Electric resonance application. Resonance in the electrical circuit is a hypermarket of knowledge. Elements of resonant chain

The resonance in physics is called a phenomenon in which the amplitudes of the system oscillation increase sharply. This happens when the coincidence of its own and external perturbation frequencies. In the mechanics, an example is a pendulum of hours. Such behavior is also characteristic of electrical circuits, including elements of active, inductive and capacitive load. Resonance of currents and stresses is very important, this phenomenon has found application in such areas of science as radio communications and industrial power supply.

Vectors and theory

To understand the meaning of the processes occurring in chains, including inductors, condensers and active resistance, should be considered a scheme of the simplest oscillatory circuit. Just as the usual pendulum alternates the energy from the potential in the kinetic state, the electrical charge in the RCL chain, accumulating in the container, flows into inductance. After that, the process occurs in the opposite direction, and it all starts first. In this case, the vector diagram is as follows: the capacitive load current is ahead of the angle π / 2 of the voltage direction, the inductive load lags behind the same angle, and the active coincides in the phase. The resulting vector has a slope relative to the abscissa, denoted by the Greek letter φ. The resonance in the AC circuit occurs when φ \u003d 0, respectively, cos φ \u003d 1. Translated from the mathematics language, this shutter means that the current passing through all the elements by phase coincides with the current in the active component of the electrical circuit.

Practical application in power supply systems

Theoretically, all these calculations are understandable, but what they mean for practical questions? A lot of things! Everyone knows that useful work In any diagram, the active component of the power is performed. At the same time, most of the consumption of energy falls on electric motors, which at any enterprise there are many, and they contain a winding in their design, which are inductive load and creating an angle φ, which is zero. In order for the reasons resonance, it is necessary to compensate for the reactive resistance so that their vector sum is zero. In practice, this is achieved by turning on the condenser, which creates the opposite shift of the current vector.

Resonance currents in radio receivers

Current resonance has both other radiotechnical applications. The oscillating circuit, which makes up the basis of each receiving device, consists of a coil of inductance and a condenser. By changing the magnitude of the electrical capacity, it is possible to ensure that the signal with the required carrier frequency will be taken selectively, and the remaining overhaul components taken on the antenna, including obstacles, will be depressed. In practice, such variable condenser looks like two sets of plates, one of which is rotated or comes out of another, increasing or reducing electric container. This creates the current resonance, and the radio receives is applied to the desired frequency.

We were convinced of the coincidence of the laws of free mechanical and electric oscillations. But the equally complete similarity of laws is also in the case of forced oscillations caused by the effect of external periodic force. In the case of electrical oscillations, the role of force plays, as we have seen in the previous paragraph, the electromotive force (abbreviated e. S). Review § 12, where we described the forced oscillations, § 13, which refers to the phenomenon of resonance, and § 14, which examines the effect of attenuation into resonant phenomena in the oscillating system. Everything that said there about mechanical forced oscillations is entirely related to electric. And here the frequency of forced oscillations in the oscillatory circuit is equal to the frequency of the existing in this circuit e. d. s. The amplitude of the forced oscillations is the greater the closer the frequency e. d. s. To the frequency of free oscillations in the circuit. At the coincidence of these frequencies, the amplitude becomes the greatest, the electric resonance is obtained: the current in the circuit and the voltage on its capacitor can very much exceed those that are obtained during tuning, i.e., away from the resonance. Resonant phenomena are the stronger and sharper than the resistance of the contour, which, thus, also plays the same role as friction in the mechanical system.

All these phenomena are easy to observe, using for obtaining a harmonic e. d. s. Urban alternating current and building an oscillating circuit, whose own frequency can be changed in both sides of the current frequency (). To avoid high resonant stresses in the circuit, which (at a voltage in the urban network) can reach several kilovolts, you should use a downstream transformer.

In fig. 53 shows the location of the instruments and the electrical scheme of the experiment (designations in the figure and the same scheme). The diagram includes a lower transformer 1, capacitor 2, chokes 3 and 4, which are inductance coils with iron cores that are needed to obtain the required large inductance. For convenience, the circuit setting the inductance is composed of the inductors of two separate coils. The setting is carried out by the fact that one of the chokes (4) the core has an air gap, the width of which can be smoothly changed within, thereby changing the overall inductance. The wider the gap, the less inductance. In signatures to fig. 53 Suitable values \u200b\u200bof all values \u200b\u200bare indicated. The voltage on the condenser is measured by a voltmeter of the AC, and the AC ammeter allows you to monitor the current in the circuit.

