Biomedical Engineering Reference
In-Depth Information
H (
j
ω
)
M
M
Stopband
Passband
Stopband
FIGURE 9.37
A realistic magnitude-frequency response for a band-pass filter. Note that the magnitude M does
not necessarily need to be one. The passband is defined as the frequency interval when the magnitude is greater
than
M
p
.
the filter and eliminates any signal or noise outside this interval. The frequencies o
1
and
o
2
are typically called cutoff frequencies for the low-pass and high-pass filters.
In reality, any real filter cannot possibly have these ideal characteristics but instead has a
smooth transition from the passband to the stopband, as shown, for example, in Figure 9.37
(the reason for this behavior is discussed in Chapter 11). Further, it is sometimes convenient
to include both amplification and filtering in the same circuit, so the maximum of the
magnitude does not need to be one, but it can be a value of
M
specified by the needs of
the application.
To determine the filter's performance, the filter is driven by a sinusoidal input. One
varies the input over the entire spectrum of interest (at discrete frequencies) and records
j
¼
M
2
the output magnitude. The critical frequencies are when
ðÞ
o
p
.
j
Hj
EXAMPLE PROBLEM 9.28
Using the low-pass filter in the following circuit, design the filter to have a gain of 5 and a
cutoff frequency of 500
rad
s
.
C
R
b
−
R
a
+
+
+
V
S
−
v
0
−
