# A Novel Battery-Supplied AFE EEG Circuit Capable of Muscle Movement Artifact Suppression
## 4 Simulation and Results: Comprehensive Analysis
### Simulation of Novel EEG-B3V3S/C1 Circuit Design
#### 4.1.1 Simulation in a 50 Hz Electrical Grid Environment
The output of the EEG circuit (V\({}_{\text{out}}\)--cyan) waveform is the output of the EEG-B3V3S/C1 circuit design. Lastly, the output of the instrumentation amplifier (V\({}_{\text{vo}}\)--red) waveform is the voltage at the output of the instrumentation amplifier. This waveform is the Fourier plane of the experiment when the Fourier transform is performed from 0 s to 3 s, and the plane is limited from 4 Hz to 30 Hz in a linear x-axis scale, in order to more closely inspect the integrity of the signal in the wavebands of interest, namely alpha, beta and theta. First and foremost, by observing Figure 21, it can be clearly assessed that the ground truth EEG signal integrity is preserved. This is apparent because in the picture, the original raw ground truth EEG signal (V\({}_{\text{eeg}}\)--pink) is magnified 300 V/V and matches exactly the output of the EEG circuit (V\({}_{\text{out}}\)--cyan) waveform of the output in the desired peaks, in the cases at 9 Hz, 10 Hz and 25 Hz, where the beta and alpha wave consecation of power exist. Simultaneously, the noise artifacts do not affect the appearance of the brain signal peaks but affect in a non-detrimental way for the BCI of neurofeedback applications the rest of the EEG frequencies in the wavebands of interest. Thus, it is apparent from the graph that the circuit output (V\({}_{\text{out}}\)--cyan) gives the magnitude and, after some processing, the energy content for the alpha, beta and theta wave bands in thirty-second intervals, while the user of the EEG circuit participates in protocols with strong compound muscle movements. In Figure 22, where the same 30 s experiment is presented, in which the Fourier transform is performed for only the first 3 s, the same observations as above still hold. So, it can safely be assumed that the circuit performs as intended both at single-digit-second intervals as well as tens-of-seconds intervals, satisfying the requirement for a wide range of neurofeedback and BCI applications. As far as EMI is concerned, by inspecting the raw EEG channel 1 signal (V\({}_{\text{ch1}}\)--blue) and raw EEG reference channel signal (V\({}_{\text{chref}}\)--green) waveforms that represent the signals collected in the electrodes, in Figure 22, the main noise is at around \(-27\) db (in this case of a 50 Hz grid at 220 V), while in the output, it is suppressed at approximately \(-74\) db, validating the theoretical predictions about the depth of the notch filter. Moreover, it is apparent that the relative amplitude of the weakened EMI signal component in the output is in the order of magnitude of an extremely weak gamma signal, so the majority of gamma signals in the 50 Hz region could be collected by the proposed novel circuit of this study. This observation, of course, is also true for the conditions in Figure 17:4  
As for Figure 23, it has the same ranges in time scale and Fourier transform as Figure 22, but it is focused on the 3 kHz region. As previously described, there is the region where the frequency component is expected to be of the ERP signal that takes place in the first second of this exemplary protocol presented earlier in the results. Indeed, a closer observation reveals that almost none of the original ground truth EEG signal (V\({}_{\text{eeg}}\)--pink) is detectable in the raw EEG reference channel (V\({}_{\text{chref}}\)--green) and raw EEG channel 1 signal (V\({}_{\text{ch1}}\)--blue) waveforms that are collected from the electrodes, and the region is significantly contaminated by high frequency noise artifacts. Notably, the circuit can recreate the frequency information and especially the peak in the Fourier plane of the ERP signal, validating that both the filtering and amplification of our proposed circuit work as intended. Figure 24 represents the spectrum of the Fourier of the same constraints in time that were outlined for Figures 20, 22 and 23. The raw EEG reference channel signal (V\({}_{\text{chref}}\)--green) waveform is the voltage measured at the reference electrode.