I am newbie in the field of....... I want to learn how to derive the equations that rule the design of LC balun. I found this equation in several papers, but was not able to derive them from the circuit topology.
I hope someone could help to this.
I would not call that circuit a "balun"! I would call it "a crappy circuit the chip manufacturer needed to come up with because he made a chip with a differential output, but most customers want single ended output".
Indeed this is a classical and simple implementation of a balun, widely used to make his job, that is exactly: a circuit the chip manufacturer needed to come up with because he made a chip with a differential output, but most customers want single ended output.
Simple: one branch make 90deg the other -90deg with an impedance ratio.