Electric Filter

an electric device that separates from the spectrum of electric oscillations supplied to its input those components that lie in some given frequency band. The components separated are the only ones that are fed through to the filter output; all other components are attenuated. Electric filters are used in multichannel communication systems, radio equipment, and automation and remote control devices, as well as in electronic measurement technology. They are suitable for any application where electric signals are transmitted in the presence of other (interfering) signals or noise differing from the transmitted signal in frequency composition. Electric filters are also used in current rectifiers to attenuate the pulsation of rectified current.

The frequency band that includes the passed components is called the passband, and the band that includes the attenuated components is called the stop band. The filtering properties of an electric filter are quantitatively described by the magnitude of attenuation contributed by the filter relative to the components of the spectrum of electric oscillations. The greater difference in attenuation between the stop band and the passband, the higher the filtering capacity.

Electric filters may be classified according to the shape of the curve describing attenuation versus frequency. Low-pass filters transmit oscillations having frequencies no higher than some cutoff frequency f_u and attenuate oscillations with frequencies higher than f_u. Conversely, high-pass filters transmit oscillations with frequencies higher than some frequency f₁, and attenuate oscillations below this limit. Band-pass filters transmit oscillations only in a finite frequency interval, from f_u to f₁. Band-elimination, or rejection filters, exhibit frequency characteristics that are the reverse of those of band-pass filters.

Figure 1. Schematic diagrams and frequency curves of several electric filters that use induction coils, capacitors, and resistors: (a) low-pass filter, (b) high-pass filter, (c) band-pass filter, (d) band-elimination filter, (e–h) respective frequency curves; (L₁, L₂ . . ., L₁₁) induction coils, (C₁, C₂ . . .,C₁₁) capacitors, (R₁, R₂ . . ., R₁₁) resistors, (f) frequency, (f_t) and (f₁₁) cutoff frequencies

The design, manufacturing technology, and operating principle of electric filters are determined primarily by the operating frequency range and by the required shape of the filters’ frequency curves. In the frequency range from several kilohertz (kHz) to tens of megahertz (MHz), and in a few cases up to several gigahertz (GHz), LC filters are widely used (Figures l,a; l,c; and 1,d). Such filters contain discrete components, such as inductance coils and capacitors. In the range from fractions of a hertz (Hz) to

Figure 2. Block diagram and time curves of a digital filter: (D) digitizer, which converts the analogue signal x(t) into a sequence of pulses (the network function) x*(t); (ADC) analogue-to-digital converter, which converts the instantaneous values of the analogue signal into the nearest discrete levels X(nT), where n = 0, 1, 2,... and T is the pulse tracking period; (C) computer, which converts the sequence of numbers (levels) X(nT) into the output function Y(nT); (DAC) digital-to-analogue converter, which converts Y(nT) into the analogue output signal y(t)

hundreds of kHz the most widely used designs have passive or active RC filters (Figure l,b), which incorporates resistors and capacitors (active filters also contain an amplifier). The operating principle of LC and RC filters is based on the dependence of capacitive and inductive reactance on the frequency of alternating current.

Electrothermal filters are used to filter signals at frequencies of fractions of Hz. They are built in the form of rods that incorporate a heat source and a thermoelectric converter. The addition of a feedback-type amplifier makes it possible to use such filters as high-pass and band-pass filters. Electromechanical filters may incorporate disk, cylinder, plate, dumbbell, or tuning-fork resonators. Their operation is based on the principle of mechanical resonance, and the application range is from several kHz to 1 MHz. Piezoelectric band-pass filters and band-elimination filters exhibit high filtering capacities. They are made from such materials as piezoelectric quartz or piezoelectric ceramics. Some designs use discrete components, such as quartz resonators combined with inductance coils and capacitors; in monolithic designs the coupling between resonators is achieved by acoustic waves—either space waves (for filters used in the range from several MHz to tens of MHz) or surface waves (for the range from several MHz to 1–2 GHz).

Digital filters constitute a special group of electric filters (Figure 2). They are frequently constructed from integrated circuits. Electric filters used in microwave technology incorporate sections of transmission lines (coaxial cables, strip lines, or metal wave guides) and are essentially distributed oscillatory systems. For the frequency range from 100 MHz to 10 GHz, serviceable filters can be designed as comb, step, and other types of filters made from strip resonators. Waveguide filters are often used in the range from several GHz to tens of GHz. They consist of waveguide sections with a raised cutoff (critical) frequency (high-pass waveguide filters) or sections containing resonant diaphragms or cavity resonators (band-pass waveguide filters).