The topology of the buck-boost circuit is shown in Fig. 4. The converter operates in CCM. The input voltage is Vin and duty ratio is D. (25 points) (a) Using inductor current iz and capacitor voltage vc as state variables and Vin as input, derive the state-space models of two operating states. (5 points) (b) Based on (a), apply the state-space averaging technique, and derive the state-space model of the buck-boost converter. (5 points) (c) Derive the input voltage to capacitor voltage transfer function (5 points) vc(s) Vin (s) vc(s) (d) Derive the duty ratio to capacitor voltage transfer function (5 points) d(s) (e) Following from (d), the converter has the following parameters: L=25 H, C=10 F, R=10 2, Vin 48 V, D=0.5, and switching frequency fs-200 kHz. Calculate the zeros and poles (in rad/s) of vc(s) d(s) (5 points) Vin L iL Fig. 4. D 1 + VC R