Electric filter

A transmission network used to selectively modify the components of a signal according to their frequencies. In most cases a filter is used to enhance signals of desired frequencies while suppressing signals of undesired frequencies. An ideal filter would pass only desired frequencies while completely suppressing all unwanted frequencies, without any dispersion in time of the frequencies. Unfortunately, ideal filters are impossible to achieve.

Electric filters are used in most electronic communication systems. Whether communication is over wire, free space, or optical fiber, multiple channels of information can be multiplexed on different frequency bands. Unwanted signals and noise are introduced along the communications path. The main function of electric filters is to separate the desired signal or channel from all others and from any noise or interference. For example, an AM radio receiver may have a low-pass filter after the antenna to separate the AM frequency band from higher frequency bands and , elsewhere in the radio, a band-pass filter to select the desired station out of the AM band.

Although electronic filters are commonly thought of as devices for conferring selectivity to communication paths, they are used in almost every part of electronic equipment, such as the damping element in phase-locked loops, cleanup devices for frequency sources, and pulse expansion and compression devices for radar. One of the simplest and most common filters is the bypass capacitor used to restrict high-frequency electronic noise.

Filters are characterized in multiple ways. The expression low-pass, Butterworth, LC describes a filter. The descriptior low-pass indicates the relation of the passed to the rejected frequencies. Butterworth describes the type of polynomials in the transfer function. LC indicates the construction method. This filter is made of inductors (L's) and capacitors (C's).

Filters are classified by the relationship of the frequencies that are selectively passed, referred to as the passband, to those which are attenuated, referred to as the stopband. An ideal low-pass filter passes all frequencies below a specified cutoff frequency and rejects those above. A high-pass filter does the opposite. An ideal band-pass filter will pass a band of frequencies while rejecting all others; a band-reject filter will reject a band of frequencies and pass all others.

An all-pass filter passes all frequencies but does, however, modify the time delay characteristics. It normally corrects delay distortions caused by other sections of a communication path.

All the above classifications are based on frequency-domain considerations. In addition, there are two terms that apply to the time-response characteristics of a filter. A finite impulse response (FIR) filter, when exposed to a change in input, will settle to a steady state within a finite amount of time. An infinite impulse response (IIR) filter will continue oscillating in a decaying manner forever.

A further consideration in classifying a filter is whether the frequency response is constant in time or varies. If it varies with time, as a function of the input signal, it's known as an adaptive filter. This type of filter finds use in speech and image enhancement and echo cancellation.

Because filters are used over wide frequency and bandwidth ranges and with such varying performance criteria, many methods have been devised for creating a filter function..

Acoustic filters include crystal, ceramic, mechanical, and surface-acoustic-wave (SAW) filters. These devices convert electrical energy to mechanical vibrations, process the signal acoustically, and then convert the energy back to an electrical form. The equations describing a mechanically vibrating resonator, where energy is cycled between kinetic motion and stress, match those of an inductor and capacitor (LC) attached in parallel, where energy is cycled between the electric field of the capacitor and the magnetic field of the inductor. However, the mechanical resonators have much higher Q's and better stability than the LC circuit. With the addition of a transducer to convert electrical energy to acoustic, the LC circuits can be replaced with mechanical resonators.

Many techniques are used to create filters. Inductors are re placed with transistor networks in active filters, discussed below, to reduce size and cost. By using an analog-to-digital converter the transfer function can be created mathematically by a digital processor. At high frequencies, transmission lines and waveguide structures replace lumped elements.

An active filter comprises resistors, capacitors, and active elements such as operational amplifiers. It's also referred to as an active-RC filter.

Active filters can realize the same filter characteristics as passive ones comprising resistor, capacitor, and inductor elements. They have, however, several advantages over their passive counterparts:

1. Active filters can provide gain, and are frequently used to simultaneously match filtering (frequency-determining) and gain specifications.

2. They are readily implemented in integrated-circuit technology, whereas the inductor element of passive filters is not readily realized. As a result, the active filter is inexpensive, and is attractive for its small size and weight. In addition, it's readily included with other signal-processing functions on a single integrated circuit.

3. The design of active filters is considerably simpler than that of passive ones. In addition, it's easy to provide for variability, which can be used to change filter characteristics by electrical input signals.

The active filter also has some disadvantages:

1. Since the active filter contains electronic components, it requires a power supply, which adds to the complexity of the realization. The electronic components also place restrictions on the level of the signals that can be applied to the filter and on the noise component that the filter may add to the filtered signal.

2. The mathematical process by which the active filter produces filtering characteristics in general requires the use of internal feedback. When this feedback is positive, the resulting filter may be very sensitive to lack of precision in component values, and the effects of aging and environmental conditions.

In general, active filters are designed with the assumption that the active elements are ideal (no parasitics). For example, the operational amplifier is assumed to have infinite gain, infinite input impedance, zero output impedance, and an infinite frequency range (gain-bandwidth). All practical filter realizations must be evaluated for the effect that the nonideal parasitics have on actual filter performance. One of the most trouble some of the parasitics is the operational-amplifier gain band width. Typically, for a given application, tuning charts may be developed which can be used to provide compensation for such operational-amplifier limitations.

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