The Lock-in Amplifier
• A lock-in amplifier is basically an amplifier
that amplifies a small frequency band
around a certain reference frequency
• A lock-in can be used to
– Measure sinusoidal voltage amplitudes and
phase
– Measure noise around a certain frequency
– Measure Power spectral density
– … etc.
The Lock-in principle
Reference
oscillator
X
Cos(wt)
Low pass
filter
X
90
degree
signal
X
Sin(wt)
Signal is V(t)=A Cos(wt+phi)
Low pass
filter
Y
The Lock-in principle
X
Cos(wt)
Low pass
filter
X
signal
Signal is
V(t)=A Cos(wt+phi)
= A*( Cos(wt)Cos(phi) - Sin(wt)*Sin(phi) )
The Lock-in principle
Amplitude = sqrt (x*x + y*y)
Phase = arctan (y/x)
Dual phase
Reference
oscillator
X
Cos(wt)
Low pass
filter
X
90
degree
signal
Y
Low pass
filter
X
Sin(wt)
Single phase
Reference
oscillator
X
Cos(wt)
Low pass
filter
X
signal
Effect of low pass filters
Effect of low pass filters
Noise is moved away from DC
The signal frequency band is moved to DC and 2f
LPF selects only the DC component
Effect of low pass filters
Time constant of the lock-in determines the LPF bandwidth
Effect of low pass filters
Rule of Thumb
Wait at least 3 times the time constant for the signal
To stabilize after something is changed (e.g. frequency)
This is assuming your sample or system responds
at least this fast
Phase Locked Loop
Choice of Frequencies to reduce line voltage
coupling
60 Hz and Harmonics
Avoid multiples of 60 Hz
Capacitive and Inductive Coupling
Multiple Modulations,
Harmonics
Example
Application examples
Impedance Measurement
Electrochemistry
Mechanical resonator
Time dependent PL
Phase interpreted as TIME