Active RC filters

Question

I was reading paragraph 4.2 of this book about Active RC filters.

It says that if we want to get a band pass filter with high selectivity (i.e. high quality factor Q) we should use resonant circuits (like RLC circuits). But, since high inductances are difficult to realize in integrated circuits, this solution cannot be used in many situations, and the alternative is that of using some active components (like Op - Amp or OTA).

What I do not understand is: why does the presence of active components guarantee sharp filter shapes (as a resonant circuit with high Q)?

Answer 1

The 'problem' is that you have not understood what he is actually saying.
In the text below he effectively says:

• Filters with high selectivity require [by definition] sharp transitions between passband and stopband.

• The realisation of such "transfer functions" mathematically requires the use of high Q components with the "mathematically represented" characteristics of inductors.

• In typical applications the required inductances are often mechanically large.

• The mathematical representation of RC components mean that filter circuits using them without amplification are only able to implement poles with Q <= 0.5.

• However, by using circuits which 'mathematically transform' the characteristics of RC circuits it is possible to implement circuit blocks which emulate the high Q behaviour of inductors.

• So, the use of RC circuits and Opamps or OTAs allow the realisation of more physically compact filters and do not require the use of inductors.

The key points here are

• Sharp filters require components with certain characteristics in order to implement the transfer functions.

  • Inductors have these characteristics

  • Resistors don't.

  • Circuit blocks using Resistors + Opamps/OTAs can be made to.

______________

Answer 2

Active filters use the Transimpedance and Inversion feedback property to make active inductors with a capacitor but very limited on current.

Passive Q of 100 is possible but critical with temperature compensation needing PTC caps to compensate for NTC inductors. Also tolerances are usually unobtainable unless using a trimcap or varicap. but not here with 158uF.

The Q factor also amplifies the need for GBW greatly even if operating at a low frequency.

Example BPF f0 =1kHz 8th order Butterworth BW =<50 Hz
I selected GBW slider =1MHz then peak gain was -29dB instead of 0dB.

The highest analog GBW is about 500MHz. There are several topologies and many free filter design tools online or downloadable. TI, AD, etc.