A.C. Fundamentals - Bandwidth of Parallel Resonant Circuit
1 Answer
In A.C. (alternating current) fundamentals, a parallel resonant circuit is a type of electrical circuit that consists of a resistor (R), an inductor (L), and a capacitor (C) connected in parallel. When operated at its resonant frequency, this circuit exhibits interesting properties, including a significant increase in impedance and a large circulating current.
The bandwidth of a parallel resonant circuit refers to the range of frequencies around the resonant frequency where the circuit's impedance remains relatively low compared to the impedance at frequencies far from the resonant frequency. In other words, the bandwidth is the range of frequencies over which the circuit exhibits resonance-related effects.
The formula to calculate the bandwidth (BW) of a parallel resonant circuit is given by:
BW = f2 - f1
Where:
BW = Bandwidth
f1 = Lower cutoff frequency
f2 = Upper cutoff frequency
The cutoff frequencies can be calculated using the following formulas:
f1 = fr / Q
f2 = fr * Q
Where:
fr = Resonant frequency of the circuit
Q = Quality factor of the circuit
The quality factor (Q) of the circuit is a dimensionless parameter that describes the sharpness of the resonance. A higher Q indicates a narrower bandwidth and a sharper resonance, while a lower Q indicates a broader bandwidth.
In summary, the bandwidth of a parallel resonant circuit is the range of frequencies around the resonant frequency within which the circuit exhibits resonance-related effects. It is determined by the quality factor (Q) of the circuit and is related to the resonant frequency (fr). A higher quality factor leads to a narrower bandwidth, while a lower quality factor results in a wider bandwidth.
The bandwidth of a parallel resonant circuit refers to the range of frequencies around the resonant frequency where the circuit's impedance remains relatively low compared to the impedance at frequencies far from the resonant frequency. In other words, the bandwidth is the range of frequencies over which the circuit exhibits resonance-related effects.
The formula to calculate the bandwidth (BW) of a parallel resonant circuit is given by:
BW = f2 - f1
Where:
BW = Bandwidth
f1 = Lower cutoff frequency
f2 = Upper cutoff frequency
The cutoff frequencies can be calculated using the following formulas:
f1 = fr / Q
f2 = fr * Q
Where:
fr = Resonant frequency of the circuit
Q = Quality factor of the circuit
The quality factor (Q) of the circuit is a dimensionless parameter that describes the sharpness of the resonance. A higher Q indicates a narrower bandwidth and a sharper resonance, while a lower Q indicates a broader bandwidth.
In summary, the bandwidth of a parallel resonant circuit is the range of frequencies around the resonant frequency within which the circuit exhibits resonance-related effects. It is determined by the quality factor (Q) of the circuit and is related to the resonant frequency (fr). A higher quality factor leads to a narrower bandwidth, while a lower quality factor results in a wider bandwidth.