The principles of radio communication. Energy of resonance. Some examples of the manifestation and application of resonance in nature and technology Application of electrical resonance in radio communication

Knowledge of physics and theory of this science is directly related to housekeeping, renovation, construction and mechanical engineering. We propose to consider what is the resonance of currents and voltages in a serial RLC circuit, what is the main condition for its formation, as well as calculation.

What is resonance?

Determination of the phenomenon by TOE: electrical resonance occurs in an electric circuit at a certain resonant frequency, when some parts of the resistances or conductivities of the circuit elements compensate each other. In some circuits, this occurs when the impedance between the input and the output of the circuit is nearly zero and the signal transfer function is close to unity. In this case, the quality factor of this circuit is very important.

Signs of resonance:

The components of the reactive current branches are equal to each other IPC \u003d IPL, the antiphase is formed only when the net active energy at the input is equal;
The current in individual branches exceeds the entire current of a particular circuit, while the branches are in phase.

In other words, resonance in an AC circuit implies a special frequency, and is determined by the values \u200b\u200bof resistance, capacitance and inductance. There are two types of resonance currents:

Consistent;
Parallel.

For series resonance, the condition is simple and characterized by minimum resistance and zero phase, it is used in reactive circuits, and it is also used by a branched circuit. Parallel resonance, or the concept of RLC, occurs when inductive and capacitive data are equal in magnitude, but cancel each other out as they are 180 degrees apart. This connection must always be equal to the specified value. It has received wider practical application. The sharp minimum impedance that it exhibits is beneficial for many electrical household appliances. The sharpness of the minimum depends on the amount of resistance.

An RLC (or circuit) circuit is an electrical circuit that consists of a resistor, an inductor, and a capacitor connected in series or in parallel. The RLC parallel oscillatory circuit got its name from the abbreviation for physical quantities, which are, respectively, resistance, inductance and capacitance. The circuit forms a harmonic oscillator for the current. Any oscillation of the current induced in the circuit attenuates over time, if the movement of directed particles is stopped by the source. This resistor effect is called damping. The presence of resistance also reduces the peak resonant frequency. Some resistance is unavoidable in real circuits, even if no resistor is included in the circuit.

Application

Almost all power electrical engineering uses just such an oscillatory circuit, say, a power transformer. Also, the circuit is necessary for setting up the operation of a TV, a capacitive generator, a welding machine, a radio receiver, it is used by the technology of "matching" television broadcasting antennas, where you need to select a narrow frequency range of some of the waves used. The RLC circuit can be used as a band-pass, notch filter, for sensors to distribute low or high frequencies.

Resonance is even used by aesthetic medicine (microcurrent therapy) and bioresonance diagnostics.

Resonance principle of currents

We can make a resonant or oscillatory circuit at a natural frequency, say, to power a capacitor, as the following diagram demonstrates:

Capacitor power circuit

The switch will be responsible for the direction of vibration.

Circuit: Resonant circuit switch

The capacitor stores all the current at the moment when the time \u003d 0. The fluctuations in the circuit are measured with ammeters.

Circuit: The current in the resonant circuit is zero

Directional particles move to the right. The inductor takes current from the capacitor.

When the polarity of the circuit returns to its original form, the current returns to the heat exchanger again.

Now the directed energy goes back into the capacitor, and the circle repeats again.

In real mixed circuit circuits, there is always some resistance that causes the amplitude of the directional particles to grow less with each circle. After several changes in the polarity of the plates, the current decreases to 0. This process is called a sinusoidal decaying waveform. How quickly this process takes place depends on the resistance in the circuit. However, the resistance does not change the frequency of the sine wave. If the resistance is high enough, the current will not fluctuate at all.

The AC designation means that when it leaves the power supply, the energy fluctuates at a specific frequency. An increase in resistance tends to reduce the maximum size of the current amplitude, but this does not lead to a change in the resonance frequency (resonant). But an eddy current process can form. After its occurrence, network interruptions are possible.

