spectrum of a trapezoidal clock signal and the associated envelope that typically bounds the
spectrum of a digital signal. For a perfectly symmetric (i.e., 50% duty cycle) digital signal,
one can verify with Fourier analysis, no even harmonics will be present in the system.
However, in reality there are sometimes significant even harmonics.
Figure 10.3: Spectrum of a digital signal showing peak envelope regions.
Note that the frequency envelope of the Fourier spectrum shown in
falls off with
frequency at a rate of -20 dB per decade (an inverse linear relationship with frequency) up to
f = 1/T
after which it falls off at a rate of -40 dB per decade (an inverse-square relationship).
Now consider the far-field radiation [
], which is directly proportional to the
square of frequency and thus increases with frequency at a rate of +40 dB per decade.
However, when the loop path is greater then /2, the effective loop area is adjusted to be a
(the constant will depend on the area calculation of the shape of the loop).
Thus at high enough frequency, the
component of the area A in
cancel with the
element, and the field will stay constant with increasing frequency. This
will happen at a frequency F = c/2
(where c is the speed of light and
is the loop length).
shows the relative radiated magnitudes of different frequencies input into a given
loop. Note that the loop will radiate frequencies with increasing efficiency up until the
antenna shrinking effect occurs at frequencies above F = c/2