The Definition of Q Factor by an Equation and How to Graph

I am currently building an EQ in an music app, and it's relatively simple:

6 bands of fixed center frequency, and a Q knob to control the Q of all bands, because we do not currently have space for separate Q knobs for each individual band.

The problem is that we need to draw an EQ graph according to the user's settings like the one usually seen on a sound board.

My current understanding is that the Y axis is measured in dB's and grows linearly, and the X axis is the frequency and grows exponentially (a Lin-Log graph, that is).

I have no problem drawing this, until the Q factor comes in. I know that Q makes the affected range larger if Q is smaller, and shrinks the affected range if Q is larger.

However, I do not not how to calculate the exact staring position and end position of the "bump" of that Peak EQ filter, if I'm given a center frequency of 1 kHz and a Q of 2.0.

What is the mathematical formula to compute the beginning and end of the curve?

• I went ahead and added a few line breaks (possibly: too many) to your two questions, simply to make them easier to read (and not one wall of text). – Marcus Müller Dec 16 '18 at 1:08
• dB is a logarithmic scale. So, with respect to amplitude (or power) the described graph would be log-log, with respect to logarithmic amplitude (or power), it is indeed lin-log. – Marcus Müller Dec 16 '18 at 1:08
• If your "Q" is the Quality Factor of a filter (I'm not well-versed in the conventions of audio terminology), then it is defined to be the ratio between passband width and center frequency. That would immediately be your formula. Does this help? – Marcus Müller Dec 16 '18 at 1:10
• Thanks for your edition! But if the Q is defined that way, what is the "passband width" then? Say I have a Q of 0.5 on frequency 2K, isn't the width going to be 2K/0.5 which is 4K? How can the width be 4K? Or is there a value range of Q and it cannot be certain number? Thanks! @MarcusMüller – Nicholas Dec 16 '18 at 4:54
• You might find these sources helpful in this - sengpielaudio.com/calculator-bandwidth.htm and sengpielaudio.com/calculator-cutoffFrequencies.htm – Juha P Dec 16 '18 at 8:19