Circuit arrangement for correcting linear and non-linear transfer characteristics of electroacustic transducers.

The invention relates to an arrangement for correcting the linear and non-linear transmission behavior of electroacoustic transducers, consisting of an electroacoustic transducer, an electrical equalizer network coupled to the electrical input terminals and an aid for adapting the equalizer network to the transducer. The electrical network has a non-linear transmission behavior and changes the electrical signal in such a way that the non-linear effects of the network and the coupled converter are compensated for. In this way, an overall system with reduced non-linear distortion and improved linear transmission behavior can be implemented. With the aid of an adaptation method and an arrangement, the parameters of the electrical network can be changed and independently adapted to the specific transmission behavior of the converter.

The causes of the nonlinear distortions in electroacoustic transducers are very different and depend on the transducer principle used in each case.

In the case of electrodynamic converters (loudspeakers, headphones, microphones, technical actuators), the displacement-dependent parameter changes cause the strongest non-linear distortions. In loudspeaker arrangements with special sound guidance, additional distortions occur in the pressure chamber and in the horn entrance due to non-linear compression and flow processes. Even with electrostatic converters (condenser microphone), the redistribution (or Migration) of the electrical charges disrupted the linear transmission behavior.

The reduction of the non-linear signal distortion leads to an improvement of the subjective auditory impression with electro-acoustic recording and reproduction of audio signals. But also in measurement technology and active noise abatement, there are sometimes considerable demands on the linearity of sensors and actuators. Non-linear distortions that occur in the anti-noise system are not compensated for by the noise and limit the effectiveness of the noise protection measure. A linearization of sound transmitters with constructive means generally leads to a reduction in efficiency and leads to increased additional expenditure for practical sound reinforcement tasks. For this reason, attempts are made to equalize the converter by means of additional electrical systems and to improve its linear and non-linear transmission behavior.

For this purpose, a negative negative feedback has been proposed in GB Patent 1,031,145 (PH 18,481) for electroacoustic sound transmitters. For this purpose, an electrical, mechanical or acoustic variable is measured on the transducer or in the surrounding sound field and converted into a variable (current or voltage) equivalent to the drive signal and added to the feed signal in the opposite phase, that is to say with negative feedback.

The negative feedback has the advantage that the exact structure of the nonlinear transmission system does not have to be known and that the functionality remains intact when the nonlinearity (aging) changes. However, the required signal pickups are expensive, fragile and have a certain transmission behavior, which must be compensated for by suitable equalizer networks. The danger of a possible positive feedback requires measures to correct the phase response ([1] Hall, DS: Design Considerations for an Accelerometer-Based Dynamic Loudspeaker Motional Feedback System. 87. Audio Eng. Soc. Conv, New York October 1989 (Preprint 2863)) . All of these problems prevent the negative feedback on electroacoustic sound transmitters from becoming widely accepted.

With regard to the practical implementation, it is advantageous to fundamentally dispense with the signal pickup on the converter and to realize a purely serial predistortion without signal feedback.

For this it is first necessary to model the non-linear transmission behavior of the converter with sufficient accuracy and to describe it using a non-linear transfer function. If the converter is now preceded by a dynamic nonlinear system which simulates the inverse nonlinear transfer function of the converter with sufficient accuracy, the overall distortions can be compensated for.

The VOLTERRA series development offers a possible starting point for modeling the non-linear converter. It is a very advantageous hand tool for describing second and third order distortions of weakly nonlinear systems with very small input signals. In the case of stronger non-linearities, the system can no longer be described by quadratic and cubic subsystems, and other elements of the VOLTERRA series must be taken into account. In order to achieve convergence, according to the Weierstrass criterion, the input signal must always be sufficiently small and limited. This theory was first applied to the converter by ([2] Kaizer, AJ: Modeling of the Nonlinear Response of an Electrodynamic Loudspeaker by a Volterra Series Expansion. J. Audio Eng. Soc. 35 (1987) 6, p. 421). In the small signal behavior, a good agreement between the measured and calculated distortions was achieved, but nonlinear effects can be observed with larger modulations, which cannot be described with quadratic and cubic transfer functions ([3] Klippel, W .: The Large-Signal-Behavior of Electro -dynamical Loudspeakers at Low Frequencies. 90th AES Convention Paris 1991, Preprint 3049).

If the VOLTERRA functionals of any causal, time-invariant, non-linear system are known, then according to ([4] Butterweck, HJ: Frequency-dependent non-linear transmission systems. Archive Electronics and Transmission Technology, Volume 21 (1967), Volume 5, p. 239) Compensation system can be derived with the inverse transfer function. Kaizer applied this method to the electrodynamic converter and proposed in EP 85200885 an "arrangement for converting an electrical signal into an acoustic signal and vice versa when using a non-linear network", which is intended to reduce the linear and non-linear distortions. This arrangement "contains at least two parallel branches, the first branch being the first order distortions ... and the other branch compensates for higher-order distortions ". This arrangement has a consistently additive structure corresponding to the series properties of the VOLTERRA development. The individual branches represent linear, quadratic, cubic or non-linear networks of higher order and compensate for the corresponding distortion products. Unfortunately, this concept only insufficiently takes into account the transducer-specific features and, in practical implementation, requires a restriction to square and cubic correction systems. Although it is possible to compensate for distortion successfully in the small signal range, the converter no longer behaves like an ideal square or cubic system and the inevitable incorrect compensation leads instead to a reduction to an increase in the distortions in the transmission signal. The insertion of higher order compensation elements extends the usable modulation range, but does not fundamentally solve the problem and leads to technically hardly realizable equalization systems. The additive parallel structure of the equalizer network, which inevitably results from the VOLTERRA modeling, leads to a universal but complex circuit structure, which has decisive disadvantages in large signal behavior.

The problem of adapting nonlinear equalizer networks to the electroacoustic transducer has not been discussed in the literature and no methods, tools or automatic processes have been developed to date.

The object of the invention is to provide for the first time an equalizer network without constant signal feedback (motional feed back), the one <u>complete</u>, <u>automatic</u> (independent) compensation of nonlinear distortions in small <u>and</u> Large signal range (up to the maximum power dissipation or in the entire deflection range of the voice coil) allows the specific features (non-linear causes of distortion) of the respective electroacoustic transducer to be better taken into account and implemented with less effort.

According to the invention, the electroacoustic sound transducer is described by an electro-mechano-acoustic equivalent circuit diagram. In this case, the structural components of the converter that are essential for signal transmission are functionally combined in concentrated active elements, each of which is characterized by a parameter (for example damping, rigidity of the suspension, electrodynamic coupling factor B1, etc.). In addition to the moving mass m of the voice coil and the membrane, all other elements of the transducer system are subject to temporal parameter changes. The changes caused by aging, fatigue and warming turn out to be long-term processes that the<u>linear</u> Change transmission characteristics of the converter, but none <u>nonlinear</u> Cause signal distortion. The parameter changes caused by the state variables deflection, current, fast, voltage and sound pressure lead to the known nonlinear distortions in the transmitted signal. The transmission behavior is fully described with a non-linear integro differential equation (IDG), from which the associated equalizer transfer function is derived by conversion and transferred directly into the circuit structure of the equalizer network.

This results in the circuit structure, which takes into account the physical peculiarities of the respective electroacoustic transducer system and allows full compensation of the nonlinear distortions.

For better understanding, the steps necessary to solve the task can also be explained with the help of signal flow plans.

This should be illustrated using the example of the electrodynamic woofer in voltage supply.

The electromechanical equivalent circuit diagram (FIG. 7a) can be transferred with the aid of the associated nonlinear IDG into an equivalent signal flow diagram (FIG. 7b) which consists of a nonlinear transmission system (152) and a subsequent linear transmission system (153). The linear subsystem (153) is composed of an electro-mechanical system (144) with the transfer function X (s) and a downstream mechano-acoustic system with the transfer function H (s).

The non-linear system (152) connected upstream of the linear transmission system (153) causes the disturbing, non-linear signal distortions.

The nonlinear system (152) contains nonlinear, dynamic transmission systems (two-port 147-151) and a linear transmission system (two-port 167), which also has the transfer function X (s) and further linking elements (139-143, 145).

The linear and non-linear transmission systems have an input and a signal output, the logic elements have two signal inputs and one signal output. The output of each transmission system is connected to the one input of a logic element. Both parts are referred to below as a three port. Each three port represents exactly one non-linear cause of distortion.

The three gates, which represent the deflection-dependent induction, the deflection-dependent damping, the electromagnetic drive and the deflection-dependent stiffness, contain adders (139, 141, 142, 143) as logic elements. Surprisingly, the deflection-dependent, electrodynamic drive leads to a multiplicative linking element (140). The three port, which describes the Doppler distortions, contains a variable delay element (145) as the link element.

