Saluki SE1022 User manual

SE1022 Digital Lock-in Amplifier
User Manual
Saluki Technology Inc.

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The document applies to following models:
SE1022 DSP Lock-in Amplifier (1 mHz to 102 kHz)
Standard Pack:
1×Main Machine
1×Power Cord
1×USB Cable
2×BNC Connection Cable
1×Spare Fuse (2A, 250VAC)
1×U Disk or CD (for User Manual and PC Software)

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Preface
Thank you for choosing Saluki Technology Products.
We devote ourselves to meeting your demands, providing you high-quality measuring instrument and the best
after-sales service. We persist with “superior quality and considerate service”, and are committed to offering
satisfactory products and service for our clients.
Document No.
SE1022-03-01
Version
Rev01 2021.07
Document Authorization
The information contained in this document is subject to change without notice. The power to interpret the contents
of and terms used in this document rests with Saluki.
Saluki Tech owns the copyright of this document which should not be modified or tampered by any organization or
individual or reproduced or transmitted for the purpose of making profit without its prior permission, otherwise
Saluki will reserve the right to investigate and affix legal liability of infringement.
Product Quality Assurance
The warranty period of the product is 36 months from the date of delivery. The instrument manufacturer will repair
or replace damaged parts according to the actual situation within the warranty period.
Product Quality Certificate
The product meets the indicator requirements of the document at the time of delivery. Calibration and measurement
are completed by the measuring organization with qualifications specified by the state, and relevant data are
provided for reference.
Quality/Settings Management
Research, development, manufacturing and testing of the product comply with the requirements of the quality and
environmental management system.
Contacts
Service Tel:
+886. 909 602 109
Website:
www.salukitec.com
Email:
[e-mail]
Address:
No. 367 Fuxing N Road, Taipei 105, Taiwan

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Content
1 Lock-in Amplifier Basics........................................................................................................................................ 6
1.1 Introduction....................................................................................................................................................6
1.2 Functional Diagram........................................................................................................................................8
1.3 Reference Channel......................................................................................................................................... 8
1.4 Phase Sensitive Detectors.............................................................................................................................. 9
1.5 Time Constants and DC Gain...................................................................................................................... 10
1.6 DC Outputs and Scaling...............................................................................................................................12
1.7 Dynamic Reserve......................................................................................................................................... 14
1.8 Signal Input Amplifier and Filters............................................................................................................... 15
1.9 Input Connections........................................................................................................................................ 16
1.10 Intrinsic Noise Sources................................................................................................................................ 17
1.11 External Noise Sources................................................................................................................................ 19
1.12 Aux In/Out................................................................................................................................................... 21
1.13 Sweep Frequency and Amplitude of Signal Generator................................................................................21
1.14 FFT Spectral Analysis..................................................................................................................................21
1.15 Multi-harmonic Detection............................................................................................................................22
2 Interfaces............................................................................................................................................................... 23
2.1 Front Panel................................................................................................................................................... 23
2.2 Rear Panel.................................................................................................................................................... 24
2.3 Main Display................................................................................................................................................25
3 Menus.................................................................................................................................................................... 28
3.1 [INPUT/FILTERS]...................................................................................................................................... 28
3.2 [REF/PHASE]..............................................................................................................................................29
3.3 [GAIN/TC]...................................................................................................................................................36
3.4 [DISPLAY].................................................................................................................................................. 38
3.5 [SAVE/RECALL].........................................................................................................................................44
3.6 [CHANNEL OUTPUT]............................................................................................................................... 44
3.7 [SAMPLE]................................................................................................................................................... 47
3.8 [AUX OUTPUT]..........................................................................................................................................49
3.9 [SYSTEM]................................................................................................................................................... 50
3.10 [AUTO SET]................................................................................................................................................54
3.11 [CONTROL]................................................................................................................................................ 55
4 Remote Programming............................................................................................................................................57

