Each harmonic amplitude drops off like 1/f, since each harmonic is a higher frequency. If you have never done one before, I strongly recommend you try this one.įor example, the amplitude of the n = 1 first harmonic is 2/(3.1416 x 1) = 0.64. This is one of the few Fourier Transforms I can do by hand. The amplitude of the odd harmonics is given by, The amplitude of the even harmonics is 0. The spectrum of an ideal 50% duty cycle square wave, with 0 psec rise time, has frequency components only at multiples of the clock frequency (harmonics). For this specific waveform, we can estimate the highest sine wave frequency needed to recreate the rise time.Ĭonsider first an ideal clock signal. We assume the signal is a 50% duty cycle clock signal that has a finite 10-90 rise time. The origin of this simple rule of thumb relating the rise time of a signal and the highest sine wave frequency we need to consider in the signal is based on a very simple type of signal. This would help guide us to identify the bandwidth of a measurement instrument needed to measure it, or the bandwidth of an interconnect needed to transport it. Because of the vagueness of the term “significant,” unless detailed qualifiers are added, the concept of bandwidth is only approximate.īandwidth is a figure of merit of a signal to give us a rough feel for the highest sine wave frequency component that might be in the signal. Remember: before you start using rules of thumb, be sure to read the Rule of Thumb #0: How to use them wisely.īandwidth is the highest sine wave frequency component that is significant in a signal.
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