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Sec. 4–8 Classification of Filters and Amplifiers 257
are replaced by an arrangement of electronic switches and capacitors that are controlled by a
digital clock signal [Schaumann et al., 1990].
Crystal filters are manufactured from quartz crystal elements, which act as a series resonant
circuit in parallel with a shunt capacitance caused by the holder (mounting). Thus, a parallel
resonant, as well as a series resonant, mode of operation is possible. Above 100 MHz the quartz
element becomes physically too small to manufacture, and below 1 kHz the size of the element
becomes prohibitively large. Crystal filters have excellent performance because of the inherently
high Q of the elements, but they are more expensive than LC and ceramic filters.
Mechanical filters use the vibrations of a resonant mechanical system to obtain the
filtering action. The mechanical system usually consists of a series of disks spaced along a
rod. Transducers are mounted on each end of the rod to convert the electrical signals to
mechanical vibrations at the input, and vice versa at the output. Each disk is the mechanical
equivalent of a high-Q electrical parallel resonant circuit. The mechanical filter usually has a
high insertion loss, resulting from the inefficiency of the input and output transducers.
Ceramic filters are constructed from piezoelectric ceramic disks with plated electrode
connections on opposite sides of the disk. The behavior of the ceramic element is similar to
that of the crystal filter element, as discussed earlier, except that the Q of the ceramic element
is much lower. The advantage of the ceramic filter is that it often provides adequate performance
at a cost that is low compared with that of crystal filters.
Surface acoustic wave (SAW) filters utilize acoustic waves that are launched and travel on
the surface of a piezoelectric substrate (slab). Metallic interleaved “fingers” have been deposited
on the substrate. The voltage signal on the fingers is converted to an acoustic signal (and vice
versa) as the result of the piezoelectric effect. The geometry of the fingers determines the
frequency response of the filter, as well as providing the input and output coupling [Dorf, 1993,
pp. 1073–1074]. The insertion loss is somewhat larger than that for crystal or ceramic filters.
However, the ease of shaping the transfer function and the wide bandwidth that can be obtained
with controlled attenuation characteristics make the SAW filters very attractive. This technology
is used to provide excellent IF amplifier characteristics in modern television sets.
SAW devices can also be tapped so that they are useful for transversal filter configurations
(Fig. 3–28) operating in the RF range. At lower frequencies, charge transfer devices
(CTDs) can be used to implement transversal filters [Gersho, 1975].
Transmission line filters utilize the resonant properties of open-circuited or shortcircuited
transmission lines. These filters are useful at UHF and microwave frequencies, at
which wavelengths are small enough so that filters of reasonable size can be constructed.
Similarly, the resonant effect of cavities is useful in building filters for microwave frequencies
at which the cavity size becomes small enough to be practical.
Filters are also characterized by the type of transfer function that is realized. The transfer
function of a linear filter with lumped circuit elements may be written as the ratio of two
polynomials,
H(f) = b 0 + b 1 (jv) + b 2 (jv) 2 + Á + b k (jv) k
(4–40)
a 0 + a 1 (jv) + a 2 (jv) 2 + Á + a n (jv) n
where the constants a i and b i are functions of the element values and v = 2pf. The parameter
n is said to be the order of the filter. By adjusting the constants to certain values,
desirable transfer function characteristics can be obtained. Table 4–3 lists three different