Experience shows the following: With a low inductance of the contour, the voltage on the condenser is a little more than the induction in the e. s, i.e. somewhat volt. Increasing inductance, we will see that the tension is growing; This increase is becoming more and more sharp as they approach the resonant inductance. With those numerical data that are specified in the signature to Fig. 53, the voltage rises above. With a further increase in inductance, the voltage falls again. The current in the circuit is changed in proportion to the voltage on the condenser and during the resonance can reach.

This experience corresponds to the mechanical experience with the cargo on the spring, which was described in § 12. There we were more convenient to change the frequency of the current force, here we are passing through the resonant setting, changing your own frequency of the oscillating system - our contour. The essence of the resonance phenomenon does not change.

Fig. 53. Obtaining an electric resonance for the urban current frequency: 1 - a transformer that reduces voltage, for example from up to, 2 - capacitor capacitor, 3 - choke, the inductance of which, and the winding resistance is equal to, 4 - throttle with alternating air gap, the inductance of which with a width and varies when changing the width of the gap on both sides of the specified (resonant) value

The role of electrical resonance in the technique is enormous. We give only one example. Essentially, the resonance is based on radio reception. Numerous radio stations emit electromagnetic waves, which put the variables in the radio receiver in the antenna. d. s. (electrical oscillations), and each radio station rules its oscillations specified frequency. If we were not able to allocate oscillation oscillations from this most complicated mixture, the fluctuations in the radio station you are interested in, then no radio cane is possible. Here and comes to the aid of electric resonance.

We connect with an antenna oscillatory circuit, for example, through inductance, as shown in Fig. 54.

The capacitance of the capacitor can be changed smoothly, thereby changing its own circuit frequency. If we configure the contour to the desired frequency, for example, then e. d. s. With the frequency, it will cause strong forced oscillations in the circuit, and all the rest e. D. S.-weak. Consequently, the resonance allows you to customize the receiver to the frequency of the selected station.

Fig. 54. Resonance allows you to tune in to the desired station and rejuvenate from all others. The arrow on the condenser indicates that the capacitance of the capacitor can be changed

Of course, in electrical engineering, as in mechanical engineering, the resonance can appear the greatest evil where it should not be. If the electrical circuit is designed to work in the absence of resonance, then the emergence of the resonance will cause an accident: the wires are split from excessively strong currents, the insulation will be broken due to high resonant voltages, etc. In the last century, when the electrical fluctuations were not yet sufficiently studied, Such accidents happened. Now we can depend on the conditions or use the resonance, or eliminate it.

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Resonance. Its application

Resonance in an electric oscillatory circuit The phenomenon of a sharp increase in the amplitude of the forced oscillations of the current force when the frequency of external alternating voltage is coincided with its own oscillating circuit frequency.

resonance Voltage Electric Medicine

Using resonance

In medicine

Magnetic-resonance tomography, or its abbreviated name MRI, is considered one of the most reliable radiation diagnostics methods. An obvious advantage of using such a method to check the condition of the body is that it is not ionizing radiation and gives fairly accurate results in the study of the muscular and articular system of the body, it helps with a high probability to diagnose various diseases of the spine and the central nervous system.

The survey process itself is quite simple and absolutely painless - everything that you will hear, only a strong noise, but the headphones will be protected well from him, who will give you the doctor before the procedure. There are only two types of inconvenience, which will not be able to avoid. First of all, it concerns those people who are afraid of closed spaces - the diagnosed patient falls on the horizontal lay and the automatic relay move it inside the narrow pipe with a strong magnetic fieldwhere it is located about 20 minutes. During diagnostics, one should not move so that the results will be more accurate as possible. The second inconvenience, which causes a resonant tomography in the study of a small pelvis, is the need for a purity of the bladder.

If your loved ones want to be present in diagnosity, they are obliged to sign the information document, according to which they are familiar with the rules of behavior in the diagnostic office and have no contraindications to find a strong magnetic field. One of the reasons for the impossibility of finding an MRI control is the presence of foreign metal components in the body.

