23.FiltersI.pptVIP

What is a filter Passive filters Some common filters Lecture 23. Filters I * * What are filters? Filters are electronic circuits which perform signal processing functions, specifically intended to remove unwanted signal components and/or enhance wanted ones. Common types of filters: Low-pass: deliver low frequencies and eliminate high frequencies High-pass: send on high frequencies and reject low frequencies Band-pass: pass some particular range of frequencies, discard other frequencies outside that band Band-rejection: stop a range of frequencies and pass all other frequencies (e.g., a special case is a notch filter) * Bode Plots of Common Filters Frequency Frequency Low Pass Frequency Band Pass Frequency Band Reject Gain Gain Gain Gain High Pass * Passive vs. Active filters Passive filters: RLC components only, but gain 1 Active filters: op-amps with RC elements, and gain 1 * Passive Filters Passive filters use R, L, C elements to achieve the desired filter Some Technical Terms: The half-power frequency is the same as the break frequency (or corner frequency) and is located at the frequency where the magnitude is 1/?2 of its maximum value The resonance frequency, ?0, is also referred to as the center frequency * First-Order Filter Circuits L + – VS C R Low Pass High Pass HR = R / (R + sL) HL = sL / (R + sL) + – VS R High Pass Low Pass GR = R / (R + 1/sC) GC = (1/sC) / (R + 1/sC) * Second-Order Filter Circuits C + – VS R Band Pass Low Pass L High Pass Band Reject Z = R + 1/sC + sL HBP = R / Z HLP = (1/sC) / Z HHP = sL / Z HBR = HLP + HHP * Higher Order Filters We can use our knowledge of circuits, transfer functions and Bode plots to determine how to create higher order filters For example, let’s outline the design of a third-order low-pass filter * Frequency Time Domain Connections First order circuit break frequency: ?break = 1/? Second order circuit characteristic equation s2 + 2??0 s + ?02 [ ? = 1/(2Q) ] (j??)2 + 2?(j??) + 1 [ ? = 1/?0 ] s