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15
sensitivity, decreasing the gain will increase the dynamic reserve.
1.8 Signal Input Amplifier and Filters
A lock-in amplifier can measure signals as small as a few nanovolts. The gain of the low noise signal amplifier should be
large enough so that the output signal can be digitized by the A/D converter without degrading the signal to noise ratio
(SNR). The analog gain of the SE1022 ranges from roughly 7 to 1000 times. Higher gains do not improve the SNR.
The overall gain (AC plus DC) is determined by the sensitivity and the distribution of the gain is set by the dynamic
reserve.
Input Noise
In SE1022, the input noise is about
Hz
nVrm
/
10
. If an amplifier has
Hz
nVrm
/
10
of input noise and a gain of
1000, the output will have
Hz
Vrm
/
10
of noise. Suppose the output of the amplifier is low-pass filtered by a single
RC filter (6 dB/oct rolloff) with 100ms time constant.
Input noise of lock-in amplifier and Johnson noise of resistors are both Gaussian in nature. That is to say, the amplitude of
noise is proportional to the square root of the noise bandwidth. A single-stage RC filter has an ENBW of 1/4T where T is
the time constant (RxC) which means that Gaussian noise is filtered with an effective bandwidth equal to ENBW. In this
case, the filter sees
Hz
Vrm
/
10
of input noise and has an ENBW of 1/(4
×
100ms) or 2.5 Hz. The voltage noise at
the filter output will be
Hz
Hz
Vrm
5
.
2
/
10
or 15.8 μVrms.
For Gaussian noise, the peak-peak noise is about 5 times the rms noise. Thus, the output noise will be about 79μVrms.
Input noise works in the same way. For sensitivities below 5μV, the value of input noise determines the output noise.
ENBW depends on the time constant and filter roll off. For example, suppose the SE1022 is set to <5 μV> full scale, <100
ms> time constant and <6dB/oct> roll off. Thus, ENBW is 2.5 Hz. This leads to 7.9nVrms input noise. At the output, this
causes about 0.16% of full scale (7.9nV/5μV). The peak to peak noise will be about 0.8% of full scale.
Assume that the signal input is from a low impedance source. The Johnson noise of resistors equals to
R
13
.
0
. Take
a 100
Ω
resistor for example, its noise is greater than the input noise of SE1022. The overall noise of multiple noise
sources is determined by the square root of the sum of the squares of the individual noise figures. For example, if a 1k
Ω
source impedance is used, the Johnson noise will be
Hz
nVrm
/
11
.
4
.
At low gains (sensitivities above 50
μ
V), the gain is not high enough to amplify the input noise to a level greater than the
noise of the A/D converter. In these cases, the output noise is mainly the A/D noise. At these sensitivities, the DC gain is
low and the noise at the output is negligible.)
Notch Filters
There are two notch filters in the signal amplifier chain in SE1022. They are pre-tuned to the line frequency and twice the