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Given:

  1. Center Frequency f0 = 2.2KHz
  2. Q factor = 5

The problem I'm facing is this: How do I calculate the 2 cutoff frequencies of this band pass filter? I'm confused because my question says "The cutoff frequency is not always the -3dB point. This is only the case for Q = 0.707".

I found a website that calculates the cutoff for a band pass, and the results were:

[F1 = 20KHz to F2= 2.4KHz].

But when I simulate the circuit in Multisim, I have a huge difference between the results:

[F1= 1kHz and F2=5kHz].

I need a way to calculate the two cutoff frequencies. The system functions are given at the end of the figures:

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Copied from Wikipedia!

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  • \$\begingroup\$ "I'm confused because my question says "The cutoff frequency is not always the -3dB point." Are you sure that this statemenet was used in conjunction with your bandpass? I think, it applies - in particular - to LOWPASS stages. \$\endgroup\$
    – LvW
    Nov 16, 2016 at 8:29

2 Answers 2

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The results Multisim gives you are correct. You can check it by using this calculator.

The cutoff frequencies are calculated by analyzing the circuit and seeing which part of it is responsible for low-/high-pass and calculating the corresponding frequencies. Check out this website for a detailed explanation!

As to the results you got from a website, they seem to be wrong or misinterpreted - your center frequency is only 2.2 kHz, but f1 is 20 kHz and f2 is 2.4 kHz - the range doesn't even cover the center frequency.

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The Q is always defined as \$Q=f_O/\Delta f_{-3dB}\$

The cutoff frequencies are always the -3dB point or voltage = 0.707 compared to peak=1

The \$|f2-f1|=\Delta f\$. which are the -3dB values.

Δf = BW\$_{ −3dB}\$ or the half-power full bandwidth

For more detail on a recent question (Oct 2021). Creating a digital PLL

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  • \$\begingroup\$ Would you call \$\Delta f \$ for the "bandwidth" @Tony? \$\endgroup\$
    – Carl
    Oct 7, 2021 at 16:00
  • \$\begingroup\$ @Carl yes that is Δf.=BW \$_{-3dB}\$ or the half-power full bandwidth \$\endgroup\$ Oct 7, 2021 at 19:02

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