## Radiated Emissions From Digital Circuits

As they operate, digital circuits constantly switch the state of lines between a high-voltage level and a low-voltage level to represent binary states. As shown in Figure 4.1a, the resulting time-domain waveform on any single line of a digital circuit can thus be idealized as a train of trapezoidal pulses of amplitude (either current I or voltage V) A, rise time tr, fall time tf (between 10 and 90% of the amplitude), pulse width t (at 50% of the amplitude), and period T.

The Fourier envelope of all frequency-domain components generated by such a periodic pulse train can be approximated by the nomogram of Figure 4.1b. The frequency spectrum is composed mainly of a series of discrete sine-wave harmonics starting at the fundamental frequency f0 = 1/T and continuing for all integer multiples of f0. The nomogram identifies two frequencies of interest. The first is f1, above which the locus of the maximum amplitudes rolls off with a 1/f slope. The second, f2, is the limit above which the locus rolls off at a more abrupt rate of 1/f2. These frequencies are located at and

= 1 = 0.32 2 nt t where t is the faster of (tr, tf).

The envelope of harmonic amplitude (in either amperes or volts) is then simplified to

20 dB/decade roll-off f1 < f < f2 40 dB/decade roll-off f2 < f  