An electrical network that will transmit signals with frequencies within certain designated ranges (pass bands) and reject or attenuate signals of other frequencies (stop or attenuation bands). The frequencies that separate the pass and stop bands are the cut-off frequencies, which have the symbols fc if there is only one cut-off frequency or f1 and f2 if more than one. Filters are classified according to the ranges of their pass or stop bands as low-pass, high-pass, band-pass and band-stop filters; the four main classifications with their corresponding frequency limits are shown in the table.
Type of filter | Pass band(s) | Stop band(s) |
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low pass | 0 – fc | fc – ∞ |
high pass | fc – ∞ | 0 – fc |
band pass | f1 – f2 | 0 – f1, f2 – ∞ |
band stop | 0 – f1, f2 – ∞ | f1 – f2 |
An ideal filter would transmit the pass band without attenuation and completely suppress the stop band, with a sharp cut-off profile. Practical filters however do attenuate the pass band, due to absorption, reflection, or radiation, which results in loss of signal power; neither do they completely suppress the stop bands. A typical curve of output voltage with frequency is shown in Fig. a for a simple low-pass filter: Vp is the peak voltage and Vm is the maximum voltage of an ideal filter. The filter attenuation is defined as the loss in signal power in decibels or nepers through the filter; the filter discrimination is the difference between the minimum value of insertion loss in a stop band and the maximum value in a pass band.
The components of a practical filter may be arranged to give the desired output curve. For example, Chebyshev and Butterworth filters are band-pass filters with different output characteristics (Fig. b). Butterworth filters have a flat response in the pass band whereas Chebyshev filters have some variation of the residual response in the pass band but have a more rapid increase of attenuation giving a sharper cut-off profile.
Filters are active or passive according to their components. Active filters contain active components, such as operational amplifiers, that introduce some gain into the signal combined with suitable R-C feedback circuits to give them the desired frequency-response characteristic. Most passive filter networks are constructed from impedances arranged in shunt and in parallel (L-C networks). Two basic arrangements are used: π-sections and T-sections (Fig. c). Composite networks are built up from these basic sections and the arrangement is termed a ladder network because of the alternation of shunt and parallel sections. Another type of configuration is the lattice filter in which the impedance elements are arranged in a bridge network (Fig. d).
The bandwidth of a band-pass or band-stop filter is the difference in hertz between two particular frequencies whose geometric mean equals that of the geometric mid-frequency of the pass or stop band. Frequencies exhibiting a particular characteristic, such as the point at which the response is three decibels below the peak value, are usually chosen.