WO1997025833A1

WO1997025833A1 - A method of correcting non-linear transfer behaviour in a loudspeaker

Info

Publication number: WO1997025833A1
Application number: PCT/DK1997/000012
Authority: WO
Inventors: Per Melchior Larsen
Original assignee: Per Melchior Larsen
Priority date: 1996-01-12
Filing date: 1997-01-10
Publication date: 1997-07-17
Also published as: AU1367697A

Abstract

A method is disclosed in order to compensate for the non-linear transfer behaviour in a loudspeaker, comprising designing a model of the physical loudspeaker which is used in a non-linear estimator (12) (observer). The estimator receives the voltage across the moving coil of the loudspeaker and the current in the coil. These signal values are used for calculating an estimate which is fed to a differential unit having two inputs, the second one of which receives a desired signal. The difference between the two signals is fed to a controller (9) which then controls the current/voltage to the loudspeaker, optionally via an amplifier (10). The non-linear signal components of the loudspeaker may be limited hereby, which results in a significant reduction in the distortion in the loudspeaker. The estimator is designed such that it also allows for the dynamic variations which exist in the non-linear component parts of the loudspeaker, e.g. owing to changed temperature conditions.

Description

A method of correcting non-linear transfer behaviour in a loudspeaker

The invention relates to a method of correcting non-lin¬ ear transfer behaviour in a loudspeaker, wherein the mov¬ ing coil of the loudspeaker is connected to a controller adapted to generate a signal for the moving coil to com¬ pensate the non-linear signal components which have oc- curred in the loudspeaker.

Musical sound systems have gone through a violent process of change during the last 10 to 20 years. Particularly because of the digital technology which has made it pos- sible to construct excellent musical sound systems in which noise sources are essentially removed. Furthermore, the musical sound systems of today are of such a quality that non-linear signal parts are virtually eliminated.

The weakest part of a modern musical sound system is still the loudspeaker, however. Much effort has been de¬ voted to the construction of loudspeakers which have the lowest possible distortion, and while this has been suc¬ cessful to a certain degree, it is well-known that loud- speakers loaded to a significant extent will distort the sound.

DE Offenlegungsschrift No. 4334040 discloses a loud¬ speaker structure whose non-linear transfer conditions are corrected by determining the physical variables of the loudspeaker on the basis of a measurement of the voltage across the moving coil and the current in it. This known manner of correcting non-linearities comprises a structure in which an adaptive linear or adaptive non- linear correction filter is connected to a detector coup¬ ling. The detector coupling emits a control signal from the terminals of the moving coil, said control signal ap¬ proximating the velocity of the moving coil. The output of the detector coupling is connected to an input of a differential amplifier, where a reference signal and the detector signal are compared to give an error signal on the output of the differential unit. This known system operates adaptively, as mentioned, which means that the system currently changes the model on the basis of which the error is calculated.

The object of the invention is to provide a structure in which non-linearities may be compensated with a very great accuracy in a loudspeaker by means of a simple cir¬ cuit structure.

The object of the invention is achieved by a method of the type defined in the opening paragraph which is char¬ acterized in that the current and optionally the voltage across the moving coil of the loudspeaker are fed to two inputs of a non-linear estimator (observer) , which repre¬ sents a model of the linear and non-linear mechanical, acoustic and electrical properties of the loudspeaker, and that the estimator has an output which is fed to a differential unit which forms the difference between a desired signal fed to the loudspeaker and the output sig¬ nal of the estimator, the differential signal being used as an input signal to the controller.

The use of a non-linear estimator representing a non-lin- ear model of the loudspeaker provides the advantage that the correction of non-linearities may take place with a very great accuracy.

Further, when the estimator and the differential unit have interposed between them a selector circuit adapted to select a signal derived from the estimator and to transfer this signal to the controller via the differen¬ tial unit, advantages of circuitry are achieved since the selector unit may be adapted to feed a suitable signal to the controller, which will be easier to construct with the necessary circuitry.

Further, it is expedient if the derived signal is se¬ lected from the non-linear signal components from the es¬ timator, since such a selection with good approximation can represent a correction signal capable of correcting the errors which originate from all non-linear compo¬ nents.

