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where λ is the wavelength of radiation and d is the spacing between two con-
secutive antennae. Draw the polar plot of the total intensity as function of the
angle θ for a spacing d = λ/2 for different values of N (2, 4, 6, and 10).
Pb. 6.49 Do the results of Pb. 6.48 suggest to you a strategy for designing a
multi-antenna system with sharp directivity? Can you think of a method,
short of moving the antennae around, that permits this array to sweep a
range of angles with maximum directivity?

Pb. 6.50 The following program simulates a 25-element array-swept radar
beam.

th=0:0.01:pi;
t=-0.5*sqrt(3):0.05*sqrt(3):0.5*sqrt(3);
N=25;
M=moviein(21);
for m=1:21;
I=(1/N^2)*(sin(N*((pi/4)*cos(th)+(pi/4)*t(m)))...
^2)./((sin((pi/4)*cos(th)+(pi/4)*t(m))).^2);
polar(th,I);
M(:,m)=getframe;
end
movie(M,10)

a. Determine the range of the sweeping angle.
b. Can you think of an electronic method for implementing this task?

6.8 Solving ac Circuits with Phasors: The Impedance Method
In Section 6.5, we examined the conventional technique for solving some sim-
ple ac circuits problems. We suggested that using phasors may speed up the
determination of the solution. This is the subject of this chapter section.
We will treat, using this technique, the simple RLC circuit already solved
through other means in order to give you a measure of the simplifications
that can be achieved in circuit analysis through this technique. We then pro-
ceed to use the phasor technique to investigate another circuit configuration:
the infinite LC ladder. The power of the phasor technique will also be put to
use when we, topologically, solve much more difficult circuit problems than
the one-loop category encountered thus far. Essentially, a straightforward

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