EP0568721A1 - Loudspeaker filter - 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

Various construction principles are used in loudspeaker construction 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 volume, but require twice the effort in the chassis area. Active systems quickly reach the thermal limits of the loudspeaker chassis involved when it comes to influencing the bass range. Active systems are also very expensive.

The present invention has for its object to realize certain acoustically favorable, or necessary for the construction of multi-way systems frequency response types in a passive speaker system, taking into account the repercussions of the speaker chassis, while taking into account the target sizes small housing volume and deep reproduction.
This object is achieved by the features listed in claim 1 - coordinated system of chassis parameters, housing volume and high-pass filter of at least 2nd degree.

The idea of the invention, the solution method and a calculated exemplary embodiment are described below for the case of the 2nd degree high-pass filter.

R₀

Gleichstromwiderstand des verwendeten Lautsprechers

f₀

Resonanzfrequenz des Chassis im nicht eingebauten Zustand

V_as

Aquivalentvolumen 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

Q_F =

R₀√ $\overline{\text{C/L}}$

Güte des Filters 2. Grades; C,L siehe Bild III

V_ab

das akkustische 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:

${\text{f}}_{\text{norm}}{\text{= f}}_{\text{gr}}\text{/f₀}$

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

${\text{C = C}}_{\text{norm}}\text{/R₀f₀}$

${\text{L = L}}_{\text{norm}}\text{R₀/f₀}$

F, y, a sind Zwischengrössen zur Vereinfachung der Formeln.
A, B sind Konstanten, die den Typus des erzielten akkustischen Gesamthochpasses 4. Grades beschreiben, z.B.

A =

2.613 , B = 3.414 für Butterworthcharakteristik

A =

2.828 , B = 4.0 für Linkwitzcharakteristik.

The following terms and abbreviations are used:

R₀

DC resistance of the loudspeaker used

f₀

Chassis resonance frequency 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 into account lead resistance or resistance of series coils of other crossover components

Q _F =

R₀√ $\overline{\text{C / L}}$

Quality of the 2nd degree filter; C, L see picture III

V _from

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

f _gr

The achievable lower limit frequency of the system standardized sizes:

${\text{f}}_{\text{standard}}{\text{= f}}_{\text{gr}}\text{/ f₀}$

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

${\text{C = C}}_{\text{standard}}\text{/ R₀f₀}$

${\text{L = L}}_{\text{standard}}\text{R₀ / f₀}$

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 akkustische Tiefpasscharakter des Chassis bleibt bei diesen Überlegungen schadlos unberücksichtigt, da das 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.

${\text{a² +1/a² + 1/Q}}_{\text{F}}{\text{Q}}_{\text{ms}}\text{F = B}$

${\text{a/FQ}}_{\text{ts}}{\text{+ 1/aQ}}_{\text{F}}\text{= C (C = A für symmetrische Polynome)}$

Dies führt zu folgenden Gleichungen:

$\text{1. y = 0.5 (B-2+√}\overline{{\text{(B+2)² - 4A²Q}}_{\text{ts}}{\text{/Q}}_{\text{ms}}}\overline{\text{)}}$

${\text{3. F = (a+1/a)/AQ}}_{\text{ts}}$

${\text{4. C}}_{\text{norm}}{\text{= Q}}_{\text{ts}}\text{a²/2pi (pi=3.1415.....)}$

${\text{5. L}}_{\text{norm}}{\text{= a²/F²Q}}_{\text{ts}}\text{2pi}$

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

${\text{7. V}}_{\text{norm}}\text{= 1/(F²-1)}$

Dabei ergeben die Lösungen, die in Gleichung 2. das Minuszeichen (Klammer) verwenden bei gleichem Gehäusevolumen höhere Grenzfrequenzen. Ebenso existieren für die Filter höherer Ordnung entsprechend mehrere Lösungen.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 4th level acoustic high pass, the following system of equations must be fulfilled:

${\text{a / Q}}_{\text{F}}{\text{+ 1 / aFQ}}_{\text{ts}}\text{= A}$

${\text{a² + 1 / a² + 1 / Q}}_{\text{F}}{\text{Q}}_{\text{ms}}\text{F = B}$

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

This leads to the following equations:

$\text{1. y = 0.5 (B-2 + √}\overline{{\text{(B + 2) ² - 4A²Q}}_{\text{ts}}{\text{/ Q}}_{\text{ms}}}\overline{\text{)}}$

${\text{3. F = (a + 1 / a) / AQ}}_{\text{ts}}$

${\text{4. C}}_{\text{standard}}{\text{= Q}}_{\text{ts}}\text{a² / 2pi (pi = 3.1415 .....)}$

${\text{5. L}}_{\text{standard}}{\text{= a² / F²Q}}_{\text{ts}}\text{2pi}$

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

${\text{7. V}}_{\text{standard}}\text{= 1 / (F²-1)}$

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

Figures I and II show the normalized volume of the housing and the cut-off frequency of the overall system of the 4th degree for Butterworth and Linkwitz tuning (Bu4, Li4), 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). The bass reflex tuning according to Thiele / Small can also be found for comparison. (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. I), but the highest cut-off frequencies in comparison (Fig. II).
Diagrams I and II 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.

A bass speaker chassis with the following parameters is now considered as an example: (e.g. subwoofer)
Q _ms = 5; f₀ = 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 akkustisch günstiger Zielfrequenzgang realisiert,
• gleichzeitig schützt die erfindungsgemäße Filterauslegung das Chassis wie ein Subsonicfilter.

The following advantages result in the case of the chassis considered:

• 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 woofer / woofer 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. In the case of passive separation of the chassis under consideration to higher frequencies, it is advisable to compensate for the impedance of the chassis 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 use several chassis - also with a common filter - to achieve higher volumes.

Claims (12)

Electrodynamic loudspeaker in a closed housing, characterized in that - the loudspeaker is operated via a passive 2nd or higher order high-pass filter, - the housing volume and the high-pass filter are adapted to the parameters of the loudspeaker used, - The adaptation of the housing volume and high-pass filter to the loudspeaker parameters takes place in such a way that certain acoustically favorable frequency responses are realized in interaction with the acoustic properties of the loudspeaker and its electrical effects on the high-pass filter. Loudspeaker according to claim 1, characterized in that the loudspeaker chassis under consideration is part of an active or passive multi-way system. Loudspeaker according to claim 1 or 2, characterized in that existing series resistances - including parasitic ones - are taken into account in the design. Loudspeaker according to one of claims 1 to 3, characterized in that the loudspeaker is connected in parallel to an RC element for compensating for the voice coil inductance. Loudspeaker according to one of claims 1 to 4, characterized in that passive low-pass filters are added to the passive high-pass filter according to the invention. Loudspeaker according to one of claims 1 to 5, characterized in that it is a subwoofer. Loudspeaker according to one of claims 1 to 5, characterized in that it is a low / low mid-range speaker in a system with or without an integrated or external subwoofer. Loudspeaker according to one of claims 1 to 5, characterized in that the inventive idea is applied to mid-range or tweeters. Loudspeaker according to one of claims 1 to 8, characterized in that the loudspeaker / high-pass / housing system is tuned to a higher than the lowest possible limit frequency. Loudspeaker according to one of claims 1 to 9, characterized in that the inventive idea is applied to the use of several chassis in the frequency band under consideration - acoustically parallel or in series (compound principle) or combined. Loudspeaker according to one of Claims 1 to 10, characterized in that the volume of the closed housing is connected to the environment and dampened by an acoustic flow resistance (eg Variovent). Loudspeaker according to one of claims 1 to 11, characterized in that the inventive idea is combined with the bandpass housing principle.

Images