In the context of electronics and electrical engineering, the term "bandwidth" refers to the range of frequencies over which a circuit or device can operate effectively. For a resonant circuit, the bandwidth is the range of frequencies around the resonant frequency where the circuit exhibits a relatively high response or a certain level of selectivity.
A resonant circuit is a combination of an inductor and a capacitor that forms a resonant frequency, also known as the natural frequency. At this frequency, the reactive components (inductor and capacitor) cancel each other out, and the circuit's impedance is purely resistive, resulting in a maximum response to the input signal.
The bandwidth of a resonant circuit is usually defined as the range of frequencies between two points on the frequency response curve where the circuit's response is, for example, 70.7% of the maximum response (corresponding to -3 dB from the peak response). These two points are often referred to as the "half-power points" or "3 dB points." The bandwidth can also be measured between other specific points, such as -20 dB from the peak.
The formula to calculate the bandwidth of a resonant circuit is:
Bandwidth = Resonant Frequency / Quality Factor
Where:
Resonant Frequency is the center frequency of the resonant circuit (the frequency where the circuit responds most strongly).
Quality Factor (Q) is a dimensionless parameter that represents the selectivity of the resonant circuit. A higher Q value indicates a narrower bandwidth and higher selectivity, while a lower Q value indicates a wider bandwidth and lower selectivity.
In summary, the bandwidth of a resonant circuit is determined by its resonant frequency and the quality factor, and it represents the range of frequencies within which the circuit exhibits a significant response.