9.2. Electro-mechano-acoustical circuit [1]

The drive unit for a horn loudspeaker is essentially a small direct-radiator loudspeaker that couples to the throat of a flaring horn as shown in Fig. 9.1. In the next part we shall discuss the characteristics of the horn itself. In this section we restrict ourselves to that part of the frequency range where the complex mechanical impedance Z MT looking into the throat of a horn is a pure resistance:
ZMT=1YMT=ρ0cSTN·s/m
image (9.1)
where
  • ρ 0 is density of air in kg/m3
  • c is velocity of sound in m/s
  • ρ 0 c   =   406 rayls at 22°C and 105   Pa ambient pressure
  • S T is area of the throat in m2
  • Y MT is mechanical admittance at the throat of the horn in m/N   s
A cross-sectional drawing of a compression drive unit for a horn loudspeaker is shown in Fig. 9.2. It has a diaphragm and voice coil with a total mass M MD , a mechanical compliance C MS , and a mechanical resistance R MS   =   1/G MS . The quantity G MS is the mechanical conductance of the diaphragm in m/N   s.
Behind the diaphragm is a back cavity that is usually filled with a soft acoustical material. At low frequencies this space acts as a compliance C MB , which can be lumped in with the compliance of the diaphragm. At high frequencies the reactance of this space becomes small so that the space behind the diaphragm becomes a mechanical radiation resistance R MB   =   1/G MB with a magnitude equal to that given in Eq. (9.1). This resistance combines with the mechanical radiation resistance of the throat, and the diaphragm must develop power both to its front and its back. Obviously, any power developed behind the diaphragm is wasted, and at high frequencies this sometimes becomes as much as one-half of the total generated acoustic power.
image
Figure 9.1 Cross section of a simple horn loudspeaker with an exponential cross section. For this design, the radius of the throat is 0.1, the radius of the mouth 1.7, and the length is 5.0 (arbitrary units).
image
Figure 9.2 Cross section of a horn compression drive unit. The diaphragm couples to the throat of the horn through a small cavity with a mechanical compliance C M1. Note that in this design, the annular channels within the phase plug meet the front cavity at nodal points so as to suppress the normal modes, which would otherwise occur [19]. Such modes would produce a somewhat uneven frequency response. 
Courtesy of Celestion.
In front of the diaphragm there is an air space or front cavity with compliance C M1. At low frequencies the air in this space behaves like an incompressible fluid, that is, ωC M1 is small, and all the air displaced by the diaphragm passes into the throat of the horn. At high frequencies, the mechanical reactance of this air space becomes sufficiently low (i.e., the air becomes compressible), so that all the air displaced by the diaphragm does not pass into the throat of the horn.
The voice coil has an electrical resistance R E and inductance L E . As stated above, Y MT is the mechanical admittance at the throat of the horn.
By inspection, we draw the admittance-type analogous circuit shown in Fig. 9.3. In this circuit, forces “flow” through the elements, and the velocity “drops” across them. The generator open-circuit voltage and resistance are e˜g image and R g . The electric current is i˜ image ; the linear velocity of the voice coil and diaphragm is u˜c image ; the linear velocity of the air at the throat of the horn is u˜T image ; and the force at the throat of the horn is f˜T image . As before, the area of the diaphragm is S D and that of the throat is S T .
image
Figure 9.3 Electro-mechano-acoustical analogous circuit of the admittance type for the drive unit. To derive this, we assume that the mechanical impedance at the horn throat is ρ 0 cS T , that is, the mechanical admittance is Y MT   =   1/(ρ 0 cS T ).
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