## 3 Results and Discussion
### DC/DC with MPPT Design
\[V_{TEG}(\Delta T)\big{|}_{P_{MAX}(\Delta T)}=\frac{1}{2}V_{\rm OC}(\Delta T) \tag{10}\]  
Recalling Equation (9) for the FOCV MPPT algorithm, the voltage divider coefficient \(K\) for the fractional open-circuit voltage sampling should be equal to 0.5, so as to guarantee the maximum power point condition for the selected multicell source. Finally, the utility and usage of the Peltier cell SPICE model have been proved by proposing a design example of a DC/DC boost converter with FOCV MPPT algorithm (Figure 11), to demonstrate how the design can be conditioned and optimized by considering a real source model instead of an ideal generator. In this design, the selected switching frequency of the PWM signal is 200 kHz, which is obtained by means of a sawtooth generator and the ideal comparator \(A_{3}\). The latter continuously performs the difference between the reference sawtooth signal and a DC voltage value coming from the MPPT feedforward network, producing an output square wave, that controls the transistor \(M_{1}\), where its duty cycle is proportional to the \(V_{B}\) voltage level. In this design example, an ideal built-in block of LISPICE has been employed regarding the sawtooth generator, while a reference for a possible real implementation can be found in [53]. As mentioned in the previous paragraph, the fractional open-circuit voltage sensing is performed by closing switches \(S_{2}\) and \(S_{3}\) and opening the switch \(S_{1}\), in order to store the maximum power point voltage level by means of the capacitor \(C_{3}\). Here, an additional 100 nF capacitor \(C_{1}\) has been added at the output of the TEG source, in order to retain the output voltage during the switching transients. For the capacitor \(C_{3}\), a value of 1 uF has been chosen, while a resistive value of 10 k\(\Omega\) has been selected for both resistors \(R_{1}\) and \(R_{2}\). The difference between the FOCV value and the instantaneous output voltage of the source is computed by means of the ideal op-amp \(A_{1}\) in differential amplifier configuration. All the resistors \(R_{3}\) and \(R_{f}\) have the same value of 200 k\(\Omega\). The PID algorithm introduced in the scheme of Figure 5 is here simplified to only a proportional contribution, represented by the non-inverting amplifier \(A_{2}\), where the gain has been set to 3, by means of the resistors \(R_{4}\) and \(R_{5}\). The inductor selection criterion is crucial for the DC/DC functionality. As a rule of thumb, the higher the inductor value, the higher the maximum achievable current at the output of the converter is, thanks to the reduced ripple. On the other hand, if the inductor value is too high, it can affect the cost and size of the solution, as well as the efficiency, because of the equivalent series resistance. Therefore, the minimum inductor value can be selected as follows, recalling Equation (6) and by considering the desired maximum output current  
Figure 11: Complete scheme of the implemented DC/DC boost converter with FCOV MPPT algorithm. \[Lmin=\frac{V_{TEG}(V_{out}-V_{TEG})}{\Delta I_{L}.f_{S}.V_{out}} \tag{11}\]  
where \(f_{S}\) is the switching frequency and \(\Delta I_{L}\) represents the predictable output ripple current. A good estimation of the ripple value is 20% to 40% of the maximum output current  
\[\Delta I_{L}=(0.2\div 0.4)\cdot I_{out,MAX}.\frac{V_{OUT}}{V_{TEG}} \tag{12}\]  
In this design example, by applying Equations (11) and (12), and considering the multicell source characterization, with a maximum operating temperature difference of 16 \({}^{\circ}\)C, the inductor value \(L\) has been fixed to 1 mH. Regarding the Op-Amps \(A_{1}\), \(A_{2}\), and \(A_{3}\), a generic component has been used, with an open-loop gain of 50k and a GBW (Gain BandWidth) of 10 MHz. The transistor \(M_{1}\) was chosen to have an \(R_{on}\) equal to 1 \(\Omega\) and a threshold voltage of 500 mV, while the diode \(D_{1}\) is a Schottky barrier with a forward voltage of 150 mV at 1 mA.