I am curious to know why at high frequencies the inductors and capacitors are designed using transmission line? Why not use coils for inductors and parallel plate etc for capacitor. Does it have something to with the component size at high frequency?
Self resonance frequency of the coils and capacitors is an issue at higher frequency.In additional to, realizing very small values-especially for coils- is pretty difficult.
Quality factor is another issue,stray and body parasitic elements around the package are also serious constraints..
So, there are many reasons to use distributed components at very high frequencies.
I would suggest you to read a good textbook on RF basics.
LC or lumped-elements resonators usually cease to work above 200-300 MHz. They are replaced with coaxial and other TEM lines. Above ~3 GHz, hollow-pipe waveguides are better as they have a lower loss.
My college textbook for this high-frequency stuff was Microwave Engineering by David Pozar. It's pretty math intensive for the derivations, but a very thorough work up on the entire microwave engineering subject. Parasitic effects of devices aren't often covered in textbooks, but are left to be understood in the lab environment, as they vary from device to device and are highly frequency- and geometry-dependent.