It is particularly expedient if the diaphragm velocity is selected as the derived signal component.

It is known in the operation of a loudspeaker that the non-linear transfer conditions of the loudspeaker change e.g. because of temperature changes in the moving coil and its windings.

Correction of the time variations and other differences between model and reality in the non-linear and linear transfer characteristic of the loudspeaker is provided according to the invention in that the current from the moving coil is fed to an additional differential unit having two inputs and one output, of which the first in¬ put receives the current from the moving coil of the loudspeaker and the second input receives a calculated estimated current, and in that the output of the addi¬ tional differential unit is connected to a correction circuit adapted to transfer a correction signal to an ad¬ ditional input of the estimator.

According to the invention, the estimator describes a state function of the equation x = F_es(x) x+ G_κl(x)-u_{spkf f where}

F (x)represents the system matrix of the estimator

=est

G__β((x) represents the input vector of the estimator

x represents the estimated state vector containing all estimated states - variables, and

u_Spkr represents the voltage across the moving coil.

Further, it is noted that the notation " ^' " throughout the formulae of the description indicates that the de¬ rived value is involved, while " ^* " indicates that an es¬ timated value is involved. Furthermore, "__" indicates that a vector is involved, while "_" indicates that a ma- trix is involved.

It is moreover expedient that the correction circuit of the estimator is a multiplier which performs the function

L • (i - H_est(x)-x), where

L represents a correction vector,

_est(-κ) represents the output vector of the estimator.

To perform the correction also from the non-linear co po- nents which occur in an amplifier connected to a loud¬ speaker, it is an advantage if, as stated in claim 8, the input signal to the estimator is obtained from the series connection of an amplifier and the loudspeaker.

When the non-linear estimator and optionally other dy¬ namics are implemented in a digital signal processor, a quick and a very accurate estimate of a desired physical quantity for controlling purposes may be obtained. The invention will now be explained more fully below with reference to an example shown in the drawing, in which

fig. 1 shows a traditional loudspeaker illustrated with the most important constructional parts,

fig. 2 shows an example of how non-linearities can occur,

fig. 3 shows a first embodiment of the use of the inven- tion,

fig. 4 shows a second embodiment of the use of the inven¬ tion,

fig. 5 shows the structure of an estimator for use in the method of the invention,

fig. 6 schematically shows the effect of the principles of the invention.

As will be seen in fig. 1 illustrating a bass loud¬ speaker, said loudspeaker consists of a magnet 1 which is incorporated in a magnetic circuit which additionally contains an iron core 2 and an air gap 8. The air gap 8 accommodates an air coil 7 to which a diaphragm 4 is se¬ cured. The diaphragm 4 is moreover secured to a chassis 3 by means of the outer suspension 5. The air coil 7 and the diaphragm 4 are additionally secured to/controlled by an inner suspension 6.

A strong magnetic field is formed in the air gap 8 in which the air coil 7 is positioned, so that when the coil is positioned in said field, electrical energy may be converted into mechanical energy by feeding a current through the coil. The diaphragm 4, which is secured to the coil, as mentioned, is the sound-producing element which converts the electrical energy from the moving coil to the air.

Fig. 2 shows two positions of the coil 7 in the air gap 8. It is shown in the centre of the figure that the coil is entirely surrounded by the air gap, while to the right in fig. 2 it is positioned somewhat outside the air gap , corresponding to the application of a force to the dia¬ phragm. As will be explained later, the force produced when a current is passed through the coil, depends non- linearly on the current, because the magnetic flux is not homogeneous at the outer edges of the iron of the core.

In fig. 3 the numeral 8 designates a filter which is a so-called equalizing filter that alters the frequency re¬ sponse to the desired one. The output of the filter 8 is coupled to the input of a differential unit whose output is coupled to a controller 9, which is additionally con¬ nected in series with a power amplifier 10 and a loud- speaker 11. The moving coil (not shown) of the loud¬ speaker 11 is connected to an estimator 12, which re¬ ceives partly the voltage across the moving coil u_spkr and partly the current i in the moving coil. An output of the estimator 12 is connected to a selector 13 adapted to provide, on the basis of the signals from the estimator, a suitable signal which may be fed to the differential unit, whose output terminal is connected to the control¬ ler 9.

