Bandwidth of a Resonant Circuit

Variables

What it means

The bandwidth (BW) of a resonant circuit is the frequency range between the two half‑power points (where the power is half of the peak, or the voltage/current amplitude is 1/√2 of the maximum). For a series RLC, BW = f₀ / Q, where f₀ is the resonant frequency and Q is the quality factor. A smaller bandwidth means a more selective circuit. This relationship is used in filter design to set the passband width. In practice, the bandwidth determines the range of frequencies that will pass with minimal attenuation. Example: For f₀=1000Hz and Q=20, the bandwidth is 1000/20 = 50Hz. This means the circuit will pass frequencies between 975Hz and 1025Hz at half‑power, providing a fairly narrow passband.

Worked example

Common mistakes

• Bandwidth: The frequency range between the lower and upper cut‑off frequencies.
• Units: Hz or rad/s – consistent with f₀.
• Selectivity: Narrower bandwidth means higher selectivity.
• Q factor: BW = f₀/Q – the reciprocal relation.
• Half‑power points: The frequencies where the output power is half the maximum.

Applications

Bandwidth (BW) of a resonant circuit is the frequency range between the half‑power points, BW = f₀/Q. A narrower bandwidth indicates higher selectivity, which is essential in radio receivers and filters. Engineers use this relationship to design circuits that pass desired frequencies and reject others. By setting the desired bandwidth, they can determine the required Q and component values. This formula is used in the design of RF filters, oscillators, and communication systems. Understanding the trade‑off between Q and bandwidth is key to many practical applications in electronics.

• RF filter and channel selectivity design
• Radio receiver front‑end tuning
• Oscillator phase noise and frequency stability
• Antenna matching and bandwidth optimisation
• Educational understanding of quality factor and selectivity