**Load-Line Analysis-of EIectrical Circuits**

Future 5.2-6 is a representation of an electrical system with a power supply and a load. The power supply produces the fixed voltage VI and supplies t(f n t i I required by. the load, whose voltage drop is V 2. The current-voltage/relationship for a-specific load is

foud from experiments to be

il = O.16(eO.12112

– 1)

Suppose that the supply resistance is RI = 30 nand the supply voltage is VI = 15 V. To select or design an adequate power supply, we need to determine how much current will be drawn from the power supply when this load is attached. Find’the voltage drop V2 as well.

•** Solution**

Using Kirchhoff’s voltage law, we obtain

The plot of this equation is a straight line caIled the load line. The load line is so named because it shows how the current drawn by the load changes as the load’s voltage changes. To find il and V2,we need to solve equations (5.2-1) and (5.2-2). Because of the

term eO.12v:z. ids not possible to obtain a solution using algebra. However, we can plot the curves corresponding to these equations and find their intersection. The MATLAB script file to do so follows, and Figure 5.2-7 shows the resulting plot.

v_2=[O:0.01:201;

i_ll=.16*(exp(0.12*v_2)-1);

i_12=-(1/30)*v_2+0.5;

plot tv.,z . i_ll,v_2, i_12) ,grid,x label (;v_2 (volts)’)

y label (‘i_l (amperes)’),axis([O 20 0 1))

g text(‘Load Line’),g text (‘Device Curve’)

From the figure we can see that’ the curves intersect at approximately.i I = 0.25 A. V 2 = 7.5 V. For a more accurate answer, change the axis statement to axis ‘([7 8 o . 2 O. 3 1 ) and obtain a new plot.

**Plot of the load line and the device curve for Example **

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