SRS Lock-In Amplifiers

SRS Lock-In Amplifiers - About Lock-In...

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About Lock-In Amplifiers Application Note #3 www Stanford Research Systems phone: (408)744-9040 www Lock-in amplifiers are used to detect and measure very small AC signals all the way down to a few nanovolts. Accurate measurements may be made even when the small signal is obscured by noise sources many thousands of times larger. Lock-in amplifiers use a technique known as phase-sensitive detection to single out the component of the signal at a specific reference frequency and phase. Noise signals, at frequencies other than the reference frequency, are rejected and do not affect the measurement. Why Use a Lock-In? Let's consider an example. Suppose the signal is a 10 nV sine wave at 10 kHz. Clearly some amplification is required to bring the signal above the noise. A good low-noise amplifier will have about 5 nV/ Hz of input noise. If the amplifier bandwidth is 100 kHz and the gain is 1000, we can expect our output to be 10 µ V of signal (10 nV × 1000) and 1.6 mV of broadband noise (5 nV/ Hz ×√ 100 kHz × 1000). We won't have much luck measuring the output signal unless we single out the frequency of interest. If we follow the amplifier with a band pass filter with a Q=100 (a VERY good filter) centered at 10 kHz, any signal in a 100 Hz bandwidth will be detected (10 kHz/Q). The noise in the filter pass band will be 50 µ V (5 nV/ Hz 100 Hz × 1000), and the signal will still be 10 µ V. The output noise is much greater than the signal, and an accurate measurement can not be made. Further gain will not help the signal-to-noise problem. Now try following the amplifier with a phase-sensitive detector (PSD). The PSD can detect the signal at 10 kHz with a bandwidth as narrow as 0.01 Hz! In this case, the noise in the detection bandwidth will be 0.5 µ V (5 nV/ Hz .01 Hz × 1000), while the signal is still 10 µ V. The signal-to-noise ratio is now 20, and an accurate measurement of the signal is possible. What is Phase-Sensitive Detection? Lock-in measurements require a frequency reference. Typically, an experiment is excited at a fixed frequency (from an oscillator or function generator), and the lock-in detects the response from the experiment at the reference frequency. In the following diagram, the reference signal is a square wave at frequency ω r . This might be the sync output from a function generator. If the sine output from the function generator is used to excite the experiment, the response might be the signal waveform shown below. The signal is V sig sin( ω r t + θ sig ) where V sig is the signal amplitude, ω r is the signal frequency, and θ sig is the signal’s phase. Lock-in amplifiers generate their own internal reference signal usually by a phase-locked-loop locked to the external reference. In the diagram, the external reference, the lock-in’s reference, and the signal are all shown. The internal reference is V L sin( ω L t + θ ref ).
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SRS Lock-In Amplifiers - About Lock-In...

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