Resonant circuit calculation

It should be noted that this phenomenon requires a very careful calculation, especially if a parallel connection is used. In order to avoid interference in technology, you need to use different formulas. They will also come in handy for solving any physics problem from the corresponding section.

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

R cf \u003d I 2 pin * R \u003d (V 2 pin / Z 2) * R.

However, remember that the power factor at resonance is cos φ \u003d 1

The resonance formula itself has the following form:

ω 0 \u003d 1 / √L * C

Zero impedance at resonance is determined using this formula:

F res \u003d 1 / 2π √L * C

The resonant vibration frequency can be approximated as follows:

F \u003d 1/2 p (LC) 0.5

Where: F \u003d frequency

L \u003d inductance

C \u003d capacity

Typically, the circuit will not oscillate unless the resistance (R) is low enough to satisfy the following requirements:

R \u003d 2 (L / C) 0.5

To obtain accurate data, you should try not to round the resulting values \u200b\u200bas a result of calculations. Many physicists recommend using a method called active current vector diagram. With the correct calculation and setting of devices, you will get good AC savings.

In an oscillating circuit with inductance L, capacitance C and resistance R, free electrical oscillations tend to damp. To prevent the oscillations from damping, it is necessary to periodically replenish the circuit with energy, then forced oscillations will arise that will not attenuate, because the external variable EMF will now support the oscillations in the circuit.

If the oscillations are supported by a source of external harmonic EMF, the frequency of which f is very close to the resonant frequency of the oscillatory circuit F, then the amplitude of electrical oscillations U in the circuit will increase sharply, that is, electrical resonance phenomenon.

Let us first consider the behavior of the capacitor C in the AC circuit. If a capacitor C is connected to the generator, the voltage U at the terminals of which changes according to the harmonic law, then the charge q on the capacitor plates will begin to change also according to the harmonic law, like the current I in the circuit. The larger the capacitance of the capacitor, and the higher the frequency f of the harmonic EMF applied to it, the greater the current I.

This fact is related to the idea of \u200b\u200bthe so-called capacitance of the capacitor XC, which it introduces into the alternating current circuit, limiting the current similar to the active resistance R, but in comparison with the active resistance, the capacitor does not dissipate energy in the form of heat.

If the resistance dissipates energy, and thus limits the current, then the capacitor limits the current simply due to the fact that it does not have time to fit more charge than the generator can give in a quarter of a period, moreover, in the next quarter of a period, the capacitor gives off energy, which has accumulated in the electric field of its dielectric, back to the generator, that is, although the current is limited, the energy is not dissipated (we will neglect the losses in the wires and in the dielectric).

Now consider the behavior of inductance L in an alternating current circuit. If, instead of a capacitor, a coil with inductance L is connected to the generator, then when a sinusoidal (harmonic) EMF is supplied from the generator to the coil terminals, it will begin to appear EMF of self-induction, since when the current through the inductance changes, the increasing magnetic field of the coil tends to prevent the growth of current (Lenz's law), that is, it turns out that the coil introduces inductive resistance XL into the AC circuit - additional to the resistance of the wire R.

The greater the inductance of a given coil, and the higher the frequency F of the generator current, the higher the inductive resistance XL and the lower the current I, because the current simply does not have time to be established, because the EMF of the self-induction of the coil interferes with it. And every quarter of the period, the energy accumulated in the magnetic field of the coil returns to the generator (we will neglect the losses in the wires for now).

In any real oscillatory circuit, inductance L, capacitance C and active resistance R are connected in series.

Inductance and capacitance act on the current in the opposite way in every quarter of the period of the harmonic EMF of the source: on the capacitor plates, although the current decreases, and as the current through the inductance rises, the current, although it experiences inductive resistance, increases and is maintained.

