Although this claim could be considered controversial, unless you are using a current source amplifier with high output impedance to drive your loudspeaker, my claim is Bl with unit (Tm) is Heresy!
Kindly let me show you why. I will start with the equation that defines a moving coil transducer's efficiency,
The expression ρ/2πc is a constant and can be replaced by the value 5.445×10−4 (m^2)s/kg for dry air.
Where ρ is the density of air and c is the speed of sound in SI units.
B is the DC magnetic flux density with unit (T).
l is the length of the voice coil winding with unit (m).
Sd is the effective area of the diaphragm with unit (m^2).
Mms is the moving mass including air load with unit (kg).
Re is the DC resistance of the voice coil with unit (Ω).
Using the transducer's efficiency equation above, the SPL at 1.0 (m) in dB can be calculated.
From the efficiency equation above a term β or the motor efficiency factor can be defined.
β = (Bl)(Bl)/Re with unit (N^2 /W)
Where Re = l /(Aσ)
σ is the electrical conductivity of the voice coil wire with unit (1/(Ωm)).
A is the cross-sectional area of the wire's conductor with unit (m^2).
Then β = (Bl)(Bl)(Aσ)/l
β = (B)(Bl)(Aσ)
But lA is the volume of the conductor, V with unit (m^3).
Then β = (B^2)(Vσ)
Looking back at the equation for transducer efficiency, η0 goes as β, Sd^2, and 1/Mms^2.
This shows that we don't care about the length of the voice coil wire, l.
What we care about is the volume of the conductor, V.
Now we can see that the SPL also depends on, β and not on Bl alone.
For example:
Motor A has a Bl of 10 (N/A).
Motor B has a Bl of 8 (N/A).
Which motor do you prefer? (Trick question!)
Motor A has an Re of 6.4 (Ω).
Motor B has an Re of 3.2 (Ω).
Then Motor A has a β = 15.6.
Motor B has a β = 20.0.
Motor B actually has 1.1 (dB) higher sensitivity with 20% less Bl!
The lesson here is clear. We don't care about Bl; what we care about is β.
With a large signal input, we can use Bl to evaluate motor linearity, Bl(x).
However for small signal evaluation Bl(0) = Bl, the force factor if considered alone is misleading at best.
Whereas β(x) allows for evaluation of both linearity and motor efficiency regardless of Re.
β is the true figure of merit for transducer motor evaluation, while Bl alone is effectively meaningless.
Final note: 1/β is also responsible for most of the damping, where Qes ≈ Qts.
Kindly let me show you why. I will start with the equation that defines a moving coil transducer's efficiency,
The expression ρ/2πc is a constant and can be replaced by the value 5.445×10−4 (m^2)s/kg for dry air.
Where ρ is the density of air and c is the speed of sound in SI units.
B is the DC magnetic flux density with unit (T).
l is the length of the voice coil winding with unit (m).
Sd is the effective area of the diaphragm with unit (m^2).
Mms is the moving mass including air load with unit (kg).
Re is the DC resistance of the voice coil with unit (Ω).
Using the transducer's efficiency equation above, the SPL at 1.0 (m) in dB can be calculated.
From the efficiency equation above a term β or the motor efficiency factor can be defined.
β = (Bl)(Bl)/Re with unit (N^2 /W)
Where Re = l /(Aσ)
σ is the electrical conductivity of the voice coil wire with unit (1/(Ωm)).
A is the cross-sectional area of the wire's conductor with unit (m^2).
Then β = (Bl)(Bl)(Aσ)/l
β = (B)(Bl)(Aσ)
But lA is the volume of the conductor, V with unit (m^3).
Then β = (B^2)(Vσ)
Looking back at the equation for transducer efficiency, η0 goes as β, Sd^2, and 1/Mms^2.
This shows that we don't care about the length of the voice coil wire, l.
What we care about is the volume of the conductor, V.
Now we can see that the SPL also depends on, β and not on Bl alone.
For example:
Motor A has a Bl of 10 (N/A).
Motor B has a Bl of 8 (N/A).
Which motor do you prefer? (Trick question!)
Motor A has an Re of 6.4 (Ω).
Motor B has an Re of 3.2 (Ω).
Then Motor A has a β = 15.6.
Motor B has a β = 20.0.
Motor B actually has 1.1 (dB) higher sensitivity with 20% less Bl!
The lesson here is clear. We don't care about Bl; what we care about is β.
With a large signal input, we can use Bl to evaluate motor linearity, Bl(x).
However for small signal evaluation Bl(0) = Bl, the force factor if considered alone is misleading at best.
Whereas β(x) allows for evaluation of both linearity and motor efficiency regardless of Re.
β is the true figure of merit for transducer motor evaluation, while Bl alone is effectively meaningless.
Final note: 1/β is also responsible for most of the damping, where Qes ≈ Qts.
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