## 2 Materials and Methods  
The behavior of a thermoelectric generator has been firstly analyzed and reported in this section, in order to understand what is the best electrical equivalent model, suitable for low-power, low-temperature difference applications. A thermoelectric generator is generally constituted by several junctions in series between semiconductors that are n-doped and p-doped, in order to achieve different Seebeck coefficients. In Figure 1, a block scheme of a single n-p couple is represented. The hot-side of the couple has a temperature \(T_{H}\) while the cold side presents a temperature \(T_{C}\), lower that \(T_{H}\) and because of the Seebeck effect, and electromotive force (emf) \(-S\Delta T\) is generated, where \(S\) is the total Seebeck coefficient, and a current I flows in the closed circuit, composed by the single n-p couple and the load \(R_{L}\). Considering the heat supplied to the hot side \(Q_{H}\) and the heat released from the cold side \(Q_{C}\), according to the first law of thermodynamics, it is possible to compute the electric power generated by the thermoelectric n-p couple as  
\[ \begin{array}{l}Q_{H}=ST_{H}I-\frac{1}{2}I^{2}R+K(T_{H}-T_{C})\\ Q_{C}=ST_{C}I+\frac{1}{2}I^{2}R\ +K(T_{H}-T_{c})\end{array} \Rightarrow W=Q_{H}-Q_{C}= SI\Delta T-I^{2}R \tag{1}\]  
where \(R\) is the electrical resistance of the thermocouple and \(K\) is its thermal conductance. Since the system is closed to a load, the total electrical power \(W\) is also equal to \(I^{2}R_{L}\), thus it is possible to express the current and voltage provided by the \(TEG\) as  
\[ \begin{array}{l}V=IR_{L}=S\Delta T-IR\\ I=\frac{S(T_{H}-T_{C})}{R+R_{L}}\end{array}  \tag{2}\]  
Therefore, the electrical model of a thermoelectric cell composed by \(N\) couples n-doped and p-doped can be simply represented by a voltage generator \(V_{TEG}=N\cdot V\) in series with an internal resistance \(R_{TEG}=N\cdot R\). However, the Seebeck coefficient S, as well as the thermal conductance \(K\) and the internal resistance of the cell are temperature dependent and, therefore, the behavior of the system is non-linear for large temperature variations. On the other hand, if the temperature variation is small, as well as the temperature difference, (as in the case of human body heat energy harvesting) the system can be considered locally linear [36; 37; 38]. As a second step of this work, a Peltier cell \(2\times 2\times 0.5\) cm model TEC1-3103 [39] was analyzed with the aim of determining a method to identify a SPICE model from the acquired data. A specific test platform was therefore created (Figure 1a), which has the role of providing a stable temperature difference between the two sides of the Peltier cell. The system consists mainly of a \(22\times 22\) cm printed circuit board on a 2 mm thick thermal-controlled aluminum support, a \(5\) mm glass plate, an aluminum heat sink to be placed on the cold side of the TEG cell, a model S01138812M fan that has the role of cooling at room temperature the heatsink, and a control system managed by a Microchip ATMEGA2560 microcontroller, which communicates via USB-Serial bus with a host PC, where it is possible to control all the parameters of the platform and visualize as well as acquire measurement information by means of a LabVIEW-based HMI (Human-Machine Interface). The Peltier cell is fixed on the glass plate through a \(150\) um double-sided thermal conductor, with thermal conductivity of \(1.5\) W (\(\mathrm{m\cdot K}\)) \({}^{-1}\), also used for fixing and thermally interfacing the cold side of the cell with the aluminum heat sink. In order to prevent the heat, coming from the surface of the aluminum plate surrounding the cell, from affecting the temperature of the heat sink and therefore of the TEG cold side, the remaining glass surface was covered with an adhesive thermal insulator having a thermal conductivity of \(0.0375\) W (\(\mathrm{m\cdot K}\))\({}^{-1}\).