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4.1 Command Syntax.........................................................................................................................................57
4.2 Detailed Command List............................................................................................................................... 57
5 Computer Operation..............................................................................................................................................69
5.1 Install Software............................................................................................................................................ 69
5.2 How to Use the Software............................................................................................................................. 71
5.3 Usage Examples...........................................................................................................................................88
6 Performance Tests................................................................................................................................................. 97
6.1 Self-Test.......................................................................................................................................................98
6.2 DC Offset..................................................................................................................................................... 98
6.3 Common Mode Rejection............................................................................................................................ 99
6.4 Amplitude Accuracy and Flatness............................................................................................................. 100
6.5 Amplitude Linearity...................................................................................................................................101
6.6 Frequency Accuracy.................................................................................................................................. 102
6.7 Sine Output Amplitude Accuracy and Flatness......................................................................................... 102
6.8 DC Outputs and Inputs...............................................................................................................................103
6.9 Input Noise.................................................................................................................................................104
6.10 Performance Test Record...........................................................................................................................105
7 Operation Examples............................................................................................................................................ 109
7.1 Simple Signal Measurements.....................................................................................................................109
7.2 Harmonics Measurements..........................................................................................................................113
7.3 Optical Spectral Measurements................................................................................................................. 117
7.4 Serial Communication................................................................................................................................119

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1 Lock-in Amplifier Basics
1.1 Introduction
The Lock-in amplifier is a device used to detect very small signals, which are always obscured by noise sources many
thousands of times lager. The lock-in amplifier can extract these small signals from noises and measure their values
accurately.
The lock-in amplifier is a weak signal detection method based on the coherence. Lock-in amplifiers use a key technique
known as phase-sensitive detection (PSD) to single out the required component of the signal. This component has the
same frequency with the reference signal and has a fixed phase differences with the reference signal. Noise signals at
other frequencies are rejected and do not affect the measurement.
The basic processing of small signals is amplification. Traditional amplifiers will amplify both the noise signals and the
required signals. If there is no band limiting or filtering, amplification will decrease the signal to noise ratio (SNR).
Therefore, filtering is needed to purify the signal and increase the SNR in order to measure the weak signal accurately.
PSD can be seen as a band-pass filter with a very narrow bandwidth. The basic modules of PSD include a multiplier
module and a low-pass filter (LPF) module, as shown in Fig.1. Sometimes PSD is described as a multiplier module
without a LPF.
Fig.1 PSD diagram
In Fig.1, SI(t) is the input signal plus noise in the time region, SR(t) is the reference signal, which has a fixed frequency
with the test signal.
Fig.2 Single-phase amplifier diagram
In Fig.2, the input signal SI(t) is defined as: SI(t) = AIsin(ωt + φ) + B(t) , where ωis the frequency of input signal, AI
sin(ωt + φ) is the test signal, B(t) is the total noise.
The reference signal SR(t) is defined as: SR(t) = ARsin(ωt + δ).
These two signals enter the PSD module for multiplication simultaneously, and the output of the PSD is defined as:

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)sin()()2cos(
2
1
)cos(
2
1
)sin()()sin()sin()()(




tAtBtAAAA
tAtBttAAtStSS
RRIRI
RRIRIpsd
In the time region, the output of the PSD consists three parts:
The first part is a DC signal. If AI, A and the phase difference (φ − δ) between the input signal and the reference
signal are constants, this part is a DC signal.
The second part is the frequency-doubled reference AC signal.
The third part is the result of multiplication of the noise and the reference. Because the sine signal is periodic and
there is no relevance between the noise signal and the reference signal. The integral of this part is zero.
In the frequency region, we can redraw these three parts:
The first part is at 0Hz, which is known as the DC component of one signal.
The second part is at 2fref Hz.
The third part is a random signal at all the frequencies, such as white noise. The frequency spectrum of white noise
does not change after any frequency drifts.
To sum up, the LPF output is defines as:
)cos(
2
1
  RIOutput AAS
Although we can determine the amplitude the amplitude of the input signal through adjusting the phase difference
)(  
, the accuracy is unsteady and insecure. In order to solve this problem, the dual phase lock-in amplifier was
invented, see Fig.3.
Fig.3 Dual Phase Lock-in Amplifier diagram
Now, we define the phase difference
 
, the LPF0 output
0Output
SX 
and LPF1 output
1Output
SY 
. Then
we calculate the amplitude R which is independent of θ:
R
I
A
YX
A
R)(2
2
22 


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The phase difference is defined as:
)/(tan 1XY

