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

2. 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)

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

4. 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

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

6. 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)

7. 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

8. Lecture 238 Frequency & Time Domain Connections First order circuit break frequency:  break = 1/  Second order circuit characteristic equation s 2 + 2  0 s +  0 2 [  = 1/(2Q) ] (j  ) 2 + 2  (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

9. 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