ECEN3713 Final
Exam 3 May 2005
1) A portion of a periodic waveform, x(t), is shown.
a) [5] What is the fundamental frequency for this waveform? [Answer: pi/3 radians/second]
b) [5] What is the DC voltage of this waveform? [Vdc = 2 volts, by inspection]
c) [5] Suppose y(t) = x(t) - (DC voltage of x(t)). Explain any
differences and similarities that you would expect to find when
comparing the Fourier Series of x(t) with the Fourier Series of
y(t). [Fourier Series of
y(t) = Fourier Series of x(t) - DC term of x(t). y(t)'s DC
component will be zero while x(t)'s will not. Otherwise, the
Fourier Series are identical.]
d) [25] Fourier Series analysis defines the amplitudes and phase shifts
required of the fundamental and its harmonics such that, when added
together, the result is the waveform x(t) shown. If the
fundamental frequency is expressed as a cosine, derive the amplitude
required of the fundamental frequency. [(2 - 2cos(2pi/3))0.5/pi]
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2a) [20] Find the Laplace Transform of the waveform, x(t), which is
zero at all times not shown. [X(s) = (3 -2e-2s + e-4s - 2e-6s)/s]
2b) [20] Let y(t) equal the first derivative of x(t), i.e. y(t) = d
x(t)/dt. Find Y(s). [Y(s)
= (3 -2e-2s + e-4s - 2e-6s)]
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3) The circuit to the right includes a simplified model of a Bipolar
Junction Transistor (the resistor and dependent current source between
the dots) with a current gain of 50. iin(t) is a unit
step function which is input at time t = 0.
[35] Find an equation for vout(t). [50u(t)]
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4) In the circuit shown, when vin(t) is a delta
function at time t = 0, the Laplace Transform of the input current was
found in Quiz 4A to be Iin(s) = 4/3 - 4s/(3s2 + 6s + 3).
[35] Find an expression for iin(t). [4/3(delta_function(t) + te-t - e-t)]
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