 
.
1.2 Functional Diagram
The functional block diagram of the SE1022 DSP Lock-In Amplifier is shown in Fig.4. On the whole, the SE1022
includes signal conditioners, reference signal generators, an algorithm module and a system control module and so on.
Fig.4 Functional Block Diagram of SE1022
1.3 Reference Channel
The reference channel is used to provide control signal which is associated with the detected signal. The SE1022 reference
input can trigger on an analog signal such as a sine wave or a TTL logic signal. The input is AC coupled and the input
impedance is 1MΩ.
Generally, both the sine wave and the TTL signal can be used as the reference signal. However, the generator's sine output
has a small and varying amplitude. Meanwhile, many function generators provide a stable TTL SYNC output which can
be used as the reference. Therefore, for frequencies below 1Hz, a TTL reference signal is required.
The SE1022 lock-in amplifier has two reference signal modes: internal reference mode and external reference mode.

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In internal reference mode, the internal oscillator generates a digitally synthesized sine wave which is used to multiply
with the input signal. The phase-locked-loop (PLL) is not used since the lock-in reference provides the excitation. The
phase noise will not affect the internal reference signal. The phase noise is extremely low. This mode can work normally
from 1mHz to 102kHz.
In external reference mode, an external sine wave or TTL logic signal can be used as the external reference signal. PLL
will be used in this mode, but it will generate a little phase jitter which may cause measurement errors.
The phase jitter means that average phase shift is zero but the instantaneous phase shift has a few milli-degrees of noise.
The phase jitter makes the reference signal plus noise at different frequencies. According to the coherence principle of
PSD, the output is not a single frequency, but a distribution of frequencies about the true reference frequency.
In fact, phase noise in the SE1022 is very low and generally has no effect. In applications that requiring no phase jitter, the
internal reference mode should be chose. Since there is no PLL in internal mode. The internal oscillator and the reference
sine waves are directly linked and there is no jitter in the measured phase.
1.4 Phase Sensitive Detectors
The PSD in the SE1022 acts as a digital multiplier as is shown in Fig.5. The input signal amplified and filtered is
converted to digital signal by a 24-bits A/D converter and then goes into the PSD. The reference sine wave is computed to
24 bit of accuracy, and the accuracy of the whole PSD is 48 bit.
The PSD module in lock-in amplifier is mainly used to implement the coherent modulation of the input signal and
reference signal. Generally, there are two kinds of phase-sensitive detectors (PSD's): digital PSD's and analog PSD's.
Traditional PSD's use an analog multiplier to multiply the input signal with the reference signal. There are many problems
associated with these, including harmonic rejection, output offsets, limited dynamic reserve and gain error. It will limit the
accuracy of PSD's and bring in various noises.
The digital PSD multiplies the digitized signal with a digitally computed reference sine wave. Because the reference sine
wave is computed to 24 bit of accuracy, the harmonics have -120 dB roll off. That is to say, the harmonics do not affect
the products of the PSD.
Fig.5 PSD diagram
Because the PSD based on analog method has temperature drift, there are always some deviation between the output and
actual result that is the uncertain system error. While the PSD based on digital method has a precise amplitude and never
change, so it will not generate any system errors. This eliminates a major source of gain error in a linear analog lock-in.
Considering that the inputs of analog multiplier are analog quantity, the reference signal will be affected by temperature

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drift. This will cause errors in the reference and greater errors in the results of coherent modulation.
The dynamic reserve of an analog PSD's is limited to about 60 dB, because there are always many background noises.
When there is a large noise signal present, 1000 times or 60dB greater than the full-scale signal, the analog PSD measures
the signal with an error. Because the lock-in amplifier is mainly used to detect weak signals, when the amplitude of
background noise is similar to or larger than the signal amplitude, the results of coherent modulation will be wrong.
To the digital PSD's, the dynamic reserve is limited by the quality of the A/D conversion. Once the input signal is
digitized, no further errors are introduced. Practically, the dynamic reserve of SE1022 can exceed 120dB.
The performance of a lock-in amplifier is largely determined by the performance of its PSD's. Almost in all respects, the
digital PSD outperforms the analog one. Besides, the digital PSD is also more convenient to modify.
1.5 Time Constants and DC Gain
The output signal of the PSD contains many signals of various frequency, such as the sum or difference between the input
signal frequency and the reference frequency. Only the signal whose frequency is exactly equal to the reference frequency
will result in a DC output.
The low pass filter (LPF) at the PSD output removes all the AC signals that unwanted, including the 2F (sum of the
signal and the reference) and the noise signals. This filter is what makes the lock-in such a narrow band detector.
Time Constants
The bandwidth setting of the low pass filter is the same as the conventional low pass filter. They are both determined by
the time constants. The calculation of the time constant is defined as:
f
TC
 2
1

