There are all sorts of resonances around us, in the world, in our culture, and in our technology. A tidal resonance causes the 55 foot tides in the Bay of Fundy. Mechanical and acoustical resonances and their control are at the center of practically every musical instrument that ever existed. Even our voices and speech are based on controlling the resonances in our throat and mouth. Technology is also a heavy user of resonance. All clocks, radios, televisions, and gps navigating systems use electronic resonators at their very core. Doctors use magnetic resonance imaging or MRI to sense the resonances in atomic nuclei to map the insides of their patients. In spite of the great diversity of resonators, they all share many common properties. In this blog, we will delve into their various aspects. It is hoped that this will serve both the students and professionals who would like to understand more about resonators. I hope all will enjoy the animations.

Origins of Newton's laws of motion

History of mechanical clocks with animations
Understanding a mechanical clock with animations
includes pendulum, balance wheel, and quartz clocks

## Friday, June 28, 2013

### 16g. Summary of analysis of a transmission line excited resonator using a circulator

 All postings by author previous: 3.16f Transient response up: Contents next: 3.17 Resonant scattering with two output channels

16g. Summary of analysis of a transmission line excited resonator using a circulator

Keywords: scattering, resonant, circulator, summary, coupling, matching, Smith chart, transmission line

Postings 3.16 through 3.16f concern the analysis of Fig. 35 of posting 3.15 using various methods of conventional circuit analysis. The results confirm the statements made in postings previous to these concerning coupling and Q's. The postings represent a sampling of the methods a person might use to calculate various aspects of a resonant structure.

Below is a listing of various aspects covered in postings 3.16 through 3.16f.

• The simple electrical LRC circuit that is equivalent to the acoustical circuit of Fig. 35 of posting 3.15.
• Why a small coupling hole in an acoustical circuit is equivalent to a coupling inductor in the electrical analog.
• Equations for Q0 and QL of an electrical LRC circuit.
• Yet another graphical way to present a resonance: as the real and imaginary parts of the impedance of the resonator as a function of frequency.
• An equation for the approximate resonant frequency of the LRC circuit with the coupling inductor and also for the value of the coupling inductor required for unity coupling.
• A polar plot of the complex impedance of an LRC resonator.
• Equations and graph of the resonance curve of the complete electrical circuit (LRC resonator plus driving source, its output resistance and the coupling inductor).
• Transmission line resonators.
• Qo of a transmission line resonator - equations and graphs.
• An electrical transmission line model for the acoustic circuit of Fig. 35.
• A Smith chart to graphically solve for the resonant frequency and required Lc for unity coupling.
• Discussion of the dilemma of how an inductor can possibly be used to match impedances.
• Differential equation for the complete circuit responding to transients such as a sinusoidal burst: equations and numerical solutions and graphs.
• SPICE simulation of burst response, including a graph that shows agreement with the differential equation solution.

 All postings by author previous: 3.16f Transient response up: Contents next: 3.17 Resonant scattering with two output channels