Prolitoil Resonance in Radio Communication

The phenomenon of electrical resonance is widely used in the implementation of radio communications. Radio waves from various transmitting stations are excited by the variables of various frequencies in the antenna of the radio, as each transmitting radio station operates at its frequency. The antenna inductance is associated with a oscillating circuit (Fig. 4.20). Due to the electromagnetic induction in the contour coil, variables of the corresponding frequencies and forced fluctuations of the current strength of the same frequency occur. But only with the resonance fluctuations in the strength of the current in the circuit and voltage in it will be significant, i.e., from oscillations of various frequencies excited in an antenna, the circuit allocates only those frequencies of which is equal to its own frequency. Setting the circuit to the desired frequency is usually carried out by changing the capacitance of the capacitor. This usually consists of tuning the radio to a specific radio station. The need to take into account the possibility of resonance in electrical chain. In some cases, the resonance in the electrical circuit can bring great harm. If the chain is not designed to work in resonance, then its occurrence can lead to an accident.

Excessively large currents can overheat wires. Large stresses lead to a breakdown of isolation.

This kind of accident often happened even relatively recently, when the laws of electrical fluctuations were poorly presented and could not be able to correctly calculate the electrical chains.

With forced electromagnetic oscillations, resonance is possible - a sharp increase in the amplitudes of fluctuations in the current and voltage fluctuations when the frequency of external alternating voltage with its own oscillation frequency is coincided. On the phenomenon of resonance, all radio communication is based.

Voltage resonance

The phenomenon of the resonance of electrical stress is observed in the circuit of a sequential oscillatory circuit consisting of a container (condenser), inductance and resistor (resistance). To ensure the energy supply of the oscillatory circuit, the sequential circuit also includes the source of the E. E. The source produces an alternating voltage with the frequency of W. With the resonance of the current circulating in the serial chain, must match the phase from E.D.S. E. This is ensured if the general resistance of the circuit Z \u003d R + J (WL - 1 / WC) will be only active, i.e. Z \u003d r. Equality:

(L - 1 / ws) \u003d 0 (1),

it is a mathematical condition of resonance in a oscillatory circuit. In this case, the value of the current in the chain will be I \u003d E / R. If you transform equality (1), we will get:

In this expression W - is the resonant frequency of the contour.

It is important that in the process of resonance, inductance voltage is equal to voltage on the condenser and is:

UL \u003d U \u003d WL * i \u003d WLE / R

The total amount of energy in inductance and tanks (magnetic and electric fields) is constant. This is explained by the fact that there is an oscillatory exchange of energy between these fields. The total amount of it at any time is invariably. At the same time, the exchange of energy between its source E and the chain does not occur. Instead, there is a continuous transformation of one type of energy to another.

For oscillatory contours, the term Quality will apply, which shows how the voltage on the reactive element (capacity or inductance) and the input voltage of the contour are applied. Quality is calculated by the formula:

For an ideal sequential circuit with zero active resistance The emergence of resonance is accompanied unlucky oscillations. In practice, the attenuation of oscillations is compensated by the contour feed from the oscillation generator with the frequency of the resonance.

Application of stress resonance

The phenomenon of oscillatory resonance is widely used in electronics. In particular, the input chain of any radio receiver is an adjustable oscillating circuit. Its resonant frequency variable by adjusting the capacitor capacitance coincides with the frequency of the radio station signal that must be accepted.

In the electric power industry, the emergence of stress resonance due to surgeons associated with unwanted consequences. For example, in the case of connecting to the generator or an intermediate transformer of a long cable line (which is an oscillatory circuit with a distributed capacity and inductance), not connected at the receiving end with the load (this is called the idle mode), the entire contour may be in the resonance state. In this situation, the voltage arising in some parts of the chain may be higher than the calculated one. It may threaten the cable insulation breakdown and its output. This situation is prevented by using auxiliary load.

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What is resonance?

Determination of the phenomenon of TOE: Electric resonance occurs in an electrical circuit at a certain resonant frequency, when some parts of the resistance or procedures of the schema elements compensate for each other. In some circuits, this happens when the impedance between the input and the output of the circuit is almost equal to zero, and the signal transmission function is close to one. At the same time, the quality of this circuit is very important.

