Odd Harmonics Exercise
Display the power spectrum of a square wave
1. Create a new VI using a template: NEW -> VI from template ->Tutorial (Getting Started) ->
Generate, Analyze, and Display.
2. Choose a 10 Hz square wave with a 50% duty cycle. Let's make it like a TTL clock - choose the
amplitude, offset, etc to make the clock oscillate between 0 and +5 volts. Generate 500 samples, as fast as
possible, at a rate of 1000 samples per second.
3. Set the parameters on the graphical indicator to your taste. You should be able to determine the period of
the square wave, and the amplitudes (0 volts and 5 volts) should be fairly evident. Run your VI - show it to
your neighbor.
4. Add a Spectral Measurements VI to the block diagram - attach a graphical indicator to its output. Wire
the 10 Hz square wave to the new spectral analyzer.
5. Measure the power spectrum in dB with no windowing. Adjust the graphical indicator to display the
power spectrum from 0 Hz to 200 Hz - show amplitudes from +10 dB to -40 dB. Run your VI - show it to
your neighbor.
Do you believe your spectrum plot?
6. Study the formula for the Fourier components of a square wave. Make a table - Fill Column 1 with the
frequencies of the fundamental and the harmonics that you expect up to 200 Hz (Don't worry about DC for
now).
7. Let's choose our 0 dB reference to be the fundamental. Calculate the expected amplitudes of the
harmonics in dB ( This will yield "dB referenced to the fundamental"). Fill these into Column 2 of your
table.
8. According to the formula, the peak value of the fundamental sine wave is the same as the square wave's
peak amplitude. Since we have applied a DC offset equal to the peak amplitude of the square wave, we
should have introduced a DC component with 0 dB relative to the fundamental. Add the DC component to
your table of expected values.
9. Compare your table of expected values with the power spectrum produced by LabVIEW. Write a one
(short) paragraph discussion of your results. Hand in your LabVIEW VI (front panel & block diagram),
your table of expected results, and your discussion.
Extra Work:
1. Change the square wave to a triangle wave. How do the frequencies of the triangle wave harmonics
compare with the square wave exercise? How about the amplitude? Are the triangle wave harmonics
stronger or weaker than those of the square wave?
2. What is the frequency of your square wave's highest harmonic? (trick question! - but recall that no
transmission line is completely lossless - you can't pass ∞ Hz). Apply a low pass filter to your square wave
- attenuate the upper end of the frequency spectrum that you are studying (say 100-200 Hz) Graph the
results in the time domain and the frequency domain. You should get a qualitative indication of what
happens to clock signals as they pass down a computer bus. What happened to your rise time? overshoot?