Talk:Circuit Idea/Relaxation versus LC Oscillators

(I would like to start the discussion about relaxation oscillations by moving here the text below from the page about LC tank) Circuit-fantasist (talk) 18:31, 24 January 2008 (UTC)

What the secret of relaxation oscillations is
Maybe, we have first to say here what the truth about relaxation oscillation is and then to discuss how to present this wisdom to visitors (these are different things). Well, let's begin with the first.

The initial point: A steady quantity
At the starting point we need a steady quantity. Where to get it from? As usual in this world, we need energy to create a quantity. We can get this energy from some power source. So, the first thing what we need (in this world) is a power source.

The problem: How to make it oscillate?
Then, we ask yourself, "How do we make the steady quantity oscillate?" But what does mean "to oscillate"? Simply speaking, to oscillate means just to make the quantity increase and decrease consecutively and regularly. How do we do this magic?

Preparing a steady quantity to be changed
It seems it's too difficult to make the very power source oscillate (power sources keep up constant their output quantities). Then, what do we do? We can act like in many situations of routine: instead to change the whole source energy we get some amount of energy from the source and store it in some "place" with the purpose to change it. As there are two kinds of energy - kinetic and potential, we can store energy in two kinds of energy accumulators (integrators). Let's do it; we have got the initial steady quantity. Examples: if we have stored a kinetic energy in an inductor, we obtain a constant current; if we have stored a potential energy in a capacitor, we obtain a constant voltage.

Changing the accumulated quantity
Now, we can begin doing the "veritable work" - to increase and decrase the steady quantity, in order to make it oscillate. How can we make it increase? Of course, by adding continuosly energy to the accumulator. And how can we make it decrease? Contrary, by subtracting continuosly energy from the accumulator. In both the cases we move, transport, transfer energy from one place to other - from the source to the accumulator and v.v.

Relaxation oscillations
(...We might explain what an LC oscillation is, if we say what it is not. Here, we might say that an LC oscillation is not a relaxation one. Only, we would explain what a "relaxation oscillation" is. This phenomenon is no less vague and mystic than the LC phenomenon (I have never met good resources about it). Now, we have opportunity to reveal the secret behind relaxation phenomenon by comparing it with LC one. After that, we may move these thoughts to the future story about relaxation oscillations...)



The basic idea. According to the powerful idea above, we might first build the simpler and more intuitive relaxation oscillator by using three elements: a flow (current) source, an accumulator of potential energy (a capacitor) and a load (a resistor). Such an arrangement operates in two stages as follows: in the first stage, we connect the current source to the accumulator and begin charging it; in the second stage, we connect the accumulator to the load (turn on the switch SW) and discharge it. Let's repeat it in other words: in a period of a relaxation oscillation, we first draw a kind of energy (usually, potential) from the flow source to fill the accumulator, then "suck dry" the energy from the accumulator and just "throw out" it to the environment. Thus, in the first stage of every period the source has to restore the energy in the accumulator.

Features. Note that the relaxation arrangement needs only one accumulator. It lies on the way of energy and serves as a buffer that interrupts temporarily the flow (only, the average flow remains constant). In this way, it intermits, tears to "pieces" the energy flow. It is interesting fact that a continuous current enters the accumulator while an intermittent current leaves it; so, we might say that a relaxation oscillator "discretisizes", "portens", "doses" the unceasing input flow of energy. At the same time, the accumulator's contents increases and decreases periodically. The shape of the curve is not sinusoidal because at the points of switching (at the peaks) the "flow-creating" quantity has a maximum magnitude. Note also that increase and decrease can have different durations. Examples of this possibility (see the analogies below) are a photoflash (slow charging, fast discharging), a toilet tank, a husband that fills slowly and continuously a family money deposit while his wife empties rapidly and regularly it:)

What does "relaxation oscillation" mean? I have been asking myself many times what the word "relaxation" means in this context. What does "relax" here? Maybe, the capacitor? If yes, when does the capacitor relax? Maybe, when we charge it (in this case, "relaxation" would mean restoring, retrieving, recreating the content of the accumulating element). Or maybe, the capacitor relaxes (returns to its initial "zero energy" state of equilibrium) when we discharge it...

Relaxation analogies. We can see many manifestations of this phenomenon in nature, routine, engineering and finally, in electronics. For example, I have a remembrance from my childhood how sometimes faulty toilet tanks began working intermittently (filling -> emptying -> filling -> emptying... up to infinity:) Similarly, imagine you were foolish enough to make a common money deposit with your wife:) Then, you begin working hard to feed up continuously the deposit. As a result, the amount of money increases continuously through time. Only, at some point your wife decides that's enough and draw out all the money accumulated. You begin working again... and she empties the deposit again... and this repeats again... and again... and again...:) Circuit-fantasist (talk) 20:06, 18 January 2008 (UTC)

LC oscillations


The basic idea. Contrary, in order to create an ideal LC oscillation (assume an LC tank without losses), we charge the accumulator only once in the beginning (by turning on the switch SW on the bottom of the figure). Then, we "suck dry" the energy from the accumulator but do not "throw it away"; instead, we convert it into an opposite kind (kinetic to potential or potential to kinetic) and store the converted energy in another accumulator. We move, transfer, convey the energy from the one accumulator to the other. After, we use this energy to restore the energy of the first accumulator instead to "suck" energy from the source (we move back the energy). By the way, maybe is more correctly to say "energy moves" rather than "we move the energy". But why the energy moves by itself? What make it move? What make it move to and fro without end? Don't you think there is something mystic in this endless "ping-pong" movement?

Implementation. For this purpose, the LC arrangement consists of two heterogenious (regarding to the two kinds of energy) accumulating elements. Each of them can either provide energy (when it serves as a source) or store the energy (when it serves as a load). When act as a source, it is a weakening, depleting, exhausting source because the other (accumulating) element "sucks out" the source's energy. The energy moves from the source to the accumulator and the source's output quantity decreases.

Similarities

 * 1) Both the oscillating circuits contain at least one accumulating element that acts either as a source or as an integrator.

Differences

 * 1) An relaxation oscillator consists of only one accumulating element while an LC oscillator consists of two accumulating elements.
 * 2) The relaxation accumulator is flow or pressure like; the LC accumulators are heterogenious (the one is flow-like and the other is pressure-like).
 * 3) An relaxation oscillator stores only one kind of energy (usually potential) in the accumulator while an LC oscillator stores two opposite kinds of energy (kinetic and potential) in the two accumulators.
 * 4) In an relaxation oscillator we "throw away" the energy while in an LC oscillator we treasure it temporarily in an additional accumulator with the purpose of future usage. That's why, LC oscillators are more economical than relaxation ones.
 * 5) Resonance phenomenon does not exist in relaxation circuit; it can be observed only in LC tank.
 * 6) In an relaxation oscillator the energy moves only in one direction (source -> accumulator -> load) while in an LC oscillator the energy changes periodically its direction (it circulates between the two elements).
 * 7) The shape of a relaxation oscillation is peaked, angular while the shape of an LC oscillation is rounded (sinusoidal). The reason of that is that at the peaks the source of a relaxation oscillator changes its output quantity with the maximum magnitude while the "source" of an LC oscillator (charged accumulator) does not change its output quantity.
 * 8) The shape of the relaxation oscillation can be asymmetrical (the increase and the decrease can have different durations) while the shape of the LC oscillation is precisely symmetrical.

Circuit-fantasist (talk) 18:31, 24 January 2008 (UTC)