Center frequency Guide, Meaning , Facts, Information and Description
The
center frequency f
0 (
resonant frequency) is the
geometric mean between the lower
cutoff frequency f
1 and the upper cutoff frequency f
2 of a frequency band. See also:
Band-pass filter. f2 - f1 is called the
bandwidth B.
Only if the
bandwidth f
2 - f
1 is very small in comparison to the center frequency it is sometimes possible to use this
arithmetic mean for calculations, but this is often calculated in mistake:
At radio stations (medium wave) the bandwidth is often only 9 kHz. A transmitter, which has 1500 kHz, is transmitting from 1495.5 kHz to 1504.5 kHz.
The exact formula gives:
and the short formula gives in this case the very close result of:
The short calculated value is always too large. If the bandwidth is given by B = f
2 - f
1, the difference is:
- .
But if for instance we are looking for the center frequency of the telephone audio band from 300 Hz to 3300 Hz, we get (3300 + 300) / 2 = "1800 Hz" for the short arithmetic mean calculation, but the root of 300 x 3300 = "995" Hz with the correct geometric mean formula. What a big difference!
That the geometric mean is not the arithmetic mean can be seen in a calculation program at the bottom in the external link. There one can compare the difference of both values.
External link
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