# Optimized Design of a Self-Biased Amplifier for Seizure Detection Supplied by Piezoelectric Nanogenerator: Metaheuristic Algorithms versus ANN-Assisted Goal Attainment Method

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Modified Recycling Folded Cascode Amplifier (MRFC)

_{15}and M

_{16}additionally contribute to the input drive, along with M

_{5}and M

_{6}. To do this, a crossover link is set up between M

_{6}–M

_{15}and M

_{7}–M

_{16}. The transistors M

_{17}and M

_{18}are included in the design to make it a single-ended structure, such that a current of $\frac{\left(k-1\right)}{10}{I}_{bias}$ flows through it. All the devices in the structure operate in weak inversion regions [39,40]. Whenever a substantial signal is employed into V

_{ref}, the transistors M

_{1}and M

_{2}are turned off, and M

_{4}will function in the deep triode region of the weak inversion. The bias current conducting through M

_{3}is imaged by k and (k − 1) into M

_{9}and M

_{10}, and then into the load capacitor C

_{L}by M

_{17}and M

_{18}. The design shows improvement in slew rate as it is multiplied by a factor of (2k − 1) than the conventional structures [41]. There is an overall increase in transconductance, gain bandwidth product, and slew rate. Higher values of k lead to the degradation of the phase-margin in the design and make it unstable. To avoid this, compensation resistors realized by transistors M

_{c1}and M

_{c2}working in deep triode regions are inserted between the gates of the current mirror [42].

#### 2.1. Drain Current Equations in Weak Inversion

#### 2.2. Adaptive Biasing Technique

_{1}–M

_{4}are as follows:

#### 2.3. Design Procedure

_{5}and M

_{8}is kept greater than the bias current to avoid no current through them.

_{5}and M

_{8}. The widths of M

_{6}and M

_{7}can be calculated from ${W}_{7}=\frac{{W}_{8}}{k}$ and ${W}_{6}=\frac{{W}_{5}}{k}$. The current flowing through M

_{10}is (2k − 1) times the current in M

_{8}, and the widths ${W}_{9}$ and ${W}_{10}$ can be estimated accordingly. The widths for transistors M

_{11}and M

_{12}are half those of M

_{9}and M

_{10}[46].

_{14}–M

_{16}can be calculated. The transistors M

_{17}–M

_{20}are $\frac{1}{k}$ times that of ${W}_{15}$ and ${W}_{16}$ [47,48].

_{1}–M

_{4}can be assessed with the design parameters: gain bandwidth product and load capacitance, as illustrated in Equation (17).

_{in}

_{(max)}and V

_{in}

_{(min)}, determine the aspect ratios of the biasing and cascode transistors. The overall area occupied by the transistors can be computed from Expression (19), where n is the maximum number of transistors involved, and ${L}_{n}$ is the length of the nth transistor [41].

## 3. Meta-Heuristic Optimization Algorithms

## 4. ANN-Assisted Goal Attainment Method

#### 4.1. ANN Fitting of the Overall Circuit Area

^{2}, an indicator of the correlation between the target values and the values predicted by the ANN, and it is calculated as follows:

**H**; the gradient, g; and the update for the solution,

**X**, can be approximated as follows:

**J**is Jacobian,

**I**is the unit matrix, and µ is scalar. When µ is zero, (24) retards to Newton’s method, which uses an approximate Hessian matrix. For a large µ, this becomes gradient descent with a small step size.

#### 4.2. Goal Attainment Method

_{i}(x), and a set of their respective design goals, ${F}_{i}^{g}$, the unscaled goal attainment problem is to minimize the maximum of ${F}_{i}\left(x\right)-{F}_{i}^{g}$. In a generalized form, after introducing the set of weights, ${w}_{i}$, the goal attainment problem aims for to find x while trying to minimize the maximum of the following:

## 5. Results and Discussion

#### 5.1. Results of Metaheuristic Algorithms

- In the Dragonfly Optimization Algorithm (DOA), the explorative and exploitative activities can be accomplished through the parameters: separation (s), alignment weight (a), cohesion weight (c), food factor (f), and enemy factor (e). These are dependent on the maximum number of iterations, which is considered to be 100 for a variable dimension of 8 and a search agent number of 80.
- In Grasshopper Optimization Algorithm (GOA), the exploration and exploitation phase are controlled by the coefficient “c” and are dependent on the number of iterations, 100 and with search agents of 50; c
_{max}and c_{min}are the maximum and minimum values that are selected as 1 and 0.00004. - In both the grey wolf optimization (GWO) and hybrid particle swarm optimization–grey wolf optimization (PSO–GWO), the number of search agents is 30 for a dimension of 8, while A and C are the coefficient vectors. However, in PSO–GWO the particle swarm algorithm parameters are also employed. Both the social learning and cognitive learning coefficients are kept as 0.5.
- In the Mayfly Optimization Algorithm (MOA), the male, female, and offspring population size for mayfly swarm agents is 20 each, and the inertia weight and weight damping ratio are taken as 0.8 and 1. The personal learning, global learning, and distance sight coefficients are selected as 1, 1.5, and 2. Moreover, nuptial dance, random flight, damping ratio, and mutation rates are 5, 1, 0.8, 0.99, and 0.01.
- In the Marine Predators Optimization Algorithm (MPOA), the value of the drifting Fish Aggregating Device (FAD) is kept as 0.2. P is a constant number and is equal to 0.5; the size of the search agents is 25, and the dimension is 8.
- In the whale optimization algorithm (WOA), the parameters a, l, and p are random numbers in the ranges [0, 2], [–1, 1], and [0, 1]. A and C are coefficient factors. The number of search agents is considered to be 200 for a dimension of 8 and iteration value of 100.

#### 5.2. Results of ANN-Assisted Goal Attainment Method

^{−7}for the min performance gradient, and μ starts from 0.001, with a decrease factor of 0.1, increase factor of 10, and a maximum of 10

^{10}. The maximum number of failed validation checks is six.

^{6}to 396.1957

^{2}. Set 8 and Set 9 deduce lower value for area in comparison to Set 4; they are 357.55 and 287.24 µm

^{2}, respectively. Set 8, however, has a power of 6.763 µW, which exceeds the circuit design limit of 5 µW. Set 9 consumes a power of 3.7032 µW, but the power consumed by Set 4 is lowest (815.62 nW). Therefore, considering all the parameters, Set 4 shows the best value with minimized area. Figure 10, Figure 11 and Figure 12 show a comparative representation of gain, phase, and noise plot for various sets by the ANN-assisted goal attainment method.

#### 5.3. Comparative Analysis of Optimization Results

^{2}, and provides a gain and phase of 41.255 dB and 61.96 degrees. In contrast to the metaheuristic optimization methods, the ANN-assisted goal attainment method provided better results. Based on the comparative analysis among the presented methods, it can be observed that the results in Set 4 show an improvement in terms of gain, power, and area. The goal to minimize the objective function (area) is achieved with better outcomes by the ANN-assisted goal attainment. A comparison of the results is shown in Table 8.

^{2}, which was unacceptably high.

#### 5.4. PENG Supply

^{2}. Generally speaking, however, while PENG appears to ensure sufficient power for some specific functionalities of implantable seizure control devices, it leaves much to be desired in regard to enabling more complex multifunctionalities. A solution to consider is a combination of a rechargeable battery and a PENG.

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**Flow diagram summarizing the protocol for determining the optimal set of circuit parameters that ensures minimal area.

**Figure 10.**Gain vs. frequency plot for circuits designed after results from ANN-assisted goal attainment method.

**Figure 13.**Schematic diagram of PENG supply for the analog front end (AFE) and signal processing block in a neurostimulator.

Parameters | Ranges |
---|---|

Slew rate (V/µs) | 1 to 10 |

Load capacitance (pF) | 5 to 10 |

Gain bandwidth product (MHz) | 1 to 10 |

Maximum input voltage (V) | 0.2 to 0.4 |

Minimum input Voltage (V) | −0.4 to −0.2 |

Power (µW) | 1 to 5 |

Input voltage (µV) | 500 to 600 |

Reference voltage (mV) | 1 to 2 |

Parameters | Value |
---|---|

Subthreshold slope, η | 1.3 |

Supply voltage | 0.6 V |

Threshold voltage, V_{t} | −0.42 V, 0.42 V |

Thermal voltage, V_{T} | 26 mV |

For NMOS λ_{n} | 0.04 V^{−1} |

For PMOS λ_{p} | 0.05 V^{−1} |

Maximum output voltage | 0.3 V |

Minimum output voltage | −0.3 V |

For NMOS, K_{n} (µ_{n} C_{ox}) | 355 × 10^{−6} mA/V^{2} |

For PMOS K_{p} (µ_{p} C_{ox}) | 75 V × 10^{−6} mA/V^{2} |

Parameters | DOA | GOA | PSO GWO | GWO | MOA | MPOA | WOA |
---|---|---|---|---|---|---|---|

