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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Lock-in amplifier ： ウィキペディア英語版 Lock-in amplifier ] A lock-in amplifier is a type of amplifier that can extract a signal with a known carrier wave from an extremely noisy environment. Depending on the dynamic reserve of the instrument, signals up to 1 million times smaller than noise components, potentially fairly close by in frequency, can still be reliably detected. It is essentially a homodyne detector followed by low pass filter that is often adjustable in cut off frequency and filter order. Whereas traditional lock-in amplifiers use analog frequency mixers and RC filters for the demodulation, state of the art instruments have both steps implemented by fast digital signal processing for example on an FPGA. Usually sine and cosine demodulation is performed simultaneously, which is sometimes also referred to as dual phase demodulation. This allows the extraction of the in-phase and the quadrature component that can then be transferred into polar coordinates, i.e. amplitude and phase, or further processed as real and imaginary part of a complex number (e.g. for complex FFT analysis). The device is often used to measure phase shift, even when the signals are large and of high signal-to-noise ratio, and do not need further improvement. Recovering signals at low signal-to-noise ratios requires a strong, clean reference signal the same frequency as the received signal. This is not the case in many experiments, so the instrument can recover signals buried in the noise only in a limited set of circumstances. The lock-in amplifier is commonly believed to be invented by Princeton University physicist Robert H. Dicke who founded the company Princeton Applied Research (PAR) to market the product. However, in an interview with Martin Harwit, Dicke claims that even though he is often credited with the invention of the device, he believes he read about it in a review of scientific equipment written by Walter C Michels, a professor at Bryn Mawr College.〔Oral History Transcript — Dr. Robert Dicke http://www.aip.org/history/ohilist/4572.html〕 This could have been a 1941 paper by Michels and Curtis, which in turn cites a 1934 paper by C. R. Cosens. Another timeless paper was written by C.A. Stutt in 1949.〔Stutt, C.A. (1949). "Low-frequency spectrum of lock-in amplifiers". MIT Technical Report (MIT) (105): 1–18. http://dspace.mit.edu/handle/1721.1/4940〕 == Basic principles == Operation of a lock-in amplifier relies on the orthogonality of sinusoidal functions. Specifically, when a sinusoidal function of frequency ''f1'' is multiplied by another sinusoidal function of frequency ''f2'' not equal to ''f1'' and integrated over a time much longer than the period of the two functions, the result is zero. Instead, when ''f1'' is equal to ''f2'' and the two functions are in phase, the average value is equal to half of the product of the amplitudes. In essence, a lock-in amplifier takes the input signal, multiplies it by the reference signal (either provided from the internal oscillator or an external source), and integrates it over a specified time, usually on the order of milliseconds to a few seconds. The resulting signal is a DC signal, where the contribution from any signal that is not at the same frequency as the reference signal is attenuated close to zero. The out-of-phase component of the signal that has the same frequency as the reference signal is also attenuated (because sine functions are orthogonal to the cosine functions of the same frequency), making a lock-in a phase-sensitive detector. For a sine reference signal and an input waveform $U\_\backslash mathrm(t)$, the DC output signal $U\_\backslash mathrm(t)$ can be calculated for an analog lock-in amplifier by: :$U\_\; \backslash int\_^t\; \}(s)\}\backslash ;\backslash mathrms$ where ''φ'' is a phase that can be set on the lock-in (set to zero by default). If the averaging time T is large enough (e.g. much larger than the signal period) to suppress all unwanted parts like noise and the variations at twice the reference frequency, the output is :$U\_\backslash cos\backslash theta$ where $V\_$ is the signal amplitude at the reference frequency and $\backslash theta$ is the phase difference between the signal and reference. Many applications of the lock-in only require recovering the signal amplitude rather than relative phase to the reference signal. For a simple so called single phase lock-in-amplifier the phase difference is adjusted (usually manually) to zero to get the full signal. More advanced, so called two phase lock-in-amplifiers have a second detector, doing the same calculation as before, but with an additional 90 degree phase shift. Thus one has two outputs: $X=V\_\backslash cos\backslash theta$ is called the 'in-phase' component and $Y=V\_\backslash sin\backslash theta$ the 'quadrature' component. These two quantities represent the signal as a vector relative to the lock-in reference oscillator. By computing the magnitude (R) of the signal vector, the phase dependency is removed: :$R=\backslash sqrt=\; V\_$. The phase can be calculated from :$\backslash tan\; \backslash theta\; =\; Y/X$. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Lock-in amplifier」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.