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Calculation of the power capacity of the sound box in the studio

like any other indoor sound reinforcement, there is a problem that the power capacity of the sound box used is determined according to the sound pressure level of the sound reinforcement place, that is, the so-called electric power. Although for a given room, the designer can determine the electrical power of the speaker he is familiar with based on experience, for an arbitrary room and a random speaker brand, it is not enough to estimate only by experience without scientific calculation. Because the power is too small, it will not reach the due loudness and clarity; And too much power will cause unnecessary waste. After all, it meets the requirements of sound reinforcement place and clarity; And too much power will cause unnecessary waste. After all, the electrical power of a loudspeaker that meets the sound pressure level requirements in the sound reinforcement place is not only related to the sensitivity level, directivity factor, directivity coefficient and other parameters of the loudspeaker, but also related to the peak factor and room constant in the sound reinforcement place. Therefore, before establishing a new studio sound reinforcement system, due calculation must be carried out

it should be pointed out that the following calculation method of electric power of speakers is also suitable for outdoor sound reinforcement, but the influence of room constant is no longer included

I. several basic concepts

before making specific calculations, let's discuss the following:

1, the directivity factor, directivity coefficient and sensitivity level of the speaker

(1). Directivity factor Q (d): it represents the multiple of the sound intensity produced by the speaker at a certain point in space than the sound intensity produced by the non directional speaker in theory. In actual calculation, it is characterized by the radiation angle V in the vertical direction and the radiation angle h in the horizontal direction:

Q (d) =180 ° ÷ SIN-1 [sin (v/2) · sin (h/2)]

where the units of V and h are degrees (°), and Q (d) is dimensionless

(2) directivity coefficient Q（ θ)： It represents the voltage generated by the deviation of the loudspeaker from its radiation axis by 0 angle, which is the multiple of the sound pressure attenuation at the same distance point along its axis. Q( θ) Given by referring to the directional characteristic pattern (or directional pattern) of the speaker in the following formula:

20 lgq（ θ)= L( θ)- L (a), i.e. Q（ θ)= 100.5[L( θ)- L (a)]

"in the future, the demand of the food industry for functional membranes such as high barrier, cooking resistance, UV resistance, light avoidance, antibacterial, breathable, oxygen resistant, etc. will continue to increase L（ θ) Is the sound pressure level of the measuring point that deviates from the axial 0 angle of the speaker, and l (a) is the sound pressure level at the same distance in the axial direction

the directional characteristic pattern of the speaker is the angle between the vertical radiation and the horizontal radiation of the speaker 1 given by the manufacturer at different test frequencies The equivalent sound pressure level curve in the included angle during the tensile test is shown in the figure

we take Figure 1 as an example to illustrate the pointing coefficient Q of point B deviated from the axial 0 angle（ θ) From the equivalent sound pressure level curve pointing to the characteristic diagram, it can be seen that the sound pressure level of point B is the same as that of point a, while the sound pressure level of point C equidistant from point B is 6dB greater than that of point B. If the sound pressure level L of point B is set（ θ)- 0dB, then the sound pressure level L (a) at point C = +6db

by 20lgq（ θ)= L( θ)- L(a)=-6dB ∴Q( θ)= 0.5

(3). Sensitivity level LS: the sound pressure level generated at 1m in its axial direction by the loudspeaker driven by 1W reference electric power (the sound source is pink noise). Unit: DB spl

from this definition, it can be seen that if LS is known, when you want to have 90dB sound pressure level LR at R (m) in the axial direction of the speaker, if you want to obtain the electric power we of the speaker at this time, just convert LR into the sound pressure level lr'at 1m in the axial direction (when only the direct sound energy in the room is considered and the reverberation sound energy is ignored, there can be: lr'-lr+20lgr). For example, the power level difference between the electric power we to be obtained and its quasi electric power (1W) can be calculated from the sound pressure level difference between lr' and ls, Then we are obtained. In other words, since the difference between lr'and LS is the difference between the sound pressure level produced by we and the sound pressure level produced by the reference electric power, there is the following quantitative relationship in calculation (note that it is not a physical concept): lr'-ls=10 LG (we/1w)

that is, 10 lgwe=lr'-ls or we=100.1 (lr'-ls)

note that since the actual listening area cannot have only one axis, we must not be in contact with Q (d) and Q（ θ) In relation to the peak factor and room constant to be discussed below, the above formula only gives an expression of we in quantity

