A variable frequency oscillator (VFO) in electronics is an oscillator whose frequency can be tuned (i.e., varied) over some range. It is a necessary component in any tunable radio transmitter and in receivers that works by the superheterodyne principle. The oscillator controls the frequency to which the apparatus is tuned. In a simple superheterodyne receiver, the incoming radio frequency signal (at frequency ) from the antenna is mixed with the VFO output signal tuned to , producing an intermediate frequency (IF) signal that can be processed downstream to extract the 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 (up-conversion), or more commonly, the difference frequency (down-conversion), . 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, and and various harmonic combinations of the input signals. These undesired signals are rejected by the IF 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 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. In a direct-conversion receiver, the VFO is tuned to the same frequency as the incoming radio frequency and Hz. Demodulation takes place at baseband using low-pass filters and amplifiers. In a radio frequency (RF) transmitter, VFOs are often used to tune the frequency of the output signal, often indirectly through a heterodyning process similar to that described above. Other uses include chirp generators for radar systems where the VFO is swept rapidly through a range of frequencies, timing signal generation for oscilloscopes and time domain reflectometers, and variable frequency audio generators used in musical instruments and audio test equipment.