Talk:Circuit Idea/How do We Create Sinusoidal Oscillations?

A dedication
I dedicate this incredible story to my former student [mailto:Kirillgenev@abv.bg Cyril] who has inspired me to start the series of stories about this great (circuit) phenomenon.

The story that I have told here is the most incredible happening in my teacher's life. I have been teaching circuitry for more than 20 years. I have been having good, responsive, clever, curious, capable and even talented students that have been helping and inspiring me in my pursuit of revealing the truth about circuits through these years. But, as a rule, my best students loose interest in the subject after passing the examination. I have been receiving sporadically emails from some of them at that when they need some help.

That's why, imagine how much I was amazed when Cyril whom I was teaching basic circuitry two years ago, came on one of my consultation hours and showed willingness for discussing circuit phenomena. In the beginning, I supposed that Cyril has just to pass some examination or he has failed to take an examination or he has to make a project... But imagine how much I was amazed when I knew that Cyril wanted just to understand circuits! He brought out a few textbooks, showed to me obscure circuit diagrams of various oscillators and told me that he had not understood anything from these explanations. He just wanted to know why, when and how oscillations arise, where currents flow, why the inductor and capacitor of an LC tank discharge completely, what make energy circulate between the two components of the LC circuit, what transistors and op-amps do in oscillating circuits, how an RC oscillator oscillates although it does not actually contain any oscillating circuit, etc. Then I started reading the vague texts and, as a result, I realized that I also do not understand them. I knew but I didn't realize the basic ideas behind these great phenomena.

It happened half a month ago; since that time I have no peace. I stopped writing temporarily the introductory methodological stories of Circuit idea and began thinking about oscillation phenomena. During my consultation hours Cyril and I discuss these famous circuits. Usually, our "brainstorming sessions" last two hours. I record them on a solid-state recorder; then I write down them on a paper and finally I use the valuable thoughts in creating circuit stories. So, I would like to dedicate this exciting introductory story about the philosophy of oscillations in this world to Cyril who has inspired me to start and then to keep this series of stories. Circuit-fantasist (talk) 17:27, 30 December 2007 (UTC)

In the beginning
Will you believe me how difficult it was for me to start this page? How do I begin writing a new story about something so simple, old, and legendary? Because it is easy to explain complex things in this world but it is so difficult to explain the simplest things. Everybody knows how an LC tank operates in terms of electricity and nobody understands why it operates just in this way. Thousands of writers have explained the concrete electrical LC circuit in thousands of sources down the years. Don't you think it's time finally to extract the general idea from the bare 2-component circuit, to reveal the philosophy behind it?

The challenge
I realize that it is a great challenge to begin writing a story about such a great phenomenon and to pretend to say something new about the topic. Those who venture to start such an adventure have to be prepared for bearing (mostly negative) reactions of others. People do not like someone to express own new ideas about old things even, if they are more than obvious. This upsets their mental equilibrium and they react to this "intervention" trying to redress the balance. Contrary, people adopt willingly, use and benefit from nobody's, conventional, approved and "reputable" ideas. I have known this truth from my experience since I have been bearing the (negative) reactions of people around me through my life...

But, in spite of all, I begin writing this incredible story about the great, not only an electrical but in the first place, a worldly phenomenon. Circuit-fantasist (talk) 10:18, 12 January 2008 (UTC)

Succession problems
Maybe, the main problem of this page is that it is based on a few preceding pages, which are not yet written. These pages are dedicated to the behavior of accumulating elements (capacitors and inductors) and to relaxation oscillations; they are included in the contents:

Stories about capacitor's behavior:

Is a Capacitor a Voltage Source? (comparison with a "real" voltage source) Making a Capacitor Integrate (building a resistive-capacitive integrator) Making a Capacitor Differentiate (building an "incorrect" capacitive and a "correct" capacitive-resistive differentiator) Discharging a Capacitor through a Capacitor (transferring instantly energy between voltage "sources")

Stories about inductor's behavior:

Is an Inductor a Current Source? (comparison with a "real" current source) Making an Inductor Integrate (building an inductive-resistive integrator) Making an Inductor Differentiate (building an "incorrect" inductive differentiator) Discharging an Inductor through an Inductor (a conflict between "incorrect" connected current sources)

Stories about relaxation oscillations:

How to Make the Voltage across a Capacitor Wiggle (creating a philosophy of the relaxation oscillator by comparing with the LC one)

Of course, it would be better to write first these simpler pages before to start the more complex page about LC tank. But what do I do when I was so eager to reveal the secret of the legendary LC tank? I have been longing for that for years; so, I have yielded to temptation:) That's why I have decided to start this page and, in order to compensate the absence of the pages above, to insert explanatory texts about capacitor's and inductor's behavior where it is needed. Later, when we write the missing pages, we might move or copy these texts to the appropriate places. Circuit-fantasist (talk) 17:48, 15 January 2008 (UTC)

What the talk page to contain
I suggest to shape this talk page as a second, enlarged and more colorful written version of the main page that to serve as a counterpart of the basic story. Here we - wikibookeans, circuit ideators, circuit philosophers and just curious visitors, might discuss more freely the subject. In the discussion page, we will comment what and how to say while in the main page we will just say it.

