The circuit below can have inputs V_i1,R, V_i1,C, V_i2,R, V_i2,C, V_i3,R and output V₁, V₂, V₃. 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?

Design a bandpass filter (with V₁ 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 V₁? Verify it.

What is the minimum modification required to get a highpass filter output at V₁? Verify it.