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2500
I(x )
0 0.0004 0.2 0.2 x 0 (b)
Now let the slit be replaced by two slits each 0.1 mm in width, separated by 1 mm
(centertocenter) and centered on the optical axis. Plot the intensity of light at the viewing
screen if the other parameters are the same as in part (a).
Similar to (a)
I(x )
0 1.6e05 1 x0 1 42. In Figure 421 is a circuit diagram of a halfwave rectifier followed by a capacitor to
smooth the response voltage. Model the diode as ideal and let the excitation be a cosine
at 60 Hz with an amplitude of 120 2 volts. Let the RC time constant be 0.1 seconds.
Then the response voltage will look as illustrated in Figure E422 . Find and plot the
magnitude of the CTFT of the response voltage. +
v i (t) +
R C  vo (t)
 Figure E421 A halfwave rectifier with a capacitive smoothing filter Solutions 635 M. J. Roberts  8/16/04 175 vo(t)
vi (t)
0.05 t 175 Figure E422 Excitation and response voltages
The response voltage has two parts, the exponential decay time and the cosinusoidal charging
time. The dividing time, td , between these two parts is set by the intersection of the cosine
and the exponential decay. The peak of the cosine is 120 2 . The decay time constant is 0.1
seconds. Therefore the dividing time is the solution of
120 2 cos(120πtd ) = 120 2e − td
0.1 or
cos(120πtd ) = e − td
0.1 This is a transcendental equation best solved numerically. This equation is simple enough
that a trialanderror method converges very quickly to a solution. That solution is
td = 15.23906 ms .
Therefore the description of the response voltage over one period is − 0t.1
, 0 < t < 15.23906 ms
e
v o1 ( t) = 120 2 2
cos(120πt) , 15.23906 < t < 16 ms
3 or − 0t.1 t − 0.00761953 t − 0.01595286 v o1 ( t) = 120 2 e rect + cos(120πt) rect 0.01523906 0.001427607 The CTFT of the response is the CTFT of this voltage convolved with a comb to make it
periodically repeat. The CTFT of one period is 0.01523906 − t − j 2πft
dt ∫ e 0.1e 0
Vo1 ( f ) = 120 2 1
+ [δ ( f...
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This note was uploaded on 06/19/2013 for the course ENSC 380 taught by Professor Atousa during the Spring '09 term at Simon Fraser.
 Spring '09
 ATOUSA

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