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

Sunday, June 10, 2007

The LRC Circuit, the classical simple resonator

Electrical engineers and physicists study the simple electronic resonant circuit, known as an LRC circuit in order to better understand simple resonators. While the typical student will study perhaps two pages of math and text on this subject, there is much more to learn for the circuit. We will start with the well known aspects, but then move into the lesser known, but still important mathematical aspects of this resonator.

Today the LRC circuit is used in many electronic devices. Historically, perhaps the first widespread use was in the early radio. Marconi and others in the period 1880-1910 used an LRC circuit to create high frequency oscillating currents in an antenna in the first practical wireless telegraph system. This device used a spark gap to create a much more intense electric impulse than possible by a regular telegraph key alone. It also caused wireless telegraph operators to be nicknamed "Sparks", since operation of these devices involved lots of sparking. The intense impulse across the spark gap excited the LRC circuit into resonance, which in turn, caused an electromagnetic wave to be launched from the attached antenna. Below is an animated version of this illustration. Click on "key" to see the action.

More detail on how the spark gap transmitter worked. Click on "step" to see the step-by-step action.

1. When the telegraph key is depressed, the battery is connected up to the left-most capacitor, Cc.
2. This allows current from the battery to flow through resistor Rc into this capacitor, charging it up at a controlled rate. During this time, the charge and voltage of this capacitor rises.
3. After a few milliseconds of this charging, the voltage rises sufficiently to arc over the spark gap. Arcing involves stripping electrons off air molecules, making them white hot. We say it ionizes the air.
4. This ionized air between the two sides of the gap, constitutes a conducting path and allows the built up charge in the left capacitor to rush across the gap into the right-most capacitor. The right-most capacitor C and inductor (or coil) L there make up a resonator. The inductor and wiring also have resistance that which we often treat as a separate resistor and label as the R in an LRC circuit, i.e. an inductor-resistor-capacitor circuit. As we shall see in a future posting, an LRC circuit is an elemental electrical resonator and will "ring" or resonate when exposed to the proper electrical impulse. This is analogous to a bell being struck with a hammer and hearing the bell ring afterwards.
5. The surging current coming across the spark gap is just such an impulse, and sets the LRC circuit into oscillations. During the oscillations, the voltage on the upper terminals of the inductor and capacitor rings or oscillates. This means that that voltage there first becomes positive, then goes negative, then positive, then negative and so, until the oscillations are damped out by the effects of the resistor and radiation losses. Because the antenna is mounted on top of the upper terminals of the capacitor and inductor, its voltage is also forced to oscillate, which in turn makes the antenna generate electromagnetic waves that propagate outwards at the speed of light. The frequency of these waves is the same as the resonant frequency of the LRC circuit that caused them. A second LRC circuit and antenna can be used to detect the waves.

All this may seem horribly complicated, like a strange Rube Goldberg machine, but it is the core of the first radios, that revolutionized communications. After the invention of the wireless telegraph, ships at sea could communicate with people on land. Eventually this lead development of radios, televisions, and cell phones, all of which use resonators at their very core to function.