And during the discharge: the discharge current of the capacitor is at first large, the voltage on its plates tends to establish a large current, and the inductance prevents an increase in the current, and the larger the inductance, the lower the discharge current will take place. In this case, the active resistance R introduces purely active losses. That is, the impedance Z of L, C and R connected in series at a source frequency f will be:

It is obvious from Ohm's law for alternating current that the amplitude of forced oscillations is proportional to the amplitude of the EMF and depends on the frequency. The total resistance of the circuit will be the smallest, and the amplitude of the current will be the largest, provided that the inductive resistance and capacitive at a given frequency are equal to each other, in this case, resonance will occur. From here it is also derived formula for the resonant frequency of the oscillating circuit:

When the EMF source, capacitance, inductance and resistance are connected in series with each other, then the resonance in such a circuit is called series resonance or voltage resonance. A characteristic feature of the voltage resonance is significant voltages on the capacitance and on the inductance, in comparison with the EMF of the source.

The reason for this picture is obvious. On the active resistance, according to Ohm's law, there will be a voltage Ur, on the capacitance Uc, on the inductance Ul, and having made the ratio of Uc to Ur, we can find the value of the quality factor Q. The voltage across the capacitance will be Q times greater than the EMF of the source, the same voltage will be applied to the inductance.

That is, the voltage resonance leads to an increase in the voltage across the reactive elements by a factor of Q, and the resonant current will be limited by the EMF of the source, its internal resistance and the active resistance of the circuit R. Thus, the resistance of the series circuit at the resonant frequency is minimal.

The phenomenon of voltage resonance is used in, for example, if it is necessary to eliminate a current component of a certain frequency from the transmitted signal, then a chain of capacitor and inductance connected in series is placed in parallel to the receiver so that the resonant frequency current of this LC chain would be closed through it and would not get to the receiver ...

Then the currents of the frequency far from the resonant frequency of the LC-chain will pass into the load without hindrance, and only currents close to the resonance in frequency will find themselves the shortest path through the LC-chain.

Or vice versa. If it is necessary to pass only a current of a certain frequency, then the LC-chain is connected in series to the receiver, then the signal components at the resonant frequency of the chain will pass to the load almost without loss, and the frequencies far from resonance will be greatly weakened and we can say that they will not get to the load at all. This principle is applicable to radio receivers, where a tunable oscillatory circuit is tuned to receive a strictly defined frequency of the desired radio station.

In general, voltage resonance in electrical engineering is an undesirable phenomenon as it causes overvoltage and equipment failure.

A simple example is a long cable line, which for some reason turned out to be not connected to the load, but at the same time is powered by an intermediate transformer. Such a line with a distributed capacitance and inductance, if its resonant frequency coincides with the frequency of the supply network, will simply be broken and fail. To prevent damage to cables from accidental voltage resonance, an auxiliary load is applied.

But sometimes the voltage resonance plays into our hands and not only in radios. For example, it happens that in rural areas, the voltage in the network has dropped unpredictably, and the machine needs a voltage of at least 220 volts. In this case, the phenomenon of voltage resonance saves.

It is enough to turn on several capacitors per phase in series with the machine (if the drive in it is an asynchronous motor), and thus the voltage on the stator windings will rise.

Here it is important to choose the right number of capacitors so that they accurately compensate with their capacitance along with the inductive resistance of the windings the voltage drop in the network, that is, by slightly bringing the circuit closer to resonance, you can raise the dropped voltage even under load.

When the EMF source, capacitance, inductance and resistance are connected in parallel with each other, then the resonance in such a circuit is called parallel resonance or resonance of currents. A characteristic feature of the resonance of currents is significant currents through the capacitance and inductance, compared to the source current.

The reason for this is obvious. The current through the active resistance according to Ohm's law will be equal to U / R, through the capacitance U / XC, through the inductance U / XL, and by making the ratio of IL to I, you can find the value of the quality factor Q. The current through the inductance will be Q times greater than the source current, the same current will flow every half a period into and out of the capacitor.

