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'''Heterodyne detection''' is a method of detecting frequency-modulated radiation by non-linear mixing with radiation of a reference frequency.

The radiation in question is most commonly either radio waves (see ]) or light (see ]). The reference radiation is known as the ]. The signal and the local oscillator are superimposed at a '''mixer'''. The mixer, which is commonly a (photo-)], has a non-linear response to the amplitude, that is, at least part of the output is proportional to the square of the input.

Let the electric field of the received signal be

:<math>E_\mathrm{sig}\cos(\omega_\mathrm\mathrm{sig}+\phi)\,</math>

and that of the local oscillator be

:<math>E_\mathrm{LO}\cos(\omega_\mathrm{LO}).\,</math>

For simplicity, assume that the output of the detector ''I'' is proportional to the square of the amplitude:
:<math>I</math><math>\propto</math> <math> \left( E_\mathrm{sig}\cos(\omega_\mathrm{sig}t+\phi) + E_\mathrm{LO}\cos(\omega_\mathrm{LO}t) \right)^2</math>

:<math>=</math>
:<math> E_\mathrm{sig}^2 (1/2)\left( 1+\cos(2\omega_\mathrm{sig}t+2\phi) \right)</math>
:<math> + E_\mathrm{LO}^2 (1/2)(1+\cos(2\omega_\mathrm{LO}t) </math>
:<math> + E_\mathrm{sig}E_\mathrm{LO} \left[
\cos((\omega_\mathrm{sig}+\omega_\mathrm{LO})t+\phi)
+ \cos((\omega_\mathrm{sig}-\omega_\mathrm{LO})t+\phi)
\right]
</math>

The output has high frequency (<math>2\omega_\mathrm{sig}</math> and <math>2\omega_\mathrm{LO}</math>) and constant components. In heterodyne detection, the high frequency components and usually the constant components are filtered out, leaving the two intermediate (beat) frequencies at <math>\omega_\mathrm{sig} + \omega_\mathrm{LO}</math> and <math>\omega\mathrm_\mathrm{sig}-\omega_\mathrm\mathrm{LO}</math>. The amplitude of these last components is proportional to the amplitude of the signal radiation. With appropriate ] the phase of the signal can be recovered as well.

==See also==

*]

]

Latest revision as of 19:03, 16 May 2017

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