Broadband signals; due either to transient events regularly repeated, such as commutator motors, or to non-periodic signals such as digital data or video

EMC emissions are regulated in the frequency domain. A sinusoidal waveform has a single frequency component. In contrast, a finite transition-time square wave, or trapezoidal wave, is rich in harmonics (that is, multiples of the fundamental frequency). It can be thought of as the sum of an infinite series of sine waves of appropriate amplitudes and frequencies; the conversion between the time and frequency domains is done with the Fourier Transform. Trapezoidal waveforms are of course very common in electronic circuits that use switching or digital techniques.

The amplitude envelope of the harmonics decreases at a rate of 20dB per frequency decade (inversely proportional to frequency) until a breakpoint is reached at 1/πt_{r}, a frequency which is determined by the rise and fall times of the trapezoid. Beyond this frequency the amplitude decreases at 40dB/decade (inversely proportional to the square of frequency). The actual amplitude of each harmonic follows a sinx/x law:

You can see this spectrum by monitoring the clock waveform in a digital circuit with a spectrum analyser. A purely symmetrical trapezoidal waveform does not contain any even harmonics; varying the duty cycle d of the square wave away from 50% (reducing the value of T in equation (1)) adds them. A low duty cycle reduces the amplitude of the lower-order harmonics and leaves the upper-order ones untouched.

Having different rise and fall times, in a real, asymmetrical, trapezoid, also adds even harmonics. The limit in this case is the sawtooth waveform which exhibits an equal mix of odd and even harmonics. The triangle wave contains only even harmonics. Real-life switching waveforms almost invariably have slightly different rise and fall times, so there is always some degree of even harmonic content, although at the lower orders it may be several tens of dB below the odd harmonics.

The spectrum analyser is most useful when many signals of different frequencies are present. Displaying the composite of such signals in the time domain would be meaningless. The analyser also is normally used with a logarithmic amplitude display, so that the dynamic range from top to bottom can be as high as 10,000:1 (80dB). This would not be either possible or desirable on an oscilloscope since it would distort the waveform.

A video demonstration can be found in

Broadband noise

The most common and aggressive sources of broadband noise are motors and other repetitive switching operations. In a DC brushed motor the current is switched from winding to winding by brushes contacting the commutator as it rotates, and each interruption of current causes a brief, fast-rise-time transient which has a very broad, continuous spectrum. Repetition of the interruptions results in pulsed noise which appears to be quasi-continuous in time. On a spectrum display, the individual pulses appear as “spikes” at discrete frequencies because the display is sweeping in time, but this is misleading because each spike is actually of short duration but contains energy across the frequency range.

A further very important source of broadband noise is due to digital or video data waveforms, which can be approximated by a random bit sequence. The spectrum of such a sequence contrasts with that of clock signals in that rather than being concentrated at a single frequency and its harmonics, it is spread nearly continuously over a wide frequency range. The spacing of the individual spectrum lines is given by the reciprocal of the repetition rate of the sequence. A truly random sequence, i.e. one which does not repeat, has a continuous spectrum. Many digital processes repeat with a period measured in milliseconds and their spectra are quasi-continuous with line spacings less than 1kHz, which is essentially broadband for EMC measurement purposes.

Because the energy from a given circuit carrying a data signal is spread widely across the spectrum, its amplitude at any one frequency is many times lower than a clock signal from a circuit with equivalent radiating parameters.

There is confusion about the difference between (for example) 10 M bit/sec signal and a 10 MHz frequency signal. They are not the same thing, and the fundamental frequency of the 10 M bit/sec signal is not 10 MHz. This figure shows an example of a 10 M bit/sec square wave and the fundamental sinewave at 5 MHz. In effect, the squarewave data rate only uses one bit width (which is one half of the full sinewave cycle) to determine the data rate. This means that a 10 M bit/sec pulse will have its odd numbered harmonics at 5 MHz, 15 MHz, 25 MHz, 35 MHz, etc.

Transients

Occasional transient events will also create a high frequency disturbance. As one-offs, the nuisance value of such disturbances only rarely justifies their limitation, and most standards don't apply specific limits to short duration phenomena. For instance, wording in CISPR 22/EN 55022 says

If the reading of the measuring receiver shows fluctuations close to the limit, the reading shall be observed for at least 15 s at each measurement frequency; the higher reading shall be recorded with the exception of any brief isolated high reading which shall be ignored.

A few requirements exist for the control e.g. of discontinuous disturbances in CISPR 14-1/EN55014-1, and the "exported transients" test of DEF STAN 59-411 DCE03.

In the automotive sector, as high-voltage electrical systems become increasingly integral to the overall vehicle electrical setup, it's vital to address transients. Take, for instance, the abrupt deactivation of inductive components, which can lead to significant voltage spikes known as kickback voltage. Consequently, automobile manufacturers have devised industry-specific standards that outline transient tests and set maximum limits on the amplitude of these transients. This is done to safeguard the robustness and dependability of the vehicle's electrical system.

The exact spectrum of a single transient depends on its rise and fall times and duration; it is continuous in the frequency domain, i.e. does not have discrete frequency components. The spectrum can if necessary be determined through a Fourier transform of the waveform.

Try your own calculation for the amplitude of the nth harmonic of a trapezoidal waveform, based on equation (1):