

  



 

           



^{( 1/ 2 )}



2 1

( ) 1

^{R C t}

o

e t R e

R

  



2

1 1 2

2

( ) 1 1 1

. ( ) 1 1

o i

E s R

T F E s CR R R Cs

s CR

      

 

T R C2 o( )

e t

2 1

R

R

t

Examples of Operational Amplifiers

E₀ E_i(s)

Z₁(s)

Z₂(s) I(s)

- +

I(s)

E₀(s) +

-

( )

2

( ) E s

o

  Z s

Examples of Complex Impedance

1 2

( ) ( ) ( ), ( ) ( ) ( )

i o

E s  Z s I s E s  Z s I s

R1 R2

C

i

i

( )

e s e s

_o

( )

Examples of Complex Impedance

ex)

1

( )

1

Z s  R

2 2

2 2

( ) 1

1 1

Z s R

R C s Cs R

 

 

2 2

1 1 2

( ) ( ) 1

( ) ( ) 1

o i

E s Z s R

E s   Z s   R R C s

2



( ) ( ) 1 ( )

I s Cs E s E s

   R

Other Examples

Differentiator/High Pass Filter Integrator/Low Pass Filter

Other Examples

Summing Amplifier Instrumentation Amplifier

End of Lecture 6-2