A lock-in amplifier (hereinafter referred to as Lock-in) is a highly sensitive data collector used to detect very weak AC signals (which can be as low as nV level), even if the noise is thousands of times higher than the signal, it can be accurate Measurement. Lock-in is a technology that uses PSD (PhaseSensitive Detector) -phase sensitive detector, only the signal that exists at a specific reference frequency can be selected; and the noise of other frequencies will not be detected.
Why use Lock-in?
As an example, suppose there is a 10nV, 10KHz sinusoidal signal. Obviously this signal needs a certain degree of amplification.
1. Use a good low-noise amplifier whose input noise is 5nV /? Hz, 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 /? Hz 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, the quality factor Q = 100, the center frequency is 10KHz, then only the signal within the 100Hz (10KHz / Q) bandwidth will be detected, at this time the signal It is still 10uV, but the noise = 5nV / √ Hzx √ 100Hz x 1000 = 50uV. Although the noise has been greatly reduced, it is still greater than the signal and cannot be accurately measured.
3. Now if you add a PSD after the amplifier; the bandwidth of the PSD can be narrowed to 0.01Hz, then the signal is still 10uV, but the noise is only 5nV / √ Hz x √ 0.01Hz x1000 = 0.5uV, the signal to noise ratio is = 10uV / 0.5uV = 20; so it has been able to make accurate measurements. What is PSD? Lock-in measurement requires a reference frequency ωr to trigger the experiment, and Lock-in detects the experimental response signal at this ωr. If the square wave output of a function generator is used as ωr, and its 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: signal phase Lock-in phase lock loop (Phase locked loop-PLL) will generate its own internal
External reference, reference signal locked externally. This internal reference signal waveform is VL Sin (ωLt + θref), VL: internal reference amplitude ωL: internal reference frequency (usually equal to ωr) θref: internal reference phase
After the signal is amplified by Lock-in, the internal reference signal is multiplied by the PSD, and the output of the PSD becomes the sum of two sine waves.
Vpsd = Vsig VL Sin (ωr + θsig) Sin (ωrt + θref) = 1/2 Vsig VL Cos [(ωr-ωL) t + (θsig-θref)]-1/2
VsigVLCos [(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 through a Low Pass Filter, the two AC signals are removed without leaving any signal. But if ωr = ωL, the component of the frequency difference becomes a DC signal, at this time Vpsd = 1/2 Vsig VLCos (θsig -θref), this is a good signal, because the DC signal is directly proportional to the amplitude of the signal source; Traditional Analog Lock-ins use Analog PSD to multiply analog signals and analog references, and low-pass filtering uses 1 or more RC filters; and in DSP Lock-in, these functions are all controlled by a powerful digital signal processor. Mathematical operation.
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 PLL to lock its internal reference oscillator (Oscillator) to the external reference signal. Since the PLL will actively follow the external reference signal, even if the frequency of the external reference signal changes, it will not affect the measurement. In optical experiments, we usually need to use an optical chopper to provide an external reference frequency for the lock-in.
Time constant
Lock-in determines the bandwidth of the low-pass filter by setting a time constant. Time constant Ï„ = 1 / 2Ï€f, f is the frequency of the filter -3dB (-3dB is 50% power attenuation) Increase the time constant, the output will become more stable, the measurement is more reliable (ie smoother -smooth); but filtering It takes about 5 time constants to reach the final value, so increasing the time constant will slow down the output response speed.
Dynamic Reserve-Dynamic Reserve (hereinafter referred to as DR)
The traditional definition of DR refers to the ratio of the maximum "tolerable" noise to the full-scale signal (expressed in dB). For example, if the full scale is 1uV, a 60dB DR finger can have a noise input of up to 1mV without overload.
Lock-in applications
â— Proportional spectroscopy (Ratiometric Spectroscopy) measurement
â— Determination of photoelectric experiment signal
â— Hall effect (Hall Effect) measurement
â— Capacitance measurement of semiconductor components
â— Fluorescence (PL-Photolumincense) spectrum measurement of semiconductor materials
â— Magnetic measurement of magnetic materials, superconductors, etc.
â— Measurement of fiber attenuation and chromatic dispersion
â— Signal detection of biosensors
â— Ultra-short time (Femtosecond) signal measurement
â— Amplifier gain (Gain), crosstalk (Crosstalk) measurement
â— Noise measurement of electronic components and light sensors (detector)
â— Mechanical vibration analysis
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