Page 277 - Complete Wireless Design

Filter Design

276 Chapter Six

when no amplitude ripple to the signal is desired within the filter’s passband;
it has medium selectivity, medium group delay variations, and a good toler-
ance to component variations. (A filter that is sensitive to component toler-
ances will exhibit an undesired altered passband in S and S due to the
21 11
normal variations in L and C values.) Chebyshev-type filters have a certain
amount of passband ripple that will be forced on the input signal as it passes
through to the filter’s output. The “Cheby” does, however, have high selectivity,
with high group delay variations being an unfortunate side effect of this
innate selectivity. Amplitude ripple and high group delay variations, in digital
signals, can cause an increased BER, so are undesired. Nonetheless, low-rip-
ple Chebyshevs can easily be designed, and the group delay variations can be
improved by widening the filter’s passband—or using fewer poles. Bessel
response filters have no ripple in their rounded passbands, and display very
low group delay, but have extremely poor selectivity and poor tolerance to com-
ponent variations.
There are many different types of LC circuit filter topologies that will fur-
nish these responses of Butterworth, Chebyshev, and Bessel. The choice
depends on the shape of the passband desired, the percent bandwidth
required, the sensitivity to component tolerances and distributed reactances,
and the ability to obtain easily realizable component values during design.
More on this later.
There are numerous terms used when filters are discussed. Below are the
most common:

Absolute attenuation—The maximum attenuation a filter is capable of at
some chosen frequency in its stopband. Measured in dB.
Bandwidth—The width (f f ) of the band of frequencies passed by a
LOW HIGH
bandpass filter at its 3-dB-down points. Measured in Hz.
Center frequency (f or f )—The exact mathematical center of a bandpass
C 0
filter. Measured in Hz.
Cutoff frequency—The point in a frequency response of a filter that is 3 dB
below the average passband response, and which keeps on falling.
Decibels of attenuation per octave (dB/octave)—Filters can be designed as to
how rapid their skirt slope falls. The decibels of attenuation per octave
specification refers to a filter’s steepness: If a filter is said to have a 15-
dB/octave slope at a 1-GHz cutoff frequency, then the attenuation within the
stopband will be 15 dB more at 2 GHz, while the filter’s stopband
attenuation at 4 GHz will be 30 dB. Knowing the required dB/octave fall of
the filter’s skirt assists the engineer in visualizing the attenuation as the
frequency increases, or decreases, from its passband.
Differential delay—The group delay variation (GDV) between two particular
frequencies, usually measured in nanoseconds. Delay equalization, either by
discrete analog or by DSP techniques, can be used to almost nullify the
effects of GDV, thus improving the BER of digital radios.

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