18 July/August 2018
attenuation in the filter’s pass-band. A perfect filter
would have no insertion loss at all, but all practical
filters have some insertion loss. The filter in Figure 3
has an IL of about 1 dB.
• Stop-band Attenuation and Notch Depth: In the
stop-band, a minimum amount of attenuation is
required of the filter. If the filter rejects a narrow
range of frequencies with a stop-band in between two
pass-bands, notch depth is the maximum attenuation
between those two pass-bands. Both of these
parameters are specified in dB.
• Input and Output Impedance: Filters have a
characteristic impedance that affects how a signal
source or load will perform when connected to the
filter. For the filter to have only the desired effect, it’s
impedance should match the impedance of whatever
it is connected to: a signal generator, a microphone,
a transmission line, or an amplifier. If the impedances
don’t match, filter performance may not be as
expected.
Filter Families and Orders
Looking through websites and books of filter designs,
you’ll notice that along with the type of frequency
response, there are other categories: Butterworth,
Chebyshev, Bessel, Elliptical, and more. These are known
as filter families. Many of the families are named for the
designer who worked out the equations describing them.
(Elliptical filters are so-named because the solutions to
functions describing them form an ellipse in Cartesian
coordinates.) Each set of equations has different solutions
that translate into different component values.
Each family of filters has a different frequency response
shape. They might all be designed to have the same cutoff
frequency but the amount of ripple in the pass- and stop-bands and the steepness of the rolloff vary quite a bit. (The
filter’s phase responses are also quite different.)
For example, compare the Chebyshev and Butterworth
low-pass filter response curves in Figure 4. Both are
low-pass filters with a cutoff frequency of 1,000 Hz. The
curves have very different shapes, though. The Butterworth
has a very smooth response with no ripple at all —
Butterworth filters are often referred to as maximally-flat
for that reason — but the rolloff is smooth and gradual,
as well. The Chebyshev filter trades a smooth response
for steeper rolloff by allowing various amounts of ripple.
The filter response in Figure 4 is known as a “1 dB ripple
Chebyshev.”
Depending on what you’re using the filter for, ripple
or gradual rolloff might be okay. The different filter families
offer choices about how the filter will perform and what
effects they have on the signals. For example, hams trying
to design an audio filter for receiving the single tones of
Morse code (CW) find that a lot of ripple means distortion
and smearing of the carefully shaped dits and dahs. At high
speeds, that can make the code “tough copy.” In that case,
it’s worth allowing a more gradual rolloff so you hear some
of the adjacent signals in order for the Morse elements
to be reproduced clearly. Each application is a little bit
PRACTICAL TECHNOLOGY FROM THE HAM WORLD
Brick-wall or Ideal Filters
The filter responses in Figure 2 vary smoothly between
the pass-band and the stop-band. This is the way a real
filter behaves. Nevertheless, you will encounter references
to “ideal” or “brick-wall” filters for which the pass-band
and stop-band responses are completely uniform or “flat.”
The transition region for such a filter is a vertical line on the
response graph with an infinite rolloff. Needless to say, these
filters can’t actually be built, although some sophisticated
digital filters get close.
n FIGURE 4. Filter responses for a Butterworth
and a Chebyshev low-pass filter. Both have
the same cutoff frequency of 1,000 Hz but have
significant differences in rolloff and ripple in the
passband. (Figure courtesy of the American Radio
Relay League.)
Attenuation - Is it Positive or
Negative?
If an output signal is smaller than the input signal, the ratio in dB
will be negative. For example, if the output is five times less powerful
than the input to a filter, that is a power ratio of - 7 dB with the minus
sign indicating a ratio less than 1. That represents an attenuation or
loss of 7 dB, with no minus sign.
The rule is that power ratios in dB have a positive or negative
value, while loss or attenuation are given without the minus sign.
The - 7 dB power ratio is a loss or attenuation of 7 dB. Similarly, if the
output was five times greater than the input, that would be a gain of 7
dB.
The minus sign isn’t used if the name of the parameter implies
whether it is present or not.