# An introduction to synchronous detection. A.Platil

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1 An introduction to synchronous detection A.Platil

2 Overview: Properties of SD Fourier transform and spectra General synchronous detector (AKA lock-in amplifier, syn. demodulator, Phase Sensitive Detector) Switching mode SD: pros and cons Sensor applications of SD: infrared pyrometer elements with chopper modulator AC mode strain gauge excitation

3 Introduction: Synchronous detection is a signal processing technique that: Makes possible extracting even weak signal in strong noise background - e.g.: Radio communication Strongly disturbed signals in industry Requires reference signal with known frequency and phase For starters: brief refresh of Fourier transform

4 Fourier transform and signal spectrum A f t Časová Time doména domain Frekvenční Freqency doména domain

5 Signal spectrum Any periodic signal can be described as a combination of harmonic signals of various amplitude and phase: x( t) = X + X sin( k ω t + ϕ ) 0 k k k = 1, 2,... Signal spectra are measured with spectral analyzers of various types, e.g. analogue swept-filter or digital FFT analyzers

6 Example1 - harmonic signal + weak noise, f = 100 Hz, spectrum consists of one peak at 100 Hz, noise floor is -90 db

7 Example 2: Combination of two harmonic signals 100 Hz and 300 Hz. Spectrum consists of two peaks.

8 Example 3: Square wave signal, spectrum consists of all odd higher harmonic components

9 1 st, 3 rd, 5 th, etc. higher harmonic components of square wave signal

10 Example 4: Amplitude modulation. Carrier frequency 50 khz, signal (information) frequency 5 khz.

11 In the spectrum of an AM-modulated signal, there is one peak of the carrier f 0 and two side-peaks at combination (additive and subtractive) frequencies f 0 +/-f m.

12 Synchronous detector can be used in situations where we know exact frequency and phase of signal. E.g. Where the experiment excitation frequency is available as reference. Excitation f Experiment produces output signal synchronous to excitation at frequencies k x f Generator Experiment Measurement (sync. detection) Reference signal f

13 ... or where the signal is modulated by known frequency before further processing - e.g.: modulating (chopper) amplifier Low level DC voltage amplification (µv) - problem: DC amplifier offset and its drift -solution: modulation of DC signal (by chopper), amplification by AC amplifier (DC offset drift is not an issue) and demodulation

14 On input: all RF signals captured by antenna, including wanted radio station at f 0 After mixer: combination frequencies f 1 a f 2. After Low-pass: only narrow band of low frequency signals Example of synchronous detection: receiver of AM radio superheterodyne receiver (simplified) Mixer (multiplier) Směšovač (násobička) Low-pass filter Dolní propust f f 2 Audio amplifier Zesílení signálu Local Referenční oscilátor (f 0 ) oscillator f 0 f 1 = f + f 0 f 2 = f f 0

15 In the mixer output, there are various combination (additive and subtractive) frequencies corresponding to signals captured by antenna Special case for f = f 0 (local oscillator is tuned to wanted station at f 0 ) subtractive frequency is zero (we get DC signal proportional to amplitude of received RF signal at f 0 )

16 Case 1: station transmits silence or a DC signal, the RF signal spectrum consists only of the station carrier, e.g. 100 khz. After mixer (multiplier) tuned exactly to 100kHz we get combination frequencies: f 1 = f + f 0 = f 0 + f 0 = 2f 0 (additive frequency, rejected by LP filter) and f 2 = f f = f 0 0 f 0 = 0 Hz The DC signal gets through LP filter to output (together with remnants of noise that fits into the LP band according to LP bandwidth) A A LP DP filtr 100 khz f 0 Hz 200 khz f Signal at mixer input Signals at mixer output, LP filter bandwidth is suggested

17 Case 2: station transmits a tune e.g. 10 khz the RF signal spectrum consists of 100 khz carrier with side bands (90 khz a 110 khz). After mixer (multiplier) with local oscillator exactly tuned to 100kHz we get combination frequencies: f 1 = f + f 0 = f 0 + f 0 = 200 khz +/- 10 khz (rejected by LP filter) and f 2 = f f = f 0 0 f 0 = 10 khz Signal 10 khz pass through LP (provided the LP has adequate BW) A A DP filtr 100 khz f 0 Hz 10 khz 200 khz f Signal at mixer input Signals at mixer output, LP filter bandwidth is suggested

18 The bandwidth of low-pass filter after mixer determines the resulting sensitive BW of the synchronous detector. The local oscillator determines the resulting center frequency of sensitive BW of the synchronous detector. Local oscillator frequency f 0 Propustné pásmo LP bandwidth frekvence frequency Tradeoff: the lower LP bandwidth, the less noise makes it to the output BUT the slower is the response to useful signal changes (useful BW)

19 Mathematical background of SD: The measured and the reference signals are: U sig sin ( ω t + Θ ) sig sig U ref sin ( ω t + Θ ) ref ref Then signal after mixer (multiplier) is: U = Mix. 1 U 2 1 U 2 = U sig sig sig U U U ref ref ref cos cos sin ( ω t + Θ ) sin( ω t + Θ ) ([ ω ω ] t + Θ Θ ) sig ([ ω + ω ] t + Θ + Θ ) sig Note: see that output amplitude is influenced by phase sig ref ref sig sig sig ref ref ref ref = } Low freq } High freq. (rejected)

20 The preceding example: detection with harmonic reference signal BUT In practice: often detection with squarewave reference (switchingmode detection) signal Phase Sensitive Detector (switching-mode detector) Signal after multiplier Signal after LP filter x reference x / -x

21 Remember phase does matter If the reference is shifted by 90, the detected signal is completely changed and the filtered value is zero (compare with previous fig.) signal Phase Sensitive Detector (switching-mode detector) Signal after multiplier Signal after LP filter x reference x / -x Note: for signal frequencies that do not match the reference frequency the system throughput is close to zero.

22 Synchronous demodulator in general: x(t) signal multiplier v(t) Mean value calculation T 1 v ( t ) T 0 output reference r(t) 1. analogue multiplier = ideal, BUT: non-linearity, expensive 2. Switching circuit BUT: sensitivity to odd harmonics v(t)=k(t).x(t) K(t)... switching funct. Low pass filter Or integrator

23 Pros and cons of switching-mode synchr. detection + : simple realization, cheap solution, even for large signals : sensitivity even to other frequencies than f ref Reason: multiplying with squarewave, the spectrum of which consists of ALL odd higher harmonics: 1 st, 3 rd, 5 th, 7 th,...

24 The resulting set of sensitive bandwidths of switching-mode SD Switching function (reference) = symmetrical squarewave Switching perioda T=2π/Ω

25 Sensor applications of SD AC biased strain-gauge bridge: Low level signals => AC signal is easier to process than DC signal (offset drift,...). Signal processing with a synchr. detector => noise rejection Switching-mode SD sensitive to other frequencies ( ) Pyrometry (contactless detection of infrared heat): Lot of noise, difficult to separate from useful signal Signal (IR radiation) from observed object is periodically interrupted with a chopping shutter Signal processing with a synchr. detector with a reference from shutter

26 Conclusion Synchronous detection enables processing of very weak signals (even orders of magnitude lower than noise) Synchronous detector is sensitive on the frequency of reference (e.g from local oscillator) in a narrow band (given by LP filter) Switching-mode detection is simple and cheap, but then we get sensitivity also on all higher odd harmonics of the reference.

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