Theory Of Lock In Modulation And Demodulation

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THE LOCK IN MODULATION IN ULTRA LOW FREQUENCYAPPLICATIONThis work want to show the validity of Lock In modulation in ULF (0.1-30Hz Ultra LowFrequency) reciver application. Transistor, vacuum tubes, resistor and other devices exhibit a lowfrequency phenomenon know as flicker noise, often called 1 noise because the mean squarefdensity is proportional to1fvv 1. Flicker noise pose serious problems for low-frequencyapplication but Lock In modulation could be the answer.Theory of Lock In Modulation and Demodulation1 General scheme of Lock In ringThe synchronous mod/demod is also called Lock In modulation(Fig.1). It is a modulation on adifferent frequency from the original signal, to transfer out of 1 noise (fig.2), where is prevailingfthe instrumental noise or pink noise. This frequency is knowing likeknee frequencyf kneef chopand it must be upper(Fig. 2), where we have the crossing from 1 noise region to whitefGaussian noise region.2Knee frequency.1

The Lock In modulation is also calling Chopping modulation, in fact it using Chopper amplifier.We know that traslate a signal in frequency is like to sample it, Lock In modulation is like asampling at Fc frequency,we have for Nyquist theorem, that Fc must be twice of maximumfrequency of the signal.The action consist to select the interest signal, modulate ,enlarging, filtering with a pass-band filterand demodulated synchronous with the modulator.The demodulated signal will be enlarging to obtain a signal noise ratioS 1 . We have theNadvantage that all the offset and the drift produces inside the Lock In are banishing here.Now we can see the frequency answer of a Lock In system with a time variant signal:{V0 cosω1t Signal InA cosω 0 t Syncronous RiferenceWhere ω 0 is chopping pulsation and ω 1 is the fondamental pulsation.The demodulated signal is:V 0 A cos ω 0 t cos ω 1 t V0 AV Acos (ω 0 ω 1 )t 0 cos (ω 0 ω 1 )t22We have Dsb-Sc (Double Side Band Suppressed Carrier) spectrum, looks like an AM spectrumwithout the unmodulated carrier impulse, the information is in the double side band (Fig 3).3 DSB-SC Spectrum2

2.2Asyncronism in Lock In Modulation.The asyncronism in Lock in modulation/demodulation is one of the most recurs tecnical problem.In fact we must to give a very syncronous signal to Modulator and Demodulator. Often the cause ofthe asyncronism is the different propagation time from the syncronous signal generator and themodulator/demodulator devices .The importance of a very syncronous reference is given from the fact that a phase differencefrom signal to demodulate and the syncronous reference will give an error on the continuoscomponent; this error is extimated to be: Φ Vout VS 1 90 φ the wave form are in Fig. 44Amplitude and phase with asyncronismThe demodulated signal, for the phase-displacement have a smaller amplitude. We can see that theamplitude is inversely proportional to the grow of phase differece. In particularly we have thesignal annulment at 90 and his multiples, where the demodulated signal is not present. For the oddmultiples of 180 we have an invertion of the sign.3

ANALOG DEVICE AD630 Balanced Modulator-DemodulatorWe have choose for our examination the Analog Device AD630. It’s a hight precision balancedmodulator which combines a flexible commutating architeture with the accuracy and temperaturestability. Its signal processing application include balanced modulation and demodulation ,synchronous detection ,Lock in amplification and square wave multiplication. Its works like aprecision Op amp with two indipendent differential input stage and a precision comparator which isused to select the active front end. (Fig 5)5 Functional block diagram.Lock In amplification is a technique which is used to separate a small, narrow band signal frominterfering noise. Very small signal can be detected in presence of large amounts of uncorrelatednoise when the frequency and the phase of the desire signal are known.Our experiment consist to realize a Lock In ring with two AD630, one like syncronous Modulatorand one like syncronous DemodulatorThe data sheet says that AD630 could be recover a small signal from 100 dB of interfering noise at1 Khz, we want to verify if is possible to recover small signal from noise at 100 Hz.4

