Trystan Casey
Electrical resonance is a phenomenon that occurs in an electrical circuit at a particular resonant frequency when the impedances or admittances of circuit elements cancel each other out. This happens when the impedance between the input and output of the circuit is low and the transfer function is close to one. Resonant circuits are often built using an inductor, such as a coil, connected in parallel to a capacitor. The response of the circuit to different frequencies depends on the inductance and capacitance of the circuit and peaks at one frequency value, where the current flow resonates most strongly with the input signal.
| Characteristics | Values |
|---|---|
| Definition | An electric circuit which has very low impedance at a certain frequency. |
| Circuit Elements | Resistor, Inductor, and Capacitor. |
| Connection | The elements can be connected in series or in parallel. |
| Impedance | In the resonance condition, the impedance in the circuit is minimum, and the current is maximum. |
| Applications | Tuning, filtering, stabilizing frequency, blocking frequencies, wireless transmission, and motors |
| Q Factor | The quality of resonance is determined by the Q factor, which is a function of resistance, inductance, and capacitance. |
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What You'll Learn
Resonant frequency
Electrical resonance occurs in an electric circuit at a particular resonant frequency when the impedances or admittances of circuit elements cancel each other out. In some circuits, this happens when the impedance between the input and output of the circuit is almost zero and the transfer function is close to one.
The resonant frequency of an RLC circuit can be calculated using the equation:
$$\displaystyle \omega = 2\pi f$$
Where $f$ is the resonance frequency in hertz, $L$ is the inductance in henries, and $C$ is the capacitance in farads.
Resonant circuits are commonly used in wireless (radio) transmission and reception, as well as in radio and television tuners to select specific frequencies. They can also be used to prevent the waste of electrical energy by using parallel resonance circuits, which maintain the same resonant current in the circuit and convert all the current into useful work.
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Impedance and admittance
In electrical engineering, impedance is the opposition to alternating current presented by the combined effect of resistance and reactance in a circuit. It is denoted by the letter "Z" and is expressed in ohms. In a direct current (DC) circuit, the opposition to current flow is called resistance, whereas in an alternating current (AC) circuit, impedance is the result of both the circuit's resistive and reactive components.
Impedance can be represented as a complex number, with the same units as resistance, and its symbol is usually Z. It may be represented by writing its magnitude and phase in the polar form |Z|∠θ. The impedance of a two-terminal circuit element is the ratio of the complex representation of the sinusoidal voltage between its terminals to the complex representation of the current flowing through it.
Admittance is the inverse of impedance and is denoted by the letter "Y." It is a measure of how easily current can flow through a circuit. In a parallel RLC circuit, admittance is calculated using the formula: Y = G + j*ω*C, where G is the conductance, ω is the angular frequency, and C is the capacitance.
In an electrical circuit, resonance occurs when there is a cancellation of admittances and impedances of the elements of the circuit at a given resonant frequency. This results in a high current flow at a specific frequency. The impedance of a circuit can be calculated using an LCR meter, which measures the inductance (L), capacitance (C), and resistance (R) of the circuit.
At resonance, the net reactance becomes zero, and the impedance is equal to the resistance in the circuit. This means that the current flowing through the circuit is at its maximum value. The condition for resonance in a series RLC circuit is given by the equation: XL = XC, where XL is the inductive reactance and XC is the capacitive reactance. This results in the impedance Z becoming zero.
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Circuit applications
Resonance in electrical circuits has a wide range of applications, particularly in the field of electrical engineering.
One of the most important applications of resonance is in radio and television receivers. Tuned circuits, such as RLC circuits, are used to select a narrow range of frequencies from ambient radio waves, allowing for the reception of specific channels. This is achieved through band-pass or band-stop filtering, where the circuit blocks certain frequencies while allowing others to pass through.
Resonance is also crucial in wireless (radio) transmission for both sending and receiving information. The interplay between capacitors and inductors in a circuit creates sustained oscillations that enable the transmission and reception of signals.