Frankly speaking, I have the feeling that the discussion page will become more interesting than the main one. That's why, I am divided in my decision of what to develop; this evening I decided to enrich the talk page with some wisdom:) Circuit-fantasist (talk) 19:36, 15 January 2008 (UTC)

What the secret of LC oscillations is
Maybe, we have first to say here what the truth about LC 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 in the figure on the right). 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 makes it move? What makes 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 acts 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) A relaxation oscillator consists of only one accumulating element while an LC oscillator consists of two accumulating elements.
 * 2) The relaxation accumulator is either flow or pressure like; the LC accumulators are heterogenious (the one is flow-like and the other is pressure-like).
 * 3) A 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 a 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 a relaxation circuit; it can be observed only in an LC tank.
 * 6) In a 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.

(to be continued...) Circuit-fantasist (talk) 08:01, 17 January 2008 (UTC)

How to reveal the truth about LC oscillations
If we assume that we have already revealed the secret of LC oscillations, now we have to decide how to present this wisdom to visitors (one thing is to understand somethning but the other thing is to explain it in the most credible, interesting and attractive way). For this purpose, we have to create a "scenario" of this story.

Starting and maintaining oscillation
In every kind of oscillator (including LC and relaxation oscillators), there must be at least 2 different components that "remember" 2 "instantaneous values": at any point in the oscillaton, there has to be at least the output voltage value, and also something else that remembers if we are going "up" or "down".
 * It sounds very philosophical. I need time to assimilate this wisdom:) Circuit-fantasist (talk) 08:57, 19 January 2008 (UTC)

Since resistors can instantaneously change current (when voltage is instantaneously changed), they are useless for "remembering".
 * I like this thought; I have inserted it into the story. Circuit-fantasist (talk) 08:57, 19 January 2008 (UTC)

Components that can be used for remembering:
 * capacitors
 * inductors
 * positive-feedback amplifiers (flip-flops, Schmitt trigger inverters, etc.)


 * David, I have finally finished this incredible story about LC oscillations and now I can reply with pleasure to your assertion. It sounds very fresh and original; as I can see, it is a sort of "informational viewpoint" at the topic about oscillators. IMO, it fits very well relaxation oscillators but it is not so suitable for explaining LC oscillators (regarding to RC oscillators, they are wrapped in mystery). An "energetical viewpoint" would fit LC oscillators quite better than the "energetical one". So, I suggest including this assertion into the page about relaxation oscillations. Well, let's exchange some thoughts about the topic.


 * First at all, it goes without saying that any oscillator has to contain a "remembering element", which represents the current state of the oscillator and which continuously changes its contents. From this viewpoint, we can think of an oscillator as a sequential circuit - e.g., a counter that increments or decrements continuously its contents (a "digital analogy"). Oscillators discussed here are analog devices; so, their "remembering elements" are analog as well. The capacitor is the simplest analog memory cell (as far as I know, the John Atanasoff's computer was based on a capacitor memory).
 * Then, we need an input source that charges gradually through time the memory element. In a case of a capacitor memory, we need a current source.
 * After, we need a comparator that compares the current magnitude with the maximum (if we are moving up) or minimum one (if we are moving down). For this purpose, we may use either two separate comparators or a comparator with hysteresis (the so called Schmitt trigger).
 * Finally, as you have said, we need a second memory element that "remembers" the comparator's condition (a comparator with hysteresis serves both as a comparing and a "remembering" element). Only, this element is a digital (discrete) memory that "remembers" only one bit.


 * Following the "scenario" above we will actually build a relaxation oscillator that will produce a triangle-shaped oscillation. If we try to apply this procedure to an LC oscillator, IMO we will obtain quite artificial and unnatural explanation. In an LC oscillator, we obtain "remembering", comparing and even "rounding" somewhat by itself. IMO, we have to look at LC oscillator rather from an "energetical viewpoint" than from this "informational viewpoint".


 * Circuit-fantasist (talk) 17:13, 31 January 2008 (UTC)

In a real LC oscillator, there also is something else that regulates how energy from the power supply is fed into the rest of the circuit -- it "pushes" the rest of the circuit.

Some people use a complicated circuit (op amps, PTR resistors, etc.) that very gently puts in just enough energy to compensate for the parasitic resistance of the LC, making as "pure" a sine wave as possible. There are a variety of less complicated circuits that are perhaps easier to understand, but generate a waveform that is more distorted from the "ideal" sine wave.

Would it help or make things more confusing to discuss an example "pusher" circuit?

--DavidCary (talk) 22:51, 18 January 2008 (UTC)


 * David, you have actually started the discussion about sustaining oscillation in an LC tank ("pushing" energy into an LC tank). I have started the talk page of this story and copied this discussion there. I suggest to continue discussing about "pushing" circuits on the new talk page.


 * Circuit-fantasist (talk) 17:04, 20 January 2008 (UTC)