2.4 N
OISE
M
EASUREMENTS
Lock-in amplifiers are capable to measure noise. They detect a signal at a certain center
frequency
ω
ref
with an equivalent noise bandwidth. For a Gaussian noise, the equivalent
noise bandwidth of a real low pass filter is the bandwidth which passes the same
amount of noise as a perfect rectangular filter with the equivalent noise band width.
The equivalent noise bandwidth of the
eLockIn
is determined by the time constant
and the slope of the used Butterworth filter. It is calculated by
B
n
=
∫
0
∞
1
1
2n
d
.
(4)
The normalized Butterworth filter noise bandwidths are:
Filter order
Bandwidth /
τ
1
1,570796
2
1,110721
4
1,026172
In order to measure noise spectra, the resulting data should be divided by the square-
root of the used bandwidth.
The integrated spectrum is taken with a time constant of 10 ms
and a slope of 24 dB (4
th
order) – bandwidth factor ~ 1,03. The
related bandwidth is then 1/10 ms = 100 Hz. In order to interpret
the result as noise in units of V/Hz
0.5
, the spectrum should be
divided by 10 Hz
0.5
(= sqrt(100 Hz)).
13 (58)
Summary of Contents for eLockIn 203
Page 52: ...7 APPENDICES 7 1 SCHEMATIC DIAGRAM OF THE SIGNAL PATHS 52 58...
Page 53: ...7 2 DIAGRAM OF THE LOCKIN AMPLIFICATION PATHS Diagram of the preamplifier switches 53 58...
Page 54: ...7 3 FRONTPANEL DIMENSIONS 54 58...
Page 55: ...7 4 INSTRUMENT SPECIFIC TEST SHEETS insert with 10 pages of data 55 58...
Page 56: ...7 5 PREAMPLIFIER CONNECTOR PINOUT 56 58...
Page 58: ...7 7 TRACEABILITY CHART 58 58...