Here f is the -3dB frequency of the low-pass filter. For example, to a one-order low pass filter of RC type, a 1s time
constant means its -3dB point occurs at 0.16Hz.
In fact, where there is an input noise, there is an output noise. By increasing the time constant, the output becomes more
stable and measurement becomes more reliable. The time constant reflects not only the stability of the system and the
accuracy, but also the respond time of the output.
The time constant also determines the equivalent noise bandwidth (ENBW). The ENBW isn't the filter -3dB pole, it is the
effective bandwidth for Gaussian noise.
Digital Filters vs Analog Filters
Analog filters have many limitations in performance. The temperature drift and non-linearity are two important problems
that limit the rolloff performance of an analog filter. A two-stage analog filter provides about a maximum rolloff of 12
dB/oct at high frequency points.

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Space and expense are also limitations. Each filter needs to have many different time constant settings. These different
settings require different components and switches to select. Each setting is costly and space consuming. A large quantity
of analog devices also bring quite complexity to the device debugging.
Considering these limitations, we choose a 47 bits digital filter to accomplish narrow band filtering. The DC amplitude is
exactly 0 dB and the equivalent value of Q exceeds 145dB.
Synchronous Filters
Another advantage of digital filtering is to do synchronous filtering. Even if the input signal has no noise, the PSD output
always contains a component at 2F (sum frequency of the signal and the reference) whose amplitude may exceed the
difference frequency component that we want. At low frequencies, increasing the time constant can attenuate the 2F
component.
In SE1022, synchronous filters are available at detection frequencies below 200 Hz. At higher frequencies, the filters are
not required because the 2F component is easily removed without using long time constants. The output of the
synchronous filter is followed by two more stages of normal filters. This combination of filters can eliminate the
harmonics of the reference signal and attenuate other noise signals.
Long Time Constants
Time constants above 100s are difficult to accomplish by using analog filters. This is simply because the capacitors
required for the RC filters are prohibitively large in value and size. Why would you use such a long time constant?
Sometimes you have no choice. If the reference is below 1 Hz with a lot of noise at low frequency, the PSD output will
contain many low frequency components. Nevertheless, the synchronous filter only filters out the harmonic component of
the reference frequency, and the followed filters filter the noise.
The SE1022 provides time constants as long as 3000s when the reference frequency is below 200 Hz, which can satisfy
most requirements of measurements.
DC Output Gain
How big is the DC output from the PSD? It depends on the dynamic reserve. With a 60 dB dynamic reserve, a noise signal
can be 1000 times (60 dB) greater than a full scale signal. At the PSD, the noise cannot exceed the input range of PSD.
For example, in an analog lock-in, the PSD input range might be 5 V. With 60 dB dynamic reserves, the signal will be
only 5 mV at the PSD input. The PSD typically has no gain so the DC output from the PSD will only be a few millivolts.
Even if the PSD had no DC output errors, amplifying this millivolt signal up to 10 V is error prone. An offset as small as 1
mV will appear as 1 V at the output. This is one of the reasons why analog lock-in does not perform well at high dynamic
reserve.
The digital lock-in does not have an analog DC amplifier, and has no DC output offset. Likewise, the digital DC amplifier
has no input offset. The output of the digital DC amplifier is simply the product of the input signal and the required gain.
This allows the SE1022 to operate with 100 dB of dynamic reserve without any outputs offset or zero drift.

