EP0568721B1 - Method of adapting the acoustic volume and the second-order high-pass filter of a loudspeaker chassis - Google Patents

Abstract

Loudspeaker in a closed enclosure. Conventional passive loudspeaker systems exhibit very large enclosures for a clean base reproduction which extends to low frequencies. Active electronic correcting systems are expensive and can only be used when loudspeaker and electronics are paired correctly. The novel passive loudspeaker system is intended to achieve at the same time predetermined frequency response characteristic, small enclosures and clean base reproduction which extends to a low frequency. The low range speaker is operated in connection with an enclosure tuned to its parameters and a tuned passive high-pass filter of at least 2nd degree. These measures result in a low cut-off frequency and small enclosure for particular acoustically advantageous frequency response characteristics. The novel loudspeaker system is particularly of interest in the field of small speakers suitable for the living room. <IMAGE>

Description

The invention relates to a method and a loudspeaker according to claims 1 and 3, respectively.

In the construction of loudspeakers, various construction principles are used for electrodynamic loudspeaker chassis: closed housings, bass reflex boxes, passive membranes, satellite / subwoofer systems, chassis with 2 coils, compound systems, transmission lines, horns and systems derived from them. Furthermore, there are active systems consisting of loudspeakers and associated electronics, in which improvements such as frequency response correction, feedback or complex output resistance of the amplifier can also be implemented. In addition to the electrodynamic loudspeaker, there are also electrostats, magnetostats, tapes and others that are less suitable for reproducing low frequencies.

The large housing is common to all possibilities if good bass reproduction is to be achieved. Compound systems do slightly better than others in terms of housing volume, but require twice the effort in the chassis area. When it comes to influencing the bass range, active systems quickly reach the thermal limits of the loudspeaker chassis involved. Active systems are also very expensive.

The present invention is based on the object, in a passive loudspeaker system with a given loudspeaker chassis, taking into account the repercussions of the loudspeaker chassis, certain acoustically favorable (low resonance quality, for example the maximum flat Butterworth characteristic), or frequency response types necessary for the construction of multi-way systems (for example Linkwitz characteristic) to be realized while taking into account the target sizes, small housing volume and deep reproduction.
This object is achieved by the features listed in claims 1 and 3, respectively.

From the American patent US-A-4 383 134 a speaker system is known which uses a high-pass filter. While there the focus is on the combination of the filter with a loudspeaker with parameters that can be set specifically (membrane mass and flexibility of the membrane suspension are brought to pre-defined values), a given loudspeaker chassis is assumed here and the housing volume and the filter for setting acoustically favorable properties are specifically dimensioned.

The idea of the invention, the solution method and a calculated exemplary embodiment are described below for the case of the 2nd level high-pass filter; the transfer to higher order filters is to be carried out analogously.

R₀ ,

Gleichstromwiderstand des verwendeten Lautsprechers f₀ Resonanzfrequenz des Chassis im nicht eingebauten Zustand

V_as

Äquivalentvolumen des Chassis

Q_ms

mechanische Resonanzgüte des Chassis im nicht eingebauten Zustand

Q_ts

gesamte Resonanzgüte des Chassis im nicht eingebauten Zustand, bestehend aus elektrischer und mechanischer Resonanzgüte unter Berücksichtigung von Zuleitungswiderständen oder Widerständen von Längsspulen weiterer Frequenzweichenbauteile

   weitere verwendete Größen:

Q_F =

R₀ $\sqrt{\text{C/L}}$

Güte des Filters 2. Grades;