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

Similar to voltage resonance, current resonance is used in various filters. But connected to the circuit, the parallel circuit acts in the opposite way than in the case of the serial one: installed parallel to the load, the parallel oscillatory circuit will allow the current of the resonant frequency of the circuit to pass into the load, since the resistance of the circuit itself at its own resonant frequency is maximum.

Installed in series with the load, the parallel oscillatory circuit will not pass the resonant frequency signal, since all the voltage will drop on the circuit, and the load will have a tiny fraction of the resonant frequency signal.

So, the main application of the resonance of currents in radio engineering is the creation of a large resistance for a current of a certain frequency in tube generators and high-frequency amplifiers.

In electrical engineering, current resonance is used to achieve a high power factor of loads that have significant inductive and capacitive components.

For example, they are capacitors connected in parallel with the windings of asynchronous motors and transformers operating under a load below rated.

Such solutions are resorted to precisely in order to achieve resonance of currents (parallel resonance), when the inductive resistance of the equipment is made equal to the capacitance of the connected capacitors at the network frequency, so that reactive energy circulates between the capacitors and the equipment, and not between the equipment and the network; so that the network gives off energy only when the equipment is loaded and consumes active power.

When the equipment is idle, the network is connected in parallel with the resonant circuit (external capacitors and the inductance of the equipment), which presents a very high complex impedance for the network and allows it to decrease.

Resonance in physics is a phenomenon in which the amplitudes of system oscillations increase sharply. This occurs when the natural and external disturbing frequencies coincide. An example in mechanics is the pendulum of a clock. This behavior is also typical for electrical circuits that include elements of active, inductive and capacitive loads. The resonance of currents and voltages is very important, this phenomenon has found application in such fields of science as radio communication and industrial power supply.

Vectors and theory

To understand the meaning of the processes occurring in circuits, including inductors, capacitors and active resistances, one should consider the scheme of the simplest oscillatory circuit. Just as an ordinary pendulum alternately transfers energy from the potential to the kinetic state, the electric charge in the RCL-chain, accumulating in the capacitor, flows into inductance. After that, the process goes in the opposite direction, and everything starts over. In this case, the vector diagram looks as follows: the capacitive load current is ahead of the voltage direction by an angle π / 2, the inductive load lags behind by the same angle, and the active load is in phase. The resulting vector has a slope with respect to the abscissa, denoted by the Greek letter φ. Resonance in the alternating current circuit occurs when φ \u003d 0, respectively, cos φ \u003d 1. Translated from the language of mathematics, this calculation means that the current passing through all the elements in phase coincides with the current in the active component of the electrical circuit.

Practical application in power supply systems

In theory, all these calculations are understandable, but what do they mean for practical questions? A lot of things! Everyone knows that useful work in any circuit is performed by the active component of the power. At the same time, most of the energy consumption is accounted for by electric motors, of which there are many in any enterprise, and they contain windings in their design, which are an inductive load and create an angle φ that is different from zero. In order for the currents to resonate, it is necessary to compensate for the reactances so that their vector sum becomes zero. In practice, this is achieved by turning on a capacitor that creates an opposite shift in the current vector.

Resonance of currents in radio receivers

The resonance of currents has another, radio engineering application. The oscillating circuit, which forms the basis of each receiving device, consists of an inductor and a capacitor. By changing the value of the electrical capacitance, it is possible to achieve that the signal with the required carrier frequency will be received selectively, and the remaining all-wave components received by the antenna, including interference, will be suppressed. In practice, such a variable capacitor looks like two sets of plates, one of which, during rotation, enters or exits the other, increasing or decreasing the electrical capacitance. This creates a resonance of the currents, and the radio receiver is tuned to the desired frequency.

