Lock in amplifier

What is a lock-in amplifier ？ 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. Obscure: adj. 昏暗的，朦胧的，不清楚的 vt. 使 … 模糊不清，掩盖；隐藏；使难理解 n. 某种模糊的或不清楚的东西

What is a lock-in amplifier ？ 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 ？

What about a Filter ？ If we follow the amplifier with a band pass filter with a Q=100 (a VERY good filter) centered at 10kHz, any signal in a 100Hz bandwidth will be detected (10kHZ/Q). Q=fc/B w Band-pass filter

What about a Filter ？

What about a Lock in?

What is a PSD? Lock-in measurements require a frequency reference. A lock-in amplifies the signal and then multiplies it by the lock-in reference using a phase-sensitive detector or multiplier. The PSD output is two AC signals, one at the difference frequency (ω s - ω r ) and the other at the sum frequency (ω s + ω r ).

What is a PSD? If the PSD output is passed through a low pass filter, the AC signals are removed. Vpsd = ½ VsVr cos(θ). It is a DC signal proportional to the signal amplitude

The basic theory of a lock-in? Theory : No correlation between noise and value signal, along with correlation between value signal and reference signal are used to implement signal detection in LIAs. Features: the AC component is amplified and output of the corresponding signal is a dc component.

Phase sensitive detection analysis. Multiplier type of phase sensitive detector 1. x(t) and r(t) are all sine waves.

Phase sensitive detection analysis If the PSD output is passed through a low pass filter ： When θ=0, the output has a maximum value. 1 ） amplitude-frequency characteristic If and θ=0 The frequency response First order RC low- pass filter is :

Phase sensitive detection analysis The amplitude frequency response is: and the phase is: The output of LPF: In the steady state:

Phase sensitive detection analysis Phase-sensitive characteristics

Phase sensitive detection analysis 2.When the input signal is sine wave and the reference is a square wave. The Fourier expansion of the square signal is Since the square wave is an even function Here a 0 =0 ， b m =0.

Phase sensitive detection analysis Then we can get: Similar results with the sine reference wave

Phase sensitive detection analysis 3.X(t) is a sine wave adding noise(single frequency) to it, and r(t) is sine wave

Phase sensitive detection analysis 4.X(t) is a sine wave adding the narrow- band noise to it. Here r(t) is a sine wave.

Phase sensitive detection analysis The output of LPF

Phase sensitive detection analysis 5.X(t) is a sine wave adding noise n(t) to it, and r(t) is square wave. Let’s discuss the third part, since the second part would be filtered out by LPF.

Phase sensitive detection analysis (1)If the n(t) is a single frequency noise, and the frequency is Wn. Only ， can the noise be filtered out.

Phase sensitive detection analysis (2) If the n(t) is a Broadband noise or higher harmonic of x(t) After passing the LPF:

Phase sensitive detection analysis The output noise not only occurs in the frequency W n =W 0, but also in ω n = （ 2n-1 ） ω 0. Obviously ， it need a band-pass filter to remove the harmonic.

Phase sensitive detection analysis 6.X(t) and r(t) are all square waves.

The design of LIA LIAs can be divided into two types: analog lock-in amplifiers (ALIAs) and digital lock-in amplifiers (DLIAs) LIA using analog electronics, which had good performance for most of the applications expect some shortcomings, such as instability, gain error, and thermal shifting. Consequently, a lot of attention has been paid to digital lock-in amplifier.

No correlation between noise and value signal is used to implement signal detection in LIAs The design of LIA No correlation between noise and value signal is used to implement signal detection in LIAs. Diagram of correlation detection.

The design of LIA The output of Two PSD: Orthogonal: adj. 正交的；直 角的 n. 正交直线

The design of LIA Orthogonal reference signal Phase-sensitive detector Low-pass filter The Key of LIA

Reference signal 1.Orthogonal reference signal The way in which the reference produce can be divided into two types （ 1 ） Using a Phase Locked Loop ( PLL ，锁相环） to follow the frequency of input signal ， and then produce two reference signal by Voltage controlled oscillators （ VCO ，压控振荡器）

Phase Locked Loops(PLL) VCO A PLL is a control system that generates an output signal whose phase and frequency is related to the phase and frequency of an input signal.

Phase-Locked Loops(PLL) Phase detector （ PD ，鉴相器） A phase detector is a circuit whose average output, is linearly proportional to the phase difference, ∆φ, between its two inputs

Voltage-controlled oscillators (VCOs) VCO is an electronic oscillator whose oscillation frequency is controlled by a voltage input V cont (from the phase detector).

Reference signal (2) Using a DDS (Direct Digital Synthesizer, 直接数字 式频率合成器 ) to produce the excitation signal and two reference signal

DDS DDS is a type of frequency synthesizer used for creating arbitrary waveforms from a single, fixed- frequency reference clock.

Frequency response of a 100-points averaging filter.

Key points The LIA need a LPF which has a low cutoff frequency. However, a lower cutoff frequency produces a longer measurement time. Hence, a trade-off between measurement error and measurement time must be found for each application.

Application-Low Level Optical Detection Disadvantage ： (1)If the offset control is not adjusted correctly, then the DC signal from the detector due to leakage current will give a non-zero output even with no optical input. (2)there is no way of separating the output signal caused by the wanted input signal from that due to stray light entering the detector. Traditional DC measurement monochromator [,mɔnəu'krəumeitə] n. 单色仪；

The Lock-In Amplifier Method This method can overcome the Shortcomings mentioned above.

Thank you!