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1.6 DC Outputs and Scaling
The SE1022 has Channel 1 and Channel 2 outputs (CH1 and CH2) on the front panel.
CH1 and CH2 Outputs and Display
The output range of CH1 and CH2 is from -10V to 10V.
The output signal is proportional to the value of the test signal and the setting scale. Otherwise, the SE1022 shows the
values of CH1 and CH2 on the front panel, including the value of X, Y, R, θof the test signal. The display interface of
SE1022 is shown in Fig.6.
SE1022 can display the value of CH1 and CH2 through bars in addition to numbers. To discover the changes of data, you
can observe the data in the time region.
Fig.6 Display Interface of SE1022
Fig.7 Polar Display Mode
Otherwise, SE1022 can use polar coordinates to display the vector combined with the co-phase and quadrature

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component of test signal. The polar display interface is shown in Fig.7. All display modes can simply adjust the display
ratio by hand operation. The auto-adjust function can optimize the display mode rapidly.
X, Y and R Output Offset and Expand
The SE1022 has the ability to offset the X, Y and R outputs, which is useful when measuring deviations in the signal
around some nominal value. The output can be offset to zero by setting the offset. Then changes in the output can be read
directly from the display or output voltages. The offset is specified as a percentage of full scale. Offsets can be set up to
100% of full scale. When the sensitivity is changed, the percentage does not change.
The X, Y and R outputs can be expanded. It's realized by multiplying the output with an expansion factor. Thus, a signal
which is only 10% of full scale can be expanded to provide 10 V rather than 1 V. The general use for expansion is to
increase the measurement resolution around some value which is not zero.
When the output does not exceed the full scale, the SE1022 can expand the output by multiplying with the expansion
factor from 1 to 256. The output with offset and expand is:
)(10)( VExpandOffset
Sents
Signal
Output 
Where <Offset> can be set up to ±100% by the digital keyboard and the minimal step is 0.01%. <Expand> can be set
from +1 to +256 by the digital keyboard and the minimal step is 1. Related display interface is shown in Fig.8.
For example, there is:
)(6)(102)2.0
1
1.0
(VV
mV
mV
Output 
Fig.8 Output Offset and Expand

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1.7 Dynamic Reserve
The definition of dynamic reserve is the ratio of the largest tolerable noise signal to the full scale signal, expressed in dB,
which is defined as:
Dynamic reserve = 20Lg(OVL/FS)(dB)
Here OVL is the total dynamic range of the input signal. FS is the dynamic range of the output signal. If the dynamic
reserve is 100 dB, the tolerable noise can be 105times the input.
The ‘tolerable' means that the noise at the dynamic reserve limit should not cause an overload anywhere in the
instrument. Overload might appear at the input of the pre-amplifier and the output of DC amplifier. We can adjust the
distribution of the gain to achieve high dynamic reserve. This means that the input signal gain at the pre-amplifier should
be set very low so the noise is not likely to overload. Then the low pass filter removes the large noise component from
the PSD output which allows the remaining DC components to be amplified to reach 10 V full scale.
This gain is distributed between AC gain before the PSD and DC gain following the PSD. The total gain is the product of
the AC gain and the DC gain. Suppose the total gain is a constant. If the AC gain increases and the DC gain decreases,
the input noise is easy to overload after AC gain. Thus, the dynamic reserve and the DC drifts decrease. In contrast, if the
AC gain decreases and the DC gain increases, the dynamic reserve increases. In this case, the output stability will
decrease and the accuracy of measurement will be lower.
The noise frequencies and amplitudes affect the accuracy of the DC output signal. Noise at the reference frequency with
large amplitude becomes part of the DC signal after the PSD. This enlarges the output error of the lock-in amplifier.
The dynamic reserve is related to noise frequency. The dynamic reserve is 0dB at reference frequency and increases
when the noise frequency moves away from the reference frequency. It reaches a maximum value when the frequency is
far enough. The dynamic reserve near the reference frequency is important to noise tolerance of the instrument.
Providing more low pass filter stages can improve the performance of the filters and then increase the dynamic reserve
close to the reference frequency. The dynamic reserve far from the reference frequency is generally high but has little
influence.
The dynamic reserve of SE1022 is greater than 120dB. High dynamic reserve will increase output noise and drift. When
the dynamic reserve is high, output noise will be increased due to the A/D converter. There is background noise at any
signal. When the signal is amplified by PSD, the output signal will contain noises. If the noise is very high, it will result
in large output noise. Otherwise, if the external noise is very low, the output is mainly affected by the noise of SE1022.
Reducing dynamic reserve and DC gain can decrease the error. Therefore, low dynamic reserve should be chosen firstly
in actual application.
In fact, the minimum reserve changes with the sensitivity (gain) of the instrument. At high gains, the minimum dynamic
reserve increases with the increase of the sensitivity. In analog lock-in amplifiers, low dynamic reserve means low output
error and drift. In SE1022, high dynamic reserve increases output noise, but not increases output error and drift.
However, if the gain of analog amplifier is high enough, the amplified intrinsic noise will be greater than the noise
generated by the A/D converter. In this case, increasing the analog gain cannot decrease the output noise. At high

