Filters

Filters - Filters Author John M Cimbala Penn State...

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Filters Author: John M. Cimbala, Penn State University Latest revision: 15 October 2007 Introduction Signals often contain noise and/or frequency components that we want to eliminate or suppress ( attenuate ). In this learning module, we discuss filters – what they do, how they work, and how to build them. Most of the filters discussed here are passive filters – they do not involve operational amplifiers and feedback loops, as do active filters , which are discussed briefly in a separate module. Types of filters A filter is used to remove some unwanted frequency components in a voltage signal . Consider a filter that modifies an input voltage signal V in to produce an output voltage V out , as sketched to the right. V in Filter V out We define the gain G of the filter as the ratio of the magnitude of the output voltage to the magnitude of the input voltage , out in GV V = . Stop band Pass band Frequency, f Gain, G = | V out |/| V in | 0 1 The gain of a filter typically ranges from 0 to 1. We categorize a filter according to its frequency response diagram a plot of gain G vs. frequency f . There are four basic types of filters: 0 o A low-pass filter lets low frequencies go through or pass , but attenuates or cuts off high frequencies. The f response diagram for an ideal low-pass filter is sketched to the right. requency Cutoff frequency, f cutoff o The range of frequencies that is passed by the filter is called the pass band . Ideally, V out / V in = 1 in the pass band – the output voltage is not affected in any way by the filter. o The range of frequencies that is cut off or stopped by the filter is called the stop band . Ideally, V out / V in = 0 in the stop band – the output voltage is completely cut off by the filter. o Real low-pass filters are not ideal, and do not cut off the high frequencies abruptly. Instead, there is a gradual roll off of the gain from 1 to 0. A typical frequency response diagram for a low-pass filter is sketched below left with linear scales for both gain and frequency. f (linear scale) G (linear scale) 0 1 f (log scale) G (log scale) 1 10 -1 10 -2 10 -3 10 -4 Low-pass filter Low-pass filter o Logarithmic scales are usually used when plotting the frequency response diagram – on both the horizontal and vertical axes, as sketched above right. o A high-pass filter lets high frequencies go through or pass , but attenuates low frequencies, as sketched below left (with log-log scales). f (log scale) G (log scale) 1 10 -1 10 -2 10 -3 10 -4 f (log scale) G (log scale) 1 10 -1 10 -2 10 -3 10 -4 High-pass filter Band-pass filter o A band-pass filter is a combination of the above two. It lets a band of frequencies go through or pass , but attenuates both low frequencies and high frequencies, as sketched above right.

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Filters - Filters Author John M Cimbala Penn State...

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