Basic Inverting Circuit vi = - vo/A ≅ 0

Ch(2) Signal Processing Circuits

Feedback is widely used in electronic circuits to improve their performance

Basic Inverting Circuit

V₁ applied to F the inverting terminal noninverting terminal F grounded

V₁ F applied in series with F R₁ V_o F feedback through R_F In an OP amp gain

A Û R_i F very very large v_o F limited to F 10 V or so

Then

v = - v /A ≅ 0

Ch(2) Signal Processing Circuits

i_i =

v

_i

/

^Ri

≅ 0

For an ideal amplifier. Closely approximated by a practical op amp,

R_i = ∞ Û R_o = 0 Û A = ∞ , V_i = 0 Û i_i = 0 The sum of the current into node a F Fig

This relation describes an inverting amplifier circuit.

conclusions

1 1

1 1 1

1

1

0

R A R

v or v

R v v R

R and V R

i V

i

_o ^{F o} _F ^F

F o

F

= + = = − = = −

+

V₁

Ch(2) Signal Processing Circuits

For an ideal amplifier in the inverting circuit v_i = 0 Û i₁ = v₁ / R₁ F independent of R_F ,

the input is isolated from the output R_iF = v₁ / i₁ = R₁

The simple circuit model for the inverting amplifier can be design as shown in Fig

For an ideal amplifier with infinite gain or practical op amp with very high gain

A_F F determined by F R₁ Û R_F An easy way to design an amplifier

Ch(2) Signal Processing Circuits

Summing Circuit

For any circuit F modified to permit multiple input, the operational amplifier F perform addition

ﺐﺳﺎﻨﻣ

Ch(2) Signal Processing Circuits

Several voltages through several resistances F input current.

In the practical case

v_i = 0 Û i_i =0

In a circuit model

the sum of i_i = i_F

I = i

₁

+ i

₂

+ ... + i

_n

= - i

F

Hence

Or

^F

o n

n

R v R

v R

v R

v + + ⋅ ⋅ ⋅ + = −

2 2 1

1

F n

F F

F

o

v iR

R v R

R v R

R

v R   =

 

+

⋅

⋅

⋅ + +

−

=

_{1 2}

Ch(2) Signal Processing Circuits

Basic Noninverting Circuit

The behavior of the basic amplifier is modified by the circuit connected as shown in Fig.

v₁ applied to noninverting F + terminal

fraction of v_o F The feedback F - terminal

the gain of the noninverting amplifier circuit

A_F F positive and equal or greater than unity.

o F a

a i

a i

i

v

R R

v R then v

v v

v i

v = = ∴ = + = = +

1 1

1

,

, 0 ,

0

1 1

1 R

R R

v

A_F = v^o = + ^F

Ch(2) Signal Processing Circuits

Home work P.P (3-7)