You can minimize your EMI/EMC and SI/PI problems by working as slow as possible. This is very well-known advice from many experts, books, and seminars: you can minimize or solve electromagnetic interference (emissions/susceptibility) and signal or power integrity problems by working as slow as possible. But many times this strategy is ignored. Why is this idea so important?
When designing or analyzing any electronic product, you can consider using the time and frequency domains. And remember, you can switch from one domain to the other.
You can calculate the frequency domain of your signal using the Fourier series (FS), the Discrete Fourier Transform (DFT) or the Fast Fourier Transform (FFT) depending on your signal, application, and your skills with math (the associate algorithms and equations are explained in any basic undergraduate course so it is not necessary to include that information in this article).
With the Fourier techniques, you can consider that your signal is composed of infinite sinusoidal signals at different frequencies (i.e., harmonics). And, for that signal, as the frequencies increase in value, their amplitudes are smaller and smaller.
In Figure 1, the FTT of a square voltage signal (i.e., clock) is calculated with my scope. Odd and even harmonics are clearly shown, with decreasing amplitudes as the frequency value increases.
But, do you really need an infinite number of frequencies to represent your signal?
A practical answer is no. Usually, we can take a limited range of frequencies to represent our signals in real applications, and this is what we call bandwidth. So bandwidth is, from a simple point of view, the maximum frequency in your signal.
Note that, from an EMI emissions point of view, as the bandwidth increases, the enclosures, wires, and PCB traces can act as efficient antennas easily.
From an EMI immunity point of view, as the bandwidth increases, your circuit will be able to respond to fast transients, so it is more susceptible.
From a Signal Integrity point of view, as the bandwidth increases, your connections (wires, PCB traces, etc.) can experience high-frequency effects as reflections, crosstalk, and delays, easily affecting the integrity of your signals.
So, if you minimize the bandwidth of your signals, you will be reducing the probability to experiment with any of those problems. And how can you reduce the bandwidth of your signals? The answer to that question is inside the EFFT (Extremely Fast Fourier Transform), a very well-known tool included in many EMC publications.
Consider, for example, the spectrum for a random digital signal as shown in Figure 2. This is a 4.5V amplitude signal with nominal frequency fo = 40MHz and 50% duty cycle (on time tON = 12.5ns).
But the important part for this signal is not in the nominal frequency. The critical part is in the rise and fall times. Considering a rise and fall time of tR = 2ns, we can draw the EFFT as the envelope of the amplitudes of harmonics in red color. The envelope is flat from low frequencies to corner frequency f1 = 1/πtON = 30.3MHz.
Then, amplitudes decrease at -20dB/dec.
At frequency f2 = 1/ πtR = 159MHz, amplitudes decrease at -40dB/dec. We call that frequency the “knee frequency,” and we consider that the energy at higher frequencies has no important contribution to your signal. That limit can be considered an estimation of the bandwidth for your signal.
An equivalent idea can be applied to any periodic (i.e., clock) or non-periodic (i.e., ESD) signals, or to digital, analog, or power signals. And note that maximum frequency is related to the rise time so it is related to how fast the switching time is (clearly it is related to dv/dt and di/dt).
In Figure 3, a 5.78MHz digital clock is analyzed with two different rise and fall times. The fast signal (A) has a rise time of around 3ns. The slow version (B) has a switching time of around 11ns.
Note in Figure 3 (right) how the bandwidth decreases when the rise time increases (114MHz to 29MHz).
So, when your signal includes high-frequency components because you are switching fast, you need to master all those high-frequency techniques (layout, matching, etc.) typical of RF designers in the wireless business. Yes, you are right, you are an RF designer!
Obviously, if your system is a high-speed system, you will need to apply those special techniques and forget about working slow, but what about if you are working faster than needed?
So, remember the advice: work as slow as possible.
