An oscillating circuit is a device designed to generate (create) electromagnetic waves. From its inception to the present, it has been used in many fields of science and technology: from everyday life to huge factories producing a wide variety of products.
What does it consist of?
The oscillation circuit consists of a coil and a capacitor. In addition, a resistor (element with variable resistance) may also be present in it. An inductor (or a solenoid, as it is sometimes called) is a rod on which several layers of the winding are wound, which, as a rule, is a copper wire. It is this element that creates oscillations in the oscillatory circuit. A rod located in the middle is often called a choke, or core, and a coil is sometimes called a solenoid.
The coil of the oscillating circuit creates oscillations only when there is a stored charge. When a current passes through it, it accumulates a charge, which then transfers to the circuit if the voltage drops.
Coil wires usually have very little resistance, which always remains constant. In the circuit of the oscillatory circuit very often there is a change in voltage and current. This change obeys certain mathematical laws:
- U = U 0 * cos (w * (tt 0 ), where
U is the voltage at a given time t,
U 0 - voltage at time t 0 ,
w is the frequency of electromagnetic waves.
Another integral component of the circuit is an electric capacitor. This is an element consisting of two plates that are separated by a dielectric. Moreover, the thickness of the layer between the plates is less than their size. This design allows you to accumulate an electric charge on the dielectric, which can then be given to the circuit.
The difference between a capacitor and a battery is that it does not transform substances under the influence of an electric current, but a direct accumulation of charge occurs in an electric field. Thus, using a capacitor, you can accumulate a sufficiently large charge, which can be given all at once. In this case, the current strength in the circuit increases significantly.
Also, the oscillating circuit consists of another element: a resistor. This element has a resistance and is designed to control the current strength and voltage in the circuit. If at a constant voltage increase the resistance of the resistor, then the current strength will decrease according to Ohm's law:
- I = U / R, where
I is the current strength
U is the voltage
R is the resistance.
Inductor
Let's take a closer look at all the intricacies of the inductance coil and better understand its function in the oscillatory circuit. As we have already said, the resistance of this element tends to zero. Thus, when connected to a DC circuit, a short circuit would occur . However, if you connect the coil to an AC circuit, it works properly. This allows us to conclude that the element resists alternating current.
But why does this happen and how does resistance arise with alternating current? To answer this question, we need to turn to such a phenomenon as self-induction. With the passage of current through the coil, an electromotive force (EMF) arises in it , which creates an obstacle to the change in current. The magnitude of this force depends on two factors: the inductance of the coil and the derivative of the current strength with respect to time. Mathematically, this dependence is expressed through the equation:
- E = -L * I '(t), where
E is the value of the EMF,
L is the magnitude of the inductance of the coil (for each coil it is different and depends on the number of winding coils and their thickness),
I '(t) is the derivative of the current strength with respect to time (rate of change of current strength).
The DC current does not change over time, so resistance does not arise when it is exposed.
But with alternating current, all its parameters are constantly changing according to a sinusoidal or cosine law, as a result of which there is an EMF that prevents these changes. Such resistance is called induction and is calculated by the formula:
- X L = w * L, where
w is the oscillation frequency of the circuit,
L is the inductance of the coil.
The current strength in the solenoid linearly increases and decreases according to various laws. This means that if you stop supplying current to the coil, it will continue to give charge to the circuit for some time. And if, at the same time, the current supply is abruptly interrupted, then a shock will occur due to the fact that the charge will try to distribute and exit the coil. This is a serious problem in industrial production. Such an effect (although not entirely related to the oscillatory circuit) can be observed, for example, when pulling the plug from the outlet. At the same time, a spark jumps in, which on such a scale is not able to harm a person. It is due to the fact that the magnetic field does not disappear immediately, but gradually dissipates, inducing currents in other conductors. On an industrial scale, the current strength is many times greater than the usual 220 volts for us, so when the circuit is interrupted in production, sparks of such strength can arise that will cause a lot of harm to both the plant and people.
A coil is the basis of what the oscillating circuit consists of. The inductances of the series connected solenoids add up. Next, we will take a closer look at all the subtleties of the structure of this element.
