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lesson38 - Lesson 38 Filters III(Variant of Section...

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Lesson 38 – Filters III (Variant of Section 12-4) (Variant of CLO 12-2) This is the last of two lessons on filter analysis and design. The first focused on first-order LP and HP. The second focuses on BP and BR. In discussing BP and BR filters start by using ideal models – students seem to grasp easily the concept when presented that way. Again re-introduce our block diagram and point out that in an ideal system |H(j ϖ )| , the filter’s gain, can be only either “1” or “0”. If the signal falls in the pass band it comes out the output unscathed ( |H(j ϖ )| = 1). If, however it falls in the stop band it does not exit at all ( | H(j ϖ )| = 0). If we look at the ideal filters, we see that the LPF will pass all signals up to ϖ LP and the HPF will pass signals greater than ϖ HP . Since the two filters are connected in cascade, only those signals that are between ϖ HP and ϖ LP will pass through both filters. Hence, we have a BPF with a Bandwidth, B, of ϖ HP ϖ LP . Once they appreciate how an ideal filter works draw in “real” filter curves so they can see what performance to expect. Next, show how they can design a BRF. There are two differences between BPF and BRF. The first is that in a BRF the two filters are connected in parallel rather in cascade – and therefore requiring a summer. The other difference is that the LP filter’s cutoff ϖ LP is the desired low frequency cutoff of the filter. In a BPF the ϖ LP is the cutoff of the HP filter. Similarly, that the HP filter’s cutoff ϖ HP is the desired high frequency cutoff of the filter. In a BPF the ϖ HP is the cutoff of the LP filter. Devote a good amount of time to actually designing a BPF. Since there will be a HPF and LPF designed, this exercise will review the earlier lesson as well as this one. Once a student understands how to design a BPF designing a BRF is not difficult. In their BPF design efforts the
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