All three gates are interconnected in a certain structure. Here, the output of the preceding link element is linked to an input of the next link element and leads to a chaining of all three-port gates contained. The three-port (147,139), which describes the electrical induction, comes first, followed by the three-port of the electrodynamic force factor (148, 140) and the three-port, which are connected with the electromagnetic drive (150, 142), the non-linear damping (141 , 149) and the stiffness (143, 151) correspond. In the last position immediately before the linear subsystem (145, 146) is the three-port (145, 167), which corresponds to the generation of the Doppler distortions in the acoustic system. The inputs of all nonlinear subsystems and of the linear transmission system (167) are connected to the signal input of the delay element (145). The transmission systems (147-151) are thus fed back without feedback via a signal feedback and the three port of the Doppler distortions. The well-known large signal effects (amplitude compression, phase shift of the fundamental oscillation and the distortion products) result from the signal feedback in the electromechanical converter part. The Doppler distortions caused by the Dreitor (145, 167) do not influence the mechanical vibration behavior (deflection of the membrane) and thus the process of creating the nonlinear distortions. Due to the different supply of the transmission systems (retroactive, non-reactive), the non-linear transmission system (152) consists of two non-linear subsystems connected in series.

The effect of this nonlinear transmission system (152), ie the occurrence of disturbing nonlinear distortions in the output signal, can be completely compensated for by a very specific equalization system which is connected upstream of the sound transmitter: According to the invention, this goal is achieved precisely in that the equalization system the transmission elements S_L (166), p_B (165), p_D (164), p_M (163), p_S (162) and X (s) (161), which correspond to the nonlinear and linear transmission systems of the converter (147 - 151, 167) in their transmission behavior. Each of these transmission elements is connected to a logic element which has exactly the inverse properties of the logic element in the corresponding converter driver, ie instead of the adders (139, 141-143) there are subtractors (156-158, 160), instead of the multiplier (140) a division element (159) and the controllable delay element (145) leads to a delay element with the opposite control characteristic. The connection of the transmission link and associated link element is referred to below as a three port.

All three gates in the equalizer network are connected in a chain in exactly the right order (in relation to the input terminals of the converter) using one of their inputs and their outputs. The input of all transmission elements (two gates 161-166), ie the other input of the three gates is connected to the output of the delay element. The three-port feed of the Doppler distortions in the converter signal flow diagram (145, 167) fed without feedback corresponds to an equalizer third-party (155, 161) which has a signal feedback. The other three-port electromechanical gates, which were connected via a signal feedback in the converter signal flow diagram, correspond to three-port gates in the equalizer network that are switched without feedback. The equalizer network thus also consists of two non-linear subsystems connected in series.

Only with this filter structure of the equalizer, which was derived by inverting and mirroring the converter system structure, do the three-ports in the converter and equalizer network fully compensate, i.e. the addition (139) is compensated for by a subtraction (160) of the same signal in the equalizer, the multiplication (140) is balanced by the division element (159) with the same signal in the equalizer. All other elements of the interference system are compensated in the same way by the mirrored interconnection of the inverse logic elements.

This results in a clearly assignable circuit structure of the equalization network for each type of electroacoustic transducer.

The following general features are common to all these circuit structures: The equalizer network consists of a chain connection (series connection) of transmission elements, with at least one transmission element (two-port) having a non-linear transmission behavior between its input and output ports.

Surprisingly, it was found that a complete compensation of certain, simultaneously acting, non-linear causes of distortion (eg Doppler distortion and force factor in the woofer or force factor and damping in the electrodynamic microphone) only by one <u>serial</u> Linking (series connection) of several non-linear transmission elements is possible (see FIG. 1).

A chain connection of the transmission links of the equalization network means that the links are mutually linked with their input and output and are thus switched on in the transmission chain (sound receiver, signal memory, transmitter, receiver, amplifier, sound transmitter). Each of these non-linear transmission elements (two-port Z₁, Z₂, Z₃) is a memoryless (frequency-independent) or dynamic (frequency-dependent) system.

Each dynamic, non-linear two-port Z contains at least one transmission sdreitor D (see FIG. 2), which corresponds to a non-linear cause of distortion in the converter and serves to compensate for the corresponding non-linear distortions.

Each Dreitor D in turn is a dynamic, non-linear transmission element with two signal inputs E₁, E₂ and an output A (see. Fig. 3). It consists of a non-linear, dynamic transmission element (two-port U) and a memory-less logic element V, which converts the two input signals into the output signal via an algebraic operation (eg addition, multiplication). One input E₁ of the Dreitor D is connected directly to one input of the logic element, the other input E₂ of the Dreitor (D) is connected via the two-port U to the second input of the logic element and the output of the logic element is connected to the output of the Dreitor ( D) coupled. The two-port U takes into account the physical properties of the variable converter parameter and its position in the active structure of the converter. If several transmission three gates are arranged between the input and output of the two gates (Z) (FIG. 2), these are connected in a chain connection using the respective input gate E 1 (18) and the output gate A (20) and the remaining input gate E 2 ( 19) of the three gates contained either connected to the input gate of the two-port Z (FIG. 2 a) or to the output port of the two-port Z (FIG. 2 b).

All dynamic, non-linear transmission elements (two-port Z, U and three-port D) are composed of dynamic, linear two-port and / or memoryless, non-linear two-port N and / or logic elements (e.g. adders, multipliers).

The free, variable parameters of the dynamic, linear two-port (linear filter parameters) and the memoryless, non-linear two-port (non-linear characteristic curves) are measured by measuring the resulting transmission behavior (converter with equalization network), with the help of a matching arrangement, which is temporarily or permanently sent to the converter equalizer System is connected, determined and so the equalization system is automatically adapted to the respective converter.

The equalizer network is initially to be further specified for the electrodynamic sound transmitter, which is operated in a bass reflex or compact box system. Starting from an electrical equivalent circuit diagram with concentrated elements, the non-linear integro differential equation (IDG) is set up, the equalizer transfer function is determined and implemented in a circuit arrangement. The nonlinear equivalent circuit diagram (see Fig. 7 a) differs from the linear in that current and deflection-dependent parameters or quantities occur.

The rigidity of the membrane suspension see_T(x) and the rigidity of the coupled air volume s_B(x) is in a constant total stiffness s_O and in a deflection-dependent overall stiffness s_G(x) summarized<maths id="math0001" num=""><math display="inline"><mrow><msub><mrow><mtext>s</mtext></mrow><mrow><mtext>O</mtext></mrow></msub><msub><mrow><mtext> + s</mtext></mrow><mrow><mtext>G</mtext></mrow></msub><msub><mrow><mtext>(x) = s</mtext></mrow><mrow><mtext>T</mtext></mrow></msub><msub><mrow><mtext>(x) + s</mtext></mrow><mrow><mtext>B</mtext></mrow></msub><mtext>(x). (1)</mtext></mrow></math><img file="EP0508392A2_D0001.tif" /></maths>

The dependence on the deflection is also evident in the acting electrodynamic transducer parameter Bl (x), in the voice coil inductance L (x), and in the electromagnetic driving force F_like(i, x) taken into account.

The elements of the mechanical-acoustic vibration system that have constant parameters are in the impedance<maths id="math0002" num=""><img file="EP0508392A2_D0002.tif" /></maths> summarized.

Using the Laplace operator s, the inverse Laplace transformation and the folding operation, the following nonlinear equation (IDQ) can be set up in the time domain from the equivalent circuit diagram when fed with a constant current source<maths id="math0003" num=""><img file="EP0508392A2_D0003.tif" /></maths>

The multiplication or division in the time domain (point) must be distinguished from the convolution. By connecting a suitable equalizer with the transfer function<maths id="math0004" num=""><math display="inline"><mrow><msub><mrow><mtext>i</mtext></mrow><mrow><mtext>L</mtext></mrow></msub><mtext>(t) = f [i (t)]</mtext></mrow></math><img file="EP0508392A2_D0004.tif" /></maths> the entire system should be linearized and the following linear equation (IDG) should be fulfilled:<maths id="math0005" num=""><math display="inline"><mrow><msub><mrow><mtext>Bl</mtext></mrow><mrow><mtext>O</mtext></mrow></msub><mtext>· I (t) = L⁻¹ {</mtext><munder accentunder="true"><mrow><mtext>J</mtext></mrow><mo>̲</mo></munder><mtext>(s)} * x (t). (4)</mtext></mrow></math><img file="EP0508392A2_D0005.tif" /></maths>

The nonlinear equalizer network must do the following transfer function for this<maths id="math0006" num=""><math display="inline"><mrow><msub><mrow><mtext>i</mtext></mrow><mrow><mtext>L</mtext></mrow></msub><msub><mrow><mtext>(t) = {i (t) + N</mtext></mrow><mrow><mtext>s</mtext></mrow></msub><msub><mrow><mtext>(x) + i (t) ² · N</mtext></mrow><mrow><mtext>M</mtext></mrow></msub><msub><mrow><mtext>(x)} · N</mtext></mrow><mrow><mtext>B</mtext></mrow></msub><mtext>(x), (5)</mtext></mrow></math><img file="EP0508392A2_D0006.tif" /></maths> With <maths id="math0007" num=""><math display="inline"><mrow><mtext>x (t) = L⁻¹ {X (s)} * i (t)</mtext></mrow></math><img file="EP0508392A2_D0007.tif" /></maths> have.

