Precise design of crossover inductor based on three-way speaker system

1 Introduction

The crossover of the speaker system is divided into two categories: pre-stage crossover and power crossover. The pre-stage crossover is the crossover generated by electronic components in the pre-stage circuit, and then the high, medium and low-frequency speaker systems are driven by their respective power amplifiers, as shown in Figure (1a), which belongs to small signal active crossover. The power crossover is a passive crossover circuit composed of inductors, capacitors and resistors located between the power amplifier and the speaker, as shown in Figure (1b).

The speaker system using power frequency division has a simple structure, low cost, and can achieve high playback quality. Therefore, it is the most widely used in modern high-fidelity playback systems. The quality of its performance is closely related to the various indicators of the speaker and the performance and accuracy of the frequency division circuit and inductor components. Accurate calculation of inductor parameters is the key to success.

2 Requirements for frequency division circuits and components

(1) The smaller the DC resistance and inductance value errors of the inductor components in the circuit, the better. In addition, it is best to use hollow inductors to make the frequency response curve flat.

(2) The loss of capacitor components in the circuit should be as small as possible. It is best to use audio-specific metallized polypropylene capacitors.

(3) Make each speaker unit distribute a relatively flat signal power and play a role in protecting the high-frequency speaker.

(4) The transmission power characteristics of each channel frequency division combination should meet the requirements of the characteristic curve shown in Figure 2 (P0 is the maximum value, P1 is the value of the corresponding frequency division points f1 and f2). The amplitude between the power at the frequency division point and the maximum power should meet the range of P1 (=0.3~0.5)P0.

(5) The loss is flat in the entire frequency band, with almost no "peaks" or "valleys".

Calculation of the parameter values ​​of the 3-way divider inductor and capacitor

The following uses the 3-way divider as an example to illustrate the calculation of its parameters, as shown in Figure 3.

(1) Calculate the crossover inductors L1, L2, L3, L4 and the crossover capacitors C1, C2, C3, C4.

In order to obtain the ideal spectrum characteristic curve, the theoretical calculation can be: C1=C4, C3=C2, L1=L3, L4=L2, the crossover frequency is f1, (f2 see Figure 2), then the crossover point ω1=2πf0, ω2=2πf2. And assume that the impedance of the high, medium and low speakers is the same as RL. The attenuation is 12 dB per octave.






(2) Experimental correction of the values ​​of C1, C2, C3, C4, L1, L2, L3, L4

For the sake of accuracy, the values ​​of C1, C2, C3, C4, L1, L2, L3, L4 can be slightly adjusted by experimental methods to meet the requirements of the design curve (see Figure 2). That is, by experimentally depicting the frequency response curve, the optimal values ​​of C1, C2, C3, C4, L1, L2, L3, and L4 can be obtained. If there are no experimental conditions, this step can be omitted. After the values ​​of the capacitor and inductor are obtained, the inductance value can be calculated.

4 The role of the optimal structural inductor

4.1 The proposal of the optimal structural inductor

The basic parameters of the hollow crossover inductor (abbreviated as inductor) are inductance and DC resistance. Generally speaking, inaccurate inductance will cause the crossover point to deviate from the design requirements and may affect the frequency response of the speaker system, which everyone pays more attention to. However, its DC resistance should not be too large, otherwise it will affect the sound quality. Usually people do not understand the influence of this resistance in the circuit and its quantitative requirements, so they do not pay enough attention to it. The following brief analysis is made.

Taking the crossover network in Figure 3 as an example, since the crossover inductor L2 of the woofer is connected in series with the load R (L woofer rated impedance), if the impedance of L2 is too large, the loss of the power amplifier output power on it will increase. At the same time, the damping effect of the internal resistance of the power amplifier on the woofer will also be greatly weakened. The former affects the effective output power of the amplifier, while the latter has an irreversible impact on the sound quality. Since the inductance of L2 in the crossover network is the largest and increases with the decrease of the crossover point, the influence of the DC resistance of L2 is quite prominent.

As for the crossover inductor L1 of the tweeter, since it is not connected in series with the load, there is no power consumption and damping problem like L2. However, it is still hoped that its impedance is as small as possible. Because it is connected in parallel with the load, it plays the role of bypassing the residual bass component from C1. If the resistance is too large, it will affect the attenuation steepness of the tweeter crossover network to the bass.

In summary, the value of the DC resistance of the inductor is theoretically as small as possible. In practical applications, the requirements for the value of the DC resistance of the inductor should be considered from the perspective of reducing its impact on the circuit. Specifically, there are two situations. For the inductor connected in series with the load (such as L2), the allowable power loss and sufficient damping should be considered; for the inductor connected in parallel with the load (such as L1), it is mainly considered from the perspective of having sufficient bypass effect.

