Resonance is one of the most common physical phenomena in nature . The resonance phenomenon can be observed in mechanical, electrical, and even thermal systems. Without resonance, we would not have radio, television, music, and even swings in playgrounds, not to mention the most effective diagnostic systems used in modern medicine. One of the most interesting and useful types of resonance in an electric circuit is voltage resonance.
Resonance circuit elements
The resonance phenomenon can occur in the so-called RLC circuit containing the following components:
- R - resistors. These devices, related to the so-called active elements of an electric circuit, convert electrical energy into heat. In other words, they remove energy from the circuit and convert it to 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 a change in speed. In an electrical circuit, a change in current. If it occurs for any reason, inductance counteracts such a change in circuit mode.
- C is the designation for capacitors, which are devices that store electrical energy, just as springs store mechanical energy. Inductance concentrates and conserves magnetic energy, while a capacitor concentrates the charge and thereby stores electrical energy.
Resonance circuit concept
The key elements of the resonant circuit are inductance (L) and capacitance (C). A resistor tends to damp, so it removes energy from the circuit. When considering the processes occurring in the oscillatory circuit, we temporarily ignore it, but we must remember that, like the friction force in mechanical systems, the electrical resistance in the chains cannot be eliminated.
Voltage resonance and current resonance
Depending on how 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 matches the natural frequency, under certain conditions, a voltage resonance arises in it. Resonance in an electrical circuit with reactive elements connected in parallel is called current resonance.
Natural frequency of the resonant circuit
We can make the system oscillate at its own 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). Please note that the top plate of the capacitor is positively charged and the bottom is negative. 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 we can trace the nature of the dependence of current on time. Note that T on our graph is the time required to complete one oscillation, which is called the "oscillation period" in electrical engineering.
Current flows clockwise (picture 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 a 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 has a negative charge (figure below).
Now the system has completely reversed, and energy begins to flow from the capacitor back to the inductance (figure below). As a result, the energy completely returns to its starting point and is ready to start the cycle anew.
The oscillation frequency can be approximated as follows:
where: F is the frequency, L is the inductance, C is the capacitance.
The process considered in this example reflects the physical essence of voltage resonance.
Stress resonance study
In real LC circuits, there is always a small resistance, which with each cycle reduces the increase in current amplitude. After several cycles, the current decreases to zero. This effect is called "attenuation of the sine wave." The current decay rate to zero depends on the resistance value in the circuit. However, the resistance does not change the oscillation frequency of the resonant circuit. If the resistance is large enough, sinusoidal oscillations in the circuit will not occur at all.
Obviously, where there is a natural frequency of oscillations, there is the possibility of exciting a resonant process. We do this by including an AC (AC) power source in the serial circuit, as shown in the figure on the left. The term "alternating" means that the output voltage of the source fluctuates with a certain frequency. If the frequency of the power supply matches the natural frequency of the circuit, voltage resonance occurs.
Conditions of occurrence
Now we consider the conditions for the emergence of 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. An increase in the resistance of the resistor in the resonant circuit increases the tendency for the current to decay 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 .
Using voltage resonance to transmit a radio signal
The phenomenon of stress resonance is not only a curious physical phenomenon. It plays an exceptional role in wireless communications technology - radio, television, and cellular telephony. The transmitters used for wireless transmission of information, without fail, contain circuits designed to resonate at a frequency specific to each device, called the carrier frequency. Using a transmitting antenna connected to the transmitter, it emits electromagnetic waves at the carrier frequency.
The antenna at the other end of the transceiver path receives this signal and feeds it to the receiver circuit, which is designed to resonate at the carrier frequency. Obviously, the antenna receives many signals at different frequencies, not to mention the 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, eliminating all unnecessary.
After detecting the amplitude-modulated (AM) radio signal, the low-frequency signal (LF) extracted from it is amplified and fed to a sound reproducing device. This simplest form of radio transmission is very sensitive to noise and interference.
To improve the quality of the received information, other, more advanced methods of transmitting the radio signal, which are also based on the use of tuned resonant systems, have been developed and successfully used.
Frequency modulation or FM radio solves many of the problems of radio transmission with an amplitude-modulated transmission signal, but this is achieved at the cost of significantly complicating the transmission system. In FM radio, system sounds in the electron path turn into small changes in the carrier frequency. The 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 speaker.
Other examples of using voltage resonance
Voltage resonance as a fundamental principle is also laid down in the circuitry of numerous filters that are widely used in electrical engineering to eliminate harmful and unnecessary signals, smooth out ripples and generate sinusoidal signals.