Since the overall system fulfills the linear equation (IDG) (4) after the equalization has been carried out in advance, the deflection-equivalent time signal x (t), which acts here as a control variable, can be implemented by a linear transfer element (low pass) with the following transfer function<maths id="math0008" num=""><img file="EP0508392A2_D0008.tif" /></maths> be replicated.

For the frequency-independent, non-linear functions N_s(x), N_M(x) and N_B(x) the following relationships can be specified for the deflection-dependent transducer parameters:<maths id="math0009" num=""><img file="EP0508392A2_D0009.tif" /></maths><maths id="math0010" num=""><img file="EP0508392A2_D0010.tif" /></maths>

Operating the electrodynamic converter system with a constant current source does, however, require more effort in the area of ​​the power amplifier by inserting a voltage-current converter and requires additional measures to ensure a balanced sound pressure amplitude frequency response, but simplifies the non-linear equalization. The predistorted input signal is expediently converted into a current signal only at the power amplifier.

In the case of voltage supply to the converter, the effect of the voice coil resistance and the voice coil inductance leads to a more complicated nonlinear differential equation and a correspondingly more complex equalization system.

The following nonlinear equation (IDG) results from the equivalent circuit diagram when power is supplied:<maths id="math0011" num=""><img file="EP0508392A2_D0011.tif" /></maths>

By connecting a suitable equalizer with the transfer function<maths id="math0012" num=""><math display="inline"><mrow><msub><mrow><mtext>u</mtext></mrow><mrow><mtext>L</mtext></mrow></msub><mtext>(t) = f [u (t)]</mtext></mrow></math><img file="EP0508392A2_D0012.tif" /></maths> the entire system should be linearized and the following linear equation (IDG) should be fulfilled:<maths id="math0013" num=""><math display="inline"><mrow><msub><mrow><mtext>Bl</mtext></mrow><mrow><mtext>O</mtext></mrow></msub><msub><mrow><mtext>· U = R</mtext></mrow><mrow><mtext>e</mtext></mrow></msub><mtext>· L⁻¹ {</mtext><munder accentunder="true"><mrow><mtext>J</mtext></mrow><mo>̲</mo></munder><msub><mrow><mtext>(s)} * x + L</mtext></mrow><mrow><mtext>O</mtext></mrow></msub><mtext>· L⁻¹ {p ·</mtext><munder accentunder="true"><mrow><mtext>J</mtext></mrow><mo>̲</mo></munder><msub><mrow><mtext>(s)} * x + Bl</mtext></mrow><mrow><mtext>O</mtext></mrow></msub><mtext>² · L⁻¹ {s} * x (11)</mtext></mrow></math><img file="EP0508392A2_D0013.tif" /></maths>

The nonlinear equalizer network must do the following transfer function for this<maths id="math0014" num=""><img file="EP0508392A2_D0014.tif" /></maths> With<maths id="math0015" num=""><math display="inline"><mrow><mtext>x (t) = L⁻¹ {X (s)} * u (t)</mtext></mrow></math><img file="EP0508392A2_D0015.tif" /></maths> and<maths id="math0016" num=""><img file="EP0508392A2_D0016.tif" /></maths> have.

Since the overall system fulfills the linear equation (IDG) (11) after the equalization has been implemented, the deflection-equivalent time signal x (t) can be carried out using a linear system (low pass) with the following transfer function<maths id="math0017" num=""><img file="EP0508392A2_D0017.tif" /></maths> from the undistorted input signal u (t) and the current i_L(t) using the linear transfer function<maths id="math0018" num=""><img file="EP0508392A2_D0018.tif" /></maths> be determined.

For the frequency-independent, non-linear functions N_s, N_M, N_D, N_L and N_B the following relationships can be specified for the displacement-dependent transducer parameters<maths id="math0019" num=""><img file="EP0508392A2_D0019.tif" /></maths><maths id="math0020" num=""><img file="EP0508392A2_D0020.tif" /></maths><maths id="math0021" num=""><math display="inline"><mrow><msub><mrow><mtext>N</mtext></mrow><mrow><mtext>L</mtext></mrow></msub><msub><mrow><mtext>(x) = L (x) - L</mtext></mrow><mrow><mtext>O</mtext></mrow></msub><mtext>.   (20)</mtext></mrow></math><img file="EP0508392A2_D0021.tif" /></maths>

The circuits of the equalizer for current and voltage supply can be derived directly from the non-linear transfer functions (5), (12). The point operations contained correspond to multiplications in the time domain. The convolution with a constant weight function corresponds to a linear system (filter) connected in the transmission path. The nonlinear functions are realized by memoryless, nonlinear two gates.

The equalizer network contains a three-port D for the desired change or compensation of the deflection-dependent rigidity_S (Fig. 9), which consists of a more linear, dynamic network X (100), a memoryless, non-linear two-port N_S (101) and an adder (103). The input E₂ (22) of the three-way monitor is connected to the input of the two-port X. The output of the two-port X, which carries a deflection-equivalent signal, is via the memoryless, non-linear two-port N_S connected to the input of an adder. The second input of the adder is connected to the input E₁ and the output of the adder and the output A of the Dreitor D._S are connected.

The equalizer network contains a three-port D for the desired change or compensation of the deflection-dependent electrodynamic coupling factor_B (Fig. 10), which consists of a more linear, dynamic network X, a memoryless, non-linear two-port N_B (104) and a multiplier (105). The input E₂ of the three-way monitor is serial via the linear two-port X and the memoryless, non-linear two-port N_B connected to the input of the multiplier. The second input of the multiplier is with the input E₁ and the output of the multiplier is with the output A of the three-phase D_S interconnect.

The equalizer network contains a three-port D for the desired change or compensation of the deflection-dependent damping_D (Fig. 11), which consists of a more linear, dynamic network X, a differentiator (108), a memoryless, non-linear two-port N_D (106) and an adder and multiplier (103, 107). The input E₂ of the three-way gate is via the two-port X with both the memoryless, non-linear two-port N_D as well as connected to the input of a differentiator. The outputs of the differentiator and the memoryless, non-linear two-port N_D are linked together via a multiplier and connected to the input of an adder. The second input of the adder is with the input E₁ and output of the adder and the output A of the Dreitor D._D interconnect.

The equalizer network contains a three-port D to compensate for the electromagnetic drive_M, which consists of a linear, dynamic network X, a memoryless, non-linear two-port N_M (110), a squaring (108), a multiplier (109), and an adder (103). The input E₂ of the three-way monitor is for sound transmitters that are fed via a constant current source (FIG. 13), both directly with the input of the squaring stage and via the two-port X with the input of the memoryless, non-linear two-port N._M connected. The outputs of the squarer and the two-port N_M are linked via a multiplier and fed to the input of an adder. The second input of the adder is at the input E 1 and the output of the adder is at the output A of the Dreitor D._M interconnected.

If the sound transmitter is operated via a voltage source (FIG. 12), the input signal of the squaring stage, which corresponds to the input current of the converter, is generated with the aid of a nonlinear network (111) according to relationship (13).

For this purpose, the deflection-equivalent signal at the output of the two-port X is sent both to a linear two-port with the transfer function I (s) and to the memoryless, non-linear two-port N_S, N_B guided. The output of the linear two-port I and the output of the two-port N_S are combined in an adder and fed to one input of a multiplier. The other input of the multiplier is with the output of the non-linear two-port N_B connected. The output of the multiplier carries the signal equivalent to the input current.

In order to compensate for the deflection-dependent inductance of a voltage-fed sound transmitter, the equalizer network contains a three-port D_L (Fig. 14), which consists of a more linear, dynamic network X, a non-linear network (111), a differentiator (112), a non-linear two-port N_L (110) and a multiplier (109) and adder (103). The input E₂ of the three-way gate is via the linear two-port X with the non-linear two-port N_L connected. The exit of the two-port N_L and the output of the current simulation (111) described above are connected to the inputs of the multiplier. The output signal is fed to one input of an adder via a differentiator. The second input of the adder is at the input E 1 and the output of the adder is at the output A of the Dreitor D._L interconnected.

In the case of simultaneous compensation of the electrodynamic drive and other converter parameters, the compensation three-way cables must be connected to one of their two inputs and the output in a chain such that in addition to the three-port D_L the inductance compensation, all other three-port inputs on the three-port D_B are connected (Fig. 4). The output of the compensation third party D_L must always be connected to the transducer inputs of the sound transmitter.

This circuitry arrangement of the compensation three-way arises directly from the analytical structure of the transfer function (large curly brackets in 5 and 12 respectively) and corresponds to the mirror symmetry between the equalizer structure (signal flow diagram in Fig. 20 a) and the active structure (signal flow diagram 7 b) of the nonlinear physical Mechanisms in the electrodynamic loudspeaker. Only in this order can the distortions caused by the deflection of the voice coil be fully compensated.

