Name:_______________________________________
HW-7: Adding sine waves, the addition of ordinates, the Fourier Theorem,
amplitude, rms amplitude, peak-to-peak amplitude, period, frequency, and spectrum.
Assigned: Friday, March 27, 2015 Due: Friday, April 3, 2015
Early credit is available! The Devil’s Deal is an option!
1. For the following wave,
what is the amplitude?
5
What is the peak-to-peak
amplitude of the wave?
4
3
What is the rms amplitude of
the wave?
v(t) volts
2
1
0
-1
-2
-3
What is the period of the
wave?
-4
time (seconds)
Note: The rms amplitude is 0.71 times the square root of the sum of the squares of the
individual components. (The rms voltage is the effective average voltage.)
Accurately sketch the spectrum of the
wave.
0.010
0.009
0.008
0.007
0.006
0.005
0.004
0.003
0.002
0.001
What is the frequency of the
wave?
0.000
-5
2. For the following waveform, a spectrum analyzer shows that the amplitude of the
fundamental is 2.5 volts and the 2nd harmonic is 0.7 volts.
What is the peak-to-peak
amplitude of the wave?
5
4
What is the rms amplitude of
the wave?
3
v(t) volts
2
What is the period of the
wave?
1
0
-1
-2
-3
-4
time (seconds)
Note: The rms amplitude is 0.71 times the square root of the sum of the squares of the
individual components. (The rms voltage is the effective average voltage.)
Accurately sketch the spectrum of the
wave.
0.010
0.009
0.008
0.007
0.006
0.005
0.004
0.003
0.002
0.001
0.000
-5
What is the frequency of the
wave?
3. For the
following waveform, a spectrum analyzer shows that the amplitude of the
fundamental is 2.5 volts and the 3rd harmonic is 0.3 volts.
What is the peak-to-peak
amplitude of the wave?
5
4
What is the rms amplitude of
the wave?
3
v(t) volts
2
What is the period of the
wave?
1
0
-1
-2
-3
-4
time (seconds)
Note: The rms amplitude is 0.71 times the square root of the sum of the squares of the
individual components. (The rms voltage is the effective average voltage.)
Accurately sketch the spectrum of the
wave.
0.010
0.009
0.008
0.007
0.006
0.005
0.004
0.003
0.002
0.001
0.000
-5
What is the frequency of the
wave?
4. For the following waveform, a spectrum analyzer shows that the amplitude of the
fundamental is 2.5 volts, the 2nd harmonic is 0.7 volts, and the 3rd harmonic is 0.7 volts.
What is the peak-to-peak
amplitude of the wave?
5
4
3
What is the rms amplitude of
the wave?
v(t) volts
2
1
0
-1
What is the period of the
wave?
-2
-3
-4
time (seconds)
Note: The rms amplitude is 0.71 times the square root of the sum of the squares of the
individual components. (The rms voltage is the effective average voltage.)
Accurately sketch the spectrum of the
wave.
0.010
0.009
0.008
0.007
0.006
0.005
0.004
0.003
0.002
0.001
What is the frequency of the
wave?
0.000
-5
5. A student has wired a circuit that produces the following waveform. In addition, a
spectrum analyzer shows that the fundamental is 3.0 volts, the 2nd harmonic is 2.50 volts,
the 3rd harmonic is 1.50 volts, and the 4th harmonic is 0.75 volts.
What is the peak-to-peak
amplitude of the wave?
5
4
What is the rms amplitude of
the wave?
3
What is the period of the
wave?
v(t) volts
2
1
0
-1
-2
-3
-4
time (seconds)
Note: The rms amplitude is 0.71 times the square root of the sum of the squares of the
individual components. (The rms voltage is the effective average voltage.)
Accurately sketch the spectrum of the
wave.
0.010
0.009
0.008
0.007
0.006
0.005
0.004
0.003
0.002
0.001
What is the frequency of the
wave?
0.000
-5
6. Are the harmonics always smaller than the fundamental? No! In this case, the
fundamental, the 2nd harmonic, the 3rd harmonic, the 4th harmonic and the 5th harmonic
are all1 volt.
What is the peak-to-peak
amplitude of the wave?
5
4
What is the rms amplitude of
the wave?
3
What is the period of the
wave?
v(t) volts
2
1
0
-1
-2
-3
-4
time (seconds)
Note: The rms amplitude is 0.71 times the square root of the sum of the squares of the
individual components. (The rms voltage is the effective average voltage.)
Accurately sketch the spectrum of the
wave.
0.010
0.009
0.008
0.007
0.006
0.005
0.004
0.003
0.002
0.001
What is the frequency of the
wave?
0.000
-5
7. A spectrum analyzer shows that the fundamental is 0.0 volts, the 3rd harmonic is 1.0
volts, the 4th harmonic is 1.50 volts, and the 5th harmonic is 1.0 volts.
What is the peak-to-peak
voltage of the wave?
5
4
What is the period of the
wave?
3
v(t) volts
2
What is the frequency of the
wave?
1
0
-1
-2
-3
-4
The rms amplitude is 0.71
times the square root of the
time (seconds)
sum of the squares of the
individual components. (The
rms voltage is the effective average voltage.) Determine the rms amplitude of the wave?
Accurately sketch the spectrum of the
wave.
0.010
0.009
0.008
0.007
0.006
0.005
0.004
0.003
0.002
0.001
0.000
-5
8. A spectrum analyzer shows that the fundamental is 1.00 volts, the 3rd harmonic is 1/3
volt (or 0.33 volts), the 5th harmonic is 1/5th volt (or 0.20) volts, the 7th harmonic is 1/7th
volt (or 0.14 volts), and the 9th harmonic is 1/9th volt (or 0.11 volts).
What is the peak-to-peak
voltage of the wave?
What is the period of the
wave?
What is the frequency of
the wave?
The rms amplitude is 0.71
times the square root of
the sum of the squares of
the individual components. (The rms voltage is the effective average voltage.)
Determine the rms amplitude of the wave?
Accurately sketch the spectrum of the
wave.
Note: The spectrum of a square wave includes the fundamental and the odd harmonics.
For the nth harmonic, the amplitude is 1/n. That is, for the third harmonic, the amplitude
is 1/3 volt = 0.33 volts; for the fifth harmonic, the amplitude is 1/5 volt = 0.20 volts; etc.