**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_{i1,R}, V_{i1,C}, V_{i2,R}, V_{i2,C}, V_{i3,R} and output V_{1}, V_{2}, V_{3}.

Determine the following:

- Transfer functions for all input-output combinations.
- The components on which the resonance frequency and the quality factor depend on.
- The components on which the zeroes depend on.
- Component values for a bandpass filter (with V
_{1}as output) with a resonance frequency of 10kHz and a quality factor of 10. Determine where you will apply the input.

- Build a bandpass filter (with V
_{1}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
_{1}? 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 V
_{1}? 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.