# Filters

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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.
Fig. 1: Defining the four broad categories of filters.
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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