# A Novel Battery-Supplied AFE EEG Circuit Capable of Muscle Movement Artifact Suppression
## 3 Materials and Methods: A Novel Proposed EEG Analog Front-End Circuit System
### EEG Sub-Circuit Modeling the Fliedge Notch Filter 50 Hz or 60 Hz  
Active notch filters are used to attenuate significant aberrations occurring at 50 and 60 Hz in EEG data. They have shown challenges in terms of adjusting the center frequency, maintaining stability, and achieving repeatability. The maximum goal that the designer could achieve is a noise level reduction of approximately 40 to 50 dB when simulating the circuits by theoretical calculations. Consequently, this design prioritizes center frequency and Q above notch depth. The Q value of a certain notch filter corresponds to the frequency at which the filter's response is attenuated by \(-3\) dB, not at the point 3 dB above the notch depth.  
This is a dual operational amplifier filter that utilizes just four high-precision components: (i) two resistors (Ro) and (ii) two capacitors (CO). These components are responsible for setting the damping factor and center frequency of the filter. RO resistance is shown as an assemblage of resistances that possess a high level of accuracy. Circuits that are used in a 50 Hz grid make use of resistors RO6 and RO10 with a resistance of 33 k\(\Omega\) as shown in Figure 13. It is necessary to place an extra 33 k\(\Omega\) resistance in parallel with RO6 and one with RO10, respectively, in order to utilize the EEG in a 60 Hz grid environment.  
The Q factor of the filter may be modified separately from the center frequency by using two resistors of equal value that are not sensitive to changes. The center frequency of the filter may be modified within a defined range without significantly reducing the depth of the notch. A greater Q factor results in a smaller stopband, but this comes at the cost of a reduced depth of notch at the desired center frequency. The equations governing the center frequency f\({}_{\rm o}\) and Quality factor Q are [35]:  
\[\rm{f_{o}=\frac{1}{2\pi R_{o}C_{Q}}} \tag{3}\]  
Figure 12: EEG sub-circuit modeling the ESD protection and the instrumentation amplifier.  
Figure 13: EEG sub-circuit modeling the Fliedge notch filter at 50 Hz or 60 Hz.  
\[\mathrm{Q}=\frac{\mathrm{R_{Q}}}{2\mathrm{R_{O}}} \tag{4}\]  
In the case of the 50 Hz grid, the (3) and (4) yield a center frequency and Quality factor of  
\[\mathrm{f_{o}}=\frac{1}{2\pi\mathrm{R_{O}}\mathrm{C_{O}}}=\frac{1}{2\pi*(3*10+2* 33)\mathrm{kT}*33\mathrm{nf}}=\frac{1}{2\pi*96\mathrm{kT}*33\mathrm{nf}}\approx 5 0.2383\mathrm{Hz}\]  
\[\mathrm{Q}=\frac{\mathrm{R_{Q}}}{2\mathrm{R_{O}}}=\frac{4.7\mathrm{M}\Omega}{2* (3*10+2*33)\mathrm{kT}\Omega}=\frac{4.7\mathrm{M}\Omega}{2*96\mathrm{kT} \Omega}\approx 24.4791\]  
\(\mathrm{Q}\approx 24.48\)  
respectively.  
In contrast, we employ the 33 k\(\Omega\) resistance parallel to RO6 and RO10 for the 60 Hz grid. Equations (3) and (4) yield a center frequency and Quality factor as follows:  
\[\mathrm{f_{o}}=\frac{1}{2\pi\mathrm{R_{O}}\mathrm{C_{O}}}=\frac{1}{2\pi*(3*10 +33+\frac{33}{33+33})\mathrm{kT}\Omega*33\mathrm{nf}}=\frac{1}{2\pi*79.5\mathrm{ k}\Omega*33\mathrm{nf}}\]  
\(\mathrm{f_{o}}\approx 60.665\mathrm{~{}Hz}\approx 60.67\mathrm{~{}Hz}\)  
\(\mathrm{Q}=\frac{\mathrm{R_{Q}}}{2\mathrm{R_{O}}}=\frac{4.7\mathrm{~{}M}\Omega }{2*(3*10+33+\frac{33}{33+33})\mathrm{kT}\Omega}=\frac{4.7\mathrm{~{}M}\Omega }{2*79.5\mathrm{~{}kT}\Omega}\approx 29.5597\)  
\(\mathrm{Q}\approx 29.56\)  
respectively. The proposed notch should theoretically achieve a notch depth of 50 dB at the center frequency calculated above.  
In Figure 13, the EEG sub-circuit modeling the Fliedge notch filter at 50 Hz or 60 Hz is depicted.