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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
HznVrm /10
. If an amplifier has
HznVrm /10
of input noise and a gain of
1000, the output will have
HzVrm /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
HzVrm /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
HzHzVrm 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 100Ωresistor 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 1kΩ
source impedance is used, the Johnson noise will be
HznVrm /11.4
.
At low gains (sensitivities above 50 μV), 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

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line frequency. When the largest noise signals are at the power line frequencies, these filters can remove noise signals at
these frequencies. Removing the largest noise before the final gain stage will reduce the dynamic reserve required to
perform a measurement.
To prevent such a situation, it is necessary to improve the signal amplifier chain. If the required dynamic reserve without
these notch filters is below 60 dB or if the minimum reserve is sufficient, then these filters do not improve the
measurement obviously.
Do not use notch filters when making measurement near the notch frequencies. Notch filters have a finite range of
attenuation, generally about 10 Hz. Thus, if the lock-in is measuring at 90Hz, do not use the 80 Hz notch filter. Otherwise,
the signal will be attenuated and the measurement will be wrong. Besides, notch filters also have effect on phase shifts
measurements.
Anti-aliasing Filters
After signal filtering and amplification, there is an anti-aliasing filter, which is required by the signal digitization process.
According to the Nyquist criterion, the sampling frequency of signal must be at least twice the highest signal frequency.
For example, the highest signal frequency is 100 kHz, then the sampling frequency is 312.5 kHz. However, signals above
156 kHz cannot reach the A/D converter. These signals would violate the Nyquist criterion and be under-sampled. The
result of under-sampling is to make the higher frequency signals appear as lower frequency signal in the digital data
stream. This would make the measurement wrong.
To avoid under-sampling, the analog signal is filtered to remove signals above 154 kHz. This filter has a flat pass
bandwidth from DC to 102 kHz so that it would not affect measurements in the operation range of the lock-in. The filter
rolls off from 102 kHz to 154 kHz and achieves an attenuation of at least 100dB above 154 kHz.
Input Impedance
The input impedance of SE1022 is 10 MΩ. If a higher input impedance is desired, the SE1022 remote preamplifier must
be used so that the SE1022 has the maximum input impedance of 100 MΩ.
1.9 Input Connections
Noises always exist in all circuits. Even if the signal is not very weak, noises exist and decrease the accuracy of
measurement. There are many methods to reduce noise. Minimizing the various noise sources can increase the accuracy of
the measurement. Besides, the effect of noise sources in the laboratory and the problem of the differential grounds
between the detector and the lock-in can be minimized by careful input connection.
There are two basic methods for input connection - the single-ended connection is more convenient while the differential
connection eliminates spurious pick-up more effectively.
Single-Ended Connection (A)

