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Unformatted text preview: BMEN 321, Dr. Maitland Practice Exam 1 ‘ September 27, 2008 This practice exam has three purposes: 1. expose you to my testing style; 2. communicate to you a NON
EXAUSTIVE set of topics that are important on the actual exam (I reserve the right and will test you on
some topics not on this practice); 3. provide structure for the review day. The length of this problem set
is not necessarily the same as the exam next Thursday. THIS WILL NOT BE TURNED IN OR GRADED 1. Short answer questions: a. For 0) = 411 [rad/s], f = [Hz]
b. True or False (circle one): Chebyscheff ﬁlters are used for their ﬂat response over the passband. c. True or False (circle one): A bandpass ﬁlter with high Q has a narrow bandwidth relative to the
center frequency. d. True or False (circle one): Bode plots are a graphical representation of the magnitude and phase
frequencydependent response of circuits. e. Write the expression for the equivalent impedance, Zeq, for three parallel passive components: R1, R2,
and C. : 2. Draw the following circuits, labeling all, elements, input and output functions and write out the transfer
functions for each. Higher order circuits can use more than one op—amp. a. Noninverting, 1St order LPF b. 2nd order inverting HPF 3. At time t=0, the switch in the circuit is open after having been in the current position for a long time. Derive
and sketch the voltage across the capacitor, Vc(t),as a function of time. Make sure to include the time at which
Vc(t) is 63% of its ﬁnal value. 4. For the Bode diagram below, magnitude and phase  ..... KCu,%<>f‘f féequeﬁcy 301cm
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Angular frequency (rad/s) a. Write the transfer function T(s) that is represented in the diagram b. Given that Vout = T(s) V0 sin (2 1r f t + (1)), where the input voltage is of the form Vin = Vosin (2 1: f t) and the magnitude and phase Bode plots provide 20 log T(s) and (1), respectively, ﬁnd Vout for the
following input signal (note the phase lag at fc is 45 degrees) Vin =10 sin (2 1t (0.01) t) + 10 sin (2 1t (1) t) + 10 sin (2 1: (100) t) Vout = 4. For the following transfer ﬁanctions, sketch an asymptotic loglog Bode magnitude plot for the gain (G(f)=20
log T(s) = 2010g(Vo/Vin)). Make sure to identify key features like cutoff frequencies, the passband, gains at
fc and maximum gain. Plot G(f), not G(w), where w=27cf S
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71C) a. (Yes, a little difﬁcult) Write the transfer function that corresponds to the plot above. Remember that T(s)=T1(s)*T2(s)* . ..
(turn) in the asymptotic Bode plot (HP and LP T(s) will get you there). Start with a higher order HP. b. F ill out the table below. You may assume asymptotic values for the magnitude, INCLUDING all cutoff
frequencies. Now you see why they are called “comer” frequencies too — the log magnitude plot turns “comers” at these frequencies. All sin and cos functions are of the form A cos[27t(f)t] where A is amplitude in [V] and f is frequency in [Hz].
Neglect phase in all cases. (6 pts) f [Hz] 10 cos[21t(3)t]
1 C08[27‘C(20)t]
1 sin[21t(2000)t] 30000 100 cos[2n(30000)t] 100000 100 cos[21t(105)t] 6. The ﬁrst ﬁgure below shows a carotid stenotic lesion. As blood passes across the stenosis, it accelerates and
creates vortices, both of which result is higher than normal ﬂow rates (frequencies). The second line of
personal health, the family doctor (you are the ﬁrst), listens for high frequency components as the ﬁrst diagnosis
of this disease. Imaging will conﬁrm. You, an engineer, decide that the frequency spectrum of the ﬂow, as
measured by an acoustic microphone is the way to go for diagnosing if these high ﬂows are present. Pieces of plaque can
break free, travel to the ' brain, and block. blood ' vessels that supply blood to the brain (‘2‘ ﬁﬁﬁﬁz‘; , if”; 5:. For the ﬂow below taken as a voltage off the microphone, draw a block diagram of the circuit that you would
build to reduce the high frequency components to a 05 V DC voltage that can be used quantitatively measure
the magnitude of the high frequency element. The peak voltage on the plot below is 1 mV. The period between
major peaks is 1 second. What frequencies is the higher component in the timebased signal below? 10100
Hz. ...
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 Fall '08
 MEISSNER

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