Resonance of stresses. What is resonance in an electrical circuit

Resonance is one of the most common physical phenomena in nature . The phenomenon of resonance can be observed in mechanical, electrical and even thermal systems. Without resonance, we would not have radio, television, music and even a swing in playgrounds, not to mention the most effective diagnostic systems used in modern medicine. One of the most interesting and useful forms of resonance in an electrical circuit is the resonance of voltages.

Elements of the resonance circuit

The phenomenon of resonance can arise in the so-called RLC-chain, which contains the following components:

• R - resistors. These devices, related to the so-called active elements of the electrical circuit, convert electric energy into thermal energy. In other words, they remove energy from the circuit and convert it into heat.
• L is the inductance. Inductance in electrical circuits is an analog of mass or inertia in mechanical systems. This component is not very noticeable in the electrical circuit, until you try to make any changes in it. In mechanics, for example, such a change is the change in speed. In the electrical circuit, the current changes. If for some reason it occurs, the inductance counteracts such a change in the mode of the circuit.
• C is the designation for capacitors, which are devices storing electrical energy in a manner similar to how the springs retain mechanical energy. Inductance concentrates and retains magnetic energy, while the capacitor concentrates the charge and thereby stores electrical energy.

The concept of a resonant circuit

The key elements of the resonant circuit are inductance (L) and capacitance (C). The resistor tends to damp the oscillations, so it removes the energy from the circuit. When considering the processes occurring in the oscillatory circuit, we temporarily ignore it, but it must be remembered that, like the frictional force in mechanical systems, the electrical resistance in the circuits can not be eliminated.

Resonance resonance and current resonance

Depending on the way the key elements are connected, the resonant circuit can be sequential and parallel. When a serial oscillatory circuit is connected to a voltage source with a signal frequency that coincides with the natural frequency, under certain conditions, a resonance of voltages arises in it. Resonance in an electrical circuit with parallel connected reactive elements is called resonance of currents.

The natural frequency of the resonant circuit

We can make the system oscillate at its own frequency. To do this, you must first charge the capacitor, as shown in the upper left figure. When this is done, the key is moved to the position shown in the same figure on the right.

At time "0" all electrical energy is stored in the capacitor, and the current in the circuit is zero (figure below). Note that the upper plate of the capacitor is charged positively, and the lower one is negative. We can not see the oscillations of the electrons in the circuit, but we can measure the current with an ammeter, and with the aid of an oscilloscope we can trace the character of the current versus time. Note that T on our graph is the time it takes to complete one oscillation, which in electrical engineering is called the "oscillation period".

The current flows clockwise (figure below). Energy is transferred from the capacitor to the inductor. At first glance, it may seem strange that the inductance contains energy, but this is similar to the kinetic energy contained in the moving mass.

The energy flow returns back to the capacitor, but note that the polarity of the capacitor has now changed. In other words, the bottom plate now has a positive charge, and the top plate - a negative charge (figure below).

Now the system has completely turned, and the energy starts to flow from the capacitor again to the inductance (figure below). As a result, energy completely returns to its starting point and is ready to start the cycle anew.

The oscillation frequency can be approximated as follows:

• F = 1 / 2π (LC) ^0.5 ,

Where: F - frequency, L - inductance, C - capacitance.

The process considered in this example reflects the physical essence of stress resonance.

Investigation of stress resonance

In real LC circuits, there is always a small resistance, which with each cycle reduces the increase in the current amplitude. After several cycles, the current decreases to zero. This effect is called "attenuation of a sinusoidal signal". The rate of attenuation of the current to a zero value depends on the value of the resistance in the circuit. However, the resistance does not change the oscillation frequency of the resonant circuit. If the resistance is large enough, no sinusoidal oscillations in the circuit will occur at all.

Obviously, where there is a natural oscillation frequency, there is the possibility of exciting a resonant process. We do this, including the AC power supply (AC) in the serial circuit, as shown in the figure to the left. The term "variable" means that the output voltage of the source fluctuates at a certain frequency. If the frequency of the power supply coincides with the natural frequency of the circuit, a resonance of the voltages arises.

Conditions of occurrence

We now consider the conditions for the appearance of a stress resonance. As shown in the last figure, we returned the resistor to the circuit. In the absence of a resistor in the circuit, the current in the resonant circuit will increase to a certain maximum value determined by the parameters of the circuit elements and the power of the power source. Increasing the resistance of the resistor in the resonant circuit increases the tendency to attenuate the current in the circuit, but does not affect the frequency of the resonant oscillations. As a rule, the voltage resonance mode does not occur if the resistance of the resonance circuit satisfies the condition R = 2 (L / C) ^0.5 .

Use of voltage resonance for radio transmission

The phenomenon of stress resonance is not only a curious physical phenomenon. It plays an exceptional role in the technology of wireless communications - radio, television, cellular telephony. Transmitters used for wireless transmission of information necessarily contain circuits designed for resonating at a frequency defined for each device, called the carrier frequency. By means of a transmitting antenna connected to the transmitter, it emits electromagnetic waves at a carrier frequency.

An antenna at the other end of the transmit-receive path receives this signal and feeds it to the receiving loop, designed to resonate at the carrier frequency. Obviously, the antenna receives a lot of signals at different frequencies, not to mention background noise. Due to the presence at the input of the receiving device tuned to the carrier frequency of the resonant circuit, the receiver selects the only correct frequency, filtering out all unnecessary ones.

After detecting the amplitude-modulated (AM) radio signal, the low-frequency signal (LF) extracted from it is amplified and fed to the sound reproducing device. This is the simplest form of radio transmission is very sensitive to noise and interference.

To improve the quality of information received, other, more advanced methods of radio signal transmission have been developed and successfully used, which are also based on the use of tuned resonant systems.

Frequency modulation or FM radio solves many of the problems of radio transmission with an amplitude-modulated transmission signal, however this is achieved at the cost of a significant complication of the transmission system. In FM radio, system sounds in the electronic path are converted into small changes in the carrier frequency. Part of the equipment that performs this conversion is called a "modulator" and is used with the transmitter.

Accordingly, a demodulator must be added to the receiver to convert the signal back to a form that can be reproduced through the loudspeaker.

Other examples of the use of voltage resonance

Resonance resonance as a fundamental principle is also embedded in the circuitry of numerous filters widely used in electrical engineering to eliminate harmful and unnecessary signals, smoothing pulsations and generating sinusoidal signals.