The most bizarre and mysterious circuits for beginners are probably the oscillators. You plug them to a power supply and they produce a periodic signal without being sure why. Along the years, huge amounts of research and effort has been invested by engineers in an attempt to fully understand how they function with whole books having been written about them.
Today, oscillators can been considered as a well understood electronic building block. However, there is still a debate about their fundamental properties. I read a recently published paper called “The Barkhausen Criterion (Observation ?)” written by a professor at DTU, where I am currently studying for my MSc, stating that the famous Barkhausen criterion is a necessary but not sufficient condition for oscillations to occur.
At any case, this is not a theoretical post. I am going to show you an easy way to design a 10 MHz sine wave Colpitts oscillator using only simple algebra and circuit theory.