====== Active RC universal filter ======
===== Goals =====
  * Understand the operation of an active RC (i.e. opamp-RC) filter

===== Lecture =====
  * [[http://www.ee.iitm.ac.in/~nagendra/EC330/201401/lectures/activeRCfilter/activeRCfilter.html|Brief introductory lecture about this experiment]]

===== References =====
  * Analog Circuits Course lectures on [[http://www.ee.iitm.ac.in/~nagendra/videolectures/doku.php?|VLSI group videolectures]]
    * [[http://www.ee.iitm.ac.in/~nagendra/shanthi_lectures/EC201/14NovEC201/14NovEC201.html|Synthesis of a second order active-RC filter with bandpass and low-pass outputs.]]
    * [[http://www.ee.iitm.ac.in/~nagendra/shanthi_lectures/EC201/15NovEC201/15NovEC201.html|Synthesis of a biquad with arbitrary numerator, the effect of finite input and output impedance of opamps in feedback amplifiers.]]

===== Preliminaries(to be done before the lab) =====
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 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<sub>1</sub> as output) with a resonance frequency of 10kHz and a quality factor of 10. Determine where you will apply the input.

{{:courses:ec330:ttbiquad.png?600}}

===== Experiment =====
  * Use LF347 quad opamp for this experiment
  * Build a bandpass filter (with V<sub>1</sub> 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<sub>1</sub>? 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)|<sup>2</sup>.
  * Modify the above circuit to get a highpass filter output at V<sub>1</sub>? 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<sub>m</sub>-C filters are used instead.