What is inductance?
The inductance of the coil of the oscillatory circuit is an individual indicator numerically equal to the electromotive force (in volts) that occurs in the circuit when the current strength changes by 1 A in 1 second. If the solenoid is connected to a direct current circuit, then its inductance describes the energy of the magnetic field, which is created by this current according to the formula:
- W = (L * I 2 ) / 2, where
W is the energy of the magnetic field.
The inductance coefficient depends on many factors: on the geometry of the solenoid, on the magnetic characteristics of the core and on the number of coils of wire. Another property of this indicator is that it is always positive, because the variables on which it depends cannot be negative.
Inductance can also be defined as the property of a conductor with current to accumulate energy in a magnetic field. It is measured at Henry (named after the American scientist Joseph Henry).
In addition to the solenoid, the oscillatory circuit consists of a capacitor, which will be discussed later.
Electric capacitor
The capacity of the oscillating circuit is determined by the capacity of the electric capacitor. About his appearance was written above. Now we will analyze the physics of the processes that take place in it.
Since the capacitor plates are made of a conductor, an electric current can flow through them. However, there is an obstacle between the two plates: a dielectric (it can be air, wood or other material with high resistance. Due to the fact that the charge cannot pass from one end of the wire to the other, it accumulates on the plates of the capacitor. This increases the power of magnetic and electric fields around it. Thus, when the charge ceases, all the electricity accumulated on the plates begins to be transferred to the circuit.
Each capacitor has a rated voltage that is optimal for its operation. If you use this element for a long time at a voltage higher than the nominal, its service life is significantly reduced. The capacitor of the oscillatory circuit is constantly subject to the influence of currents, and therefore, when choosing it, you should be extremely careful.
In addition to the conventional capacitors discussed, there are also ionistors. This is a more complex element: it can be described as something between a battery and a capacitor. As a rule, organic substances, between which there is an electrolyte, serve as the dielectric in the ionistor. Together they create a double electric layer, which allows you to accumulate in this design many times more energy than in a traditional capacitor.
What is capacitor capacity?
Capacitor capacity is the ratio of the capacitor charge to the voltage under which it is located. This value can be calculated very simply using a mathematical formula:
- C = (e 0 * S) / d, where
e 0 is the dielectric constant of the dielectric material (tabulated value),
S is the area of the capacitor plates,
d is the distance between the plates.
The dependence of the capacitance on the distance between the plates is explained by the phenomenon of electrostatic induction: the smaller the distance between the plates, the more they affect each other (according to Coulomb's law), the greater the charge on the plates and the lower the voltage. And when the voltage decreases, the value of the capacitance increases, since it can also be described by the following formula:
- C = q / U, where
q is the charge in pendants.
It is worth talking about the units of this quantity. Capacity is measured in farads. 1 farad is a fairly large value, so existing capacitors (but not ionistors) have a capacitance measured in picofarads (one trillion farad).
Resistor
The current in the oscillatory circuit also depends on the resistance of the circuit. And besides the described two elements that make up the oscillating circuit (coil, capacitor), there is also a third - a resistor. He is responsible for creating resistance. The resistor differs from other elements in that it has a lot of resistance, which in some models can be changed. In the oscillatory circuit, it performs the function of a magnetic field power regulator. You can connect several resistors in series or in parallel, thereby increasing the resistance of the circuit.
The resistance of this element also depends on the temperature, so you should be attentive to its work in the circuit, since with the passage of current it heats up.
The resistance of the resistor is measured in Ohms, and its value can be calculated by the formula:
- R = (p * l) / S, where
p is the resistivity of the material of the resistor (measured in (Ohm * mm 2 ) / m);
l is the length of the resistor (in meters);
S is the cross-sectional area (in square millimeters).
How to link contour parameters?
Now we have come close to the physics of the oscillatory circuit. Over time, the charge on the capacitor plates changes according to a second-order differential equation.
If this equation is solved, several interesting formulas follow that describe the processes that occur in the circuit. For example, the cyclic frequency can be expressed in terms of capacitance and inductance.
