Electric networks which permit unattenuated (or free) transmission of electric signals within specified frequency ranges and produce attenuation to suppress the signals outside the specified frequency ranges are termed the electric filters or simply filters.
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The frequency band or bands (range or ranges) freely transmitted by a filter is termed the transmission (or pass) band or bands of that filter. The frequency band or bands attenuated by a filter are referred to as the attenuation (or stop) band or bands of that filter.
For their operation electric filters depend on two basic facts: firstly, inductive reactance is directly proportional and capacitive reactance is inversely proportional to frequency;
secondly, in an inductive reactance the current is in quadrature lagging with voltage, while in a capacitive reactance the current is in quadrature leading with the voltage. Resistors, inductors and capacitors may be combined in many ways to make circuits that have the property of passing or rejecting either low or high frequencies or bands of frequencies.
Invented by G.A. Campbell, filters are widely used in auto- systems and television etc. Bandpass filters are employed for selecting frequency ranges corresponding to desired radio or TV station channels and bandstop filters are employed for attenuation of undesirable signals that may contaminate the desirable signal.
For example, for eliminating undesirable hum noise in dc power supplies, use of low-pass filters is made.
The performance of a filter is expressed in terms of the number of decibels (dB) the signal is amplified or reduced per frequency octave or frequency decade."
Filter networks are of four types namely low-pass, high- pass, band-pass and band-stop (or band-elimination) filters.
Low- pass filters, as the name indicates, transmit all frequencies from zero to a desired cut-off frequency (from 0 to f) and attenuate all higher frequencies (from f to infinity).
High pressure filter attenuate all frequencies from zero up to a desired cut-off frequency (f) and transmit all higher frequencies (from f to infinity).
Band- pass filters transmit a selected band of frequencies either higher or lower than the desired range or band.
Band-stop (or band- elimination) filters reject a certain range or band of frequencies and transmit all frequencies either higher or lower than the undesired range or band.
In low-pass filters, output voltage is taken across capacitor in case of R-C filter and across resistor in case of R-L filter. Cut- off frequency given by 1/2Ï€RC (in case of R-C filter) or R/2Ï€L (in case of R-L filter) occurs when (i) output voltage is 0.707 times the input voltage (ii) R = Xc or R = XL (iii) VR = VC or VR=VI and impedance phase angle = -4 - 45° in case of R-C filter and 0 = 45° in case of R-L filter.
In high-pass filters, output voltage is taken across resistor in case of R-C filter and across inductor in case of R-L filter. The cut-off frequency given by 1/2Ï€RC in case of R-C filter or by R/2Ï€L (in case of R-L filter) occurs when R = XC or R= X₁, the phase angle is 45° in case of R-C filter and -45 in case of R-L filter.
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