If the frequency of the natural oscillations of the circuit coincides with the frequency of the change in the external force, then the phenomenon of resonance occurs. In an electric oscillatory circuit, the role of an external periodic force is played by a generator, which provides a change in the electromotive force according to the harmonic law:

while natural electromagnetic oscillations occur in a circuit with a frequency ω about. if the active resistance of the circuit is small, then the natural frequency of oscillations is determined by the formula:

The current strength during forced oscillations (or the voltage across the capacitor) should reach a maximum value when the frequency of the external emf (1) is equal to the natural frequency of the oscillating circuit:

Resonance in an electric oscillatory circuit is the phenomenon of a sharp increase in the amplitude of forced current fluctuations (voltage across a capacitor, inductance coil) when the natural frequency of the circuit oscillations and the external emf coincide. Such changes at resonance can reach values \u200b\u200bof multiples of hundreds of times.

In a real oscillatory circuit, the establishment of amplitude oscillations in the circuit does not occur immediately. The maximum at resonance is obtained the higher and sharper, the lower the active resistance and the greater the inductance of the circuit:. The active resistance R plays a large role in the circuit. Indeed, it is the presence of this resistance that leads to the conversion of the energy of the electric field into the internal energy of the conductor (the conductor heats up). This suggests that the resonance in the electric oscillatory circuit should be clearly expressed at a low active resistance. In this case, the establishment of amplitude oscillations occurs gradually. So, the amplitude of the current fluctuations increases until the energy released during the period on the resistor equals the energy entering the circuit during this time. So at R → 0, the resonant value of the current increases sharply. Whereas with an increase in active resistance, the maximum value of the current strength decreases, and it makes no sense to talk about resonance at large values \u200b\u200bof R.

Figure: 2. Dependence of the amplitude of the voltage across the capacitor on the frequency of the emf:

1 - resonance curve with the resistance of the circuit R1;
2 - resonance curve at circuit resistance R2;

3 - resonance curve with the resistance of the circuit R3

The phenomenon of electrical resonance is widely used in radio communication. Radio waves from different transmitting stations excite alternating currents of different frequencies in the antenna of the radio receiver, since each transmitting radio station operates at its own frequency.
An oscillatory circuit is inductively connected to the antenna. As a result of electromagnetic induction, variable emf of the corresponding frequencies and forced oscillations of the current strength of the same frequencies appear in the loop coil. But only at resonance, the fluctuation of the current in the circuit and the voltage on the circuit will be significant. Therefore, of all the frequencies excited in the antenna, the circuit selects only oscillations whose frequency is equal to the natural frequency of the circuit. Tuning the circuit to the desired frequency ω0 is usually carried out by changing the capacitance of the capacitor.

In some cases, resonance in an electrical circuit can be harmful. So, if the circuit is not designed to work under resonance conditions, then the occurrence of resonance will lead to an accident: high voltages will lead to insulation breakdown. Accidents of this kind often happened in the 19th century, when people had a poor idea of \u200b\u200bthe laws of electrical oscillations and did not know how to calculate electrical circuits.

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Resonance. Its application

Resonance in an electric oscillatory circuit is called the phenomenon of a sharp increase in the amplitude of forced current oscillations when the frequency of the external alternating voltage coincides with the natural frequency of the oscillatory circuit.

resonance voltage electrical medicine

Using Resonance

In medicine

Magnetic resonance imaging, or its abbreviated name MRI, is considered one of the most reliable methods of radiation diagnostics. The obvious advantage of using this method to check the state of the body is that it is not ionizing radiation and gives fairly accurate results when examining the muscular and articular systems of the body, helps with a high probability of diagnosing various diseases of the spine and the central nervous system.

The examination process itself is quite simple and absolutely painless - everything that you hear is just loud noise, but it is well protected by headphones that the doctor will give you before the procedure. There are only two kinds of inconvenience that cannot be avoided. First of all, this applies to those people who are afraid of confined spaces - the diagnosed patient lies down on a horizontal bed and automatic relays move him inside a narrow tube with a strong magnetic field, where he stays for about 20 minutes. During the diagnosis, you should not move in order to get the results as accurate as possible. The second inconvenience caused by resonance imaging in the study of the small pelvis is the need for a full bladder.

