VHF / UHF Filters and Multicouplers: Application of Air Resonators

Chapter 3

Resonant Cavities

3.1. Resonance

Figure 3.1.

The phenomenon of resonance is one of the most important and one of the most general that exist in physics, and we find it in all its branches: we can think, or rather hope, that one day a resonant model of the atom will replace the planetary models in force today, thus dissipating the fabricated mystery of quantization; but it is taking time to arrive. Resonance takes place when a device under periodic oscillation presents a geometry or an arrangement such that this signal, by means of a reflection or a particular configuration, becomes in phase with itself and its amplitude increases to a maximum. This maximum is limited by a damping factor, which is exerted by friction in mechanics and by resistance in electromagnetism. The resonance can be both useful or a hindrance. In general, we can say that in mechanics we try to avoid it, even if there are examples of the opposite, whereas in physical electronics we make abundant use of it.

It is accepted in physics that all resonant systems can be modeled by a inductance and capacitance coupled together – be it in series or in parallel – and a resistance that represents the damping.

A resonant circuit is characterized by its quality coefficient in vacuum Q0 and its resonant frequency F0:

[3.1]

[3.2]

[3.3]

Any closed volume is susceptible to resonate, either acoustically or electrically, ...