The deflection of the membrane changes not only the electrical and mechanical parameters of the transducer but also the acoustic radiation conditions, i.e. the distance between the current membrane position and a fixed reception point in the main radiation direction (axis) is dependent on the deflection and leads to a different transit time of the signal in the acoustic system. In particular, high-frequency signal components with short wavelengths are impaired by the resulting phase or frequency modulation (known as the Doppler effect) and generate additional intermodulation distortions ([5] GL Beers and H.Belar, "Frequency-Modulation Distortion in Loudspeakers", J. Audio Eng. Soc ., Volume 29, pages 320-326, May 1981).

In order to also compensate for these distortions by predistortion of the electrical feed signal, this distortion mechanism is also modeled and the required transfer function of the equalization network is derived and the required circuit structure is determined. The sound pressure p (t) occurring at a reception point in the main emission direction results from folding the deflection x (t) of the membrane with the impulse response<maths id="math0022" num=""><math display="inline"><mrow><mtext>p (t) = h (t, x (t)) * x (t) (21)</mtext></mrow></math><img file="EP0508392A2_D0022.tif" /></maths> being the impulse response<maths id="math0023" num=""><img file="EP0508392A2_D0023.tif" /></maths> describes the radiation and propagation of the acoustic signal and takes into account the variable transit time of the signal in the acoustic system.

With the help of the Diracfunction δ (t) the constant acoustic impulse response h_O(t) are separated from the variable transit time, which results from the quotient of deflection x (t) and speed of sound c.

In combination with the linear transfer function of the (equalized) electromechanical transducer X (s), the relationship between the electrical input signal u_L(t) and the resulting sound pressure<maths id="math0024" num=""><img file="EP0508392A2_D0024.tif" /></maths> to be discribed.

The electrical input signal of the converter with the filter function<maths id="math0025" num=""><img file="EP0508392A2_D0025.tif" /></maths> predistorted, so the runtime changes<maths id="math0026" num=""><math display="inline"><mrow><msub><mrow><mtext>p (t) = h</mtext></mrow><mrow><mtext>O</mtext></mrow></msub><msub><mrow><mtext>(t) * L⁻¹ {X (s)} * δ (t - T</mtext></mrow><mrow><mtext>O</mtext></mrow></msub><mtext> - T₁) * u (t) (25)</mtext></mrow></math><img file="EP0508392A2_D0026.tif" /></maths> and thus compensate for the Doppler distortions in the main emission direction.

The transfer function of the equalizer (24) can be implemented in terms of circuitry with the aid of a transfer element with a variable, controllable transit time. A control-equivalent signal x (t) is required for control. This signal can with the help of a linear filter with the transfer function X (s) from the electrical signal u_L(t) can be obtained. If you consider this correction network as a three-door D_T, whose input E₁ (21) is fed with the signal u (t) and whose output A (25) leads to the converter, the control input E₂ (22) is connected to the output A. Thus, the compensation network for Doppler distortions is one of the retroactive, feedback circuit structures (see FIG. 2 b).

If other non-linear causes of distortion (eg force factor, damping, inductance) act in the electrodynamic sound transmitter, the corresponding compensation factors (see D_D (15), D_B (16), D_L (17) in Fig. 4) <u>to</u> the compensation third party of the Doppler distortions (D_T (14)). Only in this way can the control signal x (t) required for the compensation of all deflection-related distortions be obtained with the aid of a linear filter from the electrical signal and these distortions can be completely suppressed. The resulting overall equalization network thus consists of a chain connection of two non-linear, dynamic transmission elements (see two gates Z1 and Z2 in Fig. 4), the distortions of the acoustic system being compensated for in the first transmission element and the distortions of the electromechanical system in the second element. Here, too, complete symmetry properties can be seen between the structure of the equalizer (FIG. 20 a) and the active structure of the converter (signal flow diagram FIG. 7 b).

Fig. 24 shows a possibility of realizing the equalizer D_T to compensate for Doppler distortions.

The control input E2 (22) of this three port is connected to the input of the linear filter (100), which has the transfer function X (s) and at whose output a deflection-equivalent signal x (t) is produced.

The input E1 (21) is connected to the input of a delay element (138), at the output of which the input signal appears after 20 µs delay without further distortion. With the help of two adders (136, 134), a subtractor (135) and a multiplier (137), the instantaneous signal x (t) is interpolated between the instantaneous and the delayed signal.

By coupling special sound guides to the sound transmitter, the efficiency can be increased considerably and the distortion caused by deflection can be reduced. However, non-linear flow and compression processes in sound guidance can also cause strong non-linear distortions in the emitted sound. First, the physical background of these mechanisms is to be explained on the basis of a modeling of the sound transmitter with horn sound guidance, and then the equalizer transfer function and the corresponding circuit structure are derived.

At the funnel entrance, the sound flow passes through a cross-sectional jump, so that a pressure chamber is created between the vibrating membrane and the funnel entrance. The parameters of the acoustic elements friction in the funnel entrance<img file="EP0508392A2_D0027.tif" />_K and compliance of the pressure chamber <img file="EP0508392A2_D0028.tif" />_D have a dependency on acoustic state variables. With a very large sound flow q_K the flow at the funnel entrance is no longer laminar. The formation of turbulence creates further losses in addition to the viscous friction, which lead to an increase in the overall friction parameter (flow resistance).

The second non-linear mechanism is caused by the (adiabatic) compression of the air in the pressure chamber. The resilience of the enclosed air volume V increases with increasing pressure p_D in the chamber and can be described by the following relationship<maths id="math0027" num=""><img file="EP0508392A2_D0029.tif" /></maths> If all acoustic and mechanical elements are transformed to the electrical side, an equivalent electrical equivalent circuit (FIG. 8) can be specified. The linear elements of the mechano-acoustic system are in the complex impedance<maths id="math0028" num=""><img file="EP0508392A2_D0030.tif" /></maths> summarized.

The equivalent electrical quantity of the acoustic horn input impedance also appears<maths id="math0029" num=""><img file="EP0508392A2_D0031.tif" /></maths> and the equivalent nonlinear quantities of acoustic pressure chamber compliance<maths id="math0030" num=""><img file="EP0508392A2_D0032.tif" /></maths> and acoustic damping<maths id="math0031" num=""><img file="EP0508392A2_D0033.tif" /></maths> which in a constant proportion N_O, R_O and a dependent part N (i_D) and R (u_K) are split.

The following nonlinear equation (IDG) in the time domain can be derived from the equivalent circuit diagram<maths id="math0032" num=""><math display="inline"><mrow><msub><mrow><mtext>u</mtext></mrow><mrow><mtext>L</mtext></mrow></msub><mtext> - L⁻¹ {</mtext><munder accentunder="true"><mrow><mtext>W</mtext></mrow><mo>̲</mo></munder><msub><mrow><mtext>(s)} * (N (i</mtext></mrow><mrow><mtext>D</mtext></mrow></msub><msub><mrow><mtext>) · [U</mtext></mrow><mrow><mtext>K</mtext></mrow></msub><mtext>* L⁻¹ {</mtext><munder accentunder="true"><mrow><mtext>Z.</mtext></mrow><mo>̲</mo></munder><msub><mrow><mtext>(s)}] + N (i</mtext></mrow><mrow><mtext>D</mtext></mrow></msub><msub><mrow><mtext>) U</mtext></mrow><mrow><mtext>K</mtext></mrow></msub><msub><mrow><mtext>· R (u</mtext></mrow><mrow><mtext>K</mtext></mrow></msub><mtext>)) - L⁻¹ {</mtext><munder accentunder="true"><mrow><mtext>F</mtext></mrow><mo>̲</mo></munder><msub><mrow><mtext>(s)} * [u</mtext></mrow><mrow><mtext>K</mtext></mrow></msub><msub><mrow><mtext>· R (u</mtext></mrow><mrow><mtext>K</mtext></mrow></msub><mtext>)]</mtext></mrow></math><img file="EP0508392A2_D0034.tif" /></maths><maths id="math0033" num=""><math display="inline"><mrow><mtext>= L⁻¹ {</mtext><munder accentunder="true"><mrow><mtext>W</mtext></mrow><mo>̲</mo></munder><mtext>₁ (s)</mtext><munder accentunder="true"><mrow><mtext>Z.</mtext></mrow><mo>̲</mo></munder><mtext>(s) + W (s) · (</mtext><munder accentunder="true"><mrow><mtext>Z.</mtext></mrow><mo>̲</mo></munder><msub><mrow><mtext>(s) .N</mtext></mrow><mrow><mtext>O</mtext></mrow></msub><msub><mrow><mtext> + 1 / s)} * u</mtext></mrow><mrow><mtext>K</mtext></mrow></msub><mtext>   (31)</mtext></mrow></math><img file="EP0508392A2_D0035.tif" /></maths> using the convolution operation (*), the inverse Laplace transform (L⁻¹ {}), the Laplace operator (s) and the following sum impedances<maths id="math0034" num=""><img file="EP0508392A2_D0036.tif" /></maths><maths id="math0035" num=""><math display="inline"><mrow><munder accentunder="true"><mrow><mtext>F</mtext></mrow><mo>̲</mo></munder><msub><mrow><mtext>(s) = N</mtext></mrow><mrow><mtext>O</mtext></mrow></msub><mtext>·</mtext><munder accentunder="true"><mrow><mtext>W</mtext></mrow><mo>̲</mo></munder><mtext>(s) + </mtext><munder accentunder="true"><mrow><mtext>W</mtext></mrow><mo>̲</mo></munder><mtext>₁ (s), (33)</mtext></mrow></math><img file="EP0508392A2_D0037.tif" /></maths> and<maths id="math0036" num=""><img file="EP0508392A2_D0038.tif" /></maths>

