In the following switching circuit, a battery and an ultra-capacitor is connected in series to provide power to the load. A dc/dc converter is used to maintain the voltage cross the ultra-capacitor. For all the following questions, assume the circuit operates at continuous mode. 1) Derive the relationship between the load voltage, Vload, and the input voltage, Vin, as a function of the duty ratio of S1 (4 points) 2) If Vin has a constant value of 20 V and V Load needs to be controllable in the range of 30 to 40 V, what is the duty ratio range of Si. (1 points) 3) Assume R and Vin are constant, derive (2 points) a) the voltage stresses of S1, D, and the ultra-capacitor as functions of Vload, b) equation for average value of iin as a function of Vload; c) equation for average value of isi as a function of Vload, d) equation for average value of it as a function of Vload. 4) Comparing the circuit with a traditional boost converter, assume R and Vin are constant, write down a) the voltage stresses of S1, D, and the ultra-capacitor (the output capacitor in the cuit) as functions of Vload, b) equation for average value of iin as a function of Vload; c) equation for average value of isi as a function of Vload; d) equation for average value of it as a function of Vload. 5) Based on a), b), c), and d) from 3) and 4), what are the advantages of the "new" circuit you had analyzed? (1 points)