The resonance is such a chain operation mode, which includes inductive and capacitive elements in which its input resistance (input conductivity) is real. The consequence of this is the coincidence of the current phase at the inlet of the input voltage circuit.
Resonance in chains with successively connected elements
(stress resonance)
For the chain in Fig. 1 takes place
 ;
|
(1) |
 .
|
(2) |
Depending on the ratio of values \u200b\u200band three different cases are possible.
1. The circuit prevails inductance, i.e. , and consequently,
This regime corresponds to the vector diagram in fig. 2, a.
2. The circuit prevails the container, i.e. So. This case reflects the vector diagram in fig. 2, b.
3. - The case of stress resonance (Fig. 2, B).
Stress resonance condition
| . | (3) |
At the same time, as follows from (1) and (2), 
.
With the resonance of stresses or modes close to it, the current in the chain increases sharply. In the theoretical case, at r \u003d 0, its value tends to infinity. Accordingly, the increase in current increases voltages in inductive and capacitive elements that can largely exceed the power supply voltage voltage.
Let, for example, in the chain in Fig. one . Then, and, accordingly,.
The resonance phenomenon is useful in practice, in particular in radio engineering. However, if it occurs spontaneously, it can lead to emergency regimes due to the appearance of large overvoltages and overdocks.
The physical essence of the resonance lies in the periodic metabolization of the energy between the magnetic field of the inductance coil and the electric field of the capacitor, and the sum of the fields of the fields remains constant.
The essence of the case does not change if there are several inductive and capacitive elements in the chain. Indeed, in this case 
, and ratio (3) is performed for equivalent values \u200b\u200bof L E and C E.
As the analysis of equation (3) shows, the resonance mode can be achieved by changing the parameters L and C, as well as frequencies. Based on (3) for resonant frequency, you can record
 .
|
(4) |
Resonant curves Called the dependence of current and voltage from the frequency. As their example in Fig. 3 shows typical curves I (F); And for the chain in fig. 1 at u \u003d const.
An important characteristic of the resonant contour is quality Q, determined by the ratio of the inductive (capacitive) element to the input voltage:
or taking into account (4) and (5) for you can write:
 .
|
(9) |
Depending on the ratio of values \u200b\u200band, as in the sequential connection of the elements considered above, three different cases are possible.
The circuit prevails inductance, i.e. , and consequently, . This regime corresponds to the vector diagram in fig. 5, a.
Capacity prevails in the chain, i.e. So. This case illustrates a vector diagram in fig. 5 B.
Case of current resonance (Fig. 5, B).
Conduance of current resonance or
| . | (10) |
At the same time, as follows from (8) and (9), 
. Thus, when the currents are resonance, the input conductivity of the chain is minimal, and the input resistance, on the contrary, is maximally. In particular, in the absence of a chain in Fig. 4 Resistor R Its input resistance in resonance mode tends to infinity, i.e. With resonance current currents at the inlet of the chain is minimal.
The identity of relations (3) and (5) indicates that in both cases the resonant frequency is determined by the relation (4). However, the expression (4) should not be used for any resonant chain. It is valid only for the simplest schemes with a sequential or parallel compound of inductive and capacitive elements.
When determining resonant frequency In the circuit of an arbitrary configuration or, in general, the ratio of the parameters of the scheme in the resonance mode should be processed from the condition of the substance of the input resistance (input conductivity) of the chain.
For example, for the chain in Fig. 6 have
Since in resonance mode, the imaginary part must be zero, then the resonance condition has the form
,
where, in particular, there is a resonant frequency.
Resonance in a chain chain
The condition of resonance for a chain chain mixed compound Several inductive and capacitive elements concluded in the equality of zero the imaginary part of the input resistance or input conductivity determines the presence of equations in the corresponding condition of relative to several real roots, i.e. Such chains correspond to several resonant frequencies.
Phenomenon of resonance. The electrical circuit containing inductance and capacity can serve as a oscillatory circuit where the process of electrical energy oscillations occurs, moving from inductance to the container and back. In the perfect oscillatory circuit, these oscillations will be unsuccessful. When connecting the oscillating circuit to the source alternating current Corner source frequency? May be equal to an angular frequency? 0, which occurs fluctuations in electrical energy in the circuit. In this case, there is a phenomenon of resonance, i.e. coincidences of frequency of free oscillations? 0, arising in any physical system, with the frequency of forced oscillations?, Informed by this system by external forces.