2, peak factor and room constant

(1). Peak factor LP: the difference between the peak sound pressure level and the effective value sound pressure level is the peak factor, and the unit is dB SPL

generally, as long as it is not specified, the sound pressure level referred to by people is the effective value sound pressure level. Since most of the actual sound sources without sound reinforcement have a peak value of DB (the peak sound pressure level of human language signal is about 12dB higher than the effective value, and the peak value of music signal is about dB higher than the effective value), this peak value must be accumulated when determining the electrical power of the speaker according to the effective value sound wish level of the listening area. However, for every 3dB increase in sound pressure level, the electric power of the speaker will double that of the previous one. The peak value of 18db means that the electric power will be 64 times larger than the design at the effective value sound pressure level (for example, the original design of 100W electric power will be expanded to 6400w at this time!), Although this can make the whole system amplify without dynamic distortion, from a practical point of view, these excessive power reserves that are not used in most of the time are undoubtedly a huge waste. Therefore, in the actual design, we usually seek a compromise between the peak factor and the dynamic limit according to the use

(2). Room constant R: is a parameter representing the sound absorption characteristics of a room:

Where s is the total internal surface area of the room, a is the average sound absorption coefficient of the internal surface of the room, and AI is the wall and sound coefficient of the surface symbol Si

3, sound pressure level LR

as mentioned earlier, the sound pressure level LR at the distance between the indoor sound field and the speaker R is not only Q (d), q（ θ)、 Ls, LP and R are functions of electric power we. Therefore, to obtain we, we must first obtain the expression of LR at any point in the room

for the convenience of describing the problem, if we regard the sound field as an infinite space, the speaker can be regarded as a point sound source, and the sound wave it emits is not a directionless spherical wave. Obviously, at this time, for the sound source whose sound power is we, the spherical surface area is 4 л R2. The sound intensity I of the point at which the distance Wa is r can be expressed as:

i=wa/4 л R2

since the radiation of the actual speaker is directional, after considering Q (d), there is:

i=wa · Q (d)/4 л R2

when considering the deviation of this point from the axial corner of the speaker, Q has to be added（ θ) Influence:

i=wa · Q (D8. How to consider the insurance compensation pilot of key new material utilization demonstration?)· Q2( θ)/four л R2

[note that due to Q（ θ) Is a function of sound pressure, and the sound intensity is proportional to the square of sound pressure, so Q in the above formula（ θ) In the form of square]

of course, the room will not be infinite in actual use, so in addition to the direct sound intensity above, the reverberation sound intensity (4wa/r) must be superimposed on the actual sound intensity, that is:

i=wa{[q (d) · Q2（ θ)/four л R2]+4/r}

because the sound pressure level is quantitatively equal to the sound intensity (not in physical concept!) And sound intensity level L. The formula of is: lo=10 lg/1 ×, So finally there is:

lr=lw+10 lg{[q (d) · Q2（ θ)/four л R2]+4/r}

where La is the sound power level: la=10 LG wa+120

when there is only one speaker in the room above, when there are multiple speakers with the same index, the R of a point in the sound field from each speaker is different. Not only that, the included angle of the point away from the axis of each speaker will also be different, resulting in Q（ θ) It's different. At this point:

lr=lwi+10 lg{[q (d) · Q2 (0I)/4 л r2+…+Q(d)·Q2（0n))/4 л R2]+4/r}

where LWI is the sound power level of one of the speakers, q (0n) is the directivity coefficient caused by the deviation of the point from the axis of the nth speaker, and RN is the distance from the point to the nth speaker

the above formula is the expression of the sound pressure level at any point in the room under the condition of centralized speaker amplification