However, the simplest formula that allows you to calculate many unknown quantities is the Thomson formula (named after the English physicist William Thomson, who derived it in 1853):
- T = 2 * n * (L * C) 1/2 .
T is the period of electromagnetic oscillations,
L and C - respectively, the inductance of the coil of the oscillatory circuit and the capacity of the circuit elements,
n is the number pi.
Q factor
There is another important value characterizing the operation of the circuit - quality factor. In order to understand what it is, you should turn to a process such as resonance. This is a phenomenon in which the amplitude becomes maximum at a constant value of the force that this oscillation supports. The resonance can be explained with a simple example: if you start pushing the swings to the beat of their frequency, they will accelerate, and their "amplitude" will increase. And if you push out of tune, they will slow down. At resonance, a lot of energy is often dissipated. In order to be able to calculate the magnitude of losses, we came up with such a parameter as quality factor. It is a coefficient equal to the ratio of the energy in the system to the losses occurring in the circuit in one cycle.
The quality factor of the circuit is calculated by the formula:
- Q = (w 0 * W) / P, where
w 0 is the resonant cyclic oscillation frequency;
W is the energy stored in the oscillatory system;
P is power dissipation.
This parameter is a dimensionless quantity, since it actually shows the ratio of energies: stored to spent.
What is an ideal oscillating circuit
To better understand the processes in this system, physicists have come up with the so-called ideal oscillatory circuit . This is a mathematical model representing a circuit as a system with zero resistance. In it, undamped harmonic oscillations arise. Such a model allows us to obtain formulas for the approximate calculation of the parameters of the contour. One of these parameters is the total energy:
Such simplifications significantly speed up the calculations and allow you to evaluate the characteristics of the circuit with the given indicators.
How it works?
The entire cycle of the oscillatory circuit can be divided into two parts. Now we will analyze in detail the processes occurring in each part.
- The first phase: the capacitor plate, positively charged, begins to discharge, giving current to the circuit. At this moment, the current goes from a positive charge to a negative, passing through the coil. As a result, electromagnetic oscillations occur in the circuit. The current, passing through the coil, passes to the second plate and charges it positively (whereas the first plate with which the current came is charged negatively).
- Second phase: the reverse process takes place. The current passes from the positive plate (which at the very beginning was negative) to the negative, passing again through the coil. And all the charges fall into place.
The cycle is repeated until there is a charge on the capacitor. In an ideal oscillatory circuit, this process occurs endlessly, and in real, energy losses are inevitable due to various factors: heating, which occurs due to the existence of resistance in the circuit (joule heat), and the like.
Contour Design Options
In addition to simple "coil-capacitor" and "coil-resistor-capacitor" circuits, there are other options that use an oscillating circuit as the basis. This, for example, is a parallel circuit, which differs in that it exists as an element of an electrical circuit (because, if it existed separately, it would be a sequential circuit, which was discussed in the article).
There are also other types of designs, including various electrical components. For example, you can connect a transistor to the network, which will open and close the circuit with a frequency equal to the oscillation frequency in the circuit. Thus, undamped oscillations are established in the system.
Where is the oscillating circuit applied?
The most familiar application of the components of the circuit is electromagnets. They, in turn, are used in intercoms, electric motors, sensors and in many other not so ordinary areas. Another application is an oscillator. In fact, this use of the circuit is very familiar to us: in this form it is used in the microwave to create waves and in mobile and radio communications to transmit information over a distance. All this happens due to the fact that the oscillations of electromagnetic waves can be encoded in such a way that it will be possible to transmit information over long distances.
The inductor itself can be used as an element of a transformer: two coils with a different number of windings can transfer their charge using an electromagnetic field. But since the characteristics of the solenoids differ, the current indicators in the two circuits to which these two inductors are connected will differ. Thus, it is possible to convert a current with a voltage of, say, 220 volts into a current with a voltage of 12 volts.
Conclusion
We have examined in detail the principle of operation of the oscillatory circuit and each of its parts separately. We learned that the oscillatory circuit is a device designed to create electromagnetic waves. However, these are only the basics of the complex mechanics of these seemingly simple elements. You can learn more about the intricacies of the circuit and its components from the specialized literature.