Slew rate (V/µs) | 1 | 1 | 1 | 1 | 1 | 1 | 1 |

Load capacitance (pF) | 10 | 10 | 10 | 10 | 10 | 10 | 10 |

Gain bandwidth (MHz) | 2 | 2 | 2 | 2 | 2 | 2 | 2 |

Maximum input voltage (V) | 0.24023 | 0.28355 | 0.4 | 0.4 | −0.20774 | 0.25181 | 0.2 |

Minimum input voltage (V) | −0.39493 | −0.22107 | −0.2 | −0.4 | −0.3163 | −0.3163 | −0.30419 |

Power (µW) | 1 | 1 | 1 | 3 | 1 | 1 | 1 |

Input voltage (V) | 538.1976 | 500 | 500 | 600 | 500 | 566.127 | 500 |

Reference voltage (V) | 1011.664 | 1000 | 1000 | 1100 | 1000 | 1065 | 1000 |

Area (µm^{2}) | 773.71 | 773.70 | 773.71 | 793.22 | 773.695 | 773.695 | 773.71 |

Parameters | GWO | % Error | MPOA | % Error | DOA | % Error | GOA | % Error | Cadence Simulation |

Gain | 43.16 | 4.13 | 41.255 | 0.47 | 41.022 | 1.03 | 41.135 | 0.76 | 41.45 |

Phase | 53.64 | 13.82 | 61.96 | 0.45 | 62.597 | 0.57 | 60.13 | 3.39 | 62.24 |

Noise | 20.63 | 0.34 | 20.558 | 0.01 | 20.616 | 0.27 | 20.617 | 0.28 | 20.56 |

Power | 2.83 | 0.60 | 2.884 | 1.37 | 2.834 | 0.39 | 2.865 | 0.70 | 2.845 |

Bandwidth | 6.13 | 15.66 | 5.308 | 0.15 | 5.148 | 2.87 | 5.274 | 0.49 | 5.3 |

Area | 793.18 | 3.32 | 773.6955 | 5.7 | 773.6991 | 5.69 | 773.6956 | 5.69 | 820.38 |

Parameters | WOA | % Error | PSOGWO | % Error | MOA | % Error | Cadence Simulation | ||

Gain | 41.258 | 0.46 | 41.24 | 0.51 | 41.231 | 0.53 | 41.45 | ||

Phase | 61.4 | 1.35 | 61.23 | 1.623 | 60.7 | 2.47 | 62.24 | ||

Noise | 20.62 | 0.29 | 20.562 | 0.01 | 20.6 | 0.19 | 20.56 | ||

Power | 2.87 | 0.88 | 2.839 | 0.21 | 2.834 | 0.39 | 2.845 | ||

Bandwidth | 5.3088 | 0.17 | 5.3 | 0 | 5.3088 | 0.17 | 5.3 | ||

Area | 773.697 | 5.69 | 773.6964 | 5.69 | 773.6988 | 5.69 | 820.38 |

References | Gain (dB) | Phase (degrees) | Power (µW) | Noise (nV ^{2}/Hz) | Bandwidth (kHz) | Area (µm ^{2}) | Technology |
---|---|---|---|---|---|---|---|

Wattanapanitch et al. (2007) [64] | 40.85 | - | 7.56 | 41.95 | 5.32 | 3687.84 | 180 nm |

