Phase method for calculating the separation filters of acoustic systems. Encyclopedia of radio electronics and electrical engineering

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In recent years, the requirements for the quality of sound reproduction equipment have increased significantly. First of all, this refers to the width of the operating frequency range and the magnitude of nonlinear and phase distortions. The playback quality largely depends on the design of the speaker systems (AS). In particular, multi-band speakers, in which two, three or more dynamic heads are installed, are widely used to reproduce low, medium and high frequencies.

To separate the bands of the audio spectrum, dynamic heads are switched on through crossover filters of the first, second or higher order. However, as is known, it is impossible to accurately separate the frequencies of a complex audio signal at the cutoff frequency fp (Fig. 1). Therefore, there is a zone of joint action between adjacent strips of reproduction of dynamic heads. A signal with a crossover frequency fp is reproduced by both heads at approximately the same level. At other frequencies of the joint action zone, the levels of the signals applied to the heads differ sharply from each other in amplitude. For ideal sound reproduction in the zone of joint action, conditions must be provided for in-phase operation of both heads in terms of sound pressure (hereinafter - in-phase operation of the heads), i.e. there should be no phase shift between the currents of the heads, and the zone of joint action should be as large as possible less. However, these conditions are very difficult to fulfill.

First-order filters (Fig. 1, a) are simple, their amplitude-frequency characteristics (AFC) have a flat shape, and due to this, the zones of joint action of dynamic heads are relatively wide. For example, the zone of joint action of the low-frequency VA1 and medium-frequency VA2 heads is approximately equal to 50 ... 5000 Hz (Fig. 1, b).

 
Rice. 1. Simple separation filters: a - circuit diagrams; b - amplitude-frequency characteristics; c - phase-frequency characteristics

For speakers containing three dynamic heads, there may be zones of simultaneous action of all three heads (Fig. 1, b, 500 ... 5000 Hz). (The amplitude-frequency characteristics were built up to the level of signals of practical audibility of the sound of dynamic heads.)

In such crossover filters, in series with the low-frequency (LF) head BA1, the inductor L1 is switched on, the inductive resistance of which is directly proportional to the frequency. As you know, in circuits with inductive resistance, the current lags behind the applied voltage, and in circuits containing capacitance, it leads the voltage. Consequently, the amplitude of the current and the angle of shift between the current and the applied voltage do not remain constant and are in a complex frequency dependence.

For example, for simple crossover filters, the phase-frequency characteristic (PFC) has the form shown in fig. 1, c. In the joint action zone of 50 ... 5000 Hz, depending on the frequency, the angle (p of the phase shift between the currents passing through the VA1 and VA2 heads varies from 142 to 35 °, respectively. A similar picture is observed between the phase-frequency characteristics of the VA2 and VAZ heads The phase shift angle between the head currents at the edges of the joint action zone is 60 and 100 °.It is obvious that the phase shift angle between the currents of the heads BA1 - BA2, BA2 - VAZ is excessively large and depends on the frequency, therefore, the operation of the heads in phase in terms of sound pressure in zone of joint action is not provided.

If the current in the first head changes according to the law Ii sin ot, and in the second - l2 sin (o) t + cpi2), therefore, between the currents of the dynamic heads there is a phase shift by an angle (pi2 and in this case, in the surrounding space, the sound pressure will be proportional to the so-called equivalent current Ie

I_Э = I₁ sin ωt + I₂sin(ωt + φ_1-2) = I_Msin (ωt + α),

whose amplitude I_M is determined from the expression:

I_M = root.q(I₁² + I₂² + I₁I₂cos φ_1-2),

and the angle between the equivalent current and the current of the first head can be determined as follows:

tgα = (I₂sinφ_1-2) / (I₁ + I₂ cos φ_1-2),

i.e., the angle a depends not only on the phase angle between the composite currents (pi2, but also on the ratio of their amplitudes I₁ / I₂. In the zone of joint action of dynamic heads, the phase shift angle can vary from 0 to φ_1-2depending on the ratio of the amplitudes of the currents and, therefore, during sound reproduction, distortions of the original recording will be introduced.

Rice. 2. Separating filter of the second order: a - circuit diagram; b - amplitude-frequency characteristic of the low-frequency dynamic head VA1

With known parameters of the elements of the separation filter and the dynamic head, amplitude and phase-frequency characteristics can be calculated and plotted (Fig. 2 b, c).

