Active RC universal filter

• Understand the operation of an active RC (i.e. opamp-RC) filter

• Brief introductory lecture about this experiment

• Analog Circuits Course lectures on VLSI group videolectures
  • Synthesis of a second order active-RC filter with bandpass and low-pass outputs.
  • Synthesis of a biquad with arbitrary numerator, the effect of finite input and output impedance of opamps in feedback amplifiers.

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 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 V₁ as output) with a resonance frequency of 10kHz and a quality factor of 10. Determine where you will apply the input.

• Use LF347 quad opamp for this experiment
• Build 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?

• 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.