0195136047.pdf

224 ANALOG BUILDING BLOCKS AND OPERATIONAL AMPLIFIERS

is utilized in order to predict the performance of electronic systems through the use of equations. In

this chapter first models are developed for the amplifier block, then an ideal operational amplifier

is presented, and later applications of operational amplifiers are discussed.

5.1 THE AMPLIFIER BLOCK

An amplifier can be modeled as a two-port device, that is, a box with two pairs of terminals

designated as input and output, as shown in Figure 5.1.1 (a). The circuit model of the amplifier

block shown in Figure 5.1.1 (b) is developed on the basis of the following considerations:

1. Since, for most amplifiers, the input current is proportional to the input voltage, the input
   terminals in the model are connected by a resistanceRi, known as theinput resistanceof
   the amplifier.


2. Since an amplifier delivers electric power (to a speaker, for example), the output current
   can be represented by its Thévenin-source model. The Thévenin resistanceRois known as
   theoutput resistanceand the Thévenin voltage is adependent voltage source Avin, where
   Ais called theopen-circuit voltage amplification.

Thus, the amplifier block is a linear circuit block in which the output is proportional to the

input, and the amplifier is characterized by the three constantsRi,Ro,andA. The input and output

resistances may be generalized to input and output impedances in ac systems. The advantage of the

model is that all internal complexities are summarized in the three constants, thereby simplifying

the analysis of electric systems with amplifiers. Power-supply connections are usually not shown

in circuit diagrams since they would only clutter up the drawing. It is assumed, however, that

there are always connections to some power source in order to bring in the power necessary to

run the amplifier (as will be illustrated in Example 5.1.4).

EXAMPLE 5.1.1

Let the amplifier block be connected to a current source at the input terminals, as shown in Figure

E5.1.1(a), and to a load resistanceRLat its output terminals. Findvout.

+

−

+

−

Input Output

(a)

(b)

Ri

Ro

Avin

vin vout

Is Rs vin vout RL

+

−

Rs RL

+

−

+

−

Is

Figure E5.1.1