Parallel resonance, also known as anti-resonance, is a phenomenon that occurs in AC (alternating current) circuits containing inductors and capacitors. It is one of the three types of resonances that can occur in circuits, the other two being series resonance and mixed resonance.
In a parallel resonant circuit, the inductor (L) and capacitor (C) are connected in parallel with each other. The resonance occurs at a specific frequency when the reactance of the inductor equals the reactance of the capacitor, causing the impedance of the circuit to be minimized.
Here are some key points about parallel resonance:
Resonant Frequency (fâ): The resonant frequency in a parallel resonant circuit is calculated using the formula:
0
=
1
2
f
0
â
=
2Ď
LC
â
1
â
where:
0
f
0
â
is the resonant frequency.
Ď is a mathematical constant (approximately 3.14159).
L is the inductance of the inductor in henries.
C is the capacitance of the capacitor in farads.
Impedance at Resonance: At the resonant frequency, the reactances of the inductor and capacitor cancel each other out, resulting in a very low impedance in the circuit. This can lead to high currents flowing through the circuit at resonance.
Current and Voltage: In a parallel resonant circuit, the current through the inductor and capacitor branches can be quite high at resonance due to the low impedance. However, the voltage across the branches may not be very high because the total impedance of the circuit is minimized.
Frequency Response Curve: The frequency response curve of a parallel resonant circuit is characterized by a peak at the resonant frequency. This peak indicates the frequency at which the circuit's impedance is at its lowest value.
Power Factor: At resonance, the power factor of the circuit can be both leading and lagging, depending on the relative values of the inductance and capacitance.
Applications: Parallel resonance is often used in applications where a specific frequency needs to be filtered out or where a high current needs to be achieved at a particular frequency. Examples include radio tuning circuits and impedance matching networks.
Bandwidth: The bandwidth of a parallel resonant circuit is defined as the range of frequencies around the resonant frequency for which the impedance remains relatively low. It can be calculated using the formula:
=
0
BW=
Q
f
0
â
â
where
Q is the quality factor of the circuit. A higher quality factor corresponds to a narrower bandwidth.
It's important to note that parallel resonance can also pose certain challenges, such as overcurrent issues due to the low impedance at resonance. Designing circuits with appropriate damping or loading elements can help mitigate these challenges.