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It has been suggested that this article be merged into Heterodyne. (Discuss) Proposed since February 2017.

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Heterodyne detection is a method of extracting information encoded as modulation of the phase and/or frequency of an oscillating signal, by comparing that signal with a standard or reference oscillation that would have a fixed offset in frequency and phase from the signal if it carried null information. "Heterodyne" signifies more than one frequency, in contrast to the single frequency employed in homodyne detection. The heterodyne technique is commonly used in doppler radar, continuous-wave radar, telecommunications and astronomy.

The processed signals are most commonly produced by the reception of radiation in the form of either radio waves (see superheterodyne receiver) or light (see Optical heterodyne detection or interferometry). The reference signal is known as the local oscillator. The signal and the local oscillator are compared in the receiver using a type of technology suitable for the wavelength of the radiation. For radio frequency signals, a frequency mixer may be used, while for light a common mixer is a photodiode, which has a response that is linear in energy, and hence quadratic in amplitude.

Multiplicative mixer

The received signal can be represented as

${\displaystyle E_{\mathrm {sig} }\cos(\omega _{\mathrm {sig} }t+\varphi )\,}$

and that of the local oscillator can be represented as

${\displaystyle E_{\mathrm {LO} }\cos(\omega _{\mathrm {LO} }t).\,}$

For simplicity, assume that the output I of the detector is proportional to the square of the amplitude:

${\displaystyle I\propto \left(E_{\mathrm {sig} }\cos(\omega _{\mathrm {sig} }t+\varphi )+E_{\mathrm {LO} }\cos(\omega _{\mathrm {LO} }t)\right)^{2}}$

${\displaystyle ={\frac {E_{\mathrm {sig} }^{2}}{2}}\left(1+\cos(2\omega _{\mathrm {sig} }t+2\varphi )\right)}$

${\displaystyle +{\frac {E_{\mathrm {LO} }^{2}}{2}}(1+\cos(2\omega _{\mathrm {LO} }t))}$

${\displaystyle +E_{\mathrm {sig} }E_{\mathrm {LO} }\left}$

${\displaystyle =\underbrace {\frac {E_{\mathrm {sig} }^{2}+E_{\mathrm {LO} }^{2}}{2}} _{constant\;component}+\underbrace {{\frac {E_{\mathrm {sig} }^{2}}{2}}\cos(2\omega _{\mathrm {sig} }t+2\varphi )+{\frac {E_{\mathrm {LO} }^{2}}{2}}\cos(2\omega _{\mathrm {LO} }t)+E_{\mathrm {sig} }E_{\mathrm {LO} }\cos((\omega _{\mathrm {sig} }+\omega _{\mathrm {LO} })t+\varphi )} _{high\;frequency\;component}}$

${\displaystyle +\underbrace {E_{\mathrm {sig} }E_{\mathrm {LO} }\cos((\omega _{\mathrm {sig} }-\omega _{\mathrm {LO} })t+\varphi )} _{beat\;component}.}$

The output has high frequency (${\displaystyle 2\omega _{\mathrm {sig} }}$, ${\displaystyle 2\omega _{\mathrm {LO} }}$ and ${\displaystyle \omega _{\mathrm {sig} }+\omega _{\mathrm {LO} }}$) and constant components. In heterodyne detection, the high frequency components and usually the constant components are filtered out, leaving the intermediate (beat) frequency at ${\displaystyle \omega _{\mathrm {sig} }-\omega _{\mathrm {LO} }}$. The amplitude of this last component is proportional to the amplitude of the signal radiation. With appropriate signal analysis the phase of the signal can be recovered as well.

If ${\displaystyle \omega _{\mathrm {LO} }}$ is equal to ${\displaystyle \omega _{\mathrm {sig} }}$ then the beat component is a recovered version of the original signal, with the amplitude equal to the product of ${\displaystyle E_{\mathrm {sig} }}$ and ${\displaystyle E_{\mathrm {LO} }}$; that is, the received signal is amplified by mixing with the local oscillator. This is the basis for a Direct conversion receiver.

See also

• Heterodyne
• Homodyne detection
• Optical heterodyne detection

• Articles to be merged from February 2017
• Waves
• Metrology