Lock-in amplifiers are used to detect and measure very small AC signals. Accurate measurements may be made even when the small signal is obscured by noise sources many thousands of times larger.
Lock-in amplifier is a small signals detection means based on the coherence method. Lock-in amplifiers use a key technique named as phase-sensitive detection (PSD) to single out the required component of one signal. The component has the same frequency and the fixed phase differences with the reference signal. Noise signals at frequencies other than the reference frequency are rejected and do not affect the measurement.
Let's consider an example. Suppose the signal is a 10 nV sine wave at 10 kHz. A good low noise amplifier will have about 5 nV/√Hz of input noise.
① If the amplifier bandwidth is 100 kHz and the gain is 1000, then we can expect our output to be 10 ?V of signal (10 nV x 1000) and 1.6 mV of broadband noise (5 nV/√Hz x √100 kHz x 1000). We won't have much luck measuring the output signal unless we
single out the frequency of interest.
② 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 ?V (5 nV/√Hz x √100 Hz x 1000) and the signal will still be 10 ?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.
③ Now try following the amplifier with a phasesensitive 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 only 0.5 ?V (5 nV/√Hz x √.01 Hz x 1000) while the signal is still 10 ?V. The signal to noise ratio is now 20 and an accurate measurement of the signal is possible
As we said before, PSD can be seen as a very narrow bandwidth band-pass filter. The basic PSD modules include one multiplier module and one low-pass filter (LPF) module, as Fig.1 shows. Sometimes PSD is known as the multiplier module without LPF.
Fig.1 Phase sensitive detection diagram
In Fig.1, S_I (t) is the input signal plus noise in time region, S_R (t) is the reference signal which has a fixed frequency and phase.
Fig.2 Single-phase amplifier diagram
In Fig.2, the input signal S_I (t) is defined as:S_I (t)=A_I sin?〖(ωt+φ)+B(t)〗 , where ω is the input signal frequency, A_I sin?(ωt+φ) is the input signal, B(t) is the total noise. And the reference signal S_R (t) can be defined as: S_R (t)=A_R sin?(ωt+δ).
The PSD output signal is defined as:
S_psd=S_I (t) S_R (t)=A_I A_R sin?〖(ωt+φ) sin?(ωt+δ)+B(t)A_R 〗 sin?(ωt+δ)
=1/2 A_I A_R cos?〖(φ-δ)〗-1/2 A_I A_R cos?( 2ωt+φ+δ)+B(t)A_R sin?(ωt+δ)