# Higher Order Filters

Posted on Feb 5, 2014

From the discussion made so far on the filters, it may be concluded that in the stopband the gain of the filter changes at the rate of 20 db/decade for first-order filters and 40 db/decade for second-order filters. This means that as the order of the filter is increased, the actual stopband response of the filter approaches its ideal stopband char

acteristics. In general, a third-order filter produces 60 db/decade, a fourth-order filter produces 80 db/decade and so on. The simplest way to build a third-order low-pass filter is by cascading a first order filter with a second-order. Similarly a fourth-order low-pass filter can be formed by cascading two second-order low-pass filters. Although there is no limit to the order of the filter that can be formed, as the order of the filter increases, so does its size. Also the accuracy declines, in that the difference between the actual stopband response and the theoretical stopband re ­sponse increases with an increase in the order of the filter. The voltage-gain of the first section is optional, it can be set, whatever is required. The voltage-gain of the second section, however affects the flatness of the overall response. If closed-loop gain is kept 1. 586, then the overall gain will be down 6 db (3 db for each section) at the cut-off frequency. By increasing the voltage gain of the second section slightly, cumu ­lative loss of voltage gain is offset. By using an advanced mathematical derivation, it can be proved that an Af, of 2 is the critical value required for a maximally flat response. where R and C are the resistance and capacitance of each section. At cut-off frequency, the overall voltage gain is down 3 db. Above the cut-off frequency, the voltage gain drops at a rate of 60 db per decade equivalent to 18 db per...

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