How to convert voltage units to phase units from the Lock-In Amplifier
Written by Dylan Perez
Updated at April 10th, 2025
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Liquid Instrument's Lock-In Amplifier (LIA) can recover amplitude and phase information from a low signal-to-noise ratio (SNR) signal. The LIA can recover the in-phase (X) adn quadrature (Y) component of your signal, or can be switched to polar mode which will output the amplitude (R) and phase (Θ) of your signal. When the LIA is set to Θ mode, the output will be a voltage signal that is proportional to the phase of your signal. The range for the Θ component is 1 V/cycle, which means that the range of the Θ measurement is -500 mV to 500 mV.
Converting the voltage to phase is done by the formula:
(360°/V) * (VΘ) = Δɸ
where VΘ is the LIA output voltage in Θ mode and Δɸ is the phase change in units of degrees.
To prove this, a 1 MHz sine wave is sent to input A of the LIA, and demodulated with the local oscillator. A phase shift of 341.56° was added to the local oscillator to get it in phase with input A. Then, a phase shift of 90° was added to the input A signal so there is 90° of relative phase between the two signals. Then, the output is measured.
In Θ mode, the output is 250 mV. Using the equation:
(360°/V) * (0.25 V) = 90°