EEE 302 Electrical Networks II

1. EEE 302Electrical Networks II Dr. Keith E. Holbert Summer 2001 Lecture 23

2. 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 23

3. Common Filter Bode Plots Low Pass High Pass Frequency Frequency Band Reject Band Pass Frequency Frequency Lecture 23

4. 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 23

5. Class Examples • Extension Exercise E12.16 • Extension Exercise E12.17 • Extension Exercise E12.18 Lecture 23

6. First-Order Filter Circuits High Pass Low Pass R R VS + – Low Pass VS + – High Pass L C GR = R / (R + 1/sC) GC = (1/sC) / (R + 1/sC) HR = R / (R + sL) HL = sL / (R + sL) Lecture 23

7. Second-Order Filter Circuits Band Pass Z = R + 1/sC + sL HBP = R / Z HLP = (1/sC) / Z HHP = sL / Z HBR = HLP + HHP R Low Pass C VS + – Band Reject High Pass L Lecture 23

8. 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 ] s2 + BW s + 02 s2 + R/L s + 1/(LC) [series RLC] Q value also determines damping and pole types Q < ½ ( > 1) overdamped, real & unequal roots Q = ½ ( = 1) critically damped, real & equal roots Q > ½ ( < 1) underdamped, complex conjugate pair Lecture 23

9. 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 Lecture 23