Question

Explain the phase shift in Lock in Amplifier

Answer 1

Operation of a lock-in amplifier relies on the orthogonallity 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, mulipies 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.