How do you calculate the bandwidth of a resonant circuit?

To calculate the bandwidth of a resonant circuit, you need to know the resonant frequency and the quality factor.

The bandwidth of a resonant circuit is the range of frequencies around the resonant frequency where the circuit will respond with a certain level of amplitude. It is measured between the two frequencies where the amplitude drops to 70.7% of the maximum value. The bandwidth is directly proportional to the resonant frequency and inversely proportional to the quality factor.

To calculate the bandwidth, first find the resonant frequency by using the formula f = 1/(2π√LC), where L is the inductance and C is the capacitance of the circuit. Then, calculate the quality factor using the formula Q = R√C/L, where R is the resistance of the circuit. Finally, calculate the bandwidth using the formula BW = f/Q.

For example, if a resonant circuit has a resonant frequency of 1 MHz and a quality factor of 100, the bandwidth would be 10 kHz. This means that the circuit will respond with a certain level of amplitude between the frequencies of 995 kHz and 1.005 MHz.

A-Level Physics Tutor Summary: To calculate a resonant circuit's bandwidth, find the resonant frequency with f = 1/(2π√LC) and the quality factor with Q = R√C/L. The bandwidth (BW) is worked out using BW = f/Q, showing the frequency range the circuit effectively responds to. This method links bandwidth with resonant frequency and quality factor, crucial for understanding how circuits react to different frequencies.