# Low-Cost Three-Quadrant Single Solar Cell _I-V_ Tracer
## 2 Methods and Materials
### Principles of Operation
This current will only stop when the DUT reaches the open circuit forward polarisation voltage (\(V_{\text{OC}}\)), so the first and second quadrant regions travel (including the zero-voltage point); at the end of this process, the first voltage sweep (as described before) will be over. 5. Now, to perform the second voltage sweep, \(S_{2}\) is opened, and immediately, \(S_{3}\) is closed. This discharges \(C_{1}\), so \(V(C_{1})=0\) V. At this point, \(C_{2}\), whose voltage increased by means of the charge transfer process, will remain charged. 6. \(S_{2}\) has closed again while \(S_{3}\) remains closed. Now, the negative side of the DUT will stand at ground level while its positive side will be at \(V(C_{2})\). In this case, \(V(\text{DUT})\)\(=V(C_{2})\)-0, which, by design, is far higher than the \(V(\text{DUT})_{\text{OC}}\). The DUT is now forward-polarised beyond the open circuit point, and the current flows opposite to the previous cases, from \(C_{2}\) to the ground until \(V(\text{DUT})_{\text{OC}}\) is reached (decreasing from higher voltages). Consequently, the DUT is forced to travel the fourth quadrant of its \(I\)-\(V\) curve at this step. 7. Once the process ends and the current stops flowing, \(S_{4}\) is closed to discharge \(C_{2}\) completely, leaving the apparatus ready to start a new measurement from step 1 (\(S_{4}\) has opened again after the discharge). **Tracing the \(I\)-\(V\) curve of a photovoltaic cell. ** Step 4 of the described process is the beginning of the tracing. With the capacitor \(C_{1}\) charged to the source voltage (\(V_{S}\)) and the capacitor \(C_{2}\) totally discharged, we apply a positive voltage at the negative terminal of the PV cell and zero to the positive terminal; that is, a negative voltage (see Figure 2b). The starting negative value of the voltage is equal to \(-V_{S}\), so by adjusting this source voltage it is possible to start the tracing at any desired point--even capturing the avalanche zone in the right region of Figure 2b. In this case, the current will flow inside the cell mostly through the current source since the diode is reverse-biased and the parallel resistance should ideally be very high (see Figure 4a). If the avalanche zone of the diode is reached with \(-V_{S}\), the reverse current in the diode will be added to the cell current. Consequently, the current value is determined by the PV cell's short-circuit current (\(I_{SC}\)) with the possible addition of an avalanche current at the beginning of the trace. The discharge of \(C_{1}\) (due to this current) will produce the charge of \(C_{2}\), or, equivalently, move to the right, along the \(I\)-\(V\) curve (see Figure 4b). When the voltage of both capacitors is equalised, the difference across the terminals of the cell will be 0 V; so in the \(I\)-\(V\) curve, it will be at the crossing point with the current axis (\(I_{SC}\)). The cell will continue along its normal \(I\)-\(V\) curve until it reaches \(V_{OC}\), where it cannot push more electrons outside itself--so, \(V(C_{2})-V(C_{1})=V_{OC}\)--. These assumptions and graphs are also applicable to the PV module. Indeed, a PV module is just a series association of single cells (sometimes there are also parallel associations) and some bypass diodes, so the effect over the \(I\)-\(V\) curve is just to multiply the \(V_{OC}\) by the number of cells in the series and the \(I_{SC}\) by the parallel lines (in case a parallel association exists). Of course, these assumptions are only valid if all the cells are equal and are in a good state. If there are bad cells, many deformations over the \(I\)-\(V\) curve occur, but the study of these cases is beyond the scope of this paper. Figure 4: Step 4 of the process of measurements. (**a**) Equivalent circuit. (**b**) Path on the \(I\)-\(V\) curve.