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### Understanding Electrical Filter Networks: Types, Circuits, and Design ###

This lecture, led by Dr. Keith E. Holbert, explores the fundamentals of electrical filter networks, detailing their role in passing, rejecting, and attenuating signals at various frequencies. We discuss common types of filters—low-pass, high-pass, band-pass, and band-rejection (notch filters)—and their applications. The session covers both passive and active filter circuits, emphasizing their components, such as resistors, inductors, and capacitors. Practical exercises using PSpice illustrate design principles for achieving specific bandwidths and center frequencies, enhancing understanding of filter performance. ###

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### Understanding Electrical Filter Networks: Types, Circuits, and Design ###

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  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

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