EC312 Homework 14
Name: Solutions
Read: (1) Lecture 14 Notes
(2) Frenzel, Principles of Electronic Communications Systems, 3rd Ed, Ch. 2-4 and 2-2 (p.78-85, 41-52, 56)
1. Make sure your laptop has been loaded with Xirrus software:
http://wifi.xirrus.com/Wi-FiInspectorPage?leadSourceMostRecent=WiFi%20Inspector
Fill out the form online and download Wi-fi inspector version 1.2.1.4, before coming to class.
2. In the figures below, Figure 1 represents the ideal series tuned RLC circuit, and Figure 2 represents the
actual (non-ideal) circuit.
a. Using what you have learned from PE14, write the voltage divider equation for each circuit.
C
L
+
VS
RLOAD

Figure 1
Function
Generator
C
Rs
L
VDISPLAY
Rinductor
+
Rload
Vs
+
Vout =
-
Figure2
b. Will the output still be a maximum at
the same resonant frequency for both
circuits?
Yes, because the resonant frequency depends only on the values of L and C.
2. A common concern in the design of an audio amplifier is blocking the 60-Hz AC power line frequency
from the audio output. If not blocked, the 60-Hz buzz will be produced by the speakers. What type of
filter could one employ to specifically block a 60-Hz signal? Band-reject (or Band-stop)
1
3. Commonly, FM radio receivers employ a bandpass filter with a bandwidth of 200-kHz (corresponding
to bandwidth of an FM channel). Consider tuning an FM station at 104.1 MHz.
a. If the filtering were done at 104.1 MHz (fr = 104.1 MHz) , what would be the required quality
factor Q of the filter to pass a 200 kHz bandwidth.
b. Now, say we do the filtering at 10.7 MHz instead (fr = 10.7 MHz). What would Q be now?
4. Consider the filter circuit depicted to the right in which the
output is measured across the resistor.
a. What is the voltage divider equation for this circuit ? Can
you determine whether this is a high or low pass filter by
substituting values for frequency of 0 and infinity?
Voltage divider equation:
(
)
(
)
|
|
For filter response we’re primarily interested in the ratio | |, which we can calculate as
|
|
| |
|
Therefore:
|
)
√(
= 0,
= 1, i.e. High-pass filter
5. Consider the series RLC bandpass filter shown below with L = 6.366 mH,
C = 15.92 F, and R = 1 .
a. Compute the resonant frequency, the bandwidth, and Q.
√
)(
√(
(
)(
b. If the source vi has an amplitude of 2.0 Vrms, what is the average
power dissipated by R at the resonant frequency (i.e. when f=fr)?
At resonance, the circuit is purely resistive. Average power is
given by
(
)
2
)
)
c. If the frequency of the source is changed to f = 512.5 Hz, what is the power dissipated by R (it
may be useful to consider what you calculated in part a ).
For high-Q circuits (i.e.
), we can assume that the filter’s spectrum is symmetric about
and therefore the upper cutoff frequency is approximately given by
.
We know that the cutoff frequencies correspond to the half-power points (i.e. points at which the
dissipated power is half of its peak, i.e. resonant, value). Therefore the power dissipated is 2W.
6. The figure to the right shows the frequency-domain
representation of an unknown signal.
a. Is the corresponding time-domain signal periodic or
aperiodic? Justify your answer.
The time signal must be periodic because the
component frequencies are all evenly spaced (i.e.
they are harmonics of a fundamental frequency).
Single-Sided Amplitude Spectrum of y(t)
0.7
0.6
0.5
|Y(f)|
0.4
0.3
0.2
0.1
0
b. Suppose this signal was passed through a low-pass
0
1
2
3
4
5
6
7
8
9
10
Frequency (Hz)
x 10
filter with a cut-off frequency of 6 MHz. Sketch the
frequency domain representation of the filtered
signal. (Make sure to label your axes.)
The filter will attenuate all of the frequencies above 6 MHz, so only the first three frequency
components will be present in the filtered signal.
6
Single-Sided Amplitude Spectrum of y(t)
0.7
0.6
0.5
|Y(f)|
0.4
0.3
0.2
0.1
0
0
1
2
3
3
4
5
6
Frequency (Hz)
7
8
9
10
6
x 10