Electronic – the advantage of RLC low pass filter over two RC conneced in series

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I guess two RC in series should be a second order low pass filter. Because the transfer function will have s^2. And an RLC low pass filter is a second order filter for sure.

So what is the difference between to RC in series and one RLC filter.

Best Answer

What is the advantage of RLC low pass filter over two RC connected in series?

With two RC low pass filters in series, the Q can never be greater than 0.5 and therefore it cannot make use of the peaking effects you get when you use an RLC low pass filter such as this one: -

enter image description here

Picture from here.

Look at the red trace - around resonance you can achieve a peak in the response - this can be used to highly optimize filters and improve the pass band.

With a 2nd order filter made from cascading two RC filters you have limited peak control equivalent to the Q of the RLC circuit being a maximum of 0.5: -

enter image description here

The above was made to have a Q of 0.5 by increasing the series resistance to 200 ohms.

If you want the math: -

A single low pass CR stage has a transfer function of \$\dfrac{1}{1+ sCR}\$

For 2 stages and ignoring loading effects of the 2nd stage you'd get a TF of \$\dfrac{1}{(1+ sCR)^2}\$

If you rearranged this into standard form you'd get this: -

$$\dfrac{\frac{1}{C^2R^2}}{s^2 + s\frac{2}{CR} + \frac{1}{C^2R^2}}$$

And the standard form can be shown to have these equivalent parameters: -

  • \$\frac{1}{C^2R^2} = \omega_n^2\$
  • \$\frac{2}{CR} = 2\zeta\omega_n\$

If you rearranged these you'd find that \$\zeta\$ = 1 and, because \$\frac{1}{2\zeta} = Q\$, then Q = 0.5.

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