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What is a filter Passive filters Some common filters

Lecture 24. Filters II. What is a filter Passive filters Some common filters. Active Filters. All the passive filters have a gain < 1 To achieve a gain > 1, we need to utilize an op-amp based circuit to form an active filter

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What is a filter Passive filters Some common filters

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  1. Lecture 24. Filters II • What is a filter • Passive filters • Some common filters

  2. Active Filters • All the passive filters have a gain < 1 • To achieve a gain > 1, we need to utilize an op-amp based circuit to form an active filter • We can design all the common filter types using op-amp based active filters • Recall for an ideal op-amp that V+ = V– I+ = I– = 0

  3. Op Amp Model V+ Non-inverting input + Rout Vo Rin + – – Inverting input A(V+ –V–) V–

  4. Non-inverting Op-Amp Circuit + – + + – Vin Z2 Vout Z1 –

  5. Inverting Op-Amp Circuit Z2 Z1 – – + – + Vin Vout +

  6. An Integrator C R – + – + + Vin Vout – Earlier in the semester, we saw this op-amp based integrator circuit. What type of filter does it create? Does this help you to understand time and frequency domain interrelations?

  7. A Differentiator R C – + – + + Vin Vout – What type of filtering does it produce?

  8. Example • You are shopping for a stereo system, and the following specifications are quoted: • Frequency range: –6 dB at 65 Hz and 22 kHz • Frequency response: 75 Hz to 20 kHz ±3 dB • What do these specs really mean? • Note that the human hearing range is around 20 Hz to 20 kHz (audible frequencies) • Could you draw a rough Bode (magnitude) plot for the stereo system?

  9. Example: Building Filters via Cascade of RCL circuits Second-Order Filter Circuit Z = R + 1/sC + sL R HLP = (1/sC) / Z = Low Pass C VS + – L

  10. 15.3Ω 37.0Ω V1 L=1mH V2 L=1mH V3 C=2.5μF C=2.5μF V2(s)=H1(s)V1(s) V3(s)=H2(s)V2(s) Example: Building Filters via Cascade of RCL circuits • Example of last in-class exercise • 4th Order Butterworth • Cutoff- 20000 rad/sec • System function: • Implement each Hi(s), i=1,2 using RLC (series) circuit

  11. R R V1 L V2 L V3 C C V2(s)=H1(s)V1(s) V3(s)=H2(s)V2(s) Sectional 2nd Order Filters Connected by Voltage Follower • Op-Amp isolate sections of 2nd order circuits • Loading between sections can be kept low

  12. Class Examples • Problem 10-12 (p421).

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