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using the equivalent representation shown fig

Using the equivalent representation shown fig

V1 +

Op-amp

V o R1�Rf R f

Vi ≈ 0 Rf

(14.9)

Vo =

( )V1 R1

V1 R1 Vo
(a) (b)
Figure 14.16
EXAMPLE 14.4

Solution

R 5 0 0 k�

VoV1
(14.10)

620

Chapter 14

Operational Amplifiers

Figure 14.17

Probably the most used of the op-amp circuits is the summing amplifier circuit shown in Fig. 14.18a. The circuit shows a three-input summing amplifier circuit, which pro-vides a means of algebraically summing (adding) three voltages, each multiplied by a constant-gain factor. Using the equivalent representation shown in Fig. 14.18b, the output voltage can be expressed in terms of the inputs as

R f R f R
Vo � ���RV1 ��RV2 ��RV3�3

Figure 14.18

(a) V1 � �1 V, V2 � �2 V, V3 � �3 V, R1 � 500 k�, R2 � 1 M�, R3 � 1 M�. (b) V1 � �2 V, V2 � �3 V, V3 � �1 V, R1 � 200 k�, R2 � 500 k�, R3 � 1 M�.

EXAMPLE 14.5

621
14.4

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