Digital Signal Processing Reference
In-Depth Information
input step
1.0
1
−
e
−
t
/
t
0.8
0.6
10
−
12
F) = 250 ps
t
=
RC
= (50 ohms) (5
×
0.4
0.2
t
10
−
90%
= 2.195
t
500
1000
1500
2000
2500
Time, ps
Figure 8-6
If a unit step is driven into a single-pole network with time constant
τ
, the
resulting 10 to 90% rise time can be calculated.
Equation (8-8) is a good “back of the envelope” calculation that estimates the
spectral bandwidth of a digital signal with a rise/fall time of
t
10
−
90%
.
Equations (8-5) and (8-8) can be used to estimate the spectral envelope of
a trapezoidal digital signal. The spectrum of a square wave will fall off at
−
20 dB/decade, as described by (8-5). When the frequency (
f
3dB
) that corre-
sponds to the bandwidth of an edge with rise and fall times of
t
10
−
90%
is reached,
the low-pass filtering function becomes significant, and also falls off at a rate of
−
20 dB/decade. This allows us to draw the approximate spectral envelope of a
digital pulse, as shown in Figure 8-7.
t
10
−
90%
T
1/
T
0.35/
t
10
−
90%
Frequency
Figure 8-7
Approximation of the spectral envelope of a digital pulse.
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