Lecture 231 EEE 302 Electrical Networks II Dr. Keith E. Holbert Summer 2001

Lecture 232 Filter Networks Filters pass, reject, and attenuate signals at various frequencies Common types of filters: Low-pass: pass low frequencies and reject high frequencies High-pass: pass high frequencies and reject low frequencies Band-pass: pass some particular range of frequencies, reject other frequencies outside that band Band-rejection: reject a range of frequencies and pass all other frequencies (e.g., a special case is a notch filter)

Lecture 233 Common Filter Bode Plots Frequency High Pass Frequency Low Pass Frequency Band Pass Frequency Band Reject

Lecture 234 Passive Filters Passive filters use R, L, C elements to achieve the desired filter 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 We will need active filters to achieve a gain greater than unity

Lecture 235 Class Examples Extension Exercise E12.16 Extension Exercise E12.17 Extension Exercise E12.18

Lecture 236 First-Order Filter Circuits L +–+– VSVS C R Low Pass High Pass H R = R / (R + sL) H L = sL / (R + sL) +–+– VSVS R High Pass Low Pass G R = R / (R + 1/sC) G C = (1/sC) / (R + 1/sC)

Lecture 237 Second-Order Filter Circuits C +–+– VSVS R Band Pass Low Pass L High Pass Band Reject Z = R + 1/sC + sL H BP = R / Z H LP = (1/sC) / Z H HP = sL / Z H BR = H LP + H HP

Lecture 238 Frequency & Time Domain Connections First order circuit break frequency:  break = 1/  Second order circuit characteristic equation s  0 s +  0 2 [  = 1/(2Q) ] (j  )  (j  ) + 1[  = 1/  0 ] s 2 + BW s +  0 2 s 2 + R/L s + 1/(LC)[series RLC] Q value also determines damping and pole types Q 1) overdamped, real & unequal roots Q = ½ (  = 1) critically damped, real & equal roots Q > ½ (  < 1) underdamped, complex conjugate pair

Lecture 239 PSpice Design Example Repeat E12.18 using Pspice –Plot the resistor voltage in DBs –Use goal function “BPBW” to determine the band-pass filter bandwidth: BPBW(VDB(#),3)) –Use goal function “CenterFreq(VDB(#),0?)” Bandwidth design –Design circuit to achieve a bandwidth of 300 Hz Center frequency design –Design circuit for a center frequency of 100 Hz