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In the first method, the lock-in uses the A input in a single-ended mode. The lock-in detects the signal as the voltage
between the center and outer conductors of the A input only. However, there are two disadvantages of this mode.
Generally, the low level is a constant of 0V. However, grounds of different instruments may be at different potentials.
When the shield of the A cable is connected to the lock-in's ground directly, different potentials will result in a high
current, that is the ground loop. Thus, connecting via a resistor between them can avoid ground loop problems. In general,
float uses 10 kΩand ground uses 10Ω.
Besides, this mode is not sensitive to noise. The signal cable is just like an antenna. The lock-in lets the shield ‘quasi-float'
in order to sense the experiment ground and pick up the activities of the electronic in environment. In this case, the noise
came up. Unfortunately, the single-ended connection mode cannot distinguish the noise and actual signal.
Differential Connection (A-B)
The second method of connection is the differential mode. This mode has two signals cables which connect the signal
source and the lock-in's inputs. There are two high impedance power amplifiers in the lock-in. The lock-in measures the
voltage difference between the center conductors of the A and B inputs, which can avoid common voltage problems since
the shields are ignored.
In this mode, take care that the two cables travel the same path between the experiment and the lock-in. There should not
be a large loop area enclosed by the two cables. Otherwise, measurement is susceptible to magnetic pickup.
1.10 Intrinsic Noise Sources
Noise is defined as any negative factors which will affect the result of measurement. Noise is random, unpredictable and
temporary. Good experimental design should reduce the noise and improve the stability and accuracy of measurement.
There are various intrinsic noise sources which are present in all electronic signals. Some of them are unavoidable which
only can be decreased by signal averaging and a narrower bandwidth. Others can be decreased by filtering and perfect line
structures and component layout. Meanwhile, amplifier itself also produces noise at work, which can be solved by low
noise amplifier design techniques.
Johnson Noise
Every resistor generates a noise voltage across its terminals due to thermal fluctuations in the electron density within the
resistor itself. This is Johnson noise. The spectrum of the Johnson noise is flat, so the noise power is almost the same in
different frequency band (of course there is an upper limit frequency). In this case, the noise is called white noise. The
fluctuations give rise to an open-circuit noise voltage,
2
1
)4( kTRBV 
Where k=1.38×10-23J/°K is the Boltzmann's constant. T is the temperature in °Kelvin, which can be transformed to °
Celsius: °K= °C +273.16. R is the resistance in Ohms, and B is the bandwidth of the measurement in Hz.
Harry Nyquist's mathematical studies of Johnson noise revealed that the power spectrum function of Johnson noise is:

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)/(4)( 2HzVkTRfSt 
At 300°K, a resistor of 10 kΩis connected to the input of the amplifier. The voltmeter is connected to the output of the
amplifier. The open-circuit effective voltage of the filter which has a 10 kHz bandwidth is 1.3 μV.
The amplitude of Johnson noise is unpredictable in normal cases. It follows the Gaussian distribution. Johnson noise is the
minimum value of the noise voltage of any devices including detectors, signal sources and amplifiers with resistors.
Johnson noise is a typical case of wave dissipation.
Shot Noise
Because of the finite nature of the charge carriers, electric current has noise. Noise generates in the current since there is
always some non-uniformity in the electron flow. This noise is called shot noise. It appears as voltage noise when current
is passed through a resistor, or as noise in a current measurement.
If the effect between carriers is ignored, the shot noise or current noise is given by:
2/1
)2( BqII dc 
where q is the electron charge of 1.6×10-19 Coulomb, Idc is the DC current and B is the bandwidth. If Idc is 1 A DC current
and B is 10 kHz, then, I is 57 nA which is about 0.000006% of Idc. At a smaller current, the fluctuation is larger. For
example, if Idc is 1 μA and B is still 10 kHz, then, I is about 0.006% or -85 dB. If Idc is 1 pA, then, I is about 5.6% or 56
fA.
In fact, shot noise is one kind of the white noise. Its power spectrum density is given by:
)/(2)( 2HzAqldfSsl 
The formula is based on the assumption that carriers in the current do not affect each other. This assumption exits, such as
the diffusion current in the junction diode. However, for general metal, this formula cannot be used because the cross
effect between carries cannot be ignored.
Flicker Noise (1/f Noise)
In 1925, Johnson first found 1/f noise in in tube currents. The power spectrum function of this noise is proportional to 1/f.
The lower the frequency, the more serious the noise. Thus, it is also called low frequency noise. Microscopically, 1/f noise
is caused by the random value of contact resistance between two conductors. The current amplitude of 1/f noise follows
the Gaussian distribution, and the power spectrum density is proportional to 1/f which is given by:
)/()( 2
2
HzV
f
KI
fS d 
1/f noise is also called flicker noise due to the random fluctuation of the power spectrum density in active devices. It
broadens the bandwidth near the center frequency and reduces the value of Q of oscillators. 1/f noise must be considered
near the center frequency.