Signs of resonance:

The components of the reactive branches of the current are equal to each other IPC \u003d IPL, the antiphase is formed only with the equality of pure active energy at the inlet;
The current in individual branches exceeds the entire current of a certain chain, while the branches coincide in phase.

In other words, the resonance in the AC circuit implies a special frequency, and is determined by the resistance, capacity and inductance. There are two types of current resonance:

Consistent;
Parallel.

For consistent resonance, the condition is simple and characterized by minimal resistance and zero phase, it is used in reactive circuits, also applies a branched chain. Parallel resonance or the concept of the RLC contour occurs when inductive and capacitive data is equal in size, but compensate for each other, as they are at an angle of 180 degrees from each other. This compound must be constantly equal to the specified value. He got a wider practical use. The sharp minimum impedance that is characteristic of it is useful for many electrical household appliances. The sharpness of the minimum depends on the resistance value.

RLC scheme (or contour) is electrical schemewhich consists of a resistor, inductance coils, and a condenser connected in series or in parallel. The parallel oscillatory circuit RLC received its name due to the abbreviation of physical quantities, representing respectively resistance, inductance and capacity. The scheme forms a harmonic oscillator for current. Any vibration induced in the current circuit fumbles over time if the movement of directional particles is terminated by the source. This effect of the resistor is called attenuation. The presence of resistance also reduces the peak resonant frequency. Some resistance are inevitable in real schemes, even if the resistor is not included in the circuit.

Application

Almost all the power electrical engineering uses just such an oscillating circuit, say, the power transformer. Also, the scheme is necessary to configure the operation of the TV, the capacitive generator, welding machine, radio, it applies the technology "matching" of the television antennas, where you need to select a narrow frequency range of some used waves. RLC scheme can be used as a bandwall, recorder filterFor sensors for the distribution of the lower or upper frequencies.

Resonance even uses aesthetic medicine (microcurrent therapy), and bioresonance diagnostics.

The principle of resonance of currents

We can make a resonant or oscillatory scheme in our own frequency, say, to power the capacitor, as the following diagram shows:

Scheme for powering capacitor

The switch will be responsible for the direction of oscillations.

Scheme: Resonance Scheme Switch

The capacitor retains the entire current at the moment when time \u003d 0. oscillations in the chain are measured using ammeters.

Scheme: Current in the resonant scheme is zero

The directional particles move to the right side. Inductance coil takes a current from the condenser.

When the polarity of the scheme acquires the initial look, the current returns to the heat exchange device again.

Now the directional energy goes back to the condenser, and the circle is repeated again.

In real schemes of the mixed chain, there is always some resistance that causes the amplitude of directional particles to grow less with each circle. After several shifts of the polarity of the plates, the current decreases to 0. This process It is called a sinusoidal floating wave signal. How quickly this process occurs, depends on the resistance in the chain. But at the same time, the resistance does not change the frequency of the sinusoidal wave. If the resistance is high enough, the current will not fluctuate at all.

The designation of AC means that leaving the power supply, the energy varies with a certain frequency. The increase in resistance contributes to a decrease maximum size current amplitude, but this does not lead to a change in the frequency of the resonance (resonant). But it can form a dramatic process. After it occurs in the networks there are interruptions.

Calculation of resonant contour

It should be noted that this phenomenon requires a very thorough calculation, especially if a parallel connection is used. In order for the technique of no interference, you need to use various formulas. They will use you to solve any task in physics from the relevant section.

It is very important to know the value of the power in the chain. The average power dissipated in the resonant circuit can be expressed in terms of the standard voltage and current as follows:

R cf \u003d i 2 Cont * R \u003d (V 2 CONT / Z 2) * R.

At the same time, remember that the power factor with resonance is Cos Φ \u003d 1

The very formula of the resonance has the following form:

ω 0 \u003d 1 / √L * C

Zero impedance in resonance is determined using such a formula:

F cut \u003d 1 / 2π √L * C

The resonant frequency of oscillations can be approximated as follows:

F \u003d 1/2 P (LC) 0.5

Where: F \u003d Frequency

L \u003d inductance

C \u003d Capacity

As a rule, the scheme will not fluctuate if the resistance (R) is not low enough to meet the following requirements:

R \u003d 2 (L / C) 0.5

To obtain accurate data, you need to try not to round the obtained values \u200b\u200bdue to the calculations. Many physicists recommend using a method called the vector diagram of active currents. With the right calculation and adjustment of the devices, you will have good AC savings.