The treatment principle for the influence of L2 resistance on power loss and L1 resistance on bypass effect is the same, that is, the impedance R of L1 and L2 should be much smaller than the rated impedance R of the speaker (L is R

In summary, we can draw the following conclusion: For the inductor connected in series with the load, its resistance value is generally determined according to the damping requirement R≤RL/20. For example, for an 8Ω load, the resistance of L2 should not be higher than 0.4Ω; for a 4Ω load, it should not be higher than 0.2Ω. For the inductor connected in parallel with the load, its impedance value is determined according to R≤RL/10. For example, for an 8Ω load, the resistance of L1 should not be higher than 0.8Ω; for a 4Ω load, it should not be higher than 0.4Ω. According to such requirements, many famous speaker systems may not meet the indicators.

For the same inductance, its winding structure can be arbitrarily many. Therefore, there must be an optimal structural size for the air-core inductor coil, which should make the ratio of the inductance L to its resistance R L/R reach the maximum value. A set of empirical calculation formulas for reasonably winding air-core inductor coils can be found. Compared with the structural size obtained by other methods, the same inductance value has the smallest impedance value.

In fact, it is easy to judge whether the inductor structure is optimal from its appearance. If the winding cross section is roughly square and the inner diameter of the winding is 4 times the winding width (i.e. the height of the winding), then it is basically the best structure.

The inductor coil with the best structure should be material-saving, small in size, and can make the inductance and resistance meet the predetermined values ​​at the same time.

Since there is an optimal structural dimension for each inductance value and resistance value, the traditional calculation method should be abandoned to obtain and make the inductance. Because the traditional method is difficult to meet the optimal requirements without testing and correction.

The following introduces the calculation method using the empirical formula, which can meet the optimal requirements. And it is also very accurate in calculating the inductance of some special structural dimensions.

4.2 Calculation of the best structural inductance

Assume that the required inductance is L (μH) and its impedance value is R (Ω). First, find the structural parameters of the winding





Parameter b is the height (width) of the winding, which determines the inner diameter and outer diameter of the winding. Therefore, after obtaining b, the winding skeleton can be made according to Figure 4, where the outer diameter of the skeleton is appropriately increased by about 10%, and then






where N is the number of winding turns, d is the diameter of the copper core of the wire, i is the total length of the wire, and w is the total weight of the wire.

According to the copper core diameter d, the corresponding nominal diameter is selected from the wire gauge table, and a sufficient amount of high-strength enameled wire can be purchased according to the total weight of the wire.

The inductance wound by this calculation method is generally less than 5% after comparison with the experiment. It is irrelevant whether it is measured after winding, and it can basically meet the requirements of direct application.

Since the actual copper core diameter D of the wire used in the above winding method is always selected to be larger than the calculated diameter d, the inductance after winding is always lower than the calculated value. Obviously, lengthening the length of the winding wire, that is, winding more turns, can make the actual inductance closer to the calculated value. The total length of the actual winding wire can be calculated by

k=0.4[(D/d)-i] (6)

I(=i+k)i (7)

. Where k is the lengthening factor of the actual wire, I is the total length of the actual winding wire, and the length I is wound into the skeleton. D is the actual wire diameter. For example,

the optimal structural dimensions and winding parameters of a hollow inductor coil with a resistance value of 1 mH and 0.8Ω are calculated. Substituting the values ​​into equations (1) to (5), we get



The outer diameter of the central axis of the skeleton is 2b=24 mm, the distance between the two plywood of the skeleton is b=12 mm, and the outer diameter of the plywood of the skeleton is 4b=48 mm (which can be increased by 10% in actual production). The calculation results are as follows:

b=12 mm; 2b=24 mm; N=181.5 turns; d=0.75 mm; i=20.52 m; w=81 g.

If the actual diameter of the wire is D, use k=0.4 ([D/d)-i], I (=i+k)i for correction. Use this method to calculate the values ​​of L1, L2, L3, and L4, and assemble them according to the figure.

As a calculation verification, the author made a home speaker system according to the parameters of the Hi-Vi S8 plus speaker system crossover. Among them, two inductors of 0.55 mH and 0.18 mH were calculated and made according to the above results, and the measured inductance values ​​were 0.565 mH and 0.187 mH. The error does not exceed 5%. This shows that the inductance wound by this method is accurate. Usually, even if there is no inductance meter to measure, the inductance error does not exceed 5%.

Comparing this calculation method with the previous chart method, we can also appreciate the advantages of this method: less materials, small size, no need to draw charts, and small errors.