Types of Filters | Mechanical | Band Reject | Bandpass

What Are types of Filters?

The major types of LC filters in use are named after the person who discovered and developed the analysis and design method for each filter. The most widely used filters are Butterworth, Chebyshev, Cauer (elliptical), and Bessel. Each can be implemented by using the basic low- and high-pass configurations are shown previously. The different response curves are achieved by selecting the component values during the design.

Butterworth

The Butterworth filter effect has maximum flatness in response in the passband 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 filters. See Fig. 2-34 for an example of a low-pass Butterworth filter.

Chebyshev

Chebyshev (or Tchebyschev) filters have extremely good selectivity; i.e., their attenuation rate or roll-off is high, much higher than that of the Butterworth filter (see Fig. 2-34). The attenuation just outside the passband is also very high—again, better than that of the Butterworth. The main problem with the Chebyshev filter is that it has a ripple in the passband, as is evident from the figure. The response is not flat or constant, as it is with the Butterworth filter. This may be a disadvantage in some applications.

Cauer (Elliptical)

Cauer filters produce an even greater attenuation or roll-off rate than do Chebyshev filters 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 filters, Bessel circuits provide the desired frequency response (i.e., low-pass, bandpass, etc.) but have a constant time delay in the passband. Bessel filters have what is known as a flat 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 filter has lower attenuation just outside the passband.

Mechanical Filters

An older but still useful filter is the mechanical filter. This type of filter uses resonant vibrations of mechanical disks to provide the selectivity. The signal to be filtered 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 filter. 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 filters are designed to work in the 200- to the 500-kHz range and have very high Qs. Their performance is comparable to that of crystal filters. Whatever the type, passive filters are usually designed and built with discrete components although they may also be put into integrated-circuit form. A number of filter design software packages are available to simplify and speed up the design process. The design of LC filters is specialized and complex and beyond the scope of this text. However, filters can be purchased as components. These filters 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.

Band pass Filters

A bandpass filter 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 filter is shown in Fig. 2-35(a). It has both upper and lower cutoff frequencies f2 and f1, as indicated. The bandwidth of this filter is the difference between the upper and lower cutoff frequencies, or BW = f2 – 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 filter response curve is shown in Fig. 2-35(b). The simple series and parallel resonant circuits described in the previous section have a response curve like that in the figure and make good bandpass filters. 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.

types of Filters

Two types of bandpass fi lters are shown in Fig. 2-36. In Fig. 2-36(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. 2-35(b).

Remember that the bandwidth of such a circuit is a function of the resonant frequency and Q: BW = fc /Q. A parallel resonant bandpass filter is shown in Fig. 2-36(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. 2-35(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. 2-37. As sections are cascaded, the bandwidth becomes narrower and the response curve becomes steeper. An example is shown in Fig. 2-38. As indicated earlier, using multiple filter sections greatly improves the selectivity but increases the passband attenuation (insertion loss), which must be offset by added gain.

types of Filters increases the passband attenuation (insertion loss), which must be offset by added gain.
types of filter Band-reject filters, also known as bandstop filters,
types of filter Band-reject filters,

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 filters are shown in Fig. 2-39. 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. 2-39(c). A parallel version of this circuit is shown in Fig. 2-39(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 filters used in this way are often referred to as traps. Another bridge-type notch filter is the bridge-T filter shown in Fig. 2-40. 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 filter. Since L is variable, the notch is tunable. Fig. 2-41 shows common symbols used to represent RC and LC filters or any other type of filter in system block diagrams or schematics.

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