C, L

siehe Bild 3, Kondensator und Spule des Hochpaßfilters 2. Grades

V_ab

das akustische Volumen der Box, das tatsächliche Volumen liegt dann ca. 15% darunter, je nach verwendeter Bedämpfung

f_gr

die erreichbare untere Grenzfrequenz des Systems

   normierte Größen: $${\text{f}}_{\text{norm}}{\text{= f}}_{\text{gr}}{\text{/ f}}_{\text{0}}$$

$${\text{V}}_{\text{norm}}{\text{= V}}_{\text{ab}}{\text{/ V}}_{\text{as}}$$

$${\text{C = C}}_{\text{norm}}{\text{/ f}}_{\text{0}}{\text{R}}_{\text{0}}$$

$${\text{L = L}}_{\text{norm}}{\text{R}}_{\text{0}}{\text{/ f}}_{\text{0}}$$

F, y, a sind Zwischengrößen zur Vereinfachung der Formeln.The following terms and abbreviations are used:
Speaker chassis parameters:

R ₀ ,

DC resistance of the loudspeaker used f ₀ resonance frequency of the chassis when not installed

V _as

Equivalent volume of the chassis

Q _ms

Mechanical resonance quality of the chassis when not installed

Q _ts

Total resonance quality of the chassis when not installed, consisting of electrical and mechanical resonance quality, taking lead resistances or resistances of series coils of other crossover components into account

other sizes used:

Q _F =

R ₀ $\sqrt{\text{C / L}}$

Quality of the 2nd degree filter;

C, L

see picture 3, capacitor and coil of the high-pass filter 2nd degree

V _from

the acoustic volume of the box, the actual volume is approx. 15% lower, depending on the damping used

f _gr

the attainable lower limit frequency of the system

standardized sizes: $${\text{f}}_{\text{standard}}{\text{= f}}_{\text{gr}}{\text{/ f}}_{\text{0}}$$

$${\text{V}}_{\text{standard}}{\text{= V}}_{\text{from}}{\text{/ V}}_{\text{as}}$$

$${\text{C = C}}_{\text{standard}}{\text{/ f}}_{\text{0}}{\text{R}}_{\text{0}}$$

$${\text{L = L}}_{\text{standard}}{\text{R}}_{\text{0}}{\text{/ f}}_{\text{0}}$$

F, y, a are intermediate values to simplify the formulas.

A, B are constants that describe the type of the overall 4th degree acoustic high pass,
e.g. A = 2,613, B = 3,414 for Butterworth characteristic
A = 2,828, B = 4.0 for Linkwitz characteristics.

• die Schwingungsdifferentialgleichung des Lautsprecherchassis (der akustische Tiefpaßcharakter des Chassis bleibt bei diesen Überlegungen schadlos unberücksichtigt, da der Filter am unteren Übertragungsbereich arbeitet.),
• Differentialgleichungen der Hochpaßelemente,
• Zusammenhang Schalldruck - Auslenkung der Membran,
• Transformation mechanischer in elektrische Größen am Chassis,
• Knoten- und Maschengleichungen.

Now we are formulated mathematically:

• the vibration differential equation of the loudspeaker chassis (the acoustic low-pass character of the chassis is not taken into account in these considerations, since the filter works at the lower transmission range),
• Differential equations of the high-pass elements,
• Relationship between sound pressure and membrane deflection,
• Transformation of mechanical to electrical quantities on the chassis,
• Knot and mesh equations.

$${\text{a}}^{\text{2}}{\text{+ 1 / a}}^{\text{2}}{\text{+ 1 / Q}}_{\text{F}}{\text{Q}}_{\text{ms}}\text{F = B}$$

$${\text{a / F Q}}_{\text{ts}}{\text{+ 1 / a Q}}_{\text{F}}\text{= D (D = A für symmetrische Polynome)}$$

The acoustic frequency response of the entire system can be calculated from this. The system of equations and its resolution is shown using the example of the 2nd degree filter. In order to arrive at a certain type of acoustic high-pass filter of the 4th degree, the following system of equations must be fulfilled: $${\text{a / Q}}_{\text{F}}{\text{+1 / a FQ}}_{\text{ts}}\text{= A}$$

$${\text{a}}^{\text{2nd}}{\text{+ 1 / a}}^{\text{2nd}}{\text{+ 1 / Q}}_{\text{F}}{\text{Q}}_{\text{ms}}\text{F = B}$$