Resonance in the electrical circuit can be obtained in three ways: changing the angular frequency? AC source, inductance L, or C. C. C. distinguish the resonance when sequential connection L and C - voltage resonance And with their parallel connection - reasons. Corner frequency? 0, at which resonance comes, is called resonant, or own frequency oscillations of the resonant circuit.
Resonance stress. With stress resonance (Fig. 196, a) inductive resistance x l is equally capacitive x withand the impedance Z becomes equal to the active resistance R:
Z \u003d? (R 2 + [? 0 L - 1 / (? 0 c)] 2) \u003d r
In this case, the voltage on the inductance U l and the tank U c is equal to and are located in antiphase (Fig. 196, b), so when adding, they compensate for each other. If the active resistance of the chain R is small, the current in the chain increases sharply, since the chain reactive resistance X \u003d x l -x with It becomes equal to zero. At the same time, the current I coincides in phase with the voltage U and i \u003d u / r. A sharp increase in current in the chain with stress resonance causes the same increase in the voltages U L and U C, and their values \u200b\u200bcan largely exceed the voltage U of the source supplying the circuit.
Corner frequency? 0, at which there is a resonance condition, is determined from equality ? O l \u003d 1 / (? 0 s).
From here you have
? O \u003d 1 /? (LC) (74)
If you smoothly change the angular frequency? Source, the complete resistance Z is first begins to decrease, reaches the smallest value in the stress resonance (at? O), and then increases (Fig. 197, a). In accordance with this, the current I in the chain first increases, reaches the greatest value during resonance, and then decreases.
Current resonance. Current resonance may occur with parallel compound of inductance and container (Fig. 198, a). In the ideal case, when there is no active resistance in parallel branches (R 1 \u003d R 2 \u003d 0), the condition of the current resonance is the equality of the reactive resistance of branches containing inductance and capacity, i.e. ? O l \u003d 1 / (? o C). Since in the case under consideration Active conductivity G \u003d 0, current in a unbranched part
Chains with resonance I \u003d u? (G 2 + (b l -b c) 2) \u003d 0. The values \u200b\u200bof currents in branches I 1 and i 2 will be equal (Fig. 198, b), but currents will be shifted by a phase 180 ° (current IL in inductance lags in phase from the voltage U 90 °, and the current in the tank I with ahead of U 90 ° voltage). Consequently, such a resonant contour is for current I infinitely large resistance and electrical energy in the contour from the source does not come. At the same time, currents I L and I C, i.e., the process of continuous exchange of energy inside the contour takes place inside the contour. This energy moves from the inductance into the container and back.
As follows from formula (74), changing the values \u200b\u200bof the container with or inductance l, can change the frequency of oscillations? 0 electrical energy and current in the circuit, i.e., adjust the circuit to the desired frequency. If in the branches in which the inductance and capacity were included, there was no active resistance, this process of energy oscillations would continue indefinitely, i.e., there would be unlucky energy oscillations and currents I L and I s. However, real inductance coils and capacitors always absorb electrical energy (due to the presence in coils of active resistance of wires and occurrence
in the condensers of the shift currents heating dielectric), therefore, in the actual circuit, some electrical energy flows from the source and the unbranched part of the chain flows some current I.
The resonance condition in the real resonant contour containing the active resistance R 1 and R 2 will be the equality of jet conductors B L \u003d B with branches in which the inductance and capacity are included.
From fig. 198, it follows that the current I in the unbranched part of the chain coincides in phase with the voltage U, since the reactive currents of 1 L and I C are equal, but are opposed to phase, as a result of which their vector amount is zero.
If in the parallel chain in question change the frequency? About the source of alternating current, then the total resistance of the chain begins to increase, reaches the greatest value in the resonance, and then decreases (see Fig. 197, b). In accordance with this, current I begins to decrease, reaches the smallest value i min \u003d i a with resonance, and then increases.
In real oscillatory circuits containing active resistance, each fluctuation of current is accompanied by energy loss. As a result, the reported loop energy is quite quickly spent and current fluctuations are gradually faded. To obtain unlightening oscillations, it is necessary to replenish energy losses in the active resistance all the time, i.e. this circuit must be connected to the source of the alternating current of the corresponding frequency? 0.
