Buck-Boost Converter Continuous Mode of Operation
Since the switching frequency is considered to be very high, it is assumed that the current through the inductor (L) rises linearly. Hence, the relation of the voltage and current in mode 1 is given by
(29)
The inductor current falls linearly from I2 to I1 in mode 2 time T2 and is given by
(30)
The term 
, in mode 1 and mode 2 , is the peak to peak ripple current through the inductor L. From equation 29 and equation 30 the relation between the input and output voltage is obtained as
(31)
The relation between the on and off time, of the switch S1, and the total time duration is given in terms of duty ratio (D) as:
(32a)
(32b)
Substituting the values of T1 and T2 from equation 32a and equation 32b into equation 31 gives:
(33)
If the converter is assumed to be lossless, then
(34)
The switching period T obtained from equation 29 and equation 30 as:
(35)
The peak to peak ripple current 
is obtained from equation 35 as
(36)
When the switch S1 is turned on , the filter capacitor supplies the load current for the time duration T1. The average discharge current of the capacitor 
and the peak to peak ripple current of the capacitor are:
(37)