To illustrate the principles of the invention, it will be explained below how the electrical and mechanical proper¬ ties of a loudspeaker may be described.

This is done by a state equation and an output equation, respectively. The state equation may be expressed as follows:

X= F(x) x+G(x)-u_spkr

where F(x) represents the non-linear system matrix in the loudspeaker model,

G(x) represents a possible non-linear vector,

x represents the state vector in the loudspeaker model which contains all state variables,

ig represents the voltage across the moving coil in the loudspeaker.

This may also be expressed by the following formula for a selected loudspeaker (the embodiment of fig. 3) :

uspkr

x2 represents the current i in the moving coil,

x3 represents the diaphragm velocity x

x4 represents the diaphragm position x,

L represents the inductance in the moving coil,

R represents the ohmic resistance in the moving coil, Bl(x4) represents the force factor on the diaphragm as a function of the diaphragm position,

k represents a spring constant,

r represents a coefficient of friction, and

m represents the mass of the moving parts of the loud¬ speaker and the mass of the air which is moved.

The output equation may be expressed by the formula

y = H(X) ^• X + J(X) ^• U_spkr

where H(x) represents a non-linear output vector,

J(x) represents a forward factor and u_spkr represents the voltage across the moving coil in the loudspeaker.

It can be shown that the output equation may be written as follows (the embodiment of fig. 3) :

y = .uspkr

where the constituent variables represent the same as in the state equation.

It is now possible to design the estimator 12 in fig. 3 by means of the above equations so that it is an approxi¬ mated copy of the physical loudspeaker 11. Fig. 4 shows an embodiment in which also the non-lineari¬ ties of the power amplifier are incorporated in the esti¬ mator calculation of the signal which is fed to the con¬ troller, it being then possible to express the state equation as follows:

where Xi represents the integral of the voltage across the loudspeaker, while the other variables have the same meaning as in the embodiment of fig. 3.

In this case, the state equation may be expressed as fol¬ lows:

where the constituent variables represent the same as be¬ fore.

Fig. 5 is a more detailed view of the estimator connected to a physical loudspeaker 11, and additionally shows a vector 19 which is intended to measure the current in the moving coil. The estimator may mathematically be ex¬ pressed in the following manner:

SUBSTITUTESHEET i = + G_.est (^χ) -u ' + - -H-, (^χ) ^χ)

In this formula —Fest(x) represents the system matrix in the estimator,

G__κ((x) represents the input vector of the estimator, L represents a correction vector,

H_esl(x) represents the output vector of the estimator, and

x represents the estimated state vector containing all estimated states.

It is noted that the last term of the above equation,

L-G-H^-x)

where L represents a correction vector,

is an indication of the correcting nature of the estima¬ tor whose dynamics are determined by L.

Thus, constant correction in the estimator on the basis of the difference between measured and estimated currents results in an estimator design which constantly approxi¬ mates reality, i.e. the physical loudspeaker.

As will be seen in fig. 5, 18 designates a circuit in which the dynamic conditions in the physical loudspeaker are reflected. The signal from the circuit 18 is thus used for adjusting the time variations in the estimator.

It will be explained briefly below how the estimator of the invention operates.

As already mentioned, the essential aspect of the inven¬ tion is to provide a non-linear model of the physical loudspeaker where the most important non-linearities are included. The force vector, Bl (x) , is always included as a function of the diaphragm position x, since this non- linearity is the most important one. The estimator re^¬ ceives the same input signal _Ppkc as the physical loud¬ speaker, on the basis of which an estimate of the current in the moving coil called i is estimated. The estimate is compared with the real current i which is measured in a known manner. By subtracting the two currents i and i from each other, an error of the estimate of the current is calculated, and this error is then multiplied by a suitable vector L and is afterwards fed back to the loud¬ speaker model as a correction contribution. In the same manner, the estimator constantly tries to achieve a good estimate of the real current in the loudspeaker. The most interesting thing about these circumstances is that if the estimate of the current is good, and the factors in the vector L are selected correctly, the other quantities in the loudspeaker model will likewise follow the corre¬ sponding physical quantities in the loudspeaker. In other words, e.g. the diaphragm velocity x may be found merely by correcting the estimator according to the current in the moving coil. The longer the loudspeaker has been in operation, the more its dynamics are changed signifi¬ cantly, which, however, does not change the precision of e.g. the estimated diaphragm velocity x considerably, as the estimator compensates for this significant change in the physical loudspeaker. These circumstances are illus¬ trated in fig. 6, where the line "estimated variable" follows the line "true variable" closer than the line "was in loudspeaker model". It is noted in this connec- tion that the line "estimated variable" is not to illus¬ trate that the distance between the lines "true variable" and "estimated variable" becomes greater as a function of time.

