July/August 2018 17
responses are shown in Figure 2. Filters also have a phase
response that describes the phase relationship between
the input and output signals. (There is also a time-domain
response such as you would see on an oscilloscope
screen.)
Figures 2A and 2B show the high-pass and low-pass
responses. Figure 2C is a band-pass response and Figure
2D is a band-stop or notch response. Each response has a
pass-band (where signals aren’t attenuated) and a stop-band
where signals are rejected. All have many uses in radio,
mostly in attenuating unwanted signals. We’ll discuss some
of these uses later in the article.
Filter Specifications
Before using or selecting filters, you’ll
have to know how they are specified.
Beyond just the broad high- or low-pass type, you’ll have to be able to give
specific frequencies and specific levels
of attenuation. Each of these parameters
has a name and precise definition. Figure
3 shows a high-pass filter’s magnitude
response. Drawing the gray boxes on a
response graph establishes the filter’s basic
behavior.
• Cutoff Frequency: The
frequency, ƒC, at which the output signal
has one-half the power of the input signal. This is useful
in specifying where the pass-band ends and where the
stop-band begins. The cutoff frequency is also referred
to as the – 3 dB frequency because – 3 dB is equivalent
to a power ratio of one half.
• Bandwidth: If a filter passes or rejects only a range of
frequencies acting like both a high-pass and a low-pass
filter, there will be two cutoff frequencies. The higher
one is ƒH and the lower is ƒL. In Figure 2C, the two
cutoff frequencies are approximately 2 kHz and 4 kHz,
so that filter has a bandwidth of 4 – 2 = 2 kHz.
• Ripple: This is the variation in attenuation, specified
in dB, of the input signal in the filter’s
pass-band or stop-band. Figure 3 shows
a filter with about 1.5 dB of ripple in the
pass-band. Variation in the stop-band is
also called ripple.
• Rolloff: The slope of the filter’s
response in the transition region between
the pass-band and stop-band. Rolloff
is given in dB/octave (a doubling of
frequency) or dB/decade (ten times
the frequency). If the response changes
rapidly with frequency, that rolloff is
termed steep.
• Insertion Loss (IL): The minimum
PRACTICAL TECHNOLOGY FROM THE HAM WORLD
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n FIGURE 2. Four different types of filter
responses: low-pass (A); high-pass (B);
band-pass (C); and notch or band-stop (D).
(Figure courtesy of the American Radio
Relay League.)
n FIGURE 3. A filter’s key specifications
for its amplitude response. The gray
boxes establish the basic performance
(see text).
