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Mixed-Frequency Signals
31 questions By Tony R. Kuphaldt
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Question 10 of 31
Explain how the following power-line harmonic analyzer circuit works:
Harmonic # L# value C# value
1st 20 to 22 H 0.33 μF
2nd 11 to 12 H 0.15 μF
3rd 5 to 6 H 0.15 μF
4th 1.5 to 2.5 H 0.22 μF
5th 1 to 1.5 H 0.27 μF
Reveal answerEach series LC section is a resonant band-pass filter, tuned to successive harmonics of a 60 Hz sine wave. The selector switch enables a single voltmeter to measure the RMS amplitude of each harmonic.
Follow-up question: calculate the exact inductance values necessary for precise tuning of the five LC filters, for the first five harmonics of a 60 Hz waveform.
Challenge question: the voltmeter in this circuit would not have to be a true-RMS meter. It could simply be an average-responding (RMS-calibrated) voltmeter and it would work the same. Explain why.
Notes:This question provides students with some review of passive filter circuit theory, as well as insight into a practical circuit they could conceivably build as a project.
A very important design feature of this circuit is the narrow bandwidth of each harmonic “channel.” The filter pass-bands must not come close to overlapping, or else the meter response will not be exclusively indicative of the harmonic it is switched to. High Q values for each filter section ensure that the meter will only register the particular harmonic that is selected for measurement.
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Question 11 of 31
What is a harmonic frequency? If a particular electronic system (such as an AC power system) has a fundamental frequency of 60 Hz, calculate the frequencies of the following harmonics:
- 1st harmonic =
- 2nd harmonic =
- 3rd harmonic =
- 4th harmonic =
- 5th harmonic =
- 6th harmonic =
Reveal answer- 1st harmonic = 60 Hz
- 2nd harmonic = 120 Hz
- 3rd harmonic = 180 Hz
- 4th harmonic = 240 Hz
- 5th harmonic = 300 Hz
- 6th harmonic = 360 Hz
Notes:Ask your students to determine the mathematical relationship between harmonic number, harmonic frequency, and fundamental frequency. It isn’t difficult to figure out!
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Question 12 of 31
An octave is a type of harmonic frequency. Suppose an electronic circuit operates at a fundamental frequency of 1 kHz. Calculate the frequencies of the following octaves:
- 1 octave greater than the fundamental =
- 2 octaves greater than the fundamental =
- 3 octaves greater than the fundamental =
- 4 octaves greater than the fundamental =
- 5 octaves greater than the fundamental =
- 6 octaves greater than the fundamental =
Reveal answer- 1 octave greater than the fundamental = 2 kHz
- 2 octaves greater than the fundamental = 4 kHz
- 3 octaves greater than the fundamental = 8 kHz
- 4 octaves greater than the fundamental = 16 kHz
- 5 octaves greater than the fundamental = 32 kHz
- 6 octaves greater than the fundamental = 64 kHz
Notes:Ask your students if they can determine the mathematical relationship between octave number, octave frequency, and fundamental frequency. This is a bit more difficult to do than for integer harmonics, but not beyond reason if students are familiar with exponents.
Clarify for your students the fact that “octave” is not just a musical term. In electronic circuit analysis (especially filter circuits), the word “octave” is often used to represent multiples of a given frequency, usually in reference to a bandwidth (i.e. “This filter’s passband response is essentially flat over two octaves!”).
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