Although the invention has been explained in connection with the correction of non-linear transfer conditions in a loudspeaker, nothing prevents the principles of the in¬ vention from being generally applied in circuitry which is non-linear by nature and in which linearization is de¬ sired.

The decisive thing is that a dynamic model of the non¬ linear circuit may be designed, and that one or more characteristic physical quantities of the non-linear cir¬ cuit can be measured. By drafting a state function for the estimator which includes one or more physical vari¬ ables for the non-linear circuit and drafting an output equation for the non-linear circuit, it is possible to design the estimator such that the output of the non-lin¬ ear circuit is linearized in connection with various types of control circuits.

Examples of this include feedforward circuits, cascade control, state-space control/designs and the like.

Claims

P a t e n t C l a i m s :

1. A method of correcting non-linear transfer behaviour in a loudspeaker, wherein the moving coil (7) of the loudspeaker is connected to a controller (9) and a power amplifier (10) adapted to provide a signal to the moving coil (7) to limit the non-linear signal components which have occurred in the loudspeaker, c h a r a c t e r - i z e d in that the current in and optionally the volt¬ age (Us kr) across the moving coil (7) of the loudspeaker are fed to separate inputs of an estimator (12), which is built around a non-linear model circuit of the linear and non-linear mechanical, acoustic and electrical properties of the loudspeaker, and that the estimator (12) has an output which is fed to a differential unit which forms the difference between a desired signal fed to the loud¬ speaker and the output signal of the estimator, the dif¬ ferential signal being used as an input signal to the controller (9) .

2. A method according to claim 1, c h a r a c t e r ¬ i z e d in that a selector circuit (13) is additionally arranged between the estimator and the differential unit, said selector circuit being adapted to select a signal derived from the estimator and to transfer this signal to the controller via the differential unit.

3. A method according to claim 2, c h a r a c t e r - i z e d in that the derived signal is selected from the non-linear signal components from the estimator.

4. A method according to claim 3, c h a r a c t e r ¬ i z e d in that the diaphragm velocity is selected as the non-linear signal component.

5. A method according to claims 1-4, c h a r a c t e r ¬ i z e d in that the current (i) from the moving coil (7) is fed to an additional differential unit (20) having two inputs and one output, of which the first input receives the current from the moving coil of the loudspeaker and the second input receives the estimated current, and that the output of the additional differential unit is con¬ nected to a correction circuit adapted to transfer a cor¬ rection signal to an additional input of the estimator.

6. A method according to claim 1, c h a r a c t e r ¬ i z e d in that the estimator describes a state function of the formula

= l_esl& ^ + G_ai(x)-u_ipkl

where x represents the estimated state vector containing all estimated variables,

represents the system matrix of the estimator,

^u _spkr the voltage across the moving coil of the loud- speaker.

7. A method according to claim 1, c h a r a c t e r ¬ i z e d in that the correction circuit (18) of the esti¬ mator (12) is a multiplier which performs the function

L-(i-H_est(x)-x)

where L represents a correction vector, i represents the current in the moving coil of the loudspeaker,

x represents the estimated state vector, and H_est(x) represents the output vector which multiplied by the state vector in the estimator ensures that the esti^¬ mator is corrected correctly according to i - i .

8. A method according to any one of the preceding claims, c h a r a c t e r i z e d in that the input sig¬ nal to the estimator is obtained from the series connec¬ tion of an amplifier and the loudspeaker.

9. A method according to any one of the preceding claims, c h a r a c t e r i z e d in that a digital sig¬ nal processor is used as the estimator.

10. A method according to any one of the preceding claims, c h a r a c t e r i z e d in that a bass loud- speaker is used as the loudspeaker.