If your loved ones want to be present during the diagnosis, they are required to sign an information document, according to which they are familiar with the rules of conduct in the diagnostic office and have no contraindications for being near a strong magnetic field. One of the reasons for the impossibility of being in the MRI control room is the presence of foreign metal components in the body.

Usethe use of resonance in radio communications

The phenomenon of electrical resonance is widely used in radio communication. Radio waves from different transmitting stations excite alternating currents of different frequencies in the antenna of the radio receiver, since each transmitting radio station operates at its own frequency. An oscillatory circuit is inductively connected to the antenna (Fig. 4.20). Due to electromagnetic induction, variable EMF of the corresponding frequencies and forced oscillations of the current strength of the same frequencies appear in the loop coil. But only at resonance, the oscillations of the current in the circuit and the voltage in it will be significant, that is, from the oscillations of various frequencies excited in the antenna, the circuit selects only those whose frequency is equal to its natural frequency. Tuning the loop to the desired frequency is usually done 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 the electrical circuit. In some cases, resonance in an electrical circuit can be very harmful. If the circuit is not designed to operate under resonance conditions, then resonance may result in an accident.

Excessive currents can overheat the wires. Large voltages lead to insulation breakdown.

Accidents of this kind often happened relatively recently, when the laws of electrical oscillations were poorly understood and did not know how to correctly calculate electrical circuits.

With forced electromagnetic vibrations, resonance is possible - a sharp increase in the amplitude of the current and voltage fluctuations when the frequency of the external alternating voltage coincides with the natural vibration frequency. All radio communication is based on the phenomenon of resonance.

Voltage resonance

The phenomenon of the resonance of electrical voltages is observed in the circuit of a series oscillatory circuit consisting of a capacitor (capacitor), an inductance and a resistor (resistance). To ensure the energy supply of the oscillatory circuit, a source of electromotive force E is also included in the series circuit. The source produces an alternating voltage with a frequency W. At resonance, the current circulating in the series circuit must coincide in phase with the emf. E. This is ensured if the total resistance of the circuit Z \u003d R + J (WL - 1 / WС) is only active, i.e. Z \u003d R. Equality:

(L - 1 / WС) \u003d 0 (1),

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

In this expression, W - is the resonant frequency of the circuit.

It is important that in the process of resonance the voltage across the inductor is equal to the voltage across the capacitor and is:

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

The total sum of energies in inductance and capacitance (magnetic and electric fields) is constant. This is due to the fact that vibrational exchange of energy occurs between these fields. Its total amount at any moment is unchanged. In this case, 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 into another.

For oscillatory circuits, the term Q-factor is used, which shows how the voltage across the reactive element (capacitance or inductance) and the input voltage of the circuit are related. The quality factor is calculated by the formula:

For an ideal series circuit with zero resistance, the onset of resonance is accompanied by sustained oscillations. In practice, the damping of oscillations is compensated for by feeding the circuit from an oscillator with a resonant frequency.

Application of voltage resonance

The phenomenon of vibrational resonance is widely used in radio electronics. In particular, the input circuit of any radio receiver is an adjustable oscillatory circuit. Its resonant frequency, modified by adjusting the capacitance of the capacitor, coincides with the frequency of the radio station signal to be received.

In the electric power industry, the occurrence of voltage resonance due to accompanying overvoltages is fraught with undesirable consequences. For example, if a long cable line (which is an oscillating circuit with distributed capacitance and inductance) is connected to a generator or an intermediate transformer and is not connected to the load at the receiving end (this is called no-load mode), the entire circuit may be in a resonance state. In such a situation, the stresses arising in some sections of the circuit may be higher than the calculated ones. This can threaten a breakdown of the cable insulation and its failure. This situation is prevented by using an auxiliary load.

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