Goals:

Use LF347 quad opamp for this experiment

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 resonance frequency and the quality factor depend on?

Which components do the zeros depend on?

Design a bandpass filter (with V₁ 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 V₁? 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)|².

Modify the above circuit to get a highpass filter output at V₁? 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_m-C filters are used instead.