EMC Question of the Week: November 17, 2025

1-MHz trapezoidal waves with 2-ns and 50-ns transition times displayed on a digital oscilloscope in the time and frequency domains

Changing the transition times of a 1-MHz trapezoidal waveform from 2 ns to 50 ns causes the harmonics above what frequency to start falling off at 40 dB/decade instead of 20 dB/decade?  

  1. 1 MHz
  2. 7 MHz
  3. 70 MHz
  4. 80 MHz

Answer

The best answer is “b.” The knee frequency above which harmonics start falling off at 40 dB/decade is 1/πtr where tr is the transition time. In this case, the knee frequency is 1/π(50 ns) ≈ 6.4 MHz.  Note that this knee frequency is independent of the fundamental frequency. It depends only on the transition time.

The figure shows 1-MHz trapezoidal waveforms measured on a digital oscilloscope in yellow and their calculated harmonic amplitudes in purple. The upper waveform has a 2-ns transition time. Its harmonics fall off linearly with frequency (20 dB/decade). The lower waveform has a 50-ns transition time. Note that the harmonics above 10 MHz are significantly reduced. 

Both of these waveforms exhibit excellent signal integrity. In general, slowing the transition time to approximately one-tenth the bit width significantly reduces harmonics above the 10th harmonic while maintaining good signal integrity.    

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