In the oscillatory circuit, which has the inductance L, C and the resistance of R, the free electrical oscillations tend to damage. So that the oscillations do not attense, it is necessary to periodically replenish the contour of energy, then there will be forced oscillations that will not fade, because the outer variable of EDC will now maintain fluctuations in the circuit.

If the oscillations support the source of the external harmonic EMF, the frequency of which f is very close to the resonant frequency of the oscillating circuit F, then the amplitude of the electrical oscillations U in the circuit will increase dramatically, that is, it will come phenomenon of electric resonance.

Consider first the behavior of the C capacitor in the AC circuit. If to the generator, the voltage U on the leads of which changes by the harmonic law, to attach the Condenser C, then the charge Q on the condenser plays will also vary by harmonic law, as well as the current I in the chain. The greater the capacitor capacitance, and the higher the frequency F applied to it by the harmonic EMF, the greater the current I will be.

With this fact, an idea of \u200b\u200bthe so-called capacitive resistance of the capacitor XC is associated with the alternating current circuit, which limits the current is similar to the active resistance R, but in comparison with the active resistance, the capacitor does not dispel the energy in the form of heat.

If the active resistance dispels energy, and thus limits the current, then the condenser limits the current simply due to the fact that it does not have time to fit more than the generator than the generator can give a quarter of the period, besides the next quarter of the period, the condenser gives energy which has accumulated in the electric field of its dielectric, back to the generator, that is, at least the current is limited, the energy does not dissipate (losses in the wires and in dielectric negory).

Now consider the behavior of the inductance L in the AC circuit. If instead of the capacitor, connect the coil with the inductance L to the generator, which is submitted from the sinusoidal (harmonic) emf to the conclusions of the coil, - it will begin to occur in it EMF self-inductionbecause when changing the current through the inductance, the increasing magnetic field of the coil is committed to preventing the current growth (Lenza law), that is, it turns out that the coil introduces inductive resistance XL to the resistance of the wire R.

The greater the inductance of this coil, and the higher the frequency F of the current of the generator, the higher the inductive resistance of XL and less current I, because the current simply does not have time to be installed, because the emf of self-induccus the coil interferes. And every quarter of a period of energy accumulated in the magnetic field of the coil returns to the generator (losses in the wires until we neglect).

In any real oscillatory circuit, the inductance l, C and the active resistance R.

Inductance and capacity act on the current is the opposite to each quarter of the harmonic period EMF source: on the condenser plates, although the current decreases, and when the current increases through the inductance, the current is experiencing inductive resistance, but increases and is supported.

And during the discharge: the discharge current of the condenser is first large, the voltage on its plates is tended to establish a high current, and the inductance prevents the increase in current, and the more inductance, the smaller the discharge current will occur. At the same time, the active resistance R contributes purely active losses. That is, the impedance Z, successively turned on L, C and R, at the frequency of the source F, will be:

From the law of Oma for AC, it is obvious that the amplitude of the forced oscillations is proportional to the amplitude of the EDC and depends on the frequency. The total chain resistance will be the smallest, and the amplitude of the current will be the greatest, provided that the inductive resistance and capacitiveness at this frequency are equal to each other, in this case the resonance will come. From here it is displayed Formula for the resonant frequency of the oscillating circuit:

When the source of the EDS, the container, inductance and resistance are included in each other, then the resonance in such a chain is called serial resonance or stress resonance. The characteristic feature of the resonance of stresses is significant stresses on the container and inductance, compared with the EDC of the source.

The reason for the appearance of such a painting is obvious. On the active resistance according to the Ohm law, there will be a UR voltage, on the UC capacitance, on the UL inductance, and accounted for the ratio of the UC to the UR, you can find the Quality value Q. The voltage on the container will be in Q times the source of the source, the same voltage will be applied to inductance.

