Electronic – Cutoff frequency: exactly -3 db of power

cutoff frequencyfilter

I have a question which may sound strange, but still I'd like to ask community to explain that. Hope other people may find it interesting aswell.

As we know, cutoff frequency is the one frequency harmonics of which is being reduced by 3 db (or Vpp is sqrt(2) times lesser than harmonics Vpp before the filter).

This image gives more or less clear picture of that idea (consider the red line, cutoff frequency marked as fcp):

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What that means: the filter passes all harmonics of the input signal through, but some of them are being reduced in power. Harmonics of some frequency are being reduced by 3 db, this frequency is a cutoff frequency of that particular filter.

This is the defininition and the explanation of my understanding of the term. I'd be grateful for corrections, if any 🙂

Now, the question itself: the word cutoff means that something is being cut. So, we may say that harmonics of particular frequency are filtered, if Vpp reduced by 3 db or more. The question is – why exactly 3 db? Saying exactly I mean

enter image description here

Best Answer

The 3-dB cutoff is just one commonly used way to describe a filter. For some applications you might want to specify the 10-dB cutoff or 60-dB cutoff instead. It is convention that if someone says "cutoff frequency" without being more specific, they are talking about the 3-dB cutoff. You should think of the 3-dB cutoff as the frequency where the filter begins to roll off, not where it is strongly attenuating the signal.

There are a couple of practical reasons to use the 3-dB point as the conventional cut-off frequency.

  1. In a one-pole RC filter, the 3-dB frequency is conveniently found at a radian frequency of \$\dfrac{1}{RC}\$.

  2. If you draw a piecewise linear approximation to your one-pole transfer function plot, using a horizontal line segment for the low frequencies, and a 20-dB per decade sloped line for the frequencies well above cut-off, these two approximate lines will meet at the 3-dB frequency. Often when we just want to sketch a frequency response we make a Bode plot, which uses exactly this approximation.

enter image description here

(image courtesy Wikimedia)

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