====== Active RC universal filter ======
  * **Goals:**
    * Understand the operation of an active RC (i.e. opamp-RC) filter

  * Use LF347 quad opamp for this experiment
  * The circuit below can have inputs V<sub>i1,R</sub>, V<sub>i1,C</sub>, V<sub>i2,R</sub>, V<sub>i2,C</sub>, V<sub>i3,R</sub> and output V<sub>1</sub>, V<sub>2</sub>, V<sub>3</sub>. Determine the transfer functions for all input-output combinations. 
  * Which components do the resonance frequency and the quality factor depend on? 
  * Which components do the zeros depend on? 

{{:courses:ec330:ttbiquad.png?600}}

  * Design a bandpass filter (with V<sub>1</sub> as output) for a resonance frequency of 10kHz and a quality factor of 10. Where will you apply the input? (Omit all unnecessary components from the circuit) Verify its operation.
  * While keeping the circuit the same, can you take the output from a different point to realize a lowpass filter? Verify it. 
  * What are the minimum modifications required to get a notch filter output at V<sub>1</sub>? Verify it.
  * Make the minimum modifications required to obtain a maximally flat lowpass response and verify it. A maximally flat all pole lowpass response has only the highest power of ω in the denominator of |H(jω)|<sup>2</sup>.
  * Modify the above circuit to get a highpass filter output at V<sub>1</sub>? Verify it.
  * Restore the circuit to the bandpass filter in the first part. Replace the opamp LF347 with LM324 which has an identical pin configuration(hopefully you don't have a mess of wires running over the chip!) What do you see? Why?

  * **Applications:** Active RC filters are the most popular topologies of RC filters. For example, they are used as intermediate frequency filters in radio receivers(=radios, mobile phones, GPS, ...). At very high frequencies, active RC filters cannot be realized because of difficulties in realizing stable feedback loops with high gains, and g<sub>m</sub>-C filters are used instead.