Hi,
you should at least have a clue about the frequency range.
And wheter you use a catch diode (vs sync rectifying), what type and what forward voltage vs forward current. ... what efficiency to expect.
(I mean: in numbers. Not text like "best efficiency")
Please tell what documents you have read so far. Post links. Ask detailed questions.
*****
Inductor, capacitor:
There are the most basic formulae: like
* how the current behaves over time and applied voltage
* what´s the stored energy
(no need for a dedicated SMPS document so far. They are even provided by standard capacitor and inductor informationns like Wikipedia)
For example: W = 0.5 * L * I * I.
The problem is: There is no document that tells YOUR application requirements, nor YOUR ideas how it should operate.
You need to decide YOUR requirements on your own.
For sure there are already made limits. (Example, because we don´t know your application details)
With an input voltage of 1.8V and an (inductor) output voltage of 5.5V (5V + 0.5V diode) you already know the max duty cycle can be 3:1 or 75% ( : 25%).
You need to add some headroom.
***
Please don´t expect that one of us does the whole work for you.
This is not how a forum works and not how a school work is meant to be.
Usually wou show your ideas, your calculations and we help to rectify problems.
Now I gave hints, formulae, math .... but indeed this is what we expect from you.
Simple taks like dividing 5.5 by 1.8 to get 3. (Even if you used 5V instead of 5.5V ... we are here to help you)
Klaus