$${\text{a / FQ}}_{\text{ts}}{\text{+ 1 / a Q}}_{\text{F}}\text{= D (D = A for symmetric polynomials)}$$

$$\text{2.\hspace{1em}\hspace{1em}\hspace{1em}a =}\sqrt{\text{0.5 (}\mathit{\text{y}}\text{±}\sqrt{{\mathit{\text{y}}}^{\text{2}}\text{-4}}\text{)}}$$

$${\text{3.\hspace{1em}\hspace{1em}\hspace{1em}F = (a+1/a) / A Q}}_{\text{ts}}$$

$${\text{4.\hspace{1em}\hspace{1em}\hspace{1em}C}}_{\text{norm}}{\text{= Q}}_{\text{ts}}{\text{a}}^{\text{2}}\text{/ 2π}$$

$${\text{5.\hspace{1em}\hspace{1em}\hspace{1em}L}}_{\text{norm}}{\text{= a}}^{\text{2}}{\text{/ F}}^{\text{2}}{\text{Q}}_{\text{ts}}\text{2π}$$

$${\text{6.\hspace{1em}\hspace{1em}\hspace{1em}f}}_{\text{norm}}\text{= F / a}$$

$${\text{7.\hspace{1em}\hspace{1em}\hspace{1em}V}}_{\text{norm}}{\text{= 1 / (F}}^{\text{2}}\text{-1)}$$

This leads to the following equations: $$\text{1. y = 0.5 (B - 2 +}\sqrt{{\left(\text{B + 2}\right)}^{\mathrm{2nd}}{\text{-4 A}}^{\text{2nd}}{\text{Q}}_{\text{ts}}{\text{/ Q}}_{\text{ms}}}\text{)}$$

$$\text{2. a =}\sqrt{\text{0.5 (}\mathit{\text{y}}\text{±}\sqrt{{\mathit{\text{y}}}^{\text{2nd}}\text{-4}}\text{)}}$$

$${\text{3. F = (a + 1 / a) / <figure-callout id="4" label="AQ ts" filenames="imgf0001.png" state="{{state}}">AQ </figure-callout>}}_{\text{ts}}$$

$${\text{4. C}}_{\text{standard}}{\text{= Q}}_{\text{ts}}{\text{a}}^{\text{2nd}}\text{/ 2π}$$

$${\text{5. L}}_{\text{standard}}{\text{= a}}^{\text{2nd}}{\text{/ F}}^{\text{2nd}}{\text{Q}}_{\text{ts}}\text{2π}$$

$${\text{6. f}}_{\text{standard}}\text{= F / a}$$

$${\text{7. V}}_{\text{standard}}{\text{= 1 / (F}}^{\text{2nd}}\text{-1)}$$

The solutions that use the minus sign in equation 2 result in higher limit frequencies with the same housing volume. Similarly, there are several solutions for the higher order filters.

Figures 1 and 2 show the normalized volume of the housing and the cut-off frequency of the overall system of the 4th degree related to the resonance frequency for Butterworth - and Linkwitz vote (Bu4, Li4) shown, the parameter Q _ms was set to 5. (For the Linkwitz voting, the cutoff frequency refers to the -6 dB point.) For comparison with conventional solutions, the diagrams also show the voting in a closed housing without a filter (Bu2, Li2). These are calculated according to the known formulas (literature reference at the end of the description). Also for comparison is the bass reflex tuning according to Thiele / Small. (Literature reference; Q _L = 7). It can also be seen (Bu3) that a filter of the first degree (only one capacitor) does not solve the task: when adapting to the Butterworth frequency response of the third degree there are small housings (Fig. 1), but the highest cut-off frequencies in comparison (Fig. 2). Diagrams 1 and 2 also show that the adaptation according to the invention is possible over a very wide range of chassis parameters; In particular, chassis can be used whose parameters are otherwise unsuitable for an acoustically favorable housing design.

