# Lock in amplifier simulation

• SvetaP
In summary, the conversation discusses a simulation of a lock in amplifier using Matlab and the desire to test it for different signal-to-noise ratios (SNR). The speaker mentions adding white Gaussian noise to the signal and references the specifications for lock in amplifiers, which state that they can handle up to -100dB of noise. However, when adding noise with an SNR of -30dB, the lock in stops working. The speaker is confused by this discrepancy and asks for help understanding. The attached specifications for the lock in amplifier are provided and the speaker explains that they have not yet added an analog-to-digital converter (ADC) or quantization to the system. Another participant in the conversation mentions that using averaging can achieve similar results to

#### SvetaP

Hi,

I wrote a simulation of lock in amplifier using Matlab and now i want to test it for different SNR.
I added to the signal white gaussian noise. In all the spec that i read, always written that the lock in amplifier can handle -100dB of noise.

When I add a noise of SNR=-30dB the lock in stops working, when i look at the spectrum of the signal+noise i see that the component that i am looking for is covered by noise so no wonder that the lock in doesn't work.

what i don't understand how is that in spec always written that lock in works at -100dB? i think that i am missing something.

attached spec of lock in amplifier : http://infrared.als.lbl.gov/content/PDF/equipment/SR810830_specs.pdf

look at the part of dynamic reserve.

I didn't add any ADC and quantization yet. So the system only consist of sinus signal that is the signal and reference and Gaussian noise.

Thanks for any help.

If you have truly white noise you can recover any signal if you average for long enough (the SNR improves as the square root of the number of samples).. Hence, you do not even need a lock-in amplifier (although using one will make the measurement much faster).

What is the time-constant of your simulated lock-in?

You should also be able to see the peak corresponding to your signal by just averaging over many simulated spectra.

Instead of using LPF in the end of lock in , i used averaging as perfect LPF.
explanation of simulation and results attached.

#### Attachments

• Lock in simulation 1.docx
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## 1. What is a lock-in amplifier simulation?

A lock-in amplifier simulation is a computer-based model that replicates the functionality of a lock-in amplifier, which is a specialized electronic instrument used in scientific research to measure weak signals in the presence of noise. The simulation allows for testing and optimization of experimental setups before conducting actual experiments.

## 2. How does a lock-in amplifier simulation work?

A lock-in amplifier simulation works by simulating the process of signal demodulation and filtering, which is the key function of a lock-in amplifier. The simulation takes in the input signal and uses a reference signal to extract the desired signal and filter out any noise or unwanted signals. The simulation also allows for adjusting different parameters to optimize the signal extraction process.

## 3. What are the advantages of using a lock-in amplifier simulation?

Using a lock-in amplifier simulation has several advantages. It allows for testing and optimizing experimental setups without the need for physical equipment, saving time and resources. The simulation also provides a better understanding of how a lock-in amplifier works and how different parameters affect the output signal. Additionally, simulations can be easily shared and replicated, allowing for collaboration and comparison of results.

## 4. Are there any limitations to using a lock-in amplifier simulation?

While lock-in amplifier simulations offer many benefits, there are also some limitations. Simulations may not accurately reflect the behavior of physical instruments, and the results may not always be directly applicable to real experiments. Additionally, simulations are limited by the accuracy and complexity of the model used, so they may not be suitable for all experimental setups.

## 5. What are some common uses for lock-in amplifier simulations?

Lock-in amplifier simulations are commonly used in various scientific fields, including physics, chemistry, and engineering. They are particularly useful in experiments that involve measuring small signals in the presence of noise, such as in spectroscopy, microscopy, and quantum computing research. The simulations can also aid in the development and testing of new lock-in amplifier designs.