Lock-Ins for electrical measurements At low temperatures small electrical signals, small signal changes interesting physics Problems: Noise Groundloops SNR FAM-Talk October 17 th 2014 1
Types of noise Thermal noise/johnson Nyquist noise: Equilibrium phenomena Thermal motion of charges in a conductor at finite T Shot noise Due to discrete nature of charge; non-equilibrium phenomena Relevant if number of charge carriers is small Technical noise sources (power line, vibrations, etc.) 1/f noise Equal energy in each octave, falls off with 3dB per octave e.g. charge fluctuations of traps in semiconductors Dominant at low frequencies 2
Grounding and ground loop Protect equipment from ESD Ideally one ground potential; different potentials DV ground loop Counter measures: Create a new GND loop to compensate Each cable acts like an antenna twist cables Magnetic shielding Decouple signals to optical fibres Reduce stray fields from transformers 3
Lock-In Experimental situation Signal of interest: small (mostly DC) Signal burried in a noisy AC enviroment A lock-in recovers this signal To recognize signal precise reference signal Phase sensitive detector (PSD)/mixer converts AC to DC 4
Phase sensitve detection Sinousoidal input signal PSD mixes the input signal with the reference signal demodulator output No relative phase shift w demod =2w 5
Phase sensitve detection Sinousoidal input signal PSD mixes the input signal with the reference signal demodulator output No relative phase shift w demod =2w 5
Phase sensitve detection Sinousoidal input signal PSD mixes the input signal with the reference signal demodulator output No relative phase shift w demod =2w Output signal Sensitive to phase between reference and input Proportional to amplitudes w sig =w ref & no phase shift 5
Phase sensitve detection Sinousoidal input signal PSD mixes the input signal with the reference signal demodulator output No relative phase shift w demod =2w Output signal Sensitive to phase between reference and input Proportional to amplitudes w sig =w ref & no phase shift Noise adds in real life to both signals at various frequencies BUT: mean level is not affected 5
PSD - Principle I Noise adds in real life to both signals at various frequencies 1.0 3 0.5 2 1 1 2 3 4 5 time 1 1 2 3 4 5 time 0.5 1.0 w=13hz q=0 w =50Hz 2 3 4 frequency components: w=0 Hz 2w=26 Hz w ±w=63, 37 Hz 2.0 3.5 3.0 1.5 2.5 Apply low pass filter!!! +noise 2.0 1.0 1.5 1.0 0.5 0.5 0.0 0 20 1 40 2 60 3 804 100 5 9
Principle low pass filter 2.0 1.5 1.0 0.5 0.0 0 20 40 60 80 100 Cutoff frequency f c : f c =1/(2pRC) RC: time constant Bode plot/frequency response of the signal Cutoff frequency: power reduces by factor 2 3dB gain Rolloff approaches 20dB/decade First order and second order filter differ by the rolloff 10
Components of a Lock-In Signal channel: AC coupled amplifier, band pass High impedance input Reference channel: «perfect» signal generator noise free Phase shifter PSD/Mixer: Analog-, digital-, or digital switching multiplier Low pass filter and output amplifier Output: Panel meter, depending on PSD analog to digital converter (ADC), low output impedance See also: TechNote 1000 on labrepo 11
Mixer types Analog Direct multiplication Accurate Not enough dynamic range makes it hard to recover small signals in a noisy enviroment Switching mixer (PAR 124 and Signal Recovery LI) Digital Big dynamic range Demodulates harmonics Perfect multiplication Low dynamic range, would need 32bit DAC at 100kHz Improvement by time averaging but slow 12
PSD gain Switching multiplier Simple way of multiplying 2 signals: n-fet and p-fet with a square wave on gate feed signal to one FET, inverted to second FET upper FET conducts on pos. part of square wave lower FET conducts on neg. part of square wave multiplication of input signal with square wave Odd harmonics interference Use a band pass (Q=100!!!) or low pass (still some unrejected frequencies); but missing harmonics change overall result Improvement by approximation of sine wave (cancels first harmonics) our Signal Recovery model does this See also: TechNote 1001 on labrepo 13
PAR 124 Signal channel adjust prefilter prior to PSD Low pass Filter time constant preamplifier Reference channel 2Hz-210kHz ~pv 10 V calibrator and PSD See also on lab repo: Tech Talk D. Hug - 24.9.2010 14
Preamplifier Small signals need to be amplified Each preamp adds noise: nv/ Hz Choice of preamp depends on R source and f ref noise figure contours (noise/(thermal+noise)) Single ended input avoids ground loops Available preamp models for PAR 124 Differential input common mode rejection See also: TechNote 1004/1001 on labrepo 15
Signal channel Set to the same/similar frequency as the reference channel Mode sets the filter after the preamplifier Band pass: center frequency at set frequency Flat: low pass with very small roll off Notch: very steep band pass Low pass: 12dB roll off at the set frequency High pass: same as low pass Q-factor tunes the bandwidth (high Q small bandwidth) 16
PSD Dynamic reserve: when does an interfering sigal become relevant Output Dynamic range: measure for size of signal PSD modes (choose appropriate ratio between dyn. range and reserve): Low drift good output stability Normal Hi dynamic range for higher noise levels See also: Manual PAR 124 on labrepo 17
Conclusion Lock-Ins recover small signals in noisy enviroment Simple principle but hard to implement Analog vs. Digital Several filtering stages find the best combination of the settings, depending on experimental needs 18