This section analyses calculated values of time constant and capacitance.
The current and voltage of discharging capacitor are measured for a period of 90 seconds and listed in Table 1.1. From this table, voltage is plotted against time as shown in Figure 1.9. Analysis of errors and uncertainties was not possible since these values were given. However, theoretically, as time progresses, the voltage and current should decrease to nearly zero and this pattern can be seen from the table. Moreover, a graphical representation of data is able to reveal errors, but the chart of voltage-time illustrates that the data does not have significant inaccuracies.
Since the time constant is related to the point of the capacitor discharge curve where the voltage drops to 63.2%
the tangential method is applied to that point of figure 1.9 to determine the time constant graphically. Again, the time constant is computed using the inverse of the graph gradient method to the plot of vs. time. The plot is presented in figure 1.10, which exhibits linear relationship. In addition to this, a natural logarithm of voltage is derived by rearranging the equation 1.1.
At the end of the experiment, the capacitance is computed by using formula 1.4 in each of the cases.
This equation was used because the time constant, and resistance (220 kΩ) are the known values.
The tangential method estimates that the time constant approximately equals to 9.2 seconds and, therefore, the capacitance, .
While the second technique shows that the time constant, = 7.75 seconds and the capacitance . On the other hand, the inverse gradient method applied on the figure 1.10 finds the value of the time constant to be equal to 7.2 seconds, which yields a capacitance value of 33.6 μF. In brief, these are findings of the experiment.
1.2 Diode characteristics
This part incorporates the results relating to the experiments on diode characteristics. The main objective of this experiment is to approximate the diodes behaviour by utilizing the piecewise-linear model and Shockley model. As in the discharging capacitor experiment, the values were given and, therefore, errors and uncertainties can be found only from data table and graph. No significant inaccuracies were noticed in this case either. For the purpose of the experiment, the values of gained voltage and current are demonstrated in table 1.2. Furthermore, in order to determine the parameters for the first model type, the values of these current and voltage are plotted in figure (1.12). Generally, there are two parameters for this model, namely, the forward-voltage and gradient of the slope. From this chart, it was found that Vd = 0.7 [volts] and the gradient is .
The parameters that were calculated for Shockley model are the saturation current () and the ideality factor (n).
In order to determine , firstly, the natural logarithm of measured current was calculated and was plotted against the voltage (Figure 1.13). Then, the gradient of the graph is found to be . Additionally, was found to be by determining the intersection of a curve with vertical axes and inserting this value in equation (1.6). Finally, ideality factor was calculated by equation (1.7) and it equals to 1.8.
1.3 AC-to-DC converter
The final chapter scrutinizes results obtained from the simulation of the current converter circuit. By creating a virtual circuit (Figure 1.9) in Multisim software and using a transient mode, the change in voltage with respect to time was shown in Figure 1.14. After this, a voltage output was calculated, Voutput = 22.2 [volts] and, consequently, the ripple difference is defined by equation (1.8).
The second objective of this experiment is to determine a forward-voltage. As the 1N4001 general purpose diode was used, VD = 0.7 [volts]. However, the forward-voltage for this type of diode could not be used in the simulation because the latest software update simply does not include it.
The third and the last purpose of this circuit simulation is to calculate a capacitance that would decrease ripple factor to 5%. By utilizing formula 1.10, it was found that required capacitance is approximately . Then, the circuit with changed capacitor was simulated and the voltage sine-wave is shown in figure 1.14.
