====== Opamp based universal filter ======
  * 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 resonant frequency and the quality factor depend on? 
  * Which components do the zeros depend on? 

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  * Design a bandpass filter (with V<sub>1</sub> as output) for a resonant frequency of 3kHz and a quality factor of 5. 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 is the minimum modification required to get a lowpass filter output at V<sub>1</sub>? Verify it.
  * What is the minimum modification required to get a highpass filter output at V<sub>1</sub>? Verify it.