The phenomena of stress and current resonance and the oscillating circuit were very widely used in radio engineering and high-frequency installations. With the help of oscillatory contours, we obtain high frequency currents in various radio devices and high-frequency generators. The oscillating circuit is the most important element of any radio. It provides its selectivity, i.e. the ability to allocate from radio signals with different wavelengths (i.e. with different frequencies) sent by various radio stations, signals of a certain radio station.
Resonance of currents, well known as a natural current "parallel resonance" - a process or a phenomenon that flows under conditions of a parallel type of oscillatory circuit and the presence of a voltage.
In this case, the frequency of the voltage source must have a coincidence with similar contour resonance indicators.
A current resonance is a special type of chain state, when the total current indicators coincide on phase parameters with a voltage level, and the reactive is zero and the chain is consumed only active power.
This option is characteristic mainly for schemes with variable indicators of current values \u200b\u200band has not only positive properties, but also some completely undesirable qualities that are necessarily taken into account even during the design process.
A positive resonant action is a phenomenon from the field of radio engineering, automation and wire telephony. The stress resonance refers to the category of unwanted phenomena due to overvoltages. In this case, the good electric contour is considered to be the value:
The achievement of current resonance is carried out by selecting the necessary inductive or capacitive value, as well as indicators of the frequency of the feeding networks.
The current resonance is obtained by the selection of the parameters of the electrocups in the conditions of the specified frequency of the power supply, as well as by selecting the inverse indicators.
Application of current resonance
The main area of \u200b\u200bactive application of widely demanded resonant currents is presented today:
- some kinds of filtering systems, in which the current with certain frequency parameters turns out to be significant resistance indicators;
- radio engineering in the form of receivers excreasing signals intended for specific points of radio stations. The provision of significant current resistance is accompanied by a decrease in the indicators of contour voltage at maximum frequency;
- asynchronous type engines, especially functioning in terms of incomplete load;
- installations of high-precision electrical welding;
- oscillatory contours inside electronic type generators nodes;
- devices characterized by high-frequency hardening;
- reduced generator load indicators. Under such conditions, an oscillating circuit is made in the receiving transformer with the primary winding.
Chain scheme
Especially often oscillatory contours or current resonances are used in the production of modern industrial induction boiler equipment, which makes it possible to largely improve the starting indicators of the efficiency.
Standard oscillatory contours operating under conditions of current resonance mode are massively used as one of the most important nodes in modern electronic generators.
The principle of resonance of currents
The current resonance is observed inside the electrocups with parallel coil, resistor and condenser connection. The main principle of the standard current resonance is not too complicated for understanding a simple manual:
- power on the power supply is accompanied by the accumulation of charge inside the capacitor to the nominal source voltage indicators;
- turning off the supply source with the subsequent circuit of the circuit in the contour is accompanied by the process of discharge transfer to the coil part of the device;
- the current indicators passing through the coil cause the magnetic field generation and the creation of the electromotive power of self-induction, in the direction, in the countercurrent;
- the maximum value of current indicators is achieved at the stage of a complete condenser discharge;
- the entire volume of the accumulated energy tank is easily converted into a magnetic induction field;
- the coil self-induction does not provoke the stopping of charged particles, and the repeated step of charging with another type of polarity is due to the absence of a condenser countercurrent.
Resonance in a parallel chain (current resonance)
The result of this cycle is the repeated transformation of the entire coil field into a condenser charge. The definition of standard resonant frequency is carried out similarly to the calculations of the resonance of the voltage.
The present inner active component R causes a gradual focusing of the oscillatory process than and the current resonance is caused.
Current resonance in chain with alternating current
Current flow inside the electrical circuit with a serial, parallel or mixed type of connection of the elements, causes receipt various modes functioning.Thus, the resonance of the electrical circuit is a portion mode that contains the elements of an inductive and capacitive type, and the angle of the phase shift between the current values \u200b\u200band the voltage indicators are zero.
In the capacitor connected by a parallel method, an equal reactive resistance is observed than the resonance is due.
The fact that for the coil part and the capacitor is characterized by a complete absence of active resistance, and the equality of reactive resistance makes zero common currents inside the unbranched part of the electrical circuit and large current values \u200b\u200bin the branches.
