Circuit Idea/Relaxation versus LC Oscillators

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Comparing the Ideas behind Relaxation and LC Oscillators

A relaxation oscillator[edit | edit source]

The basic idea. The simpler and more intuitive relaxation oscillator consists of (Fig. 1) a flow (current) source, an accumulator of potential energy (a capacitor), a switch SW and a load (a resistor).[1] 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.

Fig. 1. A relaxation oscillator has only one accumulating element; the energy moves only in one direction.

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 are a photoflash (slow charging, fast discharging) or a toilet tank.

An LC oscillator[edit | edit source]

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).

Fig. 2. An LC oscillator has two accumulating elements; the energy circulates between them.

Implementation. For this purpose, the LC arrangement consists of two heterogeneous (regarding to the two kinds of energy) accumulating elements (Fig. 2). 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.

Relaxation versus LC oscillators[edit | edit source]

Similarities[edit | edit source]

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

Differences[edit | edit source]

  1. A 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 heterogeneous (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 the 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.

References[edit | edit source]

  1. How to Make the Voltage across a Capacitor Wiggle (creating a philosophy of the relaxation oscillator)

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