In formula (1), there are reactances of the capacitor C3, the inductor L1 and the coil of the dynamic head BA1, which are in a complex frequency dependence. As a result, in second-order filters, the phase shift angle between the dynamic head current and the applied voltage does not remain constant and varies widely depending on the frequency. So, for example, for a low-frequency crossover filter, the phase shift angle between the current of the dynamic head and the voltage applied to the filter, depending on the frequency, can vary from -10 to -270 ° at frequencies of 20 and 20000 Hz, respectively (Fig. 2, c). For a mid-frequency dynamic head, this angle can vary from +110 to -75° at frequencies of 80 and 20000 Hz (Fig. 3), and for a high-frequency one, from +135 to -50° (at 150 and 20000 Hz).

Rice. Fig. 3. Second-order mid-range separation filter: a - circuit diagram; b-dependence of the phase shift angle between the current and voltage applied to the filter: / - the main option (C4 \u40d 2 μF. L0,9 \u4d 0,75 mH, R3 \u0d XNUMX Ohm, Kd \uXNUMXd b.XNUMX Ohm, RXNUMX \uXNUMXd XNUMX)

2 - the same, but at C4 = 20 uF

3 - the same, but at C4 \u20d XNUMX microfarads (apparently a typo in the article)

4 the same, but at C4=80 uF

5 the same, but with L2 = 0,6 uF

6 the same, but with R3 = 5 ohms

Thus, the phase angle between the current of the low-frequency dynamic head and the voltage applied to the filter can change when the frequency of the applied voltage changes. by 260°, and for the midrange and tweeters, the same angle changes by 185°. This circumstance is the main reason for the out-of-phase operation of dynamic heads in the zone of their joint action.

By changing the parameters of the crossover filter elements, you can adjust the phase response of each dynamic head. Due to this, it is possible to obtain identical characteristics of the heads and, thereby, ensure the conditions for their operation in phase in the zone of joint action.

So for a low-frequency crossover filter according to the scheme of Fig. 2, and the phase-frequency characteristic undergoes the following changes:

with an increase in the capacitance of the capacitor C3 (curve 2), the central part of the characteristic shifts parallel to the left;

a decrease in the capacitance of the capacitor C3 (curve 3) shifts parallel to the central part of the characteristic to the right;

with an increase in the resistance of the resistor R1 and a decrease in the inductance of the inductor L1, the left part shifts to the region of small angles with a simultaneous shift of the central part to the right (curve 5);

the inclusion of the resistor R2 in series with the capacitor C3 shifts the right side of the characteristic (curve 4) to the region of smaller angles.

When changing the parameters of crossover filters, not only the phase-frequency characteristic is corrected, but also the amplitude-frequency characteristic is deformed. So, in fig. 2,6:

from an increase in the capacitance of the capacitor C3 (curve 2), the current amplitude slightly increases, the frequency bandwidth decreases; with a decrease in the capacitance of the capacitor C3 (curve 3), the current decreases, and the bandwidth increases;

an increase in the resistance of the resistor R1 reduces the maximum value of the current amplitude without affecting the filter bandwidth (curve 5);

a decrease in the inductance of the inductor L1 is accompanied by an increase in the current amplitude and an expansion of the filter bandwidth, etc.

The electrical circuits of crossover filters for mid-frequency and high-frequency dynamic heads can be the same, differing only in the value of the parameters of the elements (Fig. 3, a). For such a circuit, the head current value can be calculated by the formula

With the capacitance of the capacitor C4 = 40 μF for the dynamic head ZGD1, the phase-frequency characteristic is similar in shape to the characteristic of the low-frequency head, but it is shifted to the region of positive angles.

Changing the parameters of the separation filter elements affects the phase response (Fig. 3,6) as follows:

- an increase in the capacitance of the capacitor C4 (curve 4) shifts the central part of the characteristic to the low-frequency region;

- a decrease in the inductance of the inductor L2 (curve 5) shifts the central part to the region of high frequencies and the left end of the characteristic to the region of smaller values ​​of the angles φ;

- increase in the active resistance of the head R_Д(or the resistance of a resistor connected in series with it) moves the entire characteristic in parallel in the direction of increasing the current shift angle;

- an increase in the resistance of the resistor R3 (curve 6) straightens the characteristic, shifting the right and left parts towards smaller angle values.