In conditions of parallel connection of the inductive coil and the capacitor, a oscillating circuit is obtained, which is distinguished by the presence of a generator-creating oscillation that is not connected to the circuit, which makes the system closed.
The phenomenon accompanied by a sharp decrease in the amplitude of the strength of the current values \u200b\u200bof the external circuit, which is used to power the parallel condenser turned on and the conventional inductive coil under the conditions of approximation of the value of the applied voltage to the frequency of the resonance, is called a current or parallel resonance.
Calculation of resonant contour
It must be remembered that the phenomenon represented by the current resonance needs a very competent and thorough calculation of the resonant circuit. It is especially important to perform the correct and accurate calculation in the presence of a parallel compound, which will prevent the development of interference inside the system. To calculate the correct, it is required to determine the power indicators electrical network. The average standard power, which is dissipated under the conditions of the resonant circuit, can be expressed by the standard and voltage and voltage.
In resonance, the standard power factor is unit, and the calculation formula has the form:
Formula of calculation
In order to correctly determine the zero impedance in resonance conditions, it will be necessary to use the standard formula:
Resonant curves
The resonance of the oscillatory frequency is approximated by the following formula:
Resonance of the oscillating circuit
To obtain the most accurate policy of the formulas, all the value obtained during the calculation process is recommended not to be rounded. Some physicists calculate the values \u200b\u200bof the resonant circuit are carried out in accordance with the vector diagram of active current values. In this case, the competent calculation and proper setting Devices guarantees worthy savings under the condition of AC.
Resonance chains are used primarily to highlight the signal at the desired frequencies as a result of filtering other signals, so independent calculations of the contour must be extremely accurate.
Conclusion
The resonance of current values \u200b\u200bin physics is a natural phenomenon accompanied by a sharp increase in the amplitude of oscillation inside the system, which is due to the coincidence of the indicators of its own and external perturbing frequencies.
Similar phenomena characterizes electrical circuits With the presence of elements presented by loads of active, inductive and capacitive type. Thus, the current resonance is one of naive parametersWidely used in general in a number of modern industries, including industrial electrical supply and radio communication.
The phenomenon of the resonance of currents and stress is observed in the circuits of an inductive-capacitive nature. This phenomenon has found application in electronics, becoming the main ways to adjust the receiver on a certain wave. Unfortunately, the resonance can harm electrical equipment and cable lines. In physics, the resonance is the coincidence of the frequencies of several systems. Let's look at what kind of stress resonance and currents, what value it has and where is used in electrical engineering.
Reactive inductance and capacity
Inductance is the body's ability to accumulate energy in a magnetic field. It is characterized by a current lag from phase voltage. Characteristic inductive elements - choke, coils, transformers, electric motors.
Capacity is called elements that accumulate energy with electric field. For capacitive elements, the backlog of the voltage phase is characteristic. Capacitive elements: condensers, varicaps.
Their main properties are given, the nuances within this article are not taken into account.
In addition to the listed elements, others also have a certain inductance and container, for example in electrical cables distributed by its length.
Capacity and inductance in AC circuit
If in the DC circuits, the container in the general sense is a torn area of \u200b\u200bthe chain, and the inductance is a conductor, then in variable capacitors and coils are a reactive analogue of the resistor.
The reactive resistance of the inductance coil is determined by the formula:
Vector diagram:
Condenser reactive resistance:
Here W is an angular frequency, F - frequency in the sinusoidal current chain, L is inductance, C - capacity.
Vector diagram:
It should be noted that when calculating the connected sequentially jet elements use the formula:
Please note that the capacitive component is accepted with a minus sign. If there is also an active component (resistor) in the chain, then the formula of the Pythagora theorem (based on the vector diagram) is folded:
What does the reactive resistance depend on? The reactive characteristics depend on the size of the tank or inductance, as well as from the frequency of the AC.
If you look at the formula of the reactive component, it can be noted that with certain values \u200b\u200bof the capacitive or inductive component, their difference will be zero, then only active resistance will remain in the chain. But this is not all the features of such a situation.
Voltage resonance
If it is consistent with the generator to connect the condenser and the inductor coil, then, if the equality of their reactive resistance, the stress resonance will occur. In this case, the active part Z should be as small as possible.