In addition, resonance is used in oscillator circuits, which generate sinusoidal signals in communication devices. These circuits are essential for tuning and filtering applications, as they allow for the selection of specific frequencies.
Another application of resonance is in medical devices, particularly MRI machines. Resonance plays a vital role in creating accurate and detailed images for diagnostics.
Furthermore, resonance is used to enhance power transfer in electrical systems. By optimizing circuit performance, engineers can increase the efficiency of power transmission. This principle is also applied in the design of musical instruments, allowing us to hear and communicate with each other.
Overall, the understanding and application of resonance in electrical circuits are fundamental to the advancement of technology, particularly in the fields of electronics, communication, and engineering.
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Tuning and filtering
Tuning
Resonance is used for tuning in radio and television circuits to select a particular frequency from a range of frequencies. This is achieved by using a variable capacitor in a tank circuit, which allows for the selection of a specific broadcast station. The rotating dial for station selection adjusts the variable capacitor, tuning the receiver to the desired frequency. This is an example of a band-pass filter, where the series LC components pass the signal at resonance while blocking other frequencies.
Filtering
Resonant circuits are also employed in filtering applications. By utilising the resonance between inductors and capacitors, band-pass and band-stop filters can be designed. Series LC circuits provide minimum impedance at resonance, allowing signals at the resonant frequency to pass while blocking others. Conversely, parallel LC ("tank") circuits offer maximum impedance at resonance, effectively shorting out signals at the resonant frequency while allowing others to reach the load.
The two primary types of resonant band-pass filters are the series LC and parallel LC ("tank") configurations. In the series LC configuration, the low impedance at resonance allows signals to pass to the load, while at non-resonant frequencies, the signal is blocked. On the other hand, the parallel LC ("tank") circuit exhibits high impedance at resonance, enabling signals to reach the load with minimal attenuation. However, under or over the resonant frequency, the impedance drops, shorting out the signal.
Additionally, resonant circuits can be used to prevent the waste of electrical energy. By using parallel resonance, the inductor and capacitor work together, maintaining a constant resonant current and converting all the current into useful work. This configuration can enhance the efficiency of motors by minimising the waste of inductive or capacitive current.
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LCR circuits
An LCR circuit, also known as a resonant circuit, tuned circuit, or an RLC circuit, is an electrical circuit consisting of an inductor (L), capacitor (C), and resistor (R). The three elements can be connected in series or in parallel.
The LCR circuit forms a harmonic oscillator for current and resonates in a manner similar to an LC circuit. The introduction of the resistor increases the decay of oscillations, also known as damping, and reduces the peak resonant frequency.
The LCR circuit can be analysed in terms of phasors. A phasor is a rotating quantity. For an inductor (L), if we consider I to be our reference axis, then voltage leads by 90°, and for the capacitor, the voltage lags by 90°. However, the resistance, current, and voltage phasors are always in phase.
The LCR circuit has many applications as an oscillator circuit. Radio receivers and television sets use them for tuning to select a narrow frequency range from ambient radio waves. They can also be used as band-pass filters, band-stop filters, low-pass filters, or high-pass filters.
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Frequently asked questions
Electrical resonance occurs in an electric circuit when the impedances or admittances of circuit elements cancel each other out, resulting in a minimum impedance and a maximum current flow. This occurs at a particular resonant frequency.
A resonant frequency is a specific frequency at which the current flow in a circuit is at its maximum.
An LCR circuit is an electrical circuit consisting of a resistor, an inductor, and a capacitor. These components can be connected in series (end-to-end) or in parallel.
The formula for impedance in an LCR circuit is:
Z = sqrt(R^2 + (XL - 1/XC)^2)
Where:
- Z is impedance
- R is resistance
- XL is inductive reactance
- 1/XC is capacitive reactance
Resonance is used for tuning and filtering as it occurs at a specific frequency for given values of inductance and capacitance. It is also used to establish a condition of stable frequency in circuits designed to produce AC signals.
