Editing Variable-frequency oscillator (section)

==Purpose==
In a simple [[superheterodyne receiver]], the incoming radio frequency signal (at frequency <math>f_{IN}</math>) from the [[antenna (radio)|antenna]] is [[frequency mixer|''mixed'']] with the VFO output signal tuned to <math>f_{LO}</math>, producing an [[intermediate frequency]] (IF) signal that can be processed downstream to extract the [[modulation|modulated]] information. Depending on the receiver design, the IF signal frequency is chosen to be either the sum of the two frequencies at the mixer inputs ([[Heterodyne#Up and down converters|up-conversion]]), <math>f_{IN}+f_{LO}</math> or more commonly, the difference frequency (down-conversion), <math>f_{IN}-f_{LO}</math>.

In addition to the desired ''IF'' signal and its unwanted image (the mixing product of opposite sign above), the mixer output will also contain the two original frequencies, <math>f_{IN}</math> and <math>f_{LO}</math> and various [[harmonic]] combinations of the input signals. These undesired signals are rejected by the IF [[electronic filter|filter]]. If a double balanced mixer is employed, the input signals appearing at the mixer outputs are greatly attenuated, reducing the required complexity of the IF filter.

The advantage of using a VFO as a [[heterodyne|heterodyning]] oscillator is that only a small portion of the radio receiver (the sections before the mixer such as the preamplifier) need to have a wide bandwidth. The rest of the receiver can be finely tuned to the IF frequency.<ref name="Rohde88">{{citation | last=Rohde | first=Ulrich | title=Communication Receivers Principles and Design | publisher=McGraw Hill | year=1988 | isbn=0-07-053570-1 }}</ref>

In a [[direct-conversion receiver]], the VFO is tuned to the same frequency as the incoming radio frequency and <math>f_{IF}=0 </math> Hz. Demodulation takes place at baseband using [[low-pass filter]]s and [[amplifier]]s.

In a radio frequency (RF) [[transmitter]], VFOs are often used to tune the frequency of the output signal, often indirectly through a [[heterodyne|heterodyning]] process similar to that described above.<ref name="arrlhandbook"/> Other uses include [[chirp]] generators for radar systems where the VFO is swept rapidly through a range of frequencies,<ref name="ifr">{{citation | url=http://www.ifrsys.com/ats/products/prodfiles/appnotes/8404/chirp.pdf | title=Generating frequency chirp signals to test radar systems|publisher=IFR corp.}}</ref> timing signal generation for [[oscilloscope]]s and [[time domain reflectometer]]s, and variable frequency audio generators used in musical instruments and audio test equipment.