Center frequency

The center frequency f0 is the geometric mean of the upper and lower f1 f2 limit frequency ( crossover frequency ), a frequency band having a certain bandwidth filter, also known as bandpass.

Basics

The center frequency of the filter bandwidth B = f 2 - f 1 is calculated from:

Often is falsely calculated with the arithmetic means, while the frequencies in the frequency bands related logarithmically. For example, the center frequency of the telephone audio frequencies from 300 Hz to 3400 Hz is ( 3400 300 ) / 2 Hz = 1850 Hz, but the square root of 300 Hz · 3400 Hz = 1010 Hz

Properties of the center frequency

By defining the center frequency, the ratios of the cut-off frequencies are equal to the center frequency:

If f1, f0 and f2 marked on a logarithmitschen frequency scale is f0 distance compared in the middle:

Use of the arithmetic mean as an approximation

The bandwidth f2 - f1 is often small compared to the center frequency. Then you can use a good approximation to calculate the arithmetic mean:

In many broadcast stations, the bandwidth is only 9 kHz. A transmitter, which is indicated at 1500 kHz, sends here the band of kHz to 1495.5 1504.5 kHz. The approximate formula is

While with the exact formula

Determined. The computed using the approximation formula value is always too large. If denotes the bandwidth B, the deviation of the approximation formula is about

In the example given, less than 7 Hz