That is, the resonance of stress leads to an increase in the voltage on the reactive elements in Q times, and the resonance current will be limited to the EDC of the source, its internal resistance and the active resistance of the chain R. Thus, the resistance of the sequential circuit on the resonant frequency is minimal.

The phenomenon of stress resonance is used in, for example, if it is necessary to eliminate the transmitted signal of a specific frequency current, then the receiver put a chain from the connected condenser and inductance coils, so that the current frequency of this LC-chain is closed through it, and did not get to the receiver .

Then the currents of the frequency far from the resonant frequency of the LC chain will take place in the load freely, and only close to the resonance in the frequency of currents will find themselves the shortest path through the LC chain.

Or vice versa. If you need to skip the current of a certain frequency, the LC chain turns on the receiver sequentially, then the components of the signal on the resonant frequency of the chain will pass to the load almost without loss, and frequencies are far from the resonance will be very weakened and we can not say that the load will not fall at all. This principle Apply to radio receivers, where the rebuilt vibrational circuit is adjusted to the reception of a strictly defined frequency of the desired radio station.

In general, the stress resonance in electrical engineering is an undesirable phenomenon because it causes overvoltage and failure of the equipment.

As simple example You can bring a long cable line, which for some reason turned out to be not connected to the load, but it is powered by an intermediate transformer. Such a line with a distributed capacity and inductance, if its resonant frequency coincides with the frequency of the supply network, it will simply be broken and fails. To prevent the destruction of cables from random stress resonance, auxiliary load is used.

But sometimes the stress resonance plays us on hand and not only in radio receivers. For example, it happens that in the countryside, the voltage in the network has faltered unpredictably, and the machine needs a voltage of at least 220 volts. In this case, the phenomenon of stress resonance saves.

Surely consistently with the machine (if the asynchronous motor is the drive in it), turn on several capacitors per phase, and thus the voltage on the stator windings will rise.

It is important to correctly select the number of capacitors correctly so that they precisely compensated for their capacitive resistance together with the inductive resistance of the windings of the stress stage in the network, that is, slightly approaching the chain to resonance - you can lift the fallen voltage even under load.

When the EDC source, capacity, inductance and resistance are included in parallel, then the resonance in such a chain is called parallel resonance or reasons. A characteristic feature of the resonance of currents is significant currents through a container and inductance, compared with the current source.

The reason for the appearance of such a painting is obvious. Current via active resistance according to the Ohm law will be equal to U / R, through the capacity U / XC, through the inductance U / XL, and the ratio of the IL to I can be found to find the value of Q. Current through the inductance will be in Q times the source current is the same The current will flow every half of the period into the condenser and from it.

That is, the resonance of currents leads to an increase in current through the reactive elements in Q times, and the resonant EMF will be limited to the emf of the source, its internal resistance and the active resistance of the circuit R. Thus, on the resonant frequency, the resistance of a parallel oscillatory circuit is maximum.

Similar to stress resonance, current resonance is used in various filters. But the parallel contour is included in the chain, the parallel contour acts on the contrary, than in the case of serial: the parallel load, the parallel oscillatory circuit will allow the current circuit current to go into the load, since the resistance of the contour itself on its own resonant frequency is maximum.

Mounted sequentially with a load, a parallel oscillating circuit will not miss the signal of the resonant frequency, since all the voltage falls on the contour, and a meager fraction of the resonance frequency signal will have to be loaded.

Thus, the main use of the resonance of currents in radio engineering is the creation of a large resistance for a specific frequency current in lamp generators and high-frequency amplifiers.

In electrical engineering, the current resonance is used to achieve a high load coefficient of loads with significant inductive and capacitive components.

For example, constitute condensers connected in parallel winding asynchronous engines and transformers working under load below the nominal.

Such decisions are resorted to the aim of achieving resonance of currents (parallel resonance) when the inductive resistance of the equipment is made equal to the capacitive resistance of the connected capacitors at the network frequency so that the reactive energy is circulated between the capacitors and equipment, and not between the equipment and the network; So that the network gives energy only when the equipment is loaded and consumes active power.

When equipment works in idle, the network turns out to be connected parallel to the resonant contour (external capacitors and the inductance of the equipment), which represents a very large complex resistance for the network and reduces.