By connecting a suitable equalizer with the transfer function<maths id="math0037" num=""><math display="inline"><mrow><msub><mrow><mtext>u</mtext></mrow><mrow><mtext>L</mtext></mrow></msub><mtext>(t) = f [u (t)] (35)</mtext></mrow></math><img file="EP0508392A2_D0039.tif" /></maths> the entire system should be linearized and the following linear equation (IDG) should be fulfilled:<maths id="math0038" num=""><math display="inline"><mrow><mtext>u (t) = L⁻¹ {</mtext><munder accentunder="true"><mrow><mtext>W</mtext></mrow><mo>̲</mo></munder><mtext>₁ (s)</mtext><munder accentunder="true"><mrow><mtext>Z.</mtext></mrow><mo>̲</mo></munder><mtext>(s) + </mtext><munder accentunder="true"><mrow><mtext>W</mtext></mrow><mo>̲</mo></munder><mtext>(s) · [</mtext><munder accentunder="true"><mrow><mtext>Z.</mtext></mrow><mo>̲</mo></munder><msub><mrow><mtext>(s) · N</mtext></mrow><mrow><mtext>O</mtext></mrow></msub><msub><mrow><mtext> + 1 / s]} * u</mtext></mrow><mrow><mtext>K</mtext></mrow></msub><mtext>   (36)</mtext></mrow></math><img file="EP0508392A2_D0040.tif" /></maths>

The non-linear equalizer network must have the following transfer function for this:<maths id="math0039" num=""><math display="inline"><mrow><msub><mrow><mtext>u</mtext></mrow><mrow><mtext>L</mtext></mrow></msub><mtext>(t) = u (t) + L⁻¹ {</mtext><munder accentunder="true"><mrow><mtext>W</mtext></mrow><mo>̲</mo></munder><msub><mrow><mtext>(s)} * N</mtext></mrow><mrow><mtext>A</mtext></mrow></msub><msub><mrow><mtext>(i</mtext></mrow><mrow><mtext>D (t)</mtext></mrow></msub><mtext>) + L⁻¹ {</mtext><munder accentunder="true"><mrow><mtext>F</mtext></mrow><mo>̲</mo></munder><msub><mrow><mtext>(s)} * N</mtext></mrow><mrow><mtext>R</mtext></mrow></msub><msub><mrow><mtext>(u</mtext></mrow><mrow><mtext>K (t)</mtext></mrow></msub><mtext>)   (37)</mtext></mrow></math><img file="EP0508392A2_D0041.tif" /></maths> With<maths id="math0040" num=""><math display="inline"><mrow><msub><mrow><mtext>i</mtext></mrow><mrow><mtext>D</mtext></mrow></msub><msub><mrow><mtext>(t) = [u</mtext></mrow><mrow><mtext>K</mtext></mrow></msub><mtext>(t) * L⁻¹ {</mtext><munder accentunder="true"><mrow><mtext>Z.</mtext></mrow><mo>̲</mo></munder><msub><mrow><mtext>(s)}] + N</mtext></mrow><mrow><mtext>R</mtext></mrow></msub><msub><mrow><mtext>(u</mtext></mrow><mrow><mtext>K</mtext></mrow></msub><mtext>(t))}</mtext></mrow></math><img file="EP0508392A2_D0042.tif" /></maths> and<maths id="math0041" num=""><math display="inline"><mrow><msub><mrow><mtext>u</mtext></mrow><mrow><mtext>K</mtext></mrow></msub><mtext>(t) = u (t) * L⁻¹ {</mtext><munder accentunder="true"><mrow><mtext>Y</mtext></mrow><mo>̲</mo></munder><mtext>(s)}].</mtext></mrow></math><img file="EP0508392A2_D0043.tif" /></maths>

Since the overall system fulfills the linear equation (IDG) after equalization, the control signal can_K(t) by a linear system with the following transfer function<maths id="math0042" num=""><img file="EP0508392A2_D0044.tif" /></maths> be replicated.

The following relationships can be used for the frequency-independent nonlinear functions<maths id="math0043" num=""><math display="inline"><mrow><msub><mrow><mtext>N</mtext></mrow><mrow><mtext>A</mtext></mrow></msub><msub><mrow><mtext>(i</mtext></mrow><mrow><mtext>D</mtext></mrow></msub><msub><mrow><mtext>) = N (i</mtext></mrow><mrow><mtext>D</mtext></mrow></msub><msub><mrow><mtext>) · I</mtext></mrow><mrow><mtext>D</mtext></mrow></msub><mtext> ,   (39)</mtext></mrow></math><img file="EP0508392A2_D0045.tif" /></maths><maths id="math0044" num=""><math display="inline"><mrow><msub><mrow><mtext>N</mtext></mrow><mrow><mtext>R</mtext></mrow></msub><msub><mrow><mtext>(u</mtext></mrow><mrow><mtext>K</mtext></mrow></msub><msub><mrow><mtext>) = u</mtext></mrow><mrow><mtext>K</mtext></mrow></msub><msub><mrow><mtext>· R (u</mtext></mrow><mrow><mtext>K</mtext></mrow></msub><mtext>)   (40)</mtext></mrow></math><img file="EP0508392A2_D0046.tif" /></maths> specify the converter parameters.

The non-linear transfer function of the equalizer can be converted directly into a circuit. The convolution operations are performed by linear filters with the transfer functions<u>Y</u>(s), <u>F</u>(s), <u>Z.</u>(s), <u>W</u>(s) and the nonlinear functions N_A and N_R are realized by memoryless, non-linear transmission systems. The signals are linked in accordance with the algebraic structure of the equalizer function (32) with adders and multipliers.

So for the three gate D_A (Fig. 15), which causes a desired change or compensation of the adiabatic compression in the coupled sound guide of a sound transmitter, the following structure: the input E₂ of the three-way D_A is via a transmission element (115) with the input of a memoryless, non-linear transmission element N._A (114) connected. The exit of the two-port N_A is connected via the linear transmission second gate W (113) to the first input of an adder (103) and the second input of the adder is connected to the input E 1 of the three-way switch. The output of the adder is connected to the output A of the Dreitor D_A interconnected.

For the Dreitor D_R (Fig. 16), which causes a desired change or compensation of the fast-dependent flow losses in the coupled sound guide of a sound transmitter, the following circuit structure results: The input E₂ of the three-stage D_R is via a linear, dynamic transmission element Y (118) with the input of a memoryless, non-linear transmission element N_R (119) connected. The exit of the two-port N_R is connected via the linear transmission element F (120) to the first input of an adder (103) and the second input of the adder is connected to the input E 1 of the three-way switch. The output of the adder is connected to the output A of the Dreitor D_R interconnected.

The circuit can be greatly simplified at the expense of the accuracy of the compensation in certain frequency ranges. Using relationships<maths id="math0045" num=""><math display="inline"><mrow><munder accentunder="true"><mrow><mtext>Z.</mtext></mrow><mo>̲</mo></munder><mtext>(s) &lt; </mtext><munder accentunder="true"><mrow><mtext>W</mtext></mrow><mo>̲</mo></munder><mtext>₁ (s) &lt; </mtext><munder accentunder="true"><mrow><mtext>W</mtext></mrow><mo>̲</mo></munder><mtext>₂ (s), (41)</mtext></mrow></math><img file="EP0508392A2_D0047.tif" /></maths><maths id="math0046" num=""><math display="inline"><mrow><munder accentunder="true"><mrow><mtext>Z.</mtext></mrow><mo>̲</mo></munder><msub><mrow><mtext>(s) &lt;R</mtext></mrow><mrow><mtext>O</mtext></mrow></msub><mtext>,   (42)</mtext></mrow></math><img file="EP0508392A2_D0048.tif" /></maths><maths id="math0047" num=""><math display="inline"><mrow><mtext>Real part { </mtext><munder accentunder="true"><mrow><mtext>Z.</mtext></mrow><mo>̲</mo></munder><msub><mrow><mtext>​</mtext></mrow><mrow><mtext>H</mtext></mrow></msub><mtext>(s)} &lt;imaginary part { </mtext><munder accentunder="true"><mrow><mtext>Z.</mtext></mrow><mo>̲</mo></munder><msub><mrow><mtext>​</mtext></mrow><mrow><mtext>H</mtext></mrow></msub><mtext>(s)}, (43)</mtext></mrow></math><img file="EP0508392A2_D0049.tif" /></maths> can the linear network<maths id="math0048" num=""><math display="inline"><mrow><munder accentunder="true"><mrow><mtext>W</mtext></mrow><mo>̲</mo></munder><mtext>(s) ≈ s (44)</mtext></mrow></math><img file="EP0508392A2_D0050.tif" /></maths> as a simple differentiator and the linear networks<maths id="math0049" num=""><math display="inline"><mrow><munder accentunder="true"><mrow><mtext>F</mtext></mrow><mo>̲</mo></munder><mtext>(s) ≈ </mtext><munder accentunder="true"><mrow><mtext>W</mtext></mrow><mo>̲</mo></munder><mtext>₁ (s) ≈ real part (</mtext><munder accentunder="true"><mrow><mtext>W</mtext></mrow><mo>̲</mo></munder><mtext>₁ (s)) = R₁ (45)</mtext></mrow></math><img file="EP0508392A2_D0051.tif" /></maths><maths id="math0050" num=""><img file="EP0508392A2_D0052.tif" /></maths> can be designed as simple, frequency-independent amplifiers.

