# DC-DC Buck Converters with Quasi-Online Estimation of Filter Capacitor Equivalent Parameters
## 2 Materials and Methods
### Scheme Based on the Implementation of the Principle from Figure 7a  
The proposed scheme is the one in Figure 9. The converter supplies the resistive load \(R_{L}\) and C2 is the filtering capacitor. It is a 220 \(\mu\)F/50 V electrolytic capacitor. Its frequency characteristics, measured using a BK Precision RLC-bridge, are illustrated in Figure 10a,b. The transistors T-sw1, T-sw2, and T-sw3 are used to realize the switches sw1, sw2, and sw3 in Figure 7a. The LDO is a voltage regulator that provides the voltage \(u_{i}=3.291\) V for charging C2 through the resistor \(R_{ch}\). A microcontroller with computing power based on the Cortex(r)-M7 architecture was used for measuring and processing. The signal \(V_{0}(t)\) was acquired with the sampling time \(h=20\)\(\mu\)s. The microcontroller sends signals towards the LM2596 circuit and switches using the digital ports P1, P2, P3, and P4 and measures the voltage \(V_{0}\) at capacitor and load terminals using the analog port AIN. To estimate the capacitor's equivalent parameters, the microcontroller executes the successive operation of the regimes R1-R7 in Table 2. In stages III and V (Figure 8), PO2 implemented in the microcontroller calculates \(\hat{T}_{1},\ \hat{T}_{2},\ \hat{C}_{e}\) and \(\hat{R}_{se}\). To achieve a more accurate diagnosis of the capacitor's condition, a sensor S\({}_{0}\) is thermally coupled with the capacitor and interfaced with the microcontroller. The measured result is sent together with the estimated values of the capacitor parameters using a serial SOUT interface towards external assessment of C2. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline
**Regime** & **sw11** & **sw12** & **sw21** & **sw22** & **sw3** & **sw4** & **Regime** & **sw11** & **sw12** & **sw21** & **sw22** & **sw3** & **sw4** \\ \hline R1 & 1\(\uparrow\) * & 1 & 0 & 0 & 0 & 0 & R1\({}^{\prime}\) & 1 & 1\(\uparrow\) * & 0 & 0 & 0 & 0 \\ R2 & 0 & 1 & 0\(\downarrow\) & 0 & 0\(\downarrow\) & 0 & R2\({}^{\prime}\) & 1 & 0 & 0 & 0\(\downarrow\) & 0 & 0\(\downarrow\) \\ R3 & 0 & 1 & 1 & 0 & 1\(\uparrow\) & 0 & R3\({}^{\prime}\) & 1 & 0 & 0 & 1 & 0 & 1\(\uparrow\) \\ R4 & 0\(\downarrow\) & 1 & 1 & 0 & 0 & 0 & R4\({}^{\prime}\) & 1 & 0\(\downarrow\) & 0 & 1 & 0 & 0 \\ R5 & 1\(\uparrow\) * & 1 & 1 & 0 & 0 & 0 & R5\({}^{\prime}\) & 1 & 1\(\uparrow\) * & 0 & 1 & 0 & 0 \\ R6 & 0 & 1 & 1 & 0 & 0 & 0\(\downarrow\) & R6\({}^{\prime}\) & 1 & 0 & 0 & 1 & 0\(\downarrow\) & 0 \\ R7 & 0 & 1 & 1\(\uparrow\) & 0 & 0 & 1\(\uparrow\) & R7\({}^{\prime}\) & 1 & 0 & 0 & 1\(\uparrow\) & 0 \\ R8 & 0\(\downarrow\) & 1 & 0 & 0 & 0 & 0 & R8\({}^{\prime}\) & 1 & 0\(\downarrow\) & 0 & 0 & 0 & 0 \\ R9 & 1 & 1 & 0 & 0 & 0 & 0 & R9\({}^{\prime}\) & 1 & 1 & 0 & 0 & 0 & 0 \\ \hline \end{tabular}
* The meaning of the notations: 0—open, 1—closed, \(\uparrow/\downarrow\)—the switch opens/closes to switch the scheme to the new operating mode.  
\end{table} 
Table 3: Scheme regimes from Figure 7d in the estimation process. Figure 9: Buck converter scheme made based on the principle scheme in Figure 7a. Below are some practical results that validate the structure in Figure 9. Experimentally, by commuting and maintaining the Figure 9 scheme in the R4 regime from Table 2, a value of \(K=u_{i}=3.291\) V was obtained. To determine the values of \(\hat{C}_{e}\) and \(\hat{R}_{ge}\) six sets of 25 discharge/charge experiments of C2 were performed. In each set, the experiments were repeated with a frequency of 3.33 Hz. Each discharge/charge process took 40 ms. In Figure 10(a) is illustrated how the voltage \(V_{0}\) varies in an experiment, and in Figure 10(b) the corresponding characteristics \(\hat{T}_{1,3.291}(t)\) and \(\hat{T}_{2,3.291}(t)\) are represented.