Electric circuitV V R2OUT03V 11U261 7 C O A 2 CHA1 6 RINB C H B RF4 RADOA2 DOA1COMP1MEG 21 M E G 7 CHA VOUTRB1 M E G1 8 STAT1 CHB COA11 0 RINASELA SELBU3 VS-10k6R6R7R8-VS5908V-outVV 9V130OP-27A/ADVAD630J/AD20191531213145 15Vdc872V 20191512131410kVN1N2CHA CHASTAT C H B CHB RFD O A 2C O M PRAVOUTRINBRBCOA2DOA1RINA C O A 1SELA SELBR1418 VS1MEG1MEG1MEG-VSR3R4R511V U4271841617631100VV14VAD630J/AD 15VdcV1VOFF 0VAMPL 5FREQ 1000R91k0V-0V2VOFF 0VAMPL 1FREQ 1000W0WSimulazione anello0Lock IN6 Wiring diagramWe have pointing our attention around U.L.F. (0.1 30Hz) and we have chose a center frequencyof 100 Hz for our simulation.Input signalOffsetFreq.V.ampl.Sin0V100 Hz0.1-5VModulated signalOffsetFreq.V.ampl.Sin0V1 KHz5VBetween modulator and demodulator there is an Op amp to enlarge the signal , the Op amp chosenis the Analog Device Op 27 . It must to guarantee a large gainbandwidth represented by:GOL G B Kost50

where G is the gain and B the band of aplicated signal. For OP27 the gainbandwidth is about 8Mhz ; we can have good gain (100,linear) for a signal with 100 Khz band. Last but not least theOP27 have a very good noise figure.Filtering of output signalThe modulation of a signal by a sinusoidal wave generate some harmonic atnf s, (for usf 1Khzfrequency, for this reason after demodulation the signal must be filtering with a LPF(low pass filter). The output lowpass filter is a 2nd order Butterworth with Ft 150Hz :OPAmp.ApproxOrderFtGainConfig.OP77Butterworth2 150Hz1InvertenteR322kC222nR1R22-V V 7 15Vdc22k22k100nC13 V13V U5OUTN1N2V-64 1 8OutV14 15Vdc00VOP-77/ADV-Butterworth Pl 150Hz6

Now we start to simulate by Pspice , all the Lock In ring. We have to add to input signal (Testsignal) a white gaussian variable noise source, than modulated by AD630 enlarging by OP27 anddemodulate by AD630. We have to vary the test signal amplitude and to verify the correctrecovering of the test signal from varied dB of interfering noise.In the follow table the most important result:VnoiseSign/Noise GAmpVppVeff 2(1Khz )HzS(dΒ)N R 20Log 1 2 R1 1V21.26 Veff (1Khz )-2 dB6 dB21.90 Veff (1Khz )-16 dB20 dBDemod.VinSimulazione:Red Input 100 HzGreen Out DemodulatedYesHz0.3VYesHz7

Demod.VinVnoiseSign/Noise GAmpVppVeff 2(1Khz )HzS(dΒ)N R 20Log 1 2 R1 0.1V21.26 Veff (1Khz )-25 dB27dBYes0.01V 1.26 Veff 2(1Khz )-40 dB40 dBYesSimulazione:Red Input 100 HzGreen Out DemodulatedHzHz8

VnoiseSign/Noise GAmpVppVeff 2(1Khz )HzS(dΒ)N R 20Log 1 2 R1 -45 dB46 dB0.01V 1.90 Veff 2(1Khz )Demod.VinSimulazione:Red Input 100 HzGreen Out DemodulatedNoHzThe Pspice simulation given some important result, we can’t confirm the Analog Device resultobtained at 1 Khz but we could be satisfy for our -45 dB ( S (dΒ ) ) a 100 Hz.NThe Pspice simulation is limited by the white gaussian variable noise source, we must to create a“ad hoc” device to generate suitable noise because in Pspice dosn’t exist one.9

