ECEN3713 Exam
#1 15 February 2005
1) The circuit below includes a simplified model of a Bipolar Junction
Transistor (the resistor and dependent current source between the dots)
with a current gain of 50. vin(t) is a unit step
function which is input at time t = 0.
[25] Find an equation for vout(t).
[Answer: vout(t) = -50u(t).]
<<<<<>>>>>
2a) [10] x(t) = 4cos(2π10t); t > 0. Find X(s). [X(s) = 4s/(s2 + (2*π*10)2)]
2b) [15] y(t) = 4cos(2π10t); 0 < t < 0.2. Find Y(s). [Y(s) = X(s)(1 - e-0.2s)]
<<<<<>>>>>
3) Given the circuit shown,
[10] Find the voltage transfer function
H(s) = Vout(s)/Vin(s). [H(s) = (R + s)/(Rs2 + s + R)]
[10] If vin(t) = u(t), what values for R will make the
circuit oscillate? [R
> 1/2 ohm]
[5] If vin(t) = u(t) and R = 0, sketch the current flow into
the capacitor necessary to insure vout(t) = vin(t).
How much power is required? Explain. [You should sketch iin(t) as a delta function at t = 0
with value 1/C. Since the work necessary is finite and the time
interval in which the work must be done is zero (all work must occur at
a single point in time), the power required is infinite.
<<<<<>>>>>
4) A 3 volt peak unit step function is input to the system shown at
time t = 0.
[10] Find the poles associated with the output Y(s). [One pole at s = -0.1054.
Technically there's a second pole at s = 0 associated with the input.]
[15] Find the steady state output voltage of y(t) after the transient
settles down. [The
steady state output is y(t) = 30 volts]
<<<<<end>>>>>