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 playground swings, not to mention the most effective diagnostic systems used in modern medicine. One of the most interesting and useful types of resonance in an electrical circuit is voltage resonance.
Elements of a resonant circuit
The phenomenon of resonance can occur in the so-called RLC circuit containing the following components:
- R - resistors. These devices, related to the so-called active elements of the electrical circuit, convert electrical energy into thermal energy. In other words, they remove energy from the circuit and convert it into heat.
- L - inductance. Inductance inelectrical circuits - analogue of mass or inertia in mechanical systems. This component is not very noticeable in the electrical circuit until you try to make any changes to it. In mechanics, for example, such a change is a change in speed. In an electrical circuit, a change in current. If it happens for any reason, the inductance counteracts this change in circuit mode.
- C is a designation for capacitors, which are devices that store electrical energy in the same way that springs store mechanical energy. An inductor concentrates and stores magnetic energy, while a capacitor concentrates charge and thereby stores electrical energy.
The concept of a resonant circuit
The key elements of a resonant circuit are inductance (L) and capacitance (C). The resistor tends to dampen oscillations, so it removes 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 friction force in mechanical systems, electrical resistance in circuits cannot be eliminated.
Voltage resonance and current resonance
Depending on how the key elements are connected, the resonant circuit can be series and parallel. When a series oscillatory circuit is connected to a voltage source with a signal frequency coinciding with the natural frequency, under certain conditions, voltage resonance occurs in it. Resonance in an electrical circuit with parallel connectedreactive elements is called current resonance.
Natural frequency of the resonant circuit
We can make the system oscillate at its natural frequency. To do this, you first need to charge the capacitor, as shown in the upper figure on the left. 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 top plate of the capacitor is positively charged while the bottom plate is negatively charged. We cannot see the oscillations of the electrons in the circuit, but we can measure the current with an ammeter, and with the help of an oscilloscope, trace the nature of the current versus time. Note that T on our graph is the time required to complete one oscillation, which in electrical engineering is called the "oscillation period".
Current flows clockwise (picture below). Energy is transferred from the capacitor to the inductor. At first glance, it may seem strange that an inductance contains energy, but this is similar to the kinetic energy contained in a moving mass.
The energy flow returns back to the capacitor, but note that the polarity of the capacitor has now been reversed. In other words, the bottom plate now has a positive charge and the top plate a negative charge (Figurebottom).
Now the system is completely reversed and energy starts to flow from the capacitor back into the inductor (picture below). As a result, the energy returns completely to its starting point and is ready to start the cycle again.
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.
Stress Resonance Study
In real LC circuits, there is always a small amount of resistance, which reduces the increase in current amplitude with each cycle. After several cycles, the current decreases to zero. This effect is called "sinusoidal signal damping". The rate at which the current decays to zero depends on the amount of resistance in the circuit. However, the resistance does not change the oscillation frequency of the resonant circuit. If the resistance is high enough, there will be no sinusoidal oscillation in the circuit at all.
Obviously, where there is a natural oscillation frequency, there is the possibility of excitation of the resonant process. We do this by including an alternating current (AC) power supply in series, as shown in the figure on the left. The term "variable" means that the output voltage of the source fluctuates with a certainfrequency. If the frequency of the power supply matches the natural frequency of the circuit, voltage resonance occurs.
Occurrence conditions
Now we will consider the conditions for the occurrence of stress resonance. As shown in the last picture, we have returned the resistor to the loop. 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 for the current in the circuit to decay, 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.
Using voltage resonance to transmit radio signals
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 to transmit information wirelessly necessarily contain circuits designed to resonate at a specific frequency for each device, called the carrier frequency. With a transmitting antenna connected to the transmitter, it emits electromagnetic waves at a carrier frequency.
The antenna at the other end of the transceiver path receives this signal and feeds it to the receiving circuit, designed to resonate at the carrier frequency. Obviously, the antenna receives many signals at differentfrequencies, not to mention background noise. Due to the presence of a resonant circuit at the input of the receiving device, tuned to the carrier frequency of the resonant circuit, the receiver selects the only correct frequency, eliminating all unnecessary ones.
After detecting an amplitude modulated (AM) radio signal, the low frequency signal (LF) extracted from it is amplified and fed to a sound reproducing device. This is the simplest form of radio transmission and is very sensitive to noise and interference.
To improve the quality of received information, other, more advanced methods of radio signal transmission have been developed and are successfully used, which are also based on the use of tuned resonant systems.
Frequency modulation or FM radio solves many of the problems of AM radio transmission, but this comes at the cost of greatly complicating the transmission system. In FM radio, system sounds in the electronic path are converted into small changes in the carrier frequency. The piece of equipment that does 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 into a form that can be played through the loudspeaker.
More examples of using voltage resonance
Voltage 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 ripples and generating sinusoidal signals.
