Measuring of small AC signals using lock-in amplifiers. Narrow band selective amplifiers + amplitude detector. Lock-in amplifiers 3/12/2013 Physics 403 Spring 2013 1
Simplified block diagram of a lock-in amplifier Signal in Signal amplifier Signal monitor PSD * Low-pass filter DC amplifier Reference in VCO ** Reference out output * PSD - phase sensitive detector; ** VCO - voltage controlled oscillator John H. Scofield, American Journal of Physics 62 (2) 129-133 (Feb. 1994). 3/12/2013 Physics 403 Spring 2013 2
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Phase shift y j=p/4, V out =0.72V in V in =sin(wt+p/4) 0.6 0.0-0.6 V 0 sin(wt+j) j x 0.6 0.0 reference reference -0.6 0.6 output 0.0-0.6 0 100 200 300 400 500 600 700 time (msec) 3/12/2013 Physics 403 Spring 2013 4
y Phase shift j=0, E x =E in The dependence of pattern of the output signal after demodulator on phase shift between input and reference signals V 0 sin(wt+j) j x j=p/4, E x =0.72E in j=p, E x =-E in reference j=p/2, E x =0 j=3p/2, E x =0 3/12/2013 Physics 403 Spring 2013 5
. Simple math. U x U x0 sin( w1t ) 1 - input signal U sin( w t ) - reference signal r 2 2 U U U U sin( w t )sin( w t ) U 2 de mod x r x 0 1 1 2 2 x 0 cos(( w ) w t ) cos(( ) w w ) t 1 2 1 2 1 2 1 2 ω 1 ω 2 ω 1 =ω 2 =ω U x 0 2 U x 0 2 ω 1 -ω 2 ω 1 +ω 2 2ω U U cos(2 wt ) cos( ) 2 x 0 de mod 1 2 1 2 U U de mod cos( 1 ) 2 2 x 0 and after low-pass filtering 3/12/2013 Physics 403 Spring 2013 6
Two channels demodulation In many technical applications we need to measure both components (E x, E y ) of the input signal. To do this most of the modern lock-in amplifiers are equipped by two demodulators. E in =E o sin(wt+j) to E x channel y sin(wt) E y j x E x to E y channel cos(wt) 3/12/2013 Physics 403 Spring 2013 7
Analog and digital lock-ins Block-diagram of analog lock-in 3/12/2013 Physics 403 Spring 2013 8
Analog and digital lock-ins SR510 & SR530 Lock-In Amplifiers 0.5 Hz to 100 khz frequency range Current and voltage inputs Up to 80 db dynamic reserve Tracking band-pass and line filters Internal reference oscillator Four ADC inputs, two DAC outputs GPIB and RS-232 interfaces Analog lock-ins from Stanford Research Systems 3/12/2013 Physics 403 Spring 2013 9
Analog and digital lock-ins Block-diagram of digital lock-in 3/12/2013 Physics 403 Spring 2013 10
SR830 digital lock-ins GPIB V in Input amplifier + filters Main ADC DSP Output filters Ref. out Function generator clock DAC1 DAC1 DAC1 DAC1 ADC1 ADC2 ADC3 ADC4 Block-diagram of digital lock-in 3/12/2013 Physics 403 Spring 2013 11
Analog and digital lock-ins Two DSP lock-in amplifiers: SR830 from Stanford Research Systems and 7265 from Signal Recovery. The main advantages of digital lock-ins: * high phase stability; * broad frequency range; * ideal for low and ultra low frequencies (up to 0.001Hz) * harmonics up to 65,536 (7265), 19,999 (SR830). 3/12/2013 Physics 403 Spring 2013 12
: some applications (i) Applying a small test signal (locked to the reference signal) to the studied object Asinwt Tested system Lock-in reference Examples: frequency domain spectroscopy (second sound), tunneling spectroscopy (analysis of the I-V curves), dielectric spectroscopy etc. 3/12/2013 Physics 403 Spring 2013 13
: some applications (ii) Modulating of the studied signal by the signal locked to the reference signal Function generator sync output modulation Green LED LED Power supply Fluorescence response Crystal under study SR830 lock-in signal input reference input Detector Examples: fluorescence experiment 3/12/2013 Physics 403 Spring 2013 14
Examples of application 2 Transfer line 6 Lakeshore Temperature controller Heater 7 1 3 Janis gas flow cryostat T Sample DT470 V input 4 5 GPIB PC computer (HP VEE) Preamplifier I/V Lock-in SR830 Asin(wt) AC output Experimental setup for measurement of the dielectric susceptibility (electrical conductivity) in the temperature range 15-450K 3/12/2013 Physics 403 Spring 2013 15
Scanning of the frequency of the AC signal applied to transmitter we can find the frequencies of the acoustical resonance. Examples of application. Second sound experiment Receiver He4 AC drive signal Transmitter (heater) 3/12/2013 Physics 403 Spring 2013 16
Examples of application. Optical pumping 3/12/2013 Physics 403 Spring 2013 17
Examples of application. Optical pumping Function generator DMM Sweep coil 5.1kW Rb cell B 0 - main field SR830 lock-in B 0 +B 1 sin(wt) From TeachSpin detector reference 3/12/2013 Physics 403 Spring 2013 18
Examples of application. Optical pumping The choice of amplitude modulation VFG Isweep 5.1kW B k I 1 sweep sweep K sweep 0.6G/A If V FG = 1V B 1 ~ 0.12mG 3/12/2013 Physics 403 Spring 2013 19
Examples of application. Optical pumping Analog detector record (I(f)) Lock-in detector record I H (f) 3/12/2013 Physics 403 Spring 2013 20
: demo Function generator S Lock-in amplifier Noise demo lock-in 3/12/2013 Physics 403 Spring 2013 21