Basics of lock-in amplifiers
(Source: Stanford Research Systems, Inc.)
Lock-in amplifier (hereinafter referred to as Lock-in) is a highly sensitive data collector used to detect very weak AC signals (as low as nV level), and can obtain accurate even when the noise is thousands of times higher than the signal Measurement. Lock-in is a technology that uses PSD (PhaseSensitive Detector)-phase sensitive detector. Only signals that exist at a specific reference frequency can be selected; noise at other frequencies will not be detected.
Why use Lock-in?
As an example, suppose there is a sinusoidal signal of 10nV and 10KHz. Obviously, this signal needs to be amplified to some extent.
1. Use a good low-noise amplifier, whose input noise is 5nV / ÃHz, if the bandwidth is 100KHz; the gain (Gain) is 1000, then the amplified signal = 10nV x1000 = 10uV, but the broadband noise at this time = 5nV / ÃHz x√ 100KHz x 1000 = 1.6mV. Therefore, the noise intensity is much greater than the signal, and we cannot measure the signal.
2. After the amplifier, add a bandpass filter of ideal quality, with a quality factor of Q = 100 and a center frequency of 10KHz. Only signals within the 100Hz (10KHz / Q) bandwidth will be detected. At this time, the signal will be detected. It is still 10uV, but the noise is 5nV / √ Hzx √ 100Hz x 1000 = 50uV. Although the noise has been greatly reduced, it is still larger than the signal and cannot be accurately measured.
3. Now if add a PSD after the amplifier; the bandwidth of the PSD can be narrowed to 0.01Hz, although the signal is still 10uV at this time, but the noise is only 5nV / √ Hz x √ 0.01Hz x1000 = 0.5uV, the signal-to-noise ratio is = 10uV / 0.5uV = 20; therefore, accurate measurement is possible. What is PSD? Lock-in measurement requires a reference frequency ωr to trigger the experiment, and Lock-in detects the experimental response signal at ωr. If a square wave output of a Function Generator is used as ωr, and an sine wave output is used to stimulate an experiment, the relationship is shown in the figure.
The signal waveform is Vsig.Sin (ωrt + θsig), Vsig: signal amplitude (Amplitude) ωr: reference frequency θsig: phase of the signal.
The lock-in's phase locked loop (PLL) will generate its own internal reference, which is locked to an external reference signal. The internal reference signal waveform is VL Sin (ωLt + θref), VL: internal reference, amplitude ωL: internal reference frequency (usually equal to ωr), and θref: internal reference.
After the phase lock-in amplifies the signal, the internal reference signal is multiplied by the PSD, and the output of the PSD becomes the sum of two sine waves. Vpsd = Vsig VLSin (ωr + θsig) Sin (ωrt + θref) = 1/2 Vsig VL Cos [(ωr-ωL) t + (θsig-θref)]-1 / 2VsigVLCos [(ωr + ωL) t + (θsig + θref)], Vpsd is two sets of AC signals, one is the frequency difference (ωr-ωL), and the other is the frequency sum (ωr + ωL). If the PSD output passes a low pass filter, the two AC signals are removed without leaving any signals. However, if ωr = ωL, the component of the frequency difference becomes a DC signal. At this time, Vpsd = 1 / 2Vsig VLCos (θsig -θref), which is a good signal because the DC signal is directly proportional to the amplitude of the signal source; traditional Analog Lock-ins uses Analog PSD to multiply the analog signal and analog reference, and low-pass filtering uses 1 or more levels of RC filter. In DSP Lock-in, these functions are mathematically operated by a powerful digital signal processor. Come to get.
Where does the lock-in reference signal come from?
From the above discussion, we know that the Lock-in reference frequency must be equal to the signal frequency ωr = ωL; and the phase difference (θsig-θref) must also be kept constant. Lockin uses a PLL to lock its internal reference oscillator to an external reference signal. Since the PLL actively follows the external reference signal, it does not affect the measurement even if the frequency of the external reference signal changes. In optical experiments, we usually need an optical chopper to provide an external reference frequency for Lock-in.
Lock-in determines the bandwidth of the low-pass filter by setting a time constant. Time constant τ = 1 / 2πf, f is the frequency of -3dB of the filter (-3dB is the attenuation of 50% power). Increasing the time constant will make the output more stable and the measurement will be more reliable (ie, smoother-smooth); but the filtering It takes about 5 time constants to reach the final value, so increasing the time constant will slow down the response of the output.
Dynamic Reserve (hereinafter referred to as DR)
The traditional definition of DR refers to the ratio (in dB) of the maximum "tolerable" noise to the full-scale signal. For example, if the full scale is 1uV, a 60dB DR means that there can be up to 1mV of noise input without overloading.
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