The influence of changes in the parameters of the same elements on the amplitude-frequency characteristic is as follows:

- an increase in the capacitance of the capacitor C4 leads to an increase in the maximum value of the amplitude of the characteristic, a sharp increase in its unevenness, the transmission zone increases towards low frequencies;

- increase in the active resistance of the head R_Дslightly reduces the unevenness of the frequency response;

- an increase in the resistance of the resistor R4 reduces the unevenness of the frequency response and at the same time shifts it towards low frequencies;

- resistance R3 smoothes the uneven characteristics.

With known patterns of influence of changes in the parameters of the separation filters on their phase and amplitude-frequency characteristics, the creation of identical (combined) phase characteristics of low-frequency and medium-frequency dynamic heads does not present any particular difficulties.

The greatest difficulty is the coordination of the phase characteristics of the high-frequency and mid-frequency dynamic heads. Both separating filters are capacitive and, of course, the identity of their phase-frequency characteristics can occur with the same values ​​of the capacitances of the capacitors C4, and this contradicts the frequency separation condition. Therefore, one option is to install a low-capacity capacitor C4 (about 2 μF) and an inductor L2 with a small inductance (less than 0,1 mH) in the high-frequency filter. Changing the capacitance of the capacitor C4 has a dramatic effect on the phase and amplitude characteristics. In addition, resonant phenomena may appear, therefore, it is necessary to take measures to reduce the unevenness of the frequency response, for example, to connect in series with the capacitor C4 (in Fig. 3) a resistor R3 with a small resistance.

The second option for phase matching of the currents of the VA2 and VAZ heads is the construction of filters according to different schemes: For example, the VAZ head can be turned on through a third-order separation filter

Rice. Fig. 4. Schemes for measuring the impedance of the coils of dynamic heads: a - measurement by the substitution method; b - measurement with a voltage source

The procedure for calculating the phase and amplitude-frequency characteristics of acoustic systems can be as follows. Firstly, to perform the calculation, it is necessary to know the active and inductive resistances of each dynamic head at frequencies in the zone of their useful work. The active resistance can be measured with a DC bridge, an ohmmeter, or other instrument. The determination of the inductive reactance of dynamic heads is associated with some difficulties, since it is in a complex dependence on the frequency and on the conditions of mounting the head. Therefore, the inductive reactance of dynamic heads should be determined under normal conditions of their operation (mounted in a box with a closed back wall, etc.). In practice, the inductive resistance of dynamic heads is determined experimentally and by calculation. To do this, measure the impedance of the head according to the scheme of Fig. 4. Active auxiliary resistance r in the circuit of fig. 4,a should be more, and in the scheme of fig. 4,6 - less than the expected head resistance by 10...20 times. According to these schemes, the dependence of the impedance of the dynamic head on the frequency is removed.

According to the diagram in Fig. 4, and the measurement is carried out by the substitution method. By setting the frequency of the sound generator at regular intervals G, voltmeter PV measures the drop of alternating voltage across the resistance of the coil of the dynamic head VA. Then, instead of the head, a variable resistor R is turned on and, by changing its resistance, the same voltage value is obtained on it. In this case, the active resistance R is equal to the total resistance 2d1 of the dynamic head at a given frequency. The number of measurement points is determined by the type of head (LF, HF) and the unevenness of its characteristics. On the obtained value of the impedance for each frequency value, the inductive reactance of the dynamic head is determined by the formula

Xdi = short square (Zdi² - Rd²)

The output voltage level of the sound generator has almost no effect on the measurement results. So, when the voltage changes from 1 to 30 V, the impedance of the dynamic head changes by 5 ... 8%. Measurements according to the scheme of fig. 4,6 more accurate, the head impedance value is

Zdi = r Udi / Ur

According to certain values ​​of the resistance of the dynamic heads for specific frequencies and the expected parameters of the elements of the separation filters, the phase-frequency and amplitude-frequency characteristics are calculated using formulas (1) and (2). Based on the constructed amplitude characteristics, the boundary frequencies of the section and the zones of joint action of the dynamic heads are determined, as well as the unevenness of the characteristics and the need for their equalization. Based on the same characteristics, one can draw a conclusion about the steepness of the frequency separation, about the evaluation of the qualities of the crossover filters, and about the ways of the desired change (shift, narrowing, etc.).