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Total Noise
Johnson noise and shot noise are unreducible. Any resistors with a same resistance have the same Johnson noise. Shot
noise relies on the special manufacture of resistors, including its material and package technology and so on. For example,
among winding resistor, metal film, carbon resistor and pure carbon, the winding resistor has the minimum resistance. The
metal film resistor and carbon resistor have larger resistances. The pure carbon resistor has the maximum resistance of
these four. All of these noises are incoherent. The total random noise is the square root of the sum of the squares of all the
incoherent noise sources.
1.11 External Noise Sources
In addition to the intrinsic noise sources discussed previously, there are different kinds of external noise sources. Most of
these noise sources are asynchronous and not related to the reference. They do not occur at the reference frequency or its
harmonics. These noise sources affect the measurement mainly by increasing the requirement of dynamic reserve or
lengthening the time constant. However, some external noise sources are related to the reference. If they are picked up in
the signal, noise will add or subtract from the actual signal and cause errors in the measurement. Fortunately, external
noise sources can be reduced through various ways.
Capacitive Coupling
The mutual capacity between wires is often called stray capacity Cstray. An AC voltage from a nearby piece of apparatus
can couple to a detector via Cstray. Although Cstray may be very small, the coupled noise may still be larger than a weak
experimental signal and cause severe instability for the detector. The noise current is given by:
noisestrayVCI
 
Where

is 2πtimes the noise frequency, Vnoise is the amplitude of noise, and Cstray is the stray capacitance.
When the noise sources' frequency become larger, the coupling noise will be larger. If the noise source is at the reference
frequency, the noise will be quite large. The lock-in rejects noise at other frequencies, but pick-up at the reference
frequency appears as signal.
Cures for capacitive noise coupling include:
1) Remove or turn off the noise source.
2) Design the experiment to measure voltages with low impedance for most of low frequency noise sources.
3) Install capacitive shielding by placing the experiment and detector in one metal box.
Inductive Coupling
An AC current in a nearby piece of apparatus can couple to the experiment via a magnetic field. A changing AC current
gives rise to a changing magnetic field which induces voltage. The larger the frequency, the larger the electromotive force,
the greater the measurement error.

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Cures for inductively coupled noise include:
1) Remove or turn off the interfering noise source.
2) Reduce the area of the pick-up loop by using twisted pairs or coaxial cables.
3) Use magnetic shielding to prevent magnetic field from crossing the area of measurement.
Resistive Coupling or Ground Loops
The ground loop is an interference source which can generate noise voltage between the grounds. If the noise voltage is
large enough, it will cause measurement errors. Ground loop is a physic loop, which generates from many ground methods.
These grounding methods can act as a big loop wire. They pick up noises from the environment and generate voltages in
the grounding system. The 50 Hz magnetic field of the AC power is a normal noise source that the ground loop always
pickup. For distributed grounding systems, the ground voltage can cause the ground current flow in the ground loop. Since
the ground is with low impedance, noise current is always very high.
Cures for ground loop problems include:
1) Connect all grounds to the same physical point.
2) Use a heavy ground bus to reduce the resistance of ground connections.
3) Remove sources of large ground currents from the ground bus.
Microphonics
Not all noise source are electrical in origin. According to microphonic effects, mechanical noise can be transformed into
electrical noise. Physical changes in the device or cables (due to vibrations for example) will cause electrical noise over
the whole bandwidth of the lock-in.
Solutions to minimize microphonic signals:
1) Eliminate mechanical vibrations near the experiment.
2) Tie down cables carrying sensitive signals.
3) Use a low noise cable that is designed to reduce microphonic effects.
Thermocouple Effects
When two dissimilar metals contact, there will be potential difference between them. The reason for potential difference
includes: (1) different electronic work function of two metals. (2) different electron concentration of two metals.
Suppose that metal A and metal B have work functions Va and Vb respectively. The electromotive force (emf) between A
and B is:
)ln(
b
a
baab N
N
q
kT
VVV 
Where K=1.38×10-23J/K is Boltzmann's constant. T is the temperature in °Kelvin;q is the elementary charge of 1.60×10-19