Unified Modeling of PWM Converters With Regular or Tapped Inductors Using TIS-SFG Approach

On the Equivalence of the Switched Inductor and the Tapped Inductor Converters and its Application to Small Signal Modelling

“…Practical implication of the proposed equivalence hypothesis is extending the TIS-SFG modelling approach [22], conceived for the TI converters, to include switched inductor converters as well. This paper illustrates the small signal modelling of the step-down SI cell to complete the step-up SI cell counterpart model demonstrated earlier [21].…”

“…Due to the equivalence of switched inductor and tapped inductor converters, the dynamic and steady state model of the SI converters can be obtained by borrowing and adapting the models of the equivalent TI counterpart. Earlier, an approach to modelling of tapped inductor converters was suggested in [22]. The proposed Tapped Inductor Switcher with Switched Flow Graph (TIS-SFG) method relies on substituting the switching part of the converter by a prefabricated equivalent subgraph.…”

“…As mentioned above, the SIBk converter in Figure 3 is equivalent to the TIBk converter in Figure 4 which has same frequency response and steady state performance, thus, the SIBk model is identical to the model of an ideal TIBk. The latter can be derived by the TIS-SFG method [22]. First, the switching part of the converter is symbolically substituted by the TIS block, complemented by the flow graph of the linear part of the converter as shown in Figure 14b.…”

“…Hence, the small-signal averaged model of the SIBk converter can be derived by applying the equivalence conditions of Equations (5), (8), and (9) to Figure 14c to properly modify the equivalent inductance and the winding ratio. Note that the winding ratio, a in Figure 14 is defined as [22]:…”

“…Substitution of Equations (8) and (9) into Figure 14c, this leads to the model in Figure 14d. Note that here, the effect of the capacitor's equivalent series resistance (ESR), rC, is incorporated simply by modifying the transfer function of the filter and load branch, whereas the combined effect of parasitic resistances of the switch, rF, the diodes, ron, and inductors, rL, is modelled by a single inductor's equivalent series resistor, r. The derivation of the generalized equivalent series parasitic resistor, r, was presented in [22]. Here, r can be estimated as The test bench of the prototype circuit is shown in Figure 15, while the experimental waveforms of SIBk and TIBk are shown in Figures 16 and 17.…”