II. Calculation of electric power of speakers

as mentioned earlier, the calculation of electric power of speakers is carried out under the following premise: first, it is said that the independent sound pressure level of the listening area must be determined according to the purpose of the studio, and an appropriate peak factor must be set (usually, the sound pressure level in the audience area of the variety studio is 85dB, and the peak factor is taken as 10dB); Then, according to the size of the sound reinforcement room, the radiation angle between the vertical and horizontal directions of the speaker, the pointing characteristic pattern and the sensitivity level of the speaker are selected; Only after all the above conditions are determined can we enter into the calculation of the actual electric power of the speaker

at present, the centralized method is mostly used in the sound reinforcement of the studio (for example, a speaker with the same power is placed on both sides of the stage), so the actual calculation of electric power is for convenience, and only the contribution of the designed sound pressure level to the speaker on one side of the stage is considered. Therefore, the final calculation result we is the sum of the electric power of the speakers on both sides. In other words, when calculating with the above method, as long as the sound pressure level LR of the listening area is reduced by 3dB than the design value in advance, the final we is the electrical power of each side of the speaker (because for each increase or decrease of sound pressure level by 3dB, the electrical power will be doubled or halved accordingly). In this way, the practical sound pressure level expression of indoor sound field can be approximately expressed as:

lr=lw+10 lg{[Q (d) · Q2（ θ)/four л R2]+4/r}

the specific calculation steps are as follows:

1. The formula: lr=lw+10 lg{[Q (d) · Q2（ θ)/four л R2]+4/r}, will be away from welcome people from all walks of life to visit, pointing away from the speaker R (m), away from its axis（ θ) The sound pressure level LR required by the design of a certain point in the space of the angle is converted into the sound pressure level lr'1m away from the speaker but under the same deviation angle:

lr'-lr=10 lg{[q (d) · Q2（ θ)/four л]+ 4/4}-10 lg{[Q(d)·Q2( θ)/four л R2]+4/r}

where, Q2（ θ) By 20lgq（ θ)= 10lgQ2( θ)= L( θ)- L (a), obtained by referring to the pointing characteristic pattern

2. From the pointing characteristic pattern, convert the LR 'calculated above to the sound pressure level at 1m along the sound axis li:

li=lr' +[-20 LG Q（ θ)]

3. Take into account the peak factor LP, so as to obtain the peak sound pressure level Li ':

li' =li+lp

4 at 1m along the axis of the speaker. The formula: 10lgwe=li'-ls

we will give an example below

a pair of speakers placed on both sides of the stage are prepared for indoor sound reinforcement. If the coverage angles h and V of the speaker in the vertical and horizontal radiation directions are 90 degrees and 85 degrees respectively, the sensitivity level is 83db, the average sound absorption coefficient of the room is 0.2, and the internal surface area is 800m2, the effective value sound pressure level of the 3kHz signal is 86db (the peak factor is set to 10dB; the directional characteristic pattern of the speaker at 3kHz is shown in Figure 2) at a distance of 10m from the speaker axis of 30 degrees away from the speaker, and the electrical power of the speaker is calculated

1). First, calculate the room constant and the directivity factor of the speaker:

r=s · a/1-a=800 × 0.2/(.2) =200 (M2)

q (d) =180 ° ÷ SIN-1 [sin (v/2) · sin (h/s)] =180 ° ÷ SIN-1 [sin (90 °/2) · sin (85 °/2) ≈ 6.3

2). Since the sound pressure level produced by the speakers on both sides is required to be 86db, the sound pressure level produced by the speakers on one side: lr=83db. First convert the LR of 0=30 ° and 10m away from the speaker into the sound pressure 1m away from the speaker and the same deviation angle.Level LR's:

lr'=10lg{[q (d) · Q2（ θ)/four л]+ 4/R}-10lg{[Q(d)·Q2( θ)/four л r2]+4/R}+Lr=10lg{[6.3·Q2( θ)/four л]+ 4/200}-10lg{[6.3·Q2( θ)/four л 102]+4/200}+83

where, Q2（ θ) By equation 10 lgq2（ θ)= L( θ)- L (a) and directional characteristic pattern can be obtained:

10lgq2（ θ)= L( θ)- L (a) = = -6, that is, Q2（ θ)= 0.25

thus: lr'≈ 92dB

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