|Formula for the lower cutoff frequency:|
|Formula for the upper cutoff frequency:|
|Formulas mailed by Daniel Fournier|
|Formula for the Q factor:|
|Formula for the bandwidth:|
| A high filter quality means narrow-band filtering (notch), with a large Q factor.
This results in steep filter flanks with a small bandwidth.
A low filter quality means broad-band filtering, with a small Q factor.
This results in flat filter flanks with a large bandwidth.
A low Q factor gives a broad band (wide) bandwidth or a high Q factor gives a narrow band (small) bandwidth.
Q factor as a function of the bandwidth in octaves N (octave bandwidth)
| Bandwidth in
|3.0 wide||0.404 low|
|1/12 small||17.310 high|
Conversion: 'bandwidth in octaves' N to quality factor Q
Interrelationship of 'octave bandwidth' N and the quality factor Q
Formulas for conversion of bandwidth in octaves to quality factor
Questions on "Parametric filter adjustment"
Conversion table Q to N and N to Q for parametric filters
Filter slope or steepness (dB/oct) is not bandwidth
Excel conversion - quality factor Q to bandwidth in octaves N
Calculating the center frequency from a given bandwidth
Finding the filter center frequency - geometric mean
Conversion RC-pad − R × C to Corner frequency fc and Cutoff frequency to R × C − Time constant t (tau) = R × C
|3 dB implies 1/2 the power and since the power is proportional to the
square of voltage, the voltage will be 0.707 or 70.7 % of the passband voltage.
√ (0.5) = 0.707
Bandwidth for Yamaha Parametric Equalizer
|For a Yamaha parametric equalizer EQ there is the filter bandwidth of an
octave divided in 60/60 (12 semitones).
One half tone step (semitone) is then 5/60 − 01V Digital Mixing Console.
N = "bandwidth in octaves" (semi tone or half tone distance). Q = Q factor
|Filter EQ||N||Q||Interval||Filter EQ||N||Q||Interval|
|30/60||0.5||2.871||1/2 octave||120/60||2||0.667|| 2 octaves
|60/60||1||1.,414||1 octave||150/60||2.5||0.511||2.5 octaves|
|90/60||1.5||0.92||1.5 octaves||180/60||3||0.404||3 octaves|
|The "BW/60" control replicates the effect of the Behringer Pro DSP1124P - Feedback Destroyer bandwidth setting.
This control sets the bandwidth of the filter between the half-gain points with:
Note that the Behringer DSP1100 - 24 band parametric equalizer software package does NOT correctly reproduce the way the bandwidth control actually operates, its bandwidths are too small by a factor of √2.
Defining filter bandwidth in this way is not uncommon (the TMREQ filters use a similar definition).
The relationship between Q and BW for the DSP1124P is:
|Why is the bandwidth and the cutoff frequency found at the level of "−3 dB"?
Why we always take 3 dB down gain of a filter?
Full width at half maximum (FWHM).
Answer: That is the point where the energy (power) is fallen to the 1/2 value or 0.5 = 50 percent of the initial energy quantity.
There the voltage is fallen to the value of √(1/2) = 1/√2 or 0.7071 = 70.71 percent of the initial voltage as field quantity. A 3 dB voltage drop is a decrease of 29.29 % to 70,71 %.
Quality Factor Q = f0 / BW
BW = f0/Q Q = f0/BW f0= BW × Q
Please enter two values, the third value will be calculated.