Chaturvedi et al. (2011) [65] | 37 | - | 1.5 | 65.73 | 7 | 1044 | 130 nm |

Ruiz-Amaya et al. (2015) [66] | 46 | - | 1.92 | 44.17 | 7.4 | 1077.46 | 130 nm |

Kim et al. (2018) [67] | 39.2 | 49 | 2.4 | 67 | 28 | 2689.3 | 180 nm |

Gupta et al. (2021) [68] | 45.88 | - | 2.39 | 16.13 | 340 | 770.4 | 180 nm |

This work | 41.26 | 61.96 | 2.884 | 20.558 | 5.308 | 773.6955 | 180 nm |

Set 1 | Set 2 | Set 3 | Set 4 | Set 5 | |

Slew Rate (µV/s) | 1 | 0.9824 | 2.9 | 1.2 | 4.1 |

Load capacitor (pF) | 10 | 10.0181 | 5 | 5 | 5 |

GBW (MHz) | 2 | 1.8586 | 1 | 1 | 1.4 |

Vin_m ax(V) | 0.2077 | 1.0787 | 0.4 | 0.4 | 0.4 |

Vin_m in (V) | −0.3163 | −0.9466 | −0.2 | −0.2 | −0.2 |

Pdiss (µW) | 1 | 1.1667 | 1.4 | 1 | 1 |

Input Voltage (µV) | 500 | 500.0023 | 500.2 | 500 | 500 |

Reference Voltage (µV) | 1000 | 999.9999 | 1000 | 1000 | 1000 |

Area (µm^{2}) | 781.49 | 746.15 | 425.73 | 369.98 | 513.38 |

Set 6 | Set 7 | Set 8 | Set 9 | Set 10 | |

Slew Rate (µV/s) | 4.3 | 4.8 | 0.8 | 3.5 | 8.266 |

Load capacitor (pF) | 5 | 5 | 5 | 5.4 | 5 |

GBW (MHz) | 1.2 | 1.2 | 1 | 1.1 | 1 |

Vin_m ax(V) | 0.4 | 0.4 | 0.4 | 0.4 | 0.4 |

Vin_m in (V) | −0.2 | −0.2 | −0.2 | −0.2 | −0.2 |

Pdiss (µW) | 1 | 1 | 1 | 1 | 1 |

Input Voltage (µV) | 500 | 500 | 500 | 500 | 500 |

Reference Voltage (µV) | 1000 | 1000 | 1000 | 1000 | 1000 |

Area (µm^{2}) | 494.26 | 510.89 | 357.55 | 287.24 | 640.042 |

**Table 7.**Cadence simulation results for designs resulting from the use of the ANN-assisted goal attainment method.

Set 1 | Set 2 | Set 3 | Set 4 | Set 5 | |

Gain (dB) | 41.187 | 42.273 | 46.7917 | 47.7046 | 47.7658 |

Phase (degrees) | 63.119 | 63.02 | 59.33 | 46.321 | 43.146 |

Noise (µV^{2}/Hz) | 20.619 | 20.643 | 20.7773 | 20.797 | 20.525 |

Power (µW) | 2.86 | 2.682 | 2.23 | 0.81562 | 4.7027 |

Bandwidth (kHz) | 5.3297 | 5.2387 | 6.036 | 3.849 | 4.463 |

Area (µm^{2}) | 781.49 | 746.15 | 425.73 | 369.98 | 513.38 |

Set 6 | Set 7 | Set 8 | Set 9 | Set 10 | |

Gain (dB) | 47.884 | 47.8685 | 47.867 | 46.66 | 47.07 |

Phase (degrees) | 43.938 | 42.285 | 41.763 | 44.643 | 37.552 |

Noise (µV^{2}/Hz) | 20.567 | 20.557 | 20.55 | 20.472 | 20.413 |

Power (µW) | 5.20835 | 6.73429 | 6.763 | 3.7032 | 22.984 |

Bandwidth (kHz) | 4.0079 | 3.849 | 4.00793 | 4.667 | 4.2886 |

Area (µm^{2}) | 494.26 | 510.89 | 357.55 | 287.24 | 640.042 |

Metaheuristic Algorithm | ANN-Assisted Goal Attainment Method | |
---|---|---|

Gain (dB) | 41.255 | 47.7046 |

Phase (degrees) | 61.96 | 46.321 |

Noise (µV^{2}/Hz) | 20.558 | 20.797 |

Power (µW) | 2.884 | 0.81562 |

Bandwidth (kHz) | 5.308 | 3.849 |

Area (µm^{2}) | 773.6955 | 369.98 |

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## Share and Cite

**MDPI and ACS Style**

Devi, S.; Guha, K.; Jakšić, O.; Baishnab, K.L.; Jakšić, Z.
Optimized Design of a Self-Biased Amplifier for Seizure Detection Supplied by Piezoelectric Nanogenerator: Metaheuristic Algorithms versus ANN-Assisted Goal Attainment Method. *Micromachines* **2022**, *13*, 1104.
https://doi.org/10.3390/mi13071104

**AMA Style**

Devi S, Guha K, Jakšić O, Baishnab KL, Jakšić Z.
Optimized Design of a Self-Biased Amplifier for Seizure Detection Supplied by Piezoelectric Nanogenerator: Metaheuristic Algorithms versus ANN-Assisted Goal Attainment Method. *Micromachines*. 2022; 13(7):1104.
https://doi.org/10.3390/mi13071104

**Chicago/Turabian Style**

Devi, Swagata, Koushik Guha, Olga Jakšić, Krishna Lal Baishnab, and Zoran Jakšić.
2022. "Optimized Design of a Self-Biased Amplifier for Seizure Detection Supplied by Piezoelectric Nanogenerator: Metaheuristic Algorithms versus ANN-Assisted Goal Attainment Method" *Micromachines* 13, no. 7: 1104.
https://doi.org/10.3390/mi13071104