The inductor current falls linearly from I2 to I1 in time t2
(16)
where 
is the peak to peak ripple current of inductor L. From equation 15 and equation 16 it can be seen that
(17)
Substituting 
and 
gives the average output voltage
(18)
Substituting 
into equation 18 gives
(19)
If the boost converter is assumed to be lossless then
(20)
(21)
The switching period T is given by
(22)
From equation 22 the peak to peak ripple current is given by
(23)
When the switch S is on, the capacitor supplies the load current for 
. The average capacitor current during time t1 is 
and the peak to peak ripple voltage of the capacitor is
(24)
Substituting the value of t1 from equation 19 into equation 24 gives
(25)
Condition for Continuous Inductor Current and Capacitor Voltage
If IL is the average inductor current, the inductor ripple current is 
. Hence, from equation 18 and equation 23 the following expression is obtained
(26)
The critical value of the inductor is obtained from equation 26 as
(27)
If Vc is the averag capacitor voltage, the capacitor ripple voltage 
. Using equation 25 the following expression is obtained
(28)
Hence, from equation 28 the critical value of capacitance is obtained as
(29)