The electrodynamic sound receiver (microphone) also generates non-linear signal distortions when there is high sound pressure in the lower frequency range. The physical background is first explained using a model of the electrodynamic sensor with concentrated electrical and mechanical elements and then the equalizer network is derived.

All effective acoustic elements of the sensor are described by equivalent mechanical elements. With the help of a membrane with the area S_M becomes a sound pressure signal p_m(t) converted into a force signal F (t) that drives the mechanical vibration system.

The rigidity of the membrane suspension see_T(x) and the rigidity of the coupled air volume s_B(x) is in a constant total stiffness s_O and in a deflection-dependent overall stiffness s_G(x) summarized.<maths id="math0051" num=""><math display="inline"><mrow><msub><mrow><mtext>s</mtext></mrow><mrow><mtext>O</mtext></mrow></msub><msub><mrow><mtext> + s</mtext></mrow><mrow><mtext>G</mtext></mrow></msub><msub><mrow><mtext>(X) = s</mtext></mrow><mrow><mtext>T</mtext></mrow></msub><msub><mrow><mtext>(x) + s</mtext></mrow><mrow><mtext>B</mtext></mrow></msub><mtext>(x) (48)</mtext></mrow></math><img file="EP0508392A2_D0053.tif" /></maths>

The dependency on the deflection is also taken into account in the acting electrodynamic transducer parameter Bl (x) and the acoustic-mechanical total damping is divided into a constant part z_O and split into a deflection-dependent part z (x).

All elements of the mechanical-acoustic vibration system that have constant parameters are in the mechanical impedance<maths id="math0052" num=""><img file="EP0508392A2_D0054.tif" /></maths> summarized.

The amplifier connected to the sensor should have a sufficiently high internal resistance so that the resistance and inductance of the voice coil can be neglected.

Using the Laplace operator s, the inverse Laplace transform and the convolution operation, the nonlinear equation (IDG) can be set up in the time domain<maths id="math0053" num=""><math display="inline"><mrow><mtext>F (t) = v (t) * L⁻¹ {</mtext><munder accentunder="true"><mrow><mtext>e.g.</mtext></mrow><mo>̲</mo></munder><msub><mrow><mtext>(s)} + v (t) * z (x (t)) + x (t) * s</mtext></mrow><mrow><mtext>G</mtext></mrow></msub><mtext>(x (t)) (50)</mtext></mrow></math><img file="EP0508392A2_D0055.tif" /></maths>

The force F is the input variable of the transducer and the voice coil deflection x acts as a parameter-changing state variable. The voltage at the converter terminals results from<maths id="math0054" num=""><math display="inline"><mrow><msub><mrow><mtext>u</mtext></mrow><mrow><mtext>L</mtext></mrow></msub><mtext>(t) = v (t) Bl (x (t)) (51)</mtext></mrow></math><img file="EP0508392A2_D0056.tif" /></maths>

By connecting a suitable equalizer with the transfer function<maths id="math0055" num=""><math display="inline"><mrow><msub><mrow><mtext>u (t) = f [u</mtext></mrow><mrow><mtext>L</mtext></mrow></msub><mtext>(t)] (52)</mtext></mrow></math><img file="EP0508392A2_D0057.tif" /></maths> the entire system is to be linearized and the following linear equation (IDG) is to be fulfilled<maths id="math0056" num=""><img file="EP0508392A2_D0058.tif" /></maths>

The nonlinear equalizer network must do the following transfer function in the time domain<maths id="math0057" num=""><img file="EP0508392A2_D0059.tif" /></maths> with the abbreviations<maths id="math0058" num=""><img file="EP0508392A2_D0060.tif" /></maths> and<maths id="math0059" num=""><img file="EP0508392A2_D0061.tif" /></maths> have. The frequency-independent, non-linear functions result from the dependent parameters of the sensor<maths id="math0060" num=""><img file="EP0508392A2_D0062.tif" /></maths> where the auxiliary function N_U(x) the relationship<maths id="math0061" num=""><img file="EP0508392A2_D0063.tif" /></maths> enough.

The non-linear transfer function of the equalizer can be converted directly into a circuit. This circuit is a chain connection of two non-linear, dynamic two-port Z₂ and Z₃. The two-port Z₂, which immediately follows the sound receiver, contains the three-port D_BE to compensate for the electrodynamic coupling factor. That at the output of the Dreitor D_BE Connected second two-port contains the three-port to compensate for the deflection-dependent damping and the rigidity.

The Dreitor D_BE (FIG. 19) compensates for the coupling parameter which is variable in terms of deflection. The input E₂ of the Dreitor is serial via an integrating element (129), a serially coupled memoryless, non-linear transmission element N_BE (130) connected to the one input of a multiplier (131). The input E₁ is with the second multiplier input and the output of the multiplier is with the output A of the Dreitor D._BE interconnected.

The Dreitor D_SE (FIG. 17) brings about a desired change or compensation for the stiffness of the diaphragm suspension which is variable in terms of deflection. The input E₂ of the Dreitor D_SE is via an integrating element (123), a memoryless, non-linear transmission element N._SE (122) and a linear two-port Q (121) connected to the one input of an adder (103). The second input of the adder is at the input E 1 and the output of the adder is at the output A of the Dreitor D._SE interconnected.

The Dreitor D_DE (FIG. 18) brings about a desired change or compensation for the stiffness of the diaphragm suspension which is variable in terms of deflection. The input E₂ of the Dreitor D_DE is both directly with the input of a multiplier (107) and via the chain connection of an integrator (126) and a memoryless, non-linear transmission element N._DE (128) connected to the second input of the multiplier. The output of the multiplier is connected via a linear two-port Q (121) to the input of an adder, the second input of the adder is connected to the input E 1 and the output of the adder is connected to the output A of the three-stage D_DE interconnected.

In the electrostatic sensor (condenser microphone), the non-linear signal distortions arise from the action of a constant parallel capacitance C._p, by the deflection-dependent electrical attraction between the membrane and counterelectrode and by the deflection-dependent compliance of the air cushion or the membrane.

These non-linearities can also be compensated for by an equalizer network according to the basic structure described. The membrane with the area S_M converts the sound pressure signal p_m(t) into a force signal F (t), which acts on the overall compliance in the frequency range of interest.

With regard to the equalizer network, the rigidity of the membrane s_T(x), of the coupled air cushion s_B(x) and the effect of the electrical attraction in a constant total stiffness s_O and in a deflection-dependent overall stiffness s_G(x)<maths id="math0062" num=""><math display="inline"><mrow><msub><mrow><mtext>s</mtext></mrow><mrow><mtext>O</mtext></mrow></msub><msub><mrow><mtext> + s</mtext></mrow><mrow><mtext>G</mtext></mrow></msub><msub><mrow><mtext>(x) = s</mtext></mrow><mrow><mtext>T</mtext></mrow></msub><msub><mrow><mtext>(x) + S</mtext></mrow><mrow><mtext>B</mtext></mrow></msub><msub><mrow><mtext>(x) + s</mtext></mrow><mrow><mtext>A</mtext></mrow></msub><msub><mrow><mtext>(x, U</mtext></mrow><mrow><mtext>O</mtext></mrow></msub><mtext>).   (59)</mtext></mrow></math><img file="EP0508392A2_D0064.tif" /></maths> be summarized.

A polarization voltage U is between the membrane and the counter electrode of the electrostatic sensor_O constructed and the input resistance of the coupled amplifier is so high that no charges can flow off at the signal frequencies of interest. In addition to the capacity C_O a second constant parallel capacitance C acts between the membrane and the counterelectrode, which is controlled by the deflection of the membrane_p.

