Editing Beat frequency oscillator (section)

==Example==
[[File:D 1944 Rohde und Schwarz STT4032 Front Large.jpg|thumb|upright=1.0|Separate BFO oscillators were manufactured for receivers that didn't have them; a Rohde und Schwarz STI4032 from 1944.]]
[[Image:Goldschmidt tone wheel.jpg|thumb|upright=1.5|One of the first crude examples of a BFO, the Goldschmidt [[tone wheel]]. Before vacuum tube [[electronic oscillator|oscillator]]s were invented, the first CW receivers used a wheel with electrical contacts around its rim, spun at a high speed by a motor, to interrupt a current to create a radio frequency signal to beat with the incoming radio signal.  This example, at the Tuckerton transatlantic receiving station in New Jersey in 1917, created a 40 kHz signal.]]

A receiver is tuned to a [[Morse code]] signal, and the receiver's [[intermediate frequency]] ('''IF''') is ''f''<sub>IF</sub> = 45000&nbsp;Hz.  That means the dits and dahs have become pulses of a 45000&nbsp;Hz signal, which is inaudible.

To make them audible, the frequency needs to be shifted into the audio range, for instance ''f''<sub>audio</sub> = 1000&nbsp;Hz.  To achieve that, the desired BFO frequency is ''f''<sub>BFO</sub> = 44000 or 46000 Hz. 
 
When the signal at frequency ''f''<sub>IF</sub> is mixed with the BFO frequency in the [[detector (radio)|detector]] stage of the receiver, this creates two other frequencies or [[heterodyne]]s:  |''f''<sub>IF</sub> &minus; ''f''<sub>BFO</sub>|, and |''f''<sub>IF</sub> + ''f''<sub>BFO</sub>|.    The ''difference frequency'', ''f''<sub>audio</sub> = |''f''<sub>IF</sub> &minus; ''f''<sub>BFO</sub>| = 1000 Hz, is also known as the [[beat frequency]].

The other, the ''sum frequency'', ''(F<sub>if</sub> + F<sub>bfo</sub>)'' = 89000 or 91000&nbsp;Hz, is unneeded. It can be removed by a [[lowpass filter]], such as the radio's speaker, which cannot vibrate at such a high frequency.

''f''<sub>BFO</sub> = 44000 or 46000&nbsp;Hz produces the desired 1000&nbsp;Hz beat frequency and either could be used.

By varying the BFO frequency around 44000 (or 46000) Hz, the listener can vary the output audio frequency; this is useful to correct for small differences between the tuning of the transmitter and the receiver, particularly useful when tuning in [[single sideband]] (SSB) voice. The waveform produced by the BFO ''beats'' against the IF signal in the mixer stage of the receiver. Any drift of the local oscillator or the beat-frequency oscillator will affect the pitch of the received audio, so stable oscillators are used.<ref>Paul Horowitz, Winfield Hill "The Art of Electronics 2nd Ed." Cambridge University Press 1989 {{ISBN|0-521-37095-7}}, page 898</ref>

For single sideband reception,  the BFO frequency is adjusted above or below the receiver intermediate frequency, depending on which sideband is used.<ref name=ARRL/>