• Q_ms = 5; f₀ = 30 Hz
• Q_ts = 0.5; V_as = 80 Liter
• Bei Bu2 Abstimmung (Gehäuse ohne Filter) ergibt sich:
• V_ab = 80 Liter, f_grenz = 42.4 Hz.
• Bu4 Abstimmung gemäß Erfindung liefert:
• V_ab = 38 Liter, f_grenz = 30.7 Hz.

A bass speaker chassis with the following parameters is now considered as an example: (e.g. subwoofer or bass)

• Q _ms = 5; f ₀ = 30 Hz
• Q _ts = 0.5; V _as = 80 liters
• Bu2 tuning (housing without filter) results in:
• V _ab = 80 liters, f _limit = 42.4 Hz.
• Bu4 tuning according to the invention provides:
• V _ab = 38 liters, f _limit = 30.7 Hz.

• das benötigte Gehäusevolumen ist halb so groß wie bei herkömmlichen Lösungen,
• der Frequenzbereich ist um den Faktor 1.4 (eine halbe Oktave) nach unten erweitert,
• es wird ein akustisch günstiger Zielfrequenzgang realisiert,
• gleichzeitig schützt die erfindungsgemäße Filterauslegung das Chassis wie ein Subsonicfilter.

The following advantages result in the case of the chassis under consideration:

• the housing volume required is half that of conventional solutions,
• the frequency range is extended downwards by a factor of 1.4 (half an octave),
• an acoustically favorable target frequency response is realized,
• at the same time, the filter design according to the invention protects the chassis like a subsonic filter.

A preferred application arises, for example, in systems with an external or integrated subwoofer. Here, the low / low midrange connected to the subwoofer can also be controlled according to the invention, preferably as a 4th degree link joke system. Likewise, the possibility of a higher cut-off frequency resulting in equation 2 can then advantageously be used. With passive separation (through additional filter elements, in multi-way systems) of the considered chassis to higher frequencies, it is recommended to compensate the chassis impedance by means of an RC element connected in parallel. The design according to the invention enables exact frequency response characteristics as are necessary for the construction of crossovers (eg Li4). Therefore, the invention can also be used advantageously in the mid and high range.

In a further embodiment of the invention, the series resistances of the inductors or leads used are included in the design calculation. It is also possible to combine the invention with the compound principle or to use several chassis - also with a common filter - to achieve higher volumes. Furthermore, according to the statements made, it is possible to transfer the inventive idea and the calculation methodology to closed housings which are damped by an acoustic flow resistance or which are provided with a mechanical bandpass (bandpass housing).

• Lautsprecher Jahrbuch, Michael Gaedtke, Münster,
• HIFISOUND LSV, 1989, ISBN 3-9801310-1-7

Literature:

• Loudspeaker yearbook, Michael Gaedtke, Münster,
• HIFISOUND LSV, 1989, ISBN 3-9801310-1-7

Claims (13)

1. System for methodically adjusting the acoustical volume V_ab and the passive 2nd order L, C - highpass filter of an electrodynamic driver in a closed box to the total quality factor Q_ts, to the mechanical quality factor Q_ms and to the drivers resonance frequency f₀ measured without enclosure in each case, to the drivers dc resistance R_o and equivalent volume V_as and to the constants A, B and D determining the type of the achieved 4th order acoustical overall highpass, using the 2nd order highpass filter to run the driver and using the following equations for adjustment: $${\text{I)\hspace{1em}\hspace{1em}\hspace{1em}V}}_{\text{ab}}{\text{= V}}_{\text{norm}}{\text{V}}_{\text{as}}$$

   

   $${\text{II)\hspace{1em}\hspace{1em}\hspace{1em}C = C}}_{\text{norm}}{\text{/ f}}_{\text{0}}{\text{R}}_{\text{0}}$$

   

   $${\text{III)\hspace{1em}\hspace{1em}\hspace{1em}L= L}}_{\text{norm}}{\text{R}}_{\text{0}}{\text{/ f}}_{\text{0}}$$

   

   $${\text{IV)\hspace{1em}\hspace{1em}\hspace{1em}V}}_{\text{norm}}{\text{= 1 / (F}}^{\text{2}}\text{-1)}$$

