Name: parallel rlc tuning at resonance
Uploaded: 2024-07-08T13:20:02.000Z
Duration: 1 min 23 s
Channel: JoVE

Consider an AM radio tuner comprising a parallel connection of a resistor, capacitor, and inductor, which collectively contribute to the circuit&#39;s input admittance.
At resonance, the imaginary part of the admittance is zero, causing the resonant frequency to vary inversely with the square root of the product of inductance and capacitance.
At the resonant frequency, the parallel combination of the inductor and capacitor acts as an open circuit. As a result, the resistor draws minimal current, and energy oscillates between the inductor&#39;s magnetic field and the capacitor&#39;s electric field.
The frequency response indicates that the current magnitude initially decreases, reaches a minimum at the resonance frequency, and increases as the frequency increases.
At the half-power frequencies, the current is 1.4142 times the minimum current.
The bandwidth is calculated by determining the difference between the higher and lower half-power frequencies.
The quality factor, which indicates the sharpness of the resonance curve, can be expressed in terms of the reactances.
A higher quality factor yields half-power frequencies symmetrically distributed around the resonant frequency and a narrower bandwidth.

parallel resonance

The parallel RLC circuit is an arrangement where the resistor (R), inductor (L), and capacitor (C) are all connected to the same nodes and, as a result, share the same voltage across them. The parallel RLC circuit is analyzed in terms of admittance (Y), which reflects the ease with which current can flow. The admittance is given by:
<img alt="Admittance equation Y for RLC circuit; electric circuit analysis formula diagram." src="/files/ftp_upload/15145/15145_Equation_1.svg" style="text-align: center; height: 30px;" data-altupdatedat="1762173717000" data-alt="Equation 1" />
Resonance in a parallel RLC circuit occurs when the net reactance is zero, meaning the capacitive and inductive effects cancel each other out. This condition is achieved when:
<img alt="Resonance condition equation &#969;C - 1/&#969;L = 0; electrical circuit analysis formula." src="/files/ftp_upload/15145/15145_Equation_2.svg" style="text-align: center; height: 30px;" data-altupdatedat="1762173717000" data-alt="Equation 2" />
Solving for the resonant frequency gives:
<img alt="resonant frequency formula &#969;&#8320;=1/&#8730;(LC), physics equations, educational use" src="/files/ftp_upload/15145/15145_Equation_3.svg" style="text-align: center; height: 34px;" data-altupdatedat="1762173717000" data-alt="Equation 3" />
This resonant frequency is where the circuit will exhibit purely resistive behavior, and the current through the resistor will be at its maximum. The power dissipated in the circuit is maximum at resonance due to the maximum current flow. At the half-power point frequencies, the current is approximately 0.707 of the maximum current, leading to half the maximum power dissipation. The bandwidth of the parallel RLC circuit is the difference between these half-power frequencies and is found using:
<img alt="Frequency difference formula: B = &#969;&#8322; - &#969;&#8321; = 1/RC, equation for electronics study." src="/files/ftp_upload/15145/15145_Equation_4.svg" style="text-align: center; height: 30px;" data-altupdatedat="1762173717000" data-alt="Equation 4" />
The quality factor (Q) is a dimensionless parameter that compares the resonant frequency to the bandwidth, indicating the selectivity or sharpness of the resonance peak. In high-quality circuits where Q&#8805;10, the half-power frequencies can be approximated using:
<img alt="Damping frequency formula: &#969;&#8321; &#8776; &#969;&#8320;(1 - 1/2Q), relevant to oscillation analysis." src="/files/ftp_upload/15145/15145_Equation_5.svg" style="text-align: center; height: 30px;" data-altupdatedat="1762173717000" data-alt="Equation 5" />
<img alt="Static equilibrium, &#969;&#8322; &#8776; &#969;&#8320;(1 + 1/2Q) formula, diagram for resonance frequency analysis." src="/files/ftp_upload/15145/15145_Equation_6.svg" style="text-align: center; height: 30px;" data-altupdatedat="1762173717000" data-alt="Equation 6" />
 A higher Q factor signifies that the circuit is highly selective, resonating strongly at a narrow range of frequencies around the resonance frequency. This property is particularly beneficial in radio communications, allowing for filtering unwanted frequencies and minimizing interference. Parallel resonance circuits are particularly useful in filtering applications acting as band-stop or notch filters, blocking a specific frequency range while allowing others to pass. This makes them valuable in signal processing for eliminating unwanted frequencies or noise.

Parallel Resonance

Consider an AM radio tuner comprising a parallel connection of a resistor, capacitor, and inductor, which collectively contribute to the circuit&#39;s ...

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parallel rlc tuning at resonance

A parallel RLC circuit uses a resistor, inductor, and capacitor connected to the same nodes. Because they share the same voltage, the circuit is analyzed with admittance, which describes how easily current can flow. In a parallel RLC circuit, admittance helps show how the circuit responds as the frequency changes.

Resonance happens when the net reactance is zero. At that point, the capacitive and inductive effects cancel each other out. The resonant frequency is found from this condition. At resonance, the circuit behaves as a purely resistive circuit, and the current through the resistor reaches its maximum.

Power dissipation is also greatest at resonance because the current is highest. The half-power point frequencies are the points where the current is about 0.707 of the maximum current. At those frequencies, the power dissipation is half of its maximum value. The bandwidth of the parallel RLC circuit is the difference between the two half-power frequencies.

The quality factor, or Q, compares the resonant frequency with the bandwidth. It shows how sharp or selective the resonance peak is. For high-quality circuits where Q is 10 or greater, the half-power frequencies can be approximated with a simpler method. A higher Q means the circuit responds strongly to a narrow range of frequencies around resonance.

This selective behavior is useful in radio communications. It can help filter unwanted frequencies and reduce interference. Parallel resonance circuits are also used as band-stop or notch filters. In these filters, a specific frequency range is blocked while other frequencies pass through, which is useful for removing unwanted signals or noise.

Parallel RLC Tuning at Resonance

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Explore how a parallel RLC circuit behaves at resonance, including admittance, bandwidth, Q factor, and its use in radio tuning and notch filtering.

Parallel RLC Tuning at Resonance | JoVE K12

JoVE Core Electrical Engineering offers easy-to-understand animated videos that cover fundamental concepts of electric circuits along with circuit analysis techniques. It incorporates first-order and second-order circuits using operational amplifiers and circuit transformation concepts. The inclusion of practical design examples and real-world applications through scientist-in-action videos adds significant educational value, making complex concepts accessible.

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Parallel RLC Tuning at Resonance

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