Averaged-switch modeling of a boost converter with capacitor ESR The boost converter shown in Figure 1 operates in continuous conduction mode with small inductor current and capacitor voltage ripples. The output filter capacitor has an equivalent series resistance Resr. All other losses can be neglected. The objective is to derive an averaged-switch model for the “boost” switch network defined in Figure 1. +–L+−VgivR+−vcCResraveraged-switchnetwork+−v2i2i1+−v1 Figure 1: Boost converter: Resr is the equivalent series resistance of the output filter capacitor. (a) It is tempting to assume that the “boost” averaged-switch model derived in the textbook (see Fig. 7.46) can be applied in this case without any modifications. As briefly as possible explain why this is not the case. (b) Derive a large-signal averaged switch model for the switch network in the converter of Fig. 1, including the effects of Resr. Sketch the complete large-signal averaged model of the converter. Note that this example shows how it is not always possible to derive a self-contained averaged-switch model with parameters independent of the converter: parameter Resr appears both inside the averaged switch model and outside the model in the remaining part of the converter circuit. (c) Linearize the large-signal model derived in part (b) to obtain DC and small-signal AC averaged switch model. Then sketch the complete small-signal AC model of the converter (do not include DC part of the model). (d) Apply the Extra-Element Theorem to the converter model derived in part (c): consider Resr in series with C as an extra element to derive control-to-output transfer function Gvd(s) of the converter including Resr. You may simplify your results by taking into account that Resr << R. Summarize the effects of Resr on the control-to-output transfer function in comparison to an ideal boost converter in terms of:• Corner frequencies, including any additional poles or zeros • Low-frequency gain Gvd(0) • Q-factor of the poles (e) Suppose that the ideal “boost” averaged-switch model of Fig. 7.46 is applied directly to approximately model small-signal responses of the boost converter of Fig. 1. Comment on the validity of the approximate model with respect to the effects discussed in part