How do you calculate the bandwidth of a resonant circuit?

Bandwidth (BW) = f_res / Q

Where:

BW is the bandwidth of the resonant circuit in Hertz (Hz).

f_res is the resonant frequency of the circuit in Hertz (Hz).

Q is the quality factor of the circuit.

The resonant frequency (f_res) is the frequency at which the impedance of the circuit is purely resistive (minimum impedance). It is determined by the inductance (L) and capacitance (C) of the circuit and can be calculated using the formula:

f_res = 1 / (2 * π * √(L * C))

The quality factor (Q) of the circuit is a dimensionless parameter that represents the sharpness of the resonance. It is defined as the ratio of the resonant frequency (f_res) to the bandwidth (BW) of the circuit:

Q = f_res / BW

If you have the values of inductance (L) and capacitance (C) for the resonant circuit, you can calculate the resonant frequency (f_res) using the first formula and then find the bandwidth (BW) using the second formula. Alternatively, if you have the resonant frequency (f_res) and the quality factor (Q), you can rearrange the second formula to find the bandwidth (BW).

The bandwidth is determined by the Q factor (Quality factor) of the resonant circuit, which is a measure of the sharpness or selectivity of the resonance. The higher the Q factor, the narrower the bandwidth, and vice versa.

The formula to calculate the bandwidth (BW) of a resonant circuit is:

BW = f_r / Q

Where:

BW is the bandwidth in Hertz (Hz),

f_r is the resonant frequency in Hertz (Hz),

Q is the quality factor of the resonant circuit.

To find the resonant frequency (f_r) and quality factor (Q) of the circuit, you'll need to know the values of the inductance (L) and capacitance (C) components in the circuit.

Resonant Frequency (f_r):

The resonant frequency is the frequency at which the reactive components cancel each other out, resulting in a maximum response in the circuit. It is given by:

f_r = 1 / (2 * π * √(L * C))

Where:

f_r is the resonant frequency in Hertz (Hz),

L is the inductance in Henrys (H),

C is the capacitance in Farads (F),

π (pi) is a constant approximately equal to 3.14159.

Quality Factor (Q):

The quality factor is a dimensionless value that indicates how "sharp" the resonance is. It relates the energy stored in the circuit to the energy lost per cycle. The Q factor is given by:

Q = √(L / C) / R

Where:

Q is the quality factor (dimensionless),

L is the inductance in Henrys (H),

C is the capacitance in Farads (F),

R is the resistance in Ohms (Ω).

Once you have calculated the resonant frequency (f_r) and the quality factor (Q), you can use the first formula mentioned to calculate the bandwidth (BW) of the resonant circuit. Remember that the bandwidth is the range of frequencies around the resonant frequency where the circuit's response is significant. It is usually defined as the range of frequencies between the points where the circuit's response is 3 dB (decibels) below the maximum response (half-power points).