Types of Filters
The major types of LC i lters in use are named after the person who discovered and
developed the analysis and design method for each i lter. The most widely used
i lters are Butterworth, Chebyshev, Cauer (elliptical), and Bessel. Each can be implemented by using the basic low- and high-pass coni gurations shown previously. The
different response curves are achieved by selecting the component values during the
design.
Butterworth. The Butterworth i lter effect has maximum l atness in response in the
pass band and a uniform attenuation with frequency. The attenuation rate just outside the
passband is not as great as can be achieved with other types of i lters. See Fig. for
an example of a low-pass Butterworth i lter.
Chebyshev. Chebyshev (Or Tchebyschev) i lters have extremely good selectivity; i.e.,
their attenuation rate or roll-off is high, much higher than that of the Butterworth i lter. The attenuation just outside the passband is also very high—again,
better than that of the Butterworth. The main problem with the Chebyshev i lter is that
it has ripple in the passband, as is evident from the i gure. The response is not l at or
constant, as it is with the Butterworth i lter. This may be a disadvantage in some
applications.
Cauer (Elliptical). Cauer i lters produce an even greater attenuation or roll-off rate
than do Chebyshev i lters and greater attenuation out of the passband. However, they
do this with an even higher ripple in the passband as well as outside of the passband.
Bessel. Also called Thomson i lters, Bessel circuits provide the desired frequency
response (i.e., low-pass, bandpass, etc.) but have a constant time delay in the passband.
Figure;- Butterworth, elliptical, Bessel, and Chebyshev response curves
Bessel i lters have what is known as a l at group delay: as the signal frequency varies
in the passband, the phase shift or time delay it introduces is constant. In some applications,
constant group delay is necessary to prevent distortion of the signals in the passband due
to varying phase shifts with frequency. Filters that must pass pulses or wideband modulation are examples. To achieve this desired response, the Bessel i lter has lower attenuation just outside the passband.
Mechanical Filters. An older but still useful i lter is the mechanical i lter. This type
of i lter uses resonant vibrations of mechanical disks to provide the selectivity. The signal to be i ltered is applied to a coil that interacts with a permanent magnet to produce
vibrations in the rod connected to a sequence of seven or eight disks whose dimensions
determine the center frequency of the i lter. The disks vibrate only near their resonant
frequency, producing movement in another rod connected to an output coil. This coil
works with another permanent magnet to generate an electrical output. Mechanical i lters
are designed to work in the 200- to 500-kHz range and have very high Qs. Their performance is comparable to that of crystal i lters.
Whatever the type, passive i lters are usually designed and built with discrete components although they may also be put into integrated-circuit form. A number of i lter
design software packages are available to simplify and speed up the design process. The
design of LC i lters is specialized and complex and beyond the scope of this text. However, i lters can be purchased as components. These i lters are predesigned and packaged
in small sealed housings with only input, output, and ground terminals and can be used
just as integrated circuits are. A wide range of frequencies, response characteristics, and
attenuation rates can be obtained.
Bandpass Filters. A bandpass i lter is one that allows a narrow range of frequencies
around a center frequency fc
to pass with minimum attenuation but rejects frequencies
above and below this range. The ideal response curve of a bandpass i lter is shown in
Fig. (a). It has both upper and lower cutoff frequencies f2
and f1
, as indicated. The
bandwidth of this i lter is the difference between the upper and lower cutoff frequencies,
or BW 5 f2 2 f1
. Frequencies above and below the cutoff frequencies are eliminated.
The ideal response curve is not obtainable with practical circuits, but close approximations can be obtained. A practical bandpass i lter response curve is shown in Fig.(b).
The simple series and parallel resonant circuits described in the previous section have a
response curve like that in the i gure and make good bandpass i lters. The cutoff frequencies are those at which the output voltage is down 0.707 percent from the peak output
value. These are the 3-dB attenuation points.
Figure - Response curves of a bandpass fi lter. (a) Ideal. (b) Practical.
Two types of bandpass i lters are shown in Fig.(a), a series
resonant circuit is connected in series with an output resistor, forming a voltage divider.
At frequencies above and below the resonant frequency, either the inductive or the
capacitive reactance will be high compared to the output resistance. Therefore, the
output amplitude will be very low. However, at the resonant frequency, the inductive
and capacitive reactances cancel, leaving only the small resistance of the inductor. Thus
most of the input voltage appears across the larger output resistance. The response
curve for this circuit is shown in Fig.(b). Remember that the bandwidth of such
a circuit is a function of the resonant frequency and Q: BW 5 fc
/Q.
A parallel resonant bandpass i lter is shown in Fig.(b). Again, a voltage
divider is formed with resistor R and the tuned circuit. This time the output is taken
from across the parallel resonant circuit. At frequencies above and below the center
resonant frequency, the impedance of the parallel tuned circuit is low compared to that
of the resistance. Therefore, the output voltage is very low. Frequencies above and
below the center frequency are greatly attenuated. At the resonant frequency, the reactances are equal and the impedance of the parallel tuned circuit is very high compared
to that of the resistance. Therefore, most of the input voltage appears across the tuned
circuit. The response curve is similar to that shown in Fig.(b).
Improved selectivity with steeper “skirts” on the curve can be obtained by cascading
several bandpass sections. Several ways to do this are shown in Fig. As sections
are cascaded, the bandwidth becomes narrower and the response curve becomes steeper.
An example is shown in Fig. As indicated earlier, using multiple i lter sections
greatly improves the selectivity but increases the passband attenuation (insertion loss),
which must be offset by added gain.
Figure - Simple bandpass fi lters
Figure - Some common bandpass fi lter circuits.
Figure - How cascading fi lter sections narrow the bandwidth and improve
selectivity. Figure - LC tuned bandstop fi lters. (a) Shunt. (b) Series. (c) Response curve
Bnad-reject filter (bandstop filter)
Band-Reject Filters. Band-reject Filters, also known as bandstop Filters, reject a narrow band of frequencies around a center or notch frequency. Two typical LC bandstop
i lters are shown in Fig. 2-39(a), the series LC resonant circuit forms a
voltage divider with input resistor R. At frequencies above and below the center rejection
or notch frequency, the LC circuit impedance is high compared to that of the resistance.
Therefore, signals at frequencies above and below center frequency are passed with
minimum attenuation. At the center frequency, the tuned circuit resonates, leaving only
the small resistance of the inductor. This forms a voltage divider with the input resistor.
Since the impedance at resonance is very low compared to the resistor, the output signal
is very low in amplitude. A typical response curve is shown in Fig.(c).
A parallel version of this circuit is shown in Fig.(b), where the parallel resonant
circuit is connected in series with a resistor from which the output is taken. At frequencies above and below the resonant frequency, the impedance of the parallel circuit is very
low; there is, therefore, little signal attenuation, and most of the input voltage appears
across the output resistor. At the resonant frequency, the parallel LC circuit has an
extremely high resistive impedance compared to the output resistance, and so minimum
voltage appears at the center frequency. LC i lters used in this way are often referred to
as traps.
Another bridge-type notch Filter is the bridge-T Filter shown in Fig.. This Filter,
which is widely used in RF circuits, uses inductors and capacitors and thus has a steeper
response curve than the RC twin-T notch i lter. Since L is variable, the notch is tunable.
Fig. shows common symbols used to represent RC and LC i lters or any other
type of i lter in system block diagrams or schematics.
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