How do you calculate the bandwidth and Q factor of resonant circuits?

Resonant Frequency (f0):

The resonant frequency (f0) of the circuit is the frequency at which the circuit exhibits maximum response or impedance. For a series resonant circuit, it can be calculated using the formula:

f0 = 1 / (2 * π * √(L * C))

where L is the inductance in henries, C is the capacitance in farads, and π is a constant approximately equal to 3.14159.

For a parallel resonant circuit, the resonant frequency can be calculated as:

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f0 = 1 / (2 * π * √(L * C))

2. Bandwidth (BW):

The bandwidth of a resonant circuit is the range of frequencies around the resonant frequency where the circuit's response remains relatively strong. It is often defined as the frequency range between the two points where the power response is reduced to half its maximum value. This can be expressed as a percentage of the resonant frequency:

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BW = Δf / f0 * 100%

where Δf is the difference between the two frequencies where the power response is half its maximum value.

3. Quality Factor (Q):

The Quality Factor (Q) of a resonant circuit is a dimensionless parameter that represents the selectivity or sharpness of the resonant circuit's response. It can be calculated using the following formulas:

For a series resonant circuit:

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Q = R / (ω * L)

where R is the resistance in ohms, L is the inductance in henries, and ω (omega) is the angular frequency in radians per second, given by ω = 2 * π * f0.

For a parallel resonant circuit:

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Q = R * (ω * C)

where R is the resistance in ohms, C is the capacitance in farads, and ω (omega) is the angular frequency in radians per second, given by ω = 2 * π * f0.

Remember, for accurate calculations, ensure that all units are in the same system (e.g., SI units) and be consistent in your calculations.