Wiktor Wise
Electrical resonance is a phenomenon that occurs in electrical circuits, specifically in circuits with energy-storing elements like capacitors and inductors. It happens when the impedances or admittances of the circuit elements cancel each other out at a specific resonant frequency. This results in the circuit exhibiting ringing and generating higher voltages or currents than what was initially fed into it. The concept of resonance is crucial in tuning and filtering applications, such as in radio and television receivers, where it allows users to select specific frequency channels.
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What You'll Learn
Impedance and admittance
Electrical resonance occurs in an electric circuit when the impedances or admittances of circuit elements cancel each other out at a particular resonant frequency. This often happens when the impedance between the input and output of the circuit is near zero and the transfer function is close to one.
Admittance, on the other hand, is the inverse or reciprocal of impedance. It measures how easily or readily current flows through a circuit. Admittance is denoted by the symbol Y and is measured in Siemens (S) or mhos. Admittance is composed of conductance, which facilitates current flow, and susceptance, which influences the circuit's response to AC signals.
In a series RLC circuit, resonance occurs when the impedance Z term equals zero, resulting from the difference between the values of XL (inductance) and XC (capacitance). In a parallel RLC circuit, resonance occurs when the imaginary admittance term is zero.
The presence of resistance in a circuit reduces the peak resonant frequency of damped oscillation, although the resonant frequency for driven oscillations, such as in an LC circuit, remains unchanged.
Understanding admittance and impedance in series and parallel circuits is crucial for predicting circuit behaviour under different configurations. Additionally, admittance calculations allow engineers to determine essential parameters such as total current and circuit power factor.
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LC circuits
Electrical resonance occurs in an electric circuit when the impedances or admittances of circuit elements cancel each other out at a particular resonant frequency. This often happens when the impedance between the input and output of the circuit is almost zero and the transfer function is close to one.
An LC circuit, also known as a resonant circuit, tank circuit, or tuned circuit, is an electric circuit consisting of an inductor (L) and a capacitor (C) connected together. The circuit can act as an electrical resonator, storing energy and oscillating at the circuit's resonant frequency. LC circuits are used for generating signals at a particular frequency or for picking out a signal at a particular frequency from a more complex signal. This function is called a bandpass filter.
The LC circuit is an idealized model as it assumes there is no energy loss due to resistance. In reality, any practical implementation of an LC circuit will include some resistance within the components and connecting wires, leading to energy loss over time. The purpose of an LC circuit is to minimize damping, so the resistance is kept as low as possible.
The LC circuit is the simplest type of inductor-capacitor network, but more complex LC networks with additional L and C elements may have multiple resonant frequencies. LC circuits are key components in many electronic devices, especially radio equipment, where they are used in circuits such as oscillators, filters, tuners, and frequency mixers.
The characteristic frequency of an LC circuit is the frequency at which large amplitudes are built up when a driving force is applied at that frequency. This is analogous to a child on a swing, where a push that matches the natural frequency of the swing will build up a large amplitude, while a push at a different frequency will not.
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RLC circuits
Electrical resonance occurs in an electric circuit when the impedances or admittances of circuit elements cancel each other out at a particular resonant frequency. This often happens when the impedance between the input and output of the circuit is almost zero and the transfer function is close to one. Circuits exhibiting electrical resonance are widely used in wireless (radio) transmission for both transmission and reception.
An RLC circuit is an electrical circuit consisting of a resistor (R), an inductor (L), and a capacitor (C), connected in series or in parallel. The RLC name is derived from the symbols used to represent these elements in circuit diagrams, namely “R” for resistors, “L” for inductors, and “C” for capacitors. The circuit forms a harmonic oscillator for current and resonates similarly to an LC circuit. The main difference is that the presence of the resistor increases the decay of oscillations, also known as damping.
The resistor also reduces the peak resonant frequency. In a series RLC circuit, the current flowing through each component remains unchanged while the voltages vary. The voltage across a resistor is in phase with the current, while the voltage across an inductor leads the current by 90° and the voltage across a capacitor lags the current by 90°.
The two types of RLC circuits, series and parallel, each exhibit distinct characteristics, making them suitable for specific applications. While a series RLC circuit has a single loop, a parallel RLC circuit has all its passive elements connected in parallel with the input sinusoidal current source.
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Tuning and filtering
In a series RLC circuit, the impedance is minimised at resonance, while in a parallel LC ("tank") circuit, the impedance is maximised at resonance. This property is exploited in band-pass and band-stop filter designs. For example, in a series LC band-pass filter, the series LC components pass the signal at resonance while blocking signals of other frequencies. Conversely, in a parallel LC band-stop filter, the parallel LC components present a high impedance at resonance, blocking the signal at that frequency while allowing signals of other frequencies to pass through.
The Q-factor, which is influenced by resistance, determines the quality of the resonance and plays a role in the current magnification of parallel resonant circuits. Additionally, the "purity" of inductance and capacitance is crucial for the selectivity of resonant filters, as any stray resistance can reduce their ability to discriminate between frequencies accurately.
Resonance is also utilised in AC mains filters, noise filters, and radio and television tuning circuits. It is a fundamental concept in the operation of electrical and electronic circuits, particularly in wireless (radio) transmission and reception, where resonant circuits can generate higher voltages or currents than those fed into them.
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Energy-storing elements
Capacitors and inductors are dynamic elements that can absorb, store, and release energy, allowing a circuit to sustain its electrical state even without external sources actively powering it. This property of energy storage is what sets these elements apart from resistors, which are static elements as their current-voltage relationship is time-invariant.
In an electrical circuit, capacitors and inductors work in tandem to create resonance. The collapsing magnetic field of the inductor generates an electric current in its windings, which charges the capacitor. Subsequently, the discharging capacitor provides the current necessary to rebuild the magnetic field in the inductor. This cyclical process repeats continuously, resulting in electrical resonance.
The behaviour of these energy-storing elements is governed by their respective equations: for capacitance, i = C(dv/dt), and for inductance, v = L(di/dt). These equations highlight the time-dependent nature of their current-voltage relationships. The presence of these elements in a circuit introduces a dynamic dimension, enabling a broader range of functions compared to circuits composed solely of resistive elements.
The energy-storing capability of capacitors and inductors is harnessed in various applications, such as tuning in radio and television receivers. By selecting a narrow range of frequencies from ambient radio waves, these circuits facilitate users in tuning into their desired TV channels or radio stations. This utilisation of resonance underscores the importance of energy-storing elements in modern electronics and our daily lives.
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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 at a particular resonant frequency.
An RLC circuit is an electrical circuit consisting of a resistor, an inductor, and a capacitor, connected in series or in parallel.
In a series RLC circuit, the impedance Z term is equal to zero when the difference between the value of XL and XC is zero. In a parallel RLC circuit, resonance occurs when the term of the imaginary admittance is zero.
The presence of resistance reduces the peak resonant frequency of damped oscillation. However, the resonant frequency for driven oscillations, such as in an LC circuit, remains unchanged.
Electrical resonance is used in tuning and filtering applications, such as in radio and television receivers, where specific frequency ranges need to be selected. It is also used in wireless (radio) transmission for both transmission and reception.