It is worth noting that inductance and capacity has only reactive qualities in idealized examples. In the real circuits and elements there is always active resistance of conductors, even though it is extremely small.
With resonance, the energy exchange between the throttle and the condenser occurs. In ideal examples, at the initial connection of the energy source (generator), the energy accumulates in the condenser (or choke) and, after its disconnection, there are unlucky oscillations due to this exchange.
Voltages on inductance and containers are approximately the same, according to:
Where X is XC capacitive or XL inductive resistance, respectively.
The circuit consisting of inductance and capacity is called a oscillatory contour. Its frequency is calculated by the formula:
The period of oscillations is determined by the Thompson formula:
Since the reactive resistance depends on the frequency, the resistance of the inductance with increasing frequency increases, and the container drops. When the resistance is equal, then the overall resistance is much reduced, which is reflected in the chart:
The main characteristics of the contour are Quality (Q) and frequency. If you consider the contour as a quadrupole, then its transmission coefficient after simple computing is reduced to Quality:
And the voltage at the conclusions of the chain increases in proportion to the coefficient of transmission (volunteability) of the contour.
UK \u003d UVH * Q
With stress resonance, the higher the Quality, the greater the voltage on the circuit elements will exceed the voltage of the connected generator. Voltage can rise in tens and hundreds of times. This is displayed on the schedule:
Power loss in the circuit is due only to the presence of active resistance. Energy from the power supply is taken only to maintain oscillations.
The power factor will be equal to:
This formula shows that losses occur due to active power:
S \u003d P / COSF
Current resonance is observed in circuits where inductance and capacity are connected in parallel.
The phenomenon is the flow of currents of the large size between the condenser and the coil, at zero current in the unbranched part of the chain. This is explained by the fact that when the resonant frequency is reached, the general resistance z increases. Or simple language It sounds like this - at the resonance point, the maximum total value of resistance z is achieved, after which one of the resists increases, and the other decreases depending on whether the frequency increases or decreases. It is clearly displayed on the schedule:
In general, everything is similar to the previous phenomenon, the conditions for the emergence of the resonance of currents are as follows:
- The frequency of food is similar to the contour resonant.
- Conductures in inductance and containers for variable current are equal to BL \u003d BC, B \u003d 1 / X.
Application in practice
Consider what the benefits and harm of the resonance of currents and stresses. The greatest benefit of the resonance phenomenon was brought in the radio transmission equipment. Simple words, and the receiver scheme is installed coil and condenser connected to the antenna. By changing the inductance (for example, moving the core) or the size of the container (for example, an air alternating condenser), you adjust the resonant frequency. As a result, the voltage on the coil rises and the receiver catches a certain radio wave.
The harm of these phenomena can be carried in electrical engineering, for example, on cable lines. The cable is a distributed inductance and capacity distributed in length, if the long line is to submit a voltage in idling mode (when the load is not connected to the end of the cable from the power source). Therefore, there is a danger that the insulation breakage will occur, the load ballast is connected to avoid this. Also, a similar situation can lead to the failure of electronic components, measuring instruments And other electrical equipment is the dangerous effects of this phenomenon.
Conclusion
Resonance of stresses and currents is an interesting phenomenon that you need to know. It is observed only in inductively capacitive circuits. In chains with greater active resistances, it cannot arise. Let's summarize, briefly answering the main questions on this topic:
- Where and in which chains there is a phenomenon of resonance?
In inductively capacitive circuits.
- What are the conditions for the emergence of reasance and voltage resonance?
It occurs under the condition of the equality of jet resistance. In the chain there must be minimal active resistance, and the frequency of the power source is coincided with the resonant frequency of the contour.
- How to find a resonant frequency?
In both cases by the formula:w \u003d (1 / LC) ^ (1/2)
- How to eliminate phenomenon?
By increasing the active resistance in the chain or changing the frequency.
Now you know what resonance of currents and stresses, what are the conditions for its occurrence and applications in practice. To secure the material, we recommend viewing a useful video.
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.
The inductance and capacity act on the current opposite to each quarter of the period of the harmonic EMF of the 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 stresses leads to an increase in the voltage on the jet elements in Q times, and the resonant current will be limited to the EMF 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.
