Misplaced Pages

Heterodyne detection: Difference between revisions

Article snapshot taken from Wikipedia with creative commons attribution-sharealike license. Give it a read and then ask your questions in the chat. We can research this topic together.
Browse history interactively← Previous editContent deleted Content addedVisualWikitext
Revision as of 01:52, 16 February 2017 editLayzeeboi (talk | contribs)Extended confirmed users1,039 edits rewrote lede to mirror lede of Homodyne detection← Previous edit Latest revision as of 19:03, 16 May 2017 edit undoChetvorno (talk | contribs)Extended confirmed users65,424 edits Merged article into Heterodyne 
(4 intermediate revisions by 3 users not shown)
Line 1: Line 1:
#REDIRECT ] {{R from merge}}
{{{mergeto| Heterodyne|discuss=Talk: Heterodyne#Merger proposal: Heterodyne detection|date=February 2017}}
{{Technical|date=June 2011}}
'''Heterodyne detection''' is a method of extracting information encoded as ] of the ] and/or ] 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 ]. The heterodyne technique is commonly used in ], ], ] and ].

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

=Multiplicative mixer=
The received signal can be represented as

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

and that of the local oscillator can be represented as

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

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

:<math> =\frac{E_\mathrm{sig}^2}{2}\left( 1+\cos(2\omega_\mathrm{sig}t+2\varphi) \right)</math>

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

::<math> + \underbrace{E_\mathrm{sig}E_\mathrm{LO} \cos((\omega_\mathrm{sig}-\omega_\mathrm{LO})t+\varphi)}_{beat\;component}.
</math>

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

If <math>\omega_\mathrm{LO}</math> is equal to <math>\omega_\mathrm{sig} </math> then the beat component is a recovered version of the original signal, with the amplitude equal to the product of <math> E_\mathrm{sig} </math> and <math>E_\mathrm{LO} </math>; that is, the received signal is amplified by mixing with the local oscillator{{What|reason=But at double the frequency?|date=October 2016}}. This is the basis for a ].

==See also==
*]
*]
*]

{{DEFAULTSORT:Heterodyne Detection}}
]
]

Latest revision as of 19:03, 16 May 2017

Redirect to:

  • From a merge: This is a redirect from a page that was merged into another page. This redirect was kept in order to preserve the edit history of this page after its content was merged into the content of the target page. Please do not remove the tag that generates this text (unless the need to recreate content on this page has been demonstrated) or delete this page.