HW #5

Due Thursday, February 2nd (Ground Hog's Day!)

1.a) Sketch the Bode plot of the transfer function,

b) Sketch the Bode plot of the ideal low pass filter with the transfer function:

c) Now sketch theBode plot of . What is the true magnitude (in dB) of H(s) at the cut-off frequency, s=jw _c?

2 I have an LTI system in a Big Blue box (see below). I want to know the transfer function, H(s)=Y(s)/W(s).

Of course I could input a unit impulse and find the impulse response, h(t). But a unit impulse doesn't exist in the real world! A better way is to input a sinusoid and measure the sinusoidal-steady state response (both magnitude and phase). By varying the frequency of the sinusoidal input from near zero (D.C.) to near infinity (high frequency), I could make a Bode plot for my unknown LTI system!!!

a) Using the above approach at a particular frequency I have obained the following sinusoidal steady-state plot. Find the frequncy w , the magnitude |H(jw )|, and the phase angle Ð H(jw ).

b) Suppose I take many similar measurements at various frequencies and obtain the following magnitude plot. Find my unknown transfer function, H(s).

c) Now, find the response of my LTI Big Blue Box system if I set w(t)=5u(t-4).

d) Suppose a 2nd-order under damped system has the transfer function,. Find values of z and w _n then sketch the Bode plot.

e) Find the unit step response for the system in part 2d).