The relationship between the main parameters of the loudspeaker

The performance of loudspeakers is the result of the common effects of physical parameters such as electrical, mechanical, acoustic, magnetic and other physical parameters, which are determined by the performance of key components such as drum paper, elastic wave, sound loop and magnetic circuit. Some of the parameters restrict each other and therefore must be considered and designed.

1. Comprehensive design and analysis of the main parameters

The commonly used electromechanical parameters, calculation formulas and measuring methods of the loudspeaker are summarized as follows:

DC resistance Re

Determined by voice coil, it can be measured directly by DC bridge.

Resonance frequency Fo

Determined by the equivalent vibration mass Mms and equivalent Cms of the loudspeaker, see formula (5), Fo can be measured directly by Fo tester or obtained by measuring impedance curve.

The maximum impedance Zo at the resonance frequency

It is decided by voice coil, magnetic circuit, vibration system (drum paper and elastic wave), which can be measured by means of substitution or measured by impedance curve.

Zo = Re+[(BL) 2/ (Rms+Rmr)] (10)

Mechanical force resistance Rms

Determined by the internal damping of drum paper, the elastic wave and the characteristics of the glue, it can be calculated from the following formula after measuring the mechanical quality factor Qms.

Rms = (1/Qms) *SQR (Mms/Cms) (11)

Here, SQR () indicates square root of the value in brackets ().

Radiation resistance Rmr

It is determined by the caliber and frequency, and can be ignored at low frequency.

Rmr = 0.022* (f/Sd) 2 (12)

Equivalent radiant area Sd

It is only related to the caliber (equivalent radius a).

Sd = pi * A2 (13)

Electromechanical coupling factor BL

It is determined by the Bg value of magnetic circuit and the effective length L of the voice coil. It can also be calculated by using the following formula by measuring the electrical quality factor Qes.

(BL) 2 = (Re/Qes) *SQR (Mms/Cms) (14)

Equivalent vibration mass Mms

It is decided by the voice coil mass Mm1, drum paper equivalent mass Mm2 and radiation mass Mmr that Mms can be obtained by the additional mass method.

Mms=Mm1+Mm2+2Mmr

Radiation mass Mmr

It is only related to the caliber (equivalent radius a).

Mmr =2.67* Rho o* A3 (16)

Rho o=1.21kg/m3 is air density and a is the equivalent radius of loudspeaker.

Equivalent Cms

The flexibility of the supporting parts of the loudspeaker vibration system. The larger the value, the softer the loudspeaker's whole vibration system. The unit is millimeter / Newton (mm/N).

It is determined by the Cm1 of the drum paper and the Cm2 of the elastic wave, which is what we call the transformation, but the unit should be converted into an international unit system: m/N, and the change position can be measured directly by the displacement instrument. Cms can be obtained by an additional volume measurement.

Cms= (Cm1*Cm2) / (Cm1+Cm2) (17)

Equivalent volume Vas

It is only related to the equivalent compliance and the equivalent radiation area.

Vas = Rho o*c2*Sd2*Cms (18)

Here C is the sound speed in the air, c=344m/s

Mechanical quality factor Qms

It is decided by the equivalent vibration mass Mms of the vibration system, the equivalent compliance Cms and the mechanical resistance Rms. Qms can be obtained from the measurement of the impedance curve.

Qms = (1/Rms) *SQR (Mms/Cms) = (Fo/ delta f) * (Zo/Re) (19)

F is the difference between the two frequencies corresponding to SQR (Zo*Re) on the impedance curve.

Electrical quality factor Qes

The equivalent vibration mass Mms, equivalent Cms and electromechanical coupling factor BL of the vibration system are determined jointly by the measurement of the impedance curve.

Qes =[Re/ (BL) 2]*SQR (Mms/Cms) = (Fo/ delta f) *SQR (Zo*Re) / (Zo-Re) (20)

Total quality factor Qts

It is decided by mechanical quality factor Qms and electrical quality factor Qes.

Qts = (Qms*Qes) / (Qms+Qes) = (Fo/ delta f) *SQR (Re/Zo) (21)

Reference to electroacoustic conversion efficiency (ETA o)

It is determined by electromechanical coupling factor BL, equivalent radiation area Sd and equivalent vibration mass Mms.

ETA o = (rho o/2 PI C) * (BL*Sd/Mms) 2/Re (22)

Reference sensitivity level SPLo

It is directly related to the efficiency of the reference electroacoustic conversion efficiency (ETA o).

SPLo = 112+10lg ETA o (23)

Reference amplitude Zeta

It is related to the reference electroacoustics conversion efficiency, O, Pe, a and f.

Zeta = 0.481*SQR (Pe* ETA o) / (a*f) 2

These parameters can now be measured and calculated by the loudspeaker computer test system. The commonly used test systems are LMS, CLIO, MLSSA, DAAS, SYSID, LAUD, IMP and so on. In addition, some computer simulation software can also be used to design the basic parameters of the speaker, such as LEAP, CALSOD, Speaker Easy, DLC Design, AudioCad, SOUNDEASY and so on.

The power and distortion index of loudspeaker can not be directly calculated by formula, and can only be qualitatively analyzed and discussed.

The rated sinusoidal power of the loudspeaker and the pure tone audiometry power are basically determined by the maximum amplitude o of low frequency. The maximum amplitude of the general low frequency is at the resonance frequency of Fo. The maximum amplitude of the loudspeaker's low frequency depends mainly on the magnetic circuit structure and voice coil width, and of course, it is also related to the vibration system. When the loudspeaker works normally, the sound circle can not jump out of the magnetic gap, that is, there is a o less than Xmax, otherwise there will be a large nonlinear distortion (the abnormal amplitude of the amplitude), or even the damage of the ring (dead or burned). The maximum amplitude o at Fo can be calculated by the following formula:

Zeta o = 1.414*BL*I*Cms*Qts (25)

The I in the form is the current fed to the loudspeaker, I=SQR (Pe/Re). It can be seen that if the basic electromechanical parameters of the speaker (BL, Cms, Qts) are determined, the power Pe=I2*Re determined by its current I is limited by the maximum amplitude of the low frequency amplitude of zeta o < < Xmax. Conversely, if the power of the loudspeaker must reach a certain value, the equivalent compliance of the loudspeaker can not be too large, that is, Fo can not be too small. When there is (BL) 2/Re>>Rms, the formula (25) can be simplified as follows:

Zeta o = 0.225*V/ (BL*Fo) (26)

The V is the voltage to the speaker, V=SQR (Pe*Re). This formula shows more directly the relationship between the maximum amplitude zeta O and the voltage V, the electromechanical coupling factor BL and the resonance frequency Fo. Generally speaking, the total quality factor Qts's ability to control the low frequency amplitude is reflected and reflected by formula (25) and (26), and the effect of BL value is more obvious.

The low frequency sound power Pa of speakers is also limited.

Pa= Pe* ETA o=4.33* zeta 2*a 4