Any combination of passive (R, L, and C) and/or active (transistors or
operational amplifiers) elements designed to select or reject a band of
frequencies is called a filter.
In communication systems, filters are
employed to pass those frequencies containing the desired information
and to reject the remaining frequencies. In stereo systems, filters can be
used to isolate particular bands of frequencies for increased or
decreased emphasis by the output acoustical system (amplifier, speaker,
etc.). Filters are employed to filter out any unwanted frequencies, commonly called noise, due to the nonlinear characteristics of some electronic devices or signals picked up from the surrounding medium. In
general, there are two classifications of filters:
- Passive filters are those filters composed of series or parallel
combinations of R, L, and C elements.
- Active filters are filters that employ active devices such as transistors and operational amplifiers in combination with R, L, and C
elements.
The subject of
filters is a very broad one that continues to receive extensive research
support from industry and the government as new communication systems are developed to meet the demands of increased volume and
speed. There are courses and texts devoted solely to the analysis and
design of filter systems that can become quite complex and sophisticated. In general, however, all filters belong to the four broad categories
of
low-pass,
high-pass,
pass-band, and
stop-band, as depicted in Fig. 1.
For each form there are critical frequencies that define the regions
of pass-bands and stop-bands (often called reject bands). Any frequency
in the pass-band will pass through to the next stage with at least 70.7%
of the maximum output voltage. Recall the use of the 0.707 level to
define the bandwidth of a series or parallel resonant circuit (both with
the general shape of the pass-band filter).
For some stop-band filters, the stop-band is defined by conditions
other than the 0.707 level. In fact, for many stop-band filters, the condition that $Vo = 1/1000V_{max}$ (corresponding with $-60 \,dB$ in the discussion to follow) is used to define the stop-band region, with the passband continuing to be defined by the 0.707-V level. The resulting
frequencies between the two regions are then called the transition frequencies and establish the transition region.
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