This results in the relationship between deflection x and signal output voltage<maths id="math0063" num=""><img file="EP0508392A2_D0065.tif" /></maths>

By connecting a suitable equalizer with the transfer function<maths id="math0064" num=""><math display="inline"><mrow><msub><mrow><mtext>u (t) = f [u</mtext></mrow><mrow><mtext>L</mtext></mrow></msub><mtext>(t)] (61)</mtext></mrow></math><img file="EP0508392A2_D0066.tif" /></maths> the entire system should be linearized and the following linear transfer function<maths id="math0065" num=""><img file="EP0508392A2_D0067.tif" /></maths> be fulfilled. For this, the nonlinear equalizer network must have the following transfer function in the time domain.<maths id="math0066" num=""><img file="EP0508392A2_D0068.tif" /></maths> With<maths id="math0067" num=""><img file="EP0508392A2_D0069.tif" /></maths> The equalizer network is frequency-independent and corresponds to a simple, memory-free, non-linear two-port.

Now that the circuit structure of the non-linear equalizer networks has been developed for various electroacoustic transducers, the problem of adapting these equalizer networks to the transducer is now also to be solved. The nonlinear distortions in the overall system can only be reduced below 1% if the characteristic curves in the memoryless, nonlinear two-ports are brought to the optimum values ​​at least in the same order of magnitude.

According to the invention, the equalizer network has variable properties, that is to say the parameters of the equalizer network, in particular the nonlinear, memoryless two gates, can be changed via at least one control input. On the control lines of the parameter control there are aids for storing the set control value (holding circuits) in order to retain the determined parameter setting even after the adjustment process has ended. Another circuit-technical aid is activated to adapt the network. It consists of a generation part for generating an excitation signal and an analysis part for recording and evaluating a measurement signal and for generating control signals for setting the equalizer parameters.

The adapter arrangement can be designed as a control circuit or as a control circuit.

A separate adaptation is possible in the control circuit, in which the converter is initially connected to the measuring arrangement without an equalizer network with the matching arrangement, and the nonlinear converter parameters are determined and stored in the holding circuits. After measuring the converter parameters, the equalizer network is coupled to the converter again and the outputs of the holding circuits are connected to the control inputs of the equalizer network.

A simultaneous adaptation appears to be more advantageous, in which the generation part is connected to the transducer-equalizer system and the analysis part to form an electrode.

The output of the analysis section is connected to the control input of the equalization network, so that the control signals generated in the analysis section change the parameters of the equalization network and adapt the system to the converter. A main control system takes over the control and control of the subsystems during the adjustment process.

When adapting equalizer networks to sound transmitters, the generation part is connected to the input terminals of the converter via the equalizer network. The measurement signal can be derived via an impedance measurement or via an acoustic measurement. The acoustic measurement requires an additional sound receiver, but reduces the technical effort in the subsequent analysis section.

For practical implementation, it is desirable to only change the parameters of non-linear, memoryless two-ports in the equalizer network and to largely avoid changing the linear, frequency-dependent two-port parameters. In the case of the electrodynamic sound transmitter, the overall arrangement can be adapted to the transmission behavior of the two-port X by means of the three-port damping and stiffness compensation. As a result, the adaptation effort can be reduced and at the same time a desired linear overall transmission behavior can be realized.

In the analysis part, the individual distortion components are separated from the recorded measurement signal (microphone signal) with a spectral or correlation analysis and the control signals are derived.

In the correlation analysis, it is first necessary to transfer the excitation signal from the generation part into the analysis part and to form reference signals from the excitation signal. For this purpose, the excitation signal is conducted via non-linear, dynamic two-ports, which synthetically simulate the non-linear causes of distortion of the converter and separate individual distortion components. The frequency and phase position of the reference signals, but not their amplitude, is important for the correlation analysis. The measurement signal and a reference signal are fed to the two inputs of the correlator. The correlator consists of a multiplier and a downstream low-pass filter. The correlation signal is used directly to control the equalizer network.

The adaptation process is carried out with various signal modulations in order to achieve the best possible match and ultimately compensation in the small and large signal range. In the case of a step-by-step excitation signal, the optimal equalizer parameters intended for lower modulation can be adopted and only the curve sections relevant for the extended modulation range can be changed.

In the event that the converter equalizer system has reached its modulation limits and, for example, the deflection of the voice coil or the power supplied and converted into heat can destroy the converter, the arrangement of a non-linear, dynamic two-port Z is recommended_SS in the equalizer network. The two-port Z_SS has the same structure as the other nonlinear equalizer blocks. It contains non-linear, dynamic three-port D_SS to limit the level and to limit the power.

Between the input E₁ and the output A of the three-port a controllable, non-linear network H is connected, which has, for example, a high-pass characteristic. The input E₂ is via a linear network O, via a memoryless, non-linear two-port N_O and connected to the control input of the two-port H via a further linear two-port B.

To implement the deflection protection, the linear two-port O has the transfer function X (s) and generates a deflection-equivalent signal. The non-linear two-port N_O is a rectifier and the downstream two-port has a low-pass characteristic.

In order to limit the power loss in the converter, the linear two-port O has a transfer function derived from the electrical input impedance. The non-linear two-port N_O contains a squarer and the subsequent linear two-port B is an integrator, the integration time of which corresponds to the heating-up time (determined by thermal capacity and thermal conductivity) of the converter.

A change in the linear transmission properties of the two-port H (e.g. lowering of the bass signals through a high-pass filter) prevents the converter from being destroyed or the generation of nonlinear distortions when the modulation limit (max. Deflection, max. Power loss) is reached.

Show in the drawings<ul id="ul0001" list-style="none"><li>1: the basic circuit diagram of the solution according to the invention of the equalizer network for the sound transmitter (a) and the sound receiver (b),</li><li>2a a non-interacting interconnection of individual non-linear, dynamic three-port doors D to form a two-port Z, FIG. 2 b: retroactive interconnection of individual non-linear, dynamic three-port doors D to form a two-port Z,</li><li>3: internal structure of a non-linear, dynamic Dreitor D,</li><li>4: Structure of the equalizer network for an electrodynamic sound transmitter,</li><li>5: structure of the equalizer network for an electrodynamic microphone,</li><li>6: structure of the equalizer network for a condenser microphone,</li><li>7 a: electromechanical equivalent circuit diagram for an electrodynamic sound transmitter,</li><li>7 b: Description of the transmission behavior of an electrodynamic sound transmitter with a signal flow plan,</li><li>8: equivalent circuit diagram of the electroacoustic transducer with horn sound guide (pressure chamber loudspeaker),</li><li>Fig. 9: Dreitor D_S to compensate the deflection-dependent stiffness in a sound transmitter,</li><li>Fig. 10: Dreitor D_B to compensate for the deflection-dependent, electrodynamic drive in a sound transmitter,</li><li>Fig. 11: Dreitor D_D to compensate the deflection-dependent damping in a sound transmitter,</li><li>Fig. 12: Dreitor D_MU to compensate for the electromagnetic drive in a sound transmitter with constant voltage supply,</li><li>Fig. 13: Dreitoritor D_MI to compensate for the electromagnetic drive in a sound transmitter with constant current supply,</li><li>Fig. 14: Dreitor D_L to compensate for the deflection-dependent inductance in a sound transmitter,</li><li>Fig. 15: Dreitoritor D_A to compensate for the adiabatic compression in the coupled sound guide of a sound transmitter,</li><li>Fig. 16: Dreitor D_R to compensate for the turbulent flow in the coupled sound guide of a sound transmitter,</li><li>Fig. 17: Dreitor D_SE to compensate for the deflection-dependent stiffness of an electrodynamic sound receiver, Fig. 18: Dreitor D_DE to compensate for the deflection-dependent damping of an electrodynamic sound receiver,</li><li>Fig. 19: Dreitor D_BE to compensate for the deflection-dependent, electrodynamic drive in a sound receiver,</li><li>20 a: rough structure (signal flow diagram) of an equalization system for the electrodynamic loudspeaker,</li><li>20 b: exemplary embodiment of an equalizer network for an electrodynamic loudspeaker to compensate for the deflection-dependent stiffness, damping and the coupling factor,</li><li>21: exemplary embodiment of a controllable, memoryless, non-linear two-port,</li><li>22: basic circuit diagram of the arrangement for independent, automatic adaptation of the equalizer network to the converter,</li><li>Fig. 23: Exemplary embodiment for the automatic matching arrangement.</li><li>Fig. 24: Three port D_T to compensate the deflection-dependent transit time (Doppler effect) for a sound transmitter,</li></ul> In the drawings, the numbers represent the following elements: Equalizer network (1), sound transmitter (2), sound receiver (3), linear and non-linear transmission systems (4, 5, 6, 8, 9, 10), amplifier (7), input of the two-port Z (11), output of the two-port Z (12), non-linear, dynamic transmission drives D (14, 15, 16, 17), inputs of the first three-port (18, 19), output of the last three-port (20), input E 1 of the three-port D (21), input E 2 of the three-port D (22), non-linear transmission system U (23), linking element (24), Output A of the three-port D (25), memoryless, non-linear two-port N_K (26), equalizer network (27), multiplier (28, 33), adder (29, 30), input of the equalizer (31), output of the equalizer (32), linear network with the transfer function X (s) (34), memoryless, non-linear two-port (35, 37, 38), differentiator (36), control inputs for changing parameters (39, 40, 41), control input for operating point changeover (42), relay (43), changeover switch (44, 45, 46), input the changeable, memoryless, non-linear two-port N (47), Holding circuits (48, 49, 50, 51, 52), adders (53, 54, 55, 56), multipliers (57, 58, 59), voltage-controlled amplifiers (60, 61, 62, 63), output of the non-linear two-port N (64), tone generators (65, 66), adders (67), linear network with the input voltage deflection transfer function of the converter (68, 69), multipliers (70, 71, 72), linear networks with the transfer function of the converter ( 73, 74), generation part (75), analysis part (76), multiplier (77, 78, 79, 80), Low-pass filters (81, 82, 83, 84), differentiators (85, 86), changeover switches (87), relays (88), main control system (89), voltage-controlled amplifier VCA (91), audio input (93), multiplier (95), Dreitor D_MI to compensate for electromagn. Drive with constant voltage supply (96), three-port D_MU to compensate for electromagn. Actuator with power supply (97), three-port D_L for inductance compensation (98), three gate D_S for stiffness compensation (99), linear network X to simulate the deflection (100), memoryless, non-linear two-port N_S (101), Dreitor D_B to the electrodyn. Drive compensation (102), adder (103), memoryless, non-linear two-port N_B (104), multiplier (105), memoryless, non-linear two-port N_D (106), multiplier (107), differentiator (108), three-port D_D for damping compensation (109), memoryless, non-linear two-port N_M (110), dynamic two-port to simulate the converter input current (111), differentiator (112), linear network W (113), memoryless, non-linear network N_A (114), dynamic two-port (115), three-port D_A to compensate for adiabatic compression (116), three port D_R to compensate for turbulent flow (117), linear network Y (118), memoryless, non-linear two-port N_R (119), linear network F (120), linear network Q (121), memoryless, non-linear two-port N_SE (122), integrator 1 / s (123), three-port D_SE for stiffness compensation (124), three port D_DE for damping compensation (125), integrator 1 / s (126), memoryless, non-linear two-port N_DE (128), integrator (129), memoryless, non-linear two-port N_BE (130), multiplier (131), three port D_BE to compensate for the electrodyn. Drive (132), three-door D_T to compensate for the deflection-dependent transit time in the acoustic system, adders (134), subtractors (135), adders (136), multipliers (137), delay elements with constant delay time (138), adders (139), multipliers (140), adders (142 - 143), linear transmission system X (s) (144), transmission element with variable, controllable transit time (145), linear transmission system (146), non-linear transmission systems (147-152), linear transmission system (153), Signal input (154), delay element with opposite control characteristic (155), subtracting elements (156-158, 160), dividing element (159), linear transmission system (161), non-linear transmission elements (162-166), linear transmission system (167), squarer (168 ), Multiplier (169).

