Analyze the frequency domain envelope of a square wave having variable frequency, duty cycle and rise time.
The frequency domain envelope rolls off at a rate of6 dB per octave or 20 dB per decade.The initial roll off starts at a frequency defined at 1 / ( * pulse width).Slowing the rise and fall time of the square wave will cause an additional 20 dB of attenuation to start at a frequency defined at 1 / ( * rise time).All even numbered n-Th. terms will be in the null for a 50 % duty cycle, but slight changes away from 50 % causes the minimum level and frequency of the null to shift dramatically.Note:The vertical blue marker is the location of the n-th user defined harmonic of the fundamental frequency ( fo ).
Change the "Fundamental Frequency"variable to observe the start point of the 20 dB per decade roll.A higher fundamental causes the roll off to start at a higher frequency.Set the frequency back to 10 MHz and adjust the duty cycle from 50 % to 51%.Notice how this decreases the width and depth of the null for just a 1 % change in duty cycle and how it shifts the frequency of the null for a larger change.This is one reason why some signal amplitudes change greatly from sample to sample.Set the duty cycle to 50 % again and adjust the "Rise Time" variable to some portion of the pulse width.Notice how this change adds additional attenuation (20 dB / decade) at the frequency defined at 1 /( * rise time).The null will be less dominate and also changed in frequency.The pulse width variable,
base, is equal to the period times the duty cycle.
base assumes zero rise and fall time.Keep the user defined rise time,
r, less than
base.
The example assumes afall time equal to the rise time.Finally, try a very narrow pulse to similate a unit impulse function Notice how the frequency domain envelope remains flat further out in frequency.This should be expected since the 20 dB roll off doesn't start until 1 /( * pulse width.Narrow pulse widths can be the result of reflections do to an improperly terminated transmission line.