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The main parameters of lock-in amplifiers

The main parameters of lock-in amplifiers include full scale input level, overload, minimum discernible signal, input total dynamic range, output dynamic range and dynamic reserve.

In weak signal detection, depending on the specific circumstances, people have different requirements on performance. For example, in temperature detection, low-frequency applications are usually needed due to the hysteresis of thermal effects. But to weak signal detection in the field of radio frequency, it requires that the device can be able to respond to high-speed signals. In biological testing experiments, the signal to noise ratio is generally low, at this time the devices need to  have a good signal extraction capability. In optical applications, it is often necessary to detect weak current signals, which in turn requires the device to have current amplification capability. In short, the requirements of the lock-in amplifier are varied. For the sake of uniformity, the main performance parameters of the lock-in amplifier are summarized and concentrated as follows.

1. Full Scale Input Level(FS)

FS also called full scale input sensitivity. It is used to characterize the measurement sensitivity of lock-in amplifier. It has a voltage dimension, which is related to the total gain of the system, as follows:


Where OUTmax is the output full scale value, such as 10V. Atotal  is the total gain of the system, for example, 107. then the FS of the system is 1uV. FS actually represents amplification of the system. 
It should be noted here that "output" refers to a representation of the useful signal measured by lock-in amplifier. This representation is generally the rms value of the input signal. Sometimes for the application's needs, the output may be obtained by scaling the rms value of the useful signal. OE series lock-in amplifiers can measure 1Vrms input signal directly. Sensitivity from 1nVrms-1Vrms is calibrated with the order of 1-2-5. Users can easily adjust the size of the signal.   

2. Overload(OVL)

OVL is defined as the input level at overload or critical overload at either stage of the lock-in amplifier. Because weak signal detection usually deals with low signal-to-noise input, overload often occurs when the noise voltage spikes. Therefore, OVL can be understood as the maximum input noise voltage level that the system allows, that is the system's maximum noise margin.

3. Minimum Discernible Signal(MDS)

MDS is defined as the smallest input signal that can be recognized by the output, which can be interpreted as the resolution of the system to the small signal. The main factors affecting the MDS include system internal noise, temperature drift, etc. The result may be fluctuating due to internal noise and temperature drift. The MDS is defined as the minimum input at which the output can stabilize at a certain percentage of fluctuation. For example, a 100 nV pure signal was input. Prolonged monitoring showed that the result was stable within the error in 10%.  In the instrument nominal temperature range, such as 20 ℃ ~ 30 ℃, it is also stable in this range. Moreover, when the input is below 100 nV, it can not achieve the stability within this error range using the same observation method. Then MDS is defined as 100nV. Note that, MDS is usually defined in terms of time drift in China while it's usually defined strictly with both time drift and drift in foreign countries.

4. Input Total Dynamic Range

For the given FS (ie, the given gain setting), input total dynamic range is the decibel value of the ratio of OVL to MDS, that is :      

input total dynamic range=20lg(OVL/MDS)(dB)

As mentioned above, the OVL nominates the noise margin of the lock-in amplifier, while the MDS indicates the minimum signal that the lock-in amplifier can resolve. Therefore, the input total dynamic range can be understood as the ability that a lock-in amplifier to extract useful signals from noise. Therefore, the higher the resolution, the greater the noise margin, the greater the input total dynamic range. The input total dynamic range of OE1022 is more than100dB. In its measurement range, OE1022 can accurately detect the signal out in various harsh noises, so it's universal for a variety of test sites.

5. Output Dynamic Range

This parameter is defined as the decibel value of the ratio of FS to MDS, that is :

Output dynamic range=20lg(FS/MDS)(dB)

The output dynamic range indicates the dynamic range of the useful input signal that the lock-in amplifier can detect. That is, the input valid signal can fluctuate within this range without either causing the lock-in amplifier to be indistinguishable or exceeding the maximum output range.

6.OE1022 Dynamic Reserve(DR)

DR is defined as the decibel value of the ratio of OVL to FS, as shown in the following equation:      


OVL indicates the input total dynamic range and FS indicates the output dynamic range. A dynamic reserve of 100 dB means the system can tolerate 105 times more noise than the useful signal.   
In fact, the dynamic reserve capacity should ensure not to be overload during the entire experiment. Overloading may occur at the input of the preamplifier and the signal output of the DC amplifier. High dynamic reserve can be achieved by adjusting gain distribution. The previous stage magnification is set to a smaller value to prevent noise overload. After most of the noise has been filtered out by the PSD and lowpass filters, the DC magnification is set to a larger value, amplifying the signal to full scale.
Input signal of the lock-in amplifier requires AC amplification before the PSD process, and DC amplification after the PSD process. With a constant total gain, if the AC gain is increased and the DC gain is reduced, AC amplification of the input noise will easily make the PSD overload, the dynamic reserve reduced and the output DC drift decreased. On the other hand, if the DC gain is increased and AC gain is reduced, the dynamic reserve is increased, so that the lock-in amplifier has good anti-interference ability. However, this is at the expense of output stability and will reduce the measurement accuracy. 
The output accuracy of DC amplification is affected by the frequency and amplitude of the noise.  Noise that has larger amplitude and the same frequency with signal  will change into a DC signal after through the PSD.  Then it will output directly when it pass through the low-pass filter so it  affects the output result
Dynamic reserve is related to noise frequency. The dynamic reserve is 0 at the reference frequency. the dynamic reserve increases when it's away from the reference frequency, and the maximum dynamic reserve can be reached when far enough from the reference frequency. The dynamic reserve around the reference frequency is extremely important for the instrument's noise margin. Increasing the number of low-pass filters can increase the filtering effect, thereby increasing the dynamic reserve near the reference frequency. The dynamic reserve away from the reference frequency is generally relatively large, but it has little effect.  
The dynamic reserve of OE1022 is more than 100dB, but high dynamic reserve will produce output noise and drift. When dynamic reserve is high, , the output error increases due to the noise of the analog-to-digital converter.  Because of the noise floor present in all sources, noise is mixed when the PSD  extracting signal. If the noise is high, it produces a large output error in a high dynamic reserve measurement. If the external noise is small, its output is mainly affected by the own noise of OE1022. At this point you can reduce the output error by reducing dynamic reserve and DC gain. Therefore, in practical applications, we should make full use of low dynamic reserve. 
Under certain measurement accuracy, there is a minimum of dynamic reserve.The higher the accuracy requirement, the greater the minimum.  In analog lock-in amplifiers, low dynamic reserve means less output error and drift. To OE1022,  high dynamic reserve does not increase the output error and drift, but will increase the output noise. However, if the gain of the analog amplifier before the A / D converter is large enough, its self noise is larger than that of the A / D converter. In this way, the output is mainly affected by the input noise. Therefore, increasing the analog gain, that is reducing the dynamic reserve, does not reduce the output noise. In the case of extremely high resolution, increasing the gain does not improve the signal-to-noise ratio, so we can reduce the gain to increase the dynamic reserve.