Then the phase characteristics are built and special attention is paid to their convergence in the zone of joint action of the dynamic heads. After analyzing the constructed characteristics and in the presence of any shortcomings, based on the known nature of the effect of changing the elements of separation filters on their characteristics, a correction option is outlined and the characteristics are calculated again. The characteristics obtained are built, analyzed, etc. until the required results are obtained. Then all elements of the acoustic system are mounted and electrical tests are carried out.

According to the above method, we determined the parameters of separation filters for an acoustic system based on dynamic heads: 6GD2 (L1 = 7,9 mH, R2 = 1 Ohm, C3 \u30d 5,5 μF, Rd \u1d 1,45 Ohm, R1 \u2d 1,3 Ohm); ZGD4 (L1 = 4 mH, R60 = 6,8 ohm, C3 = 2 μF, Rd1 ohm, R2 = 0,08 ohm); 4GDZ (L0,5 = 4 mH, R2 = 8,70 Ohm, C3 = 1uF, Rd = XNUMXm, RXNUMX = XNUMX Ohm).

On fig. Figures 5 and 6 show the measured characteristics of the low-frequency (LF - 6GD2) and mid-frequency (MF-ZGD1) dynamic heads. As you can see, the cutoff frequency f_P1 = 400 Hz, the joint action zone is 80...2000 Hz, and the shift angle between the phase-frequency characteristics is 150...190°. Therefore, it is necessary to reverse the polarity of switching on one of the dynamic heads ("turn" the current by 180°). As will become clear from matching the mid-frequency head with the high-frequency one, the polarity of the inclusion of the mid-frequency head should be changed (Fig. 6, inverted mid-range characteristic). In this case, the phase shift angle between the head currents is 30 and 10°, respectively, at frequencies of 80 and 2000 Hz. For a more accurate combination of characteristics in the zone of 500 ... 2000 Hz, the resistance R2 should be increased to 1,3 Ohm (see Fig. 2, a). Similarly, the phase characteristics of the medium and high-frequency dynamic heads are matched.

As a result of matching the phase characteristics of low, medium and high-frequency dynamic heads, it seems possible to create an acoustic system with high-quality reproduction of the entire frequency range and an "apparent" extension of the reproducible frequency range.

In the manufacture of separation filters as capacitors C3 and C4, it is necessary to use paper capacitors for an operating voltage of at least 100 V, for example, MBGP2 for 160 V. Resistors R1-R4 can be made with a wire with a diameter of 0,4 ... 0,6 mm from any high-resistance alloy ; winding is bifilar.

The inductor in the high-frequency filter is made on any cylindrical frame with a copper wire with a diameter of 0,6. ..0,8mm (about 140 turns). The inductor L2 of the midrange filter (approximately 240 turns) is made with a wire with a diameter of 0,8 mm, the active resistance of which should not exceed the resistance of the resistor R4, since the active total resistance of the inductor winding and additional resistor is indicated in the diagram under R4. If the value of the inductance is insufficient for the required value of active resistance, a small ferrite core is inserted into the coil.

The inductor L1 of the low-pass filter is made on a medium-sized frame (outer diameter 25 ... 30 mm) with a 0,8 mm wire. The active resistance of the winding is 1,45 ohms. To increase the inductance, a U-shaped ferrite core is inserted into the coil from a horizontal scanning transformer. Cores made of other materials (transformer steel, carbonyl iron, etc.) should not be used, since they show a dependence of the inductance value on the strength or frequency of the current. This can lead to non-linear distortion.

The connecting wires in the filters must have a cross section of at least 0,8 mm², and for connection with amplifying equipment - at least 1,5 mm². This is necessary to reduce voltage and power losses in the wires and eliminate possible mutual influences between the filters.

It is absolutely unacceptable to use separate elements in the circuits of two filters, for example, the high-frequency filter capacitor C4 should be connected after a similar mid-frequency filter capacitor (as is often done in practice). If this condition is not met, mutual influences appear on the amplitude and especially on the phase-frequency characteristics.

Author: A. Vakhrameev; Publication: cxem.net

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