EMC Question of the Week: November 24, 2025
Which signal has the strongest harmonic at 425 MHz if they both have the same amplitude and a 50% duty cycle?
- 5 MHz clock with a 1 ns transition time
- 25 MHz clock with a 3 ns transition time
- either of the above (they're equal)
- 100 MHz clock with a 40 ps transition time
Answer
The best answer is “b.” 425 MHz is the 17th harmonic of the 25 MHz clock. If the peak-to-peak voltage of the trapezoidal waveform were 1 volt, the amplitude of the 17th harmonic would be 5.0 mV. 425 MHz is the 85th harmonic of the 5 MHz clock. If the peak-to-peak voltage of the trapezoidal waveform were 1 volt, the amplitude of the 85th harmonic would be 3.9 mV. The 100 MHz clock does not have a harmonic at 425 MHz.
For high harmonics like these, the amplitude can vary greatly with minor changes in the duty cycle and/or the transition time. For example, if the 25 MHz clock transition time was 2.3 ns, or the duty cycle was 47%, the amplitude of the harmonic at 425 MHz would have dropped to less than 1 mV and the 5 MHz clock would have been the stronger source of emissions.
Rather than calculating the precise value of these upper harmonics, it is much more meaningful to calculate the envelope of the harmonics. The envelope is not subject to small variations in the waveform and can be used to make worst-case calculations. At frequencies higher than 1/πtr, the amplitude of the envelope proportional to the fundamental frequency and inversely proportional to the transition time. For this example, the factor of 5 increase in the clock frequency more than made up for the factor of 3 increase in the transition time. So, the envelope of the 25 MHz clock harmonics was higher than the envelope of the 5 MHz clock harmonics despite having the longer transition time.
The LearnEMC website has an online calculator to determine the harmonics of a trapezoidal waveform as well as the amplitude of the envelop.
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