   

   $${\text{V)\hspace{1em}\hspace{1em}\hspace{1em}C}}_{\text{norm}}{\text{= Q}}_{\text{ts}}{\text{a}}^{\text{2}}\text{/ 2π}$$

   

   $${\text{VI)\hspace{1em}\hspace{1em}\hspace{1em}L}}_{\text{norm}}{\text{= a}}^{\text{2}}{\text{/ F}}^{\text{2}}{\text{Q}}_{\text{ts}}\text{2π}$$

   

   $${\text{VII)\hspace{1em}\hspace{1em}\hspace{1em}F = (a+1/a) / A Q}}_{\text{ts}}$$

   

   $$\text{VIII)\hspace{1em}\hspace{1em}\hspace{1em}a =}\sqrt{\text{0.5 (}\mathit{\text{y}}\text{±}\sqrt{{\mathit{\text{y}}}^{\text{2}}\text{-4}}\text{)}}$$

   

   $$\text{IX)\hspace{1em}\hspace{1em}\hspace{1em}y = 0.5 (B - 2 +}\sqrt{{\left(\text{B+2}\right)}^2{\text{-4 A}}^{\text{2}}{\text{Q}}_{\text{ts}}{\text{/Q}}_{\text{ms}}}\text{)}$$

   

   $${\text{X)\hspace{1em}\hspace{1em}\hspace{1em}a / Q}}_{\text{F}}{\text{+ 1 / a F Q}}_{\text{ts}}\text{= A}$$

   

   $${\text{XI)\hspace{1em}\hspace{1em}\hspace{1em}a}}^{\text{2}}{\text{+ 1 / a}}^{\text{2}}{\text{+ 1 / Q}}_{\text{F}}{\text{Q}}_{\text{ms}}\text{F = B}$$

   

   $${\text{XII)\hspace{1em}\hspace{1em}\hspace{1em}a / F Q}}_{\text{ts}}{\text{+ 1 / a Q}}_{\text{F}}\text{= D}$$

   

   $${\text{XIII)\hspace{1em}\hspace{1em}\hspace{1em}Q}}_{\text{F}}{\text{= R}}_{\text{0}}\sqrt{\text{C/L}}$$

   

   with

   L, C:   inductor, capacitor of the 2nd order highpass filter

   Q_F:   quality factor of the 2nd order filter

   V_norm:   normalized enclosure volume

   L_norm:   normalized inductivity of inductor L

   C_norm:   normalized capacity of capacitor C

   F, y, a:   variables to make formulas easier
2. System according to claim 1, comprising the minus sign is used in equation VIII) to achieve a higher cut-off frequency.
3. Loudspeaker, obtainable by the system of one of the claims 1 or 2.
4. Loudspeaker according to claim 3, comprising existing series resistors are regarded in the calculations.
5. Loudspeaker according to one of the claims 3 or 4, comprising a RC network is added in parallel to compensate for voice coil inductivity.
6. Loudspeaker according to one of the claims 3 through 5, comprising passive low-pass filters are added to the passive highpass filter according to the invention.
7. Loudspeaker according to one of the claims 3 through 6, comprising the loudspeaker being a subwoofer.
8. Loudspeaker according to one of then claim 3 through 7, comprising the driver under consideration being a bass / bass-midrange driver in a system with or without external or integrated subwoofer.
9. Loudspeaker according to one of the claims 3 through 7, comprising the spirit of the invention being applicated to midrange drivers or tweeters.
10. Loudspeaker according to one of the claims 3 through 9, comprising there are several drivers acoustically parallel or in series or combined in the frequency range under consideration.
11. Loudspeaker according to one of the claims 3 through 10, comprising the enclosure volume being connected to the outside by means of a flow resistor.
12. Loudspeaker according to one of the claims 3 through 11, comprising the invention being combined with band-pass enclosure principle.
13. System according to one of the claims 1 or 2, comprising the constants are chosen to A = D.

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