0195136047.pdf

1.2 LUMPED-CIRCUIT ELEMENTS 23

v

B

A

RL

RS

vL

iL

iL

−

Source −

+

Load

Figure 1.2.3Power transfer between source and load.Note:RL= 0

implies short circuit;vL=0 andiL=RvSandRL→•implies open

circuit;iL=0 andvL=v.

which leads to the following equation:

(RL+RS)^2 − 2 RL(RL+RS)= 0 (1.2.12)

The solution of Equation (1.2.12) is given by

RL=RS (1.2.13)

That is to say, in order to transfer maximum power to a load, the load resistance must bematched
to the source resistance or, in other words, they should be equal to each other.
A problem related to power transfer is that ofsource loading. Figure 1.2.4(a) illustrates a
practical voltage source (i.e., an ideal voltage source along with a series internal source resistance)
connected to a load resistance; Figure 1.2.4(b) shows a practical current source (i.e., an ideal
current source along with a parallel or shunt internal source resistance) connected to a load
resistance. It follows from Figure 1.2.4(a) that

vL=v−vint=v−iLRS (1.2.14)

wherevintis the internal voltage drop within the source, which depends on the amount of current
drawn by the load. As seen from Equation (1.2.14), the voltage actually seen by the loadvL
is somewhat lower than theopen-circuit voltageof the source. When the load resistanceRLis
infinitely large, the load currentiLgoes to zero, and the load voltagevLis then equal to the
open-circuit voltage of the sourcev. Hence, it is desirable to have as small an internal resistance
as possible in a practical voltage source.
From Figure 1.2.4(b) it follows that
iL=i−iint=i−

vL

RS

(1.2.15)

whereiintis the internal current drawn away from the load because of the presence of the internal
source resistance. Thus the load will receive only part of theshort-circuit currentavailable from
the source. When the load resistanceRLis zero, the load voltagevLgoes to zero, and the load

v

(a)

RL

RS

vL

vint

iL

+−

−

Voltage source −

+

Load

i

(b)

RL

RS

vL

iint

iL

Current source −

+

Load

Figure 1.2.4Source-loading

effects.