Now we pass to realize realy the same circuit simulated by Pspice . The wiring diagram is at Fig. 7, we want to find a confirmation at what we have simulateC4 V V 11U4271841617631100C11n VCHA CHASTATSCHBCHB RFDOA2COMPRA VOUTRINBRBCOA2DOA1RINA- COA1SELAVSSELBC28R21n0201915121314R10V 7210k10k0OUT36V- N1N2 4 1 8C3591nV-1nVAD630J/AD111nU26 V17 COA2SCHA16 RINB CHBRF4 RADOA2DOA1COMP27 CHA VOUT18 STAT RB1 CHB COA110 RINASELAVSSELBV U3-C5020191531213145out908OP-27A/ADC600V 100 Hz Input signalNoise Gen Input1n0VAD630J/ADV131Khz Cloch Input 15VdcV14 15Vdc0V-7 Wiring diagram10

The circuit was made on a Bread Board , (Fig. 8).8 Components on the Bread BoardOn the Bread Board we have four In/Out gate at 50 Ohm SMB connection.1: NOISE: Input from noise generator2:INPUT: Input 100 Hz test signal.3:OSCILLATOR: Syncronous refernce for Modulator-Demodulator at 1 Khz4:OUTPUT: Output of demodulated signal.There is a dual power suply tower 15V –15V too.We have test every single circuit components and then all Lock In ring.The not-inverted OpAmp OP27 gain is: R G 20 Log ( 1 2 R1 ) 20 Log ( 1 1kΩ 100Ω ) 21dΒThe INPUT test signal was a 100Hz and the amplitude was varied from 500mV to down.Then we varied noise source intensity and the test signal amplitude to verify correct recovering ofthe test signal.11

We have verify the correct recovering of signal until: S 20dΒ . N The oscilloscope wave form are at Fig. 9, on the 1st channel there is the modulated signal at 1 Khz,on the 2nd channel the test signal correctly demodulated. and enlarging.9 Modulated Vs DemodulatedThe zoom of the oscilloscope wave form are in Fig.10 and Fig. 11.10 Zoom of Channel 111 Zoom of Channel 2.12

SThe object of our work is to find the maximum signal noise ratio where the signal is N correctly recoveryThe Analog device Data Sheet give a border of –100dB a 10 Khz.The Pspice simulation confirming the superiority of Lock In modulation for U.L.F. applicationSand give a –45dB . N The carring out of the circuit and the simulation haven’t permit to confirm the result of the software,Swe can recovering monocromatic signal only until 20 N dB .The experimental result is the worst but is at the same time more interesting.SIn fact the recovering of small signal in U.L.F band with 20 N dB is a great resultimpossible to obtain with other tecnical devices.Another part of this works and some application are on line at www.qsl.net/iw2lla.Thanks a lot to Ing. Jader Monari andl’Ing Marco Poloni from Istituto di radioastronomia CNR(Italian National Research Council ) of Medicina (Bo) and Ing. Stelio Montebugnoli generalmanager of the istitute .Bibliografy:C. Vignali (I4VIL):Radio Rivista 10/2002-Ricevitori a rivelazione SincronaF.P.Panter:Modulation-Noise and Spectral analysis – Mc Graw Hill 1985Monari-Guidi-Poloni : Circuito di riferimento per Mod/Dem Lock InMarco Poloni: Tesi di LaureaAnalog Device AD630 Data SheetAuthor:IW2LLA Dott. Ing. Andrea GhediAndrea Ghedi 2003 Pubblication only for hamand no profit use.13

application but Lock In modulation could be the answer. Theory of Lock In Modulation and Demodulation 1 General scheme of Lock In ring The synchronous mod/demod is also called Lock In modulation(Fig.1). It is a modulation on a different frequency from the original signal, to transfer out of f 1 noise (fig.2), where is prevailing

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