# DC-DC Buck Converters with Quasi-Online Estimation of Filter Capacitor Equivalent Parameters
## 2 Materials and Methods
### Principle Schemes  
From the point of view of the continuous supply of the converter load, the proposed schemes are of two categories: schemes with short-term disconnection of the load from the converter and schemes without disconnection of the load from the converter. The schemes in Figure 7a,b belong to the first category, and those in Figure 7c,d to the second category. The load and the filter capacitor are connected to the converter via terminal T. In all schemes, the filter capacitor is modeled by the serial equivalent circuit \(R_{se}-C_{e}\). POs are implemented in the measurement and processing (EMP) device. They calculate the estimates \(\hat{C}_{e}\) and \(\hat{R}_{se}\) by processing the voltage at the capacitor terminals denoted, as appropriate, by \(V_{0},\ V_{01},\ V_{02}\). The values of \(R_{ext1},\ R_{ext2},\ R_{1}\) and \(R_{2}\) are chosen considering the requirements mentioned at the end of Appendix A. Schemes in the second category have the advantage of not including the converter load in the capacitor discharge sequences, thereby not being constrained by the requirements of Appendix A. In the schemes of the first category, the parameters of the capacitor are obtained during a discharge/charge process using PO2 of Equation (8). The charging of the capacitor is carried out at the voltage \(u_{i}\) from a stabilized voltage source and not from the converter. When switches sw1 and sw2 are in the ON position and sw3 is in the OFF position, the circuits are in normal operation mode (DC-DC mode). Switching sw1 from the OFF position to the ON position results in transients at the load level. Figure 7: Principle schemes used for the realization of DC-DC buck converters with the estimation of the equivalent parameters of the filter capacitors: (**a,b**) Schemes with the monitoring of the discharging and charging of the capacitor using PO2 (**c,d**) Schemes with monitoring of two distinct discharges using PO. Figure 8 illustrates the \(V_{0}(t)\) signal in an estimation cycle associated with a discharge/charge process corresponding to the schemes in Figure 7a,b. During the I interval, the schemes operate in DC-DC mode. In intervals III and V, PO2 estimates the equivalent time constants. In intervals II and IV, of duration \(t_{n}\), PO2 acquires the voltage \(V_{0}(t)\) but does not calculate \(\hat{T}_{1e}\) and \(\hat{T}_{2e}\). The VI interval corresponds to a transient regime of DC-DC mode restoration. Table 2 shows the sequence of switch states and regimes for an estimation cycle of the scheme in Figure 7a. In second-category schemes, capacitor parameters are obtained using the discrete-time variant of PO (2) during two separate discharges of the capacitor through resistors \(R_{ext1}\) and \(R_{ext2}\), which have different values. Between discharges, the monitored capacitor is recharged via the T terminal from the converter when the T-sw1 switch is closed and the LM2596 is ON. Reconnections of the capacitor to the converter result in this case also with transient regimes at the load level. In Figure 7d, the filtering is performed using a capacitance created by connecting two capacitors in parallel. Each capacitor is monitored separately. During monitoring of one capacitor, the other capacitor provides filtering by remaining connected to the converter. This option is advantageous for at least two reasons: (i) the scheme ensures filtering throughout the estimation; (ii) the transients caused by the disconnection and reconnection of the capacitors to the converter are mitigated. The principle can be generalized for batteries of filter capacitors or schemes where \"dividing\" the filter capacity in at least two capacities can offer technical benefits. Table 3 shows for the scheme in Figure 7d the sequence of regimes that occur when estimating the parameters of capacitor 1 (regimes R1-R9) and of capacitor 2 (regimes R1'-R9').