The invention will be explained in the following using an exemplary embodiment and with reference to Figures 20, 21, 22 and 23. A simple example was chosen for reasons of clarity. The principle can be applied analogously to other and several parameters. An electrodynamic cone loudspeaker (2), mounted in a compact housing, is fed via a constant current source. With this loudspeaker, the electrodynamic drive proves to be the decisive cause of the distortion, so that only a non-linear converter parameter has to be compensated for. The equalizer network used is shown in FIG. 20. It allows correction of the electrodynamic drive, the damping and the rigidity of the converter parameters. The network contains a linear low-pass filter (34) of second order X (s), a differentiator s (36), three memoryless, non-linear two-port N_S (35), N_B (38), N_D (37) and three multipliers (33, 28, 95) and two adding stages (29, 30). The input of the adder (30) and the input of the low pass X (34) are connected to the input (31) of the equalizer network. The output of the low-pass filter X (34), which carries a deflection-equivalent signal, is connected to all inputs of the memoryless, non-linear two-ports (35, 37, 38) and the differentiating element (36) as well as to one input of the multiplier (95) . The second input of the multiplier (95) is connected to the output of the non-linear two-port N_S (35) linked. The output of the multiplier (95) is superimposed in the adder (30) with the undistorted signal. The output of the differentiator (36) and the output of the non-linear two-port N_D (37) are connected to the inputs of the multiplier (33). The output of the multiplier is linked to the predistorted signal via the adder (29) and to the one input of the multiplier (28). The second input of the multiplier (28) is connected to the output of the memoryless two-port N_B (38) connected. The output of the multiplier (28) is connected to the loudspeaker via an amplifier (7) with constant current supply.

The linear network is constructed as an active RC filter. The quality and the resonance frequency of the second order low-pass filter X (s) is determined in accordance with the desired linear transmission behavior. With the help of the three-port D contained in the equalizer circuit_D and D_S the entire system can be corrected to the required linear properties for any loudspeaker with different resonance frequency and quality. The correspondence between the low-pass function X (s) and the linear transmission behavior of the overall arrangement is a necessary prerequisite for the functionality of the nonlinear equalizer.

Since in the present example the loudspeaker has no stiffness and damping non-linearities, only constant values ​​in the two gates N_S (35) and N_D (37) filed. The non-linear characteristic of the memoryless two-port N_B (38) must, however, be adapted to the converter.

According to Fig. 21, each of these memoryless non-linear two-ports consists of a parallel connection of individual branches, each branch containing an exponentiation element (57, 58, 59) and a voltage-controlled amplifier (60, 61, 62, 63), which are connected via an adder element (53 , 54, 55, 56) before the exit (64) are summarized. In accordance with the Taylor series development, the order of the powers increases from branch to branch and the gain change of the VCA enables the approximation of any curve shape. A hold circuit (48, 49, 50, 51, 42) is connected to the control inputs of the amplifiers and stores the optimally set control voltage after the adjustment process. The control voltage of the linear (49, 60) and cubic branches (51, 58, 62) change the asymmetry of the characteristic. If the gain in the even-order potentiometers (61, 63) is increased, the symmetrical changes in the characteristic curve increase.

The control lines of the even and odd systems are each connected to a changeover switch (44, 45, 46) which are switched simultaneously by the main control unit (89) via the relay (43). The rotors of the changeover switches lead to the constant (39), symmetrical (41) and asymmetrical (40) correction inputs. In addition to the signal input and output, the changeable non-linear "two-port" also contains a control line (42) with which the changeover switch can be switched and various operating points can be selected in the characteristic curves. For very small input signals at the equalizer-converter system, the coefficients of the linear (49) and quadratic (50) elements are optimized in the lowest operating point. The order of the Taylor series approach or the number of parallel branches in the memoryless, non-linear two-port determines the number of additional operating points. They are appropriately distributed over the further modulation range of the converter.

The generating part (75) consists of two signal generators (65, 66) which generate a sinusoidal tone near the resonance frequency and a second higher-frequency tone. Both signals are added in an adder stage (67) and output to the equalizer network (1) via a voltage-controlled amplifier (91) via the changeover switch (87). The main control unit (89) establishes this connection via the relay (88) during the adaptation process and switches back to the normal signal input (93) after adaptation. The equalizer network (1) is connected to the converter (2) via a DC voltage-transmitting amplifier (7).

A microphone (3) is used to measure the sound pressure in the vicinity of the loudspeaker during the adjustment process and the electrical microphone signal is fed to the analysis part (76). The analysis part contains a correlator for each parameter to be adjusted, which was implemented with the aid of a multiplier (77, 78, 79, 80) and a downstream free pass (81, 82, 83, 84). The microphone signal is routed to one input of the correlator and a reference signal derived from the excitation signal to the other input. The amplitude of the reference signals is arbitrary and has no information value. However, the frequency and phase position of the reference signals correspond to the fundamental tones, harmonics or intermodulations in the microphone signal. The reference signal R (f₁) and R (f₂) at the multipliers (77, 78) is obtained by linear filtering (68, 89) with the transfer function X (s) of the linear two-port of the equalizer circuit from the excitation signal.

The reference signal R (f 1) is linked in the correlator (77, 81) with the microphone signal, then passed through a differentiator (85) to the control input (39) of the memory-free, non-linear two-port stiffness compensation. In the same way, the reference signal R (f₂) is fed to the correlator (78, 82) and its output is connected via a differentiating element (86) to the control input (39) of the damping compensation. Both control signals make the constant portion of the memoryless, non-linear two-port N_S and N_D changed so that the linear transmission behavior (resonance frequency and quality) of the equalizer network converter system matches the transmission behavior X (s) and the output signal at the integrators (81) and (82) becomes maximum.

The reference signals R (f₁ + f₂) and R (2 · f₁ + f₂) are synthetically generated in an electronic replica of the nonlinear converter. This network is a circuit implementation of the modeling of the transmission behavior with the VOLTERRA series.

First, the signals f 1 and f 2 are passed through linear filters X (68, 89), multiplied together in (72) and filtered again with the linear transfer function of the converter (74). The reference signal R (f 1 + f 2) obtained in this way corresponds in phase and frequency to the intermodulations generated by asymmetries in the characteristic curve of the electrodynