# 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 raw EEG channel 1 signal (V\({}_{\text{ch1}}\)--blue) waveform is the voltage measured at the channel 1 electrode. The output of the EEG circuit (V\({}_{\text{out}}\)--cyan) waveform is the output of the EEG-B3V3S/C1 circuit design. The output of the instrumentation amplifier (V\({}_{\text{vo}}\)--red) waveform is the voltage at the output of the instrumentation amplifier, magnified 1.5 times. The ground  
truth EEG signal (V\({}_{\text{eeg}}\)--pink) waveform depicts the EEG ground truth signal contained in channel 1, magnified 300 times. The last two depictions' magnification serves as a quantitative graphical measurement of the gain of the first amplification stage gain and the overall gain of the circuit. First and foremost, it is evident that the real gain of the high-pass filter sub-circuit following the instrumentation amplifier is approximately 1.5 V/V, as can be seen from the magnification of the output of the instrumentation amplifier (V\({}_{\text{vo}}\)--red), which is a value very close to the theoretical prediction of 1.59 V/V, verifying the accuracy of our design. Additionally, the real gain of the output of the EEG circuit (V\({}_{\text{out}}\)--cyan) is approximately 300 V/V, very close to the theoretical prediction of 316.01 V/V (199 * 1.59 = 316.01), which aligns with the predefined design requirements of the proposed circuit design. As it is depicted in Figure 24, the ERP signal is well preserved and denoised in the output of the signal. Notably, it can be clearly assessed that both the EMI and the muscle noise are significantly reduced. The raw EEG channel 1 signal (V\({}_{\text{chl}}\)--blue) and raw EEG reference channel signal (V\({}_{\text{chr}}\)--green) peaks that exist in the vicinity of 50 Hz are reduced to a magnitude that is in the order of magnitude or less than the brain signal. Muscle artifacts are negligibly affecting the output signal. Afterwards, in the same product of FFT analysis from the previous sub-section, the Fourier spectrum was examined in a bigger range from 10 mHz to 3 kHz, studying the same waveforms in the entire circuit's output bandwidth, as specified in the requirements of the proposed circuit design (0.5 kHz to 3 kHz). The aim of this approach was to confirm that in any range from 0.5 Hz to 3 kHz, including the frequency range of special interest from 4 Hz to 30 Hz, the ground truth EEG signal integrity is maintained, and at the same time, the noise artifacts do not influence the distinctiveness of the brain signal peaks. In Figure 25, again, it is evident that the peaks in the alpha, beta and theta wave bands and of the ERP signal of the output of the instrumentation amplifier (V\({}_{\text{vo}}\)--red), the output of the EEG circuit (V\({}_{\text{out}}\)--cyan) and the ground truth EEG signal (V\({}_{\text{eeg}}\)--pink) brain waves are all aligned. The muscle noise is suppressed and can have a significant presence in the output only in the frequency ranges below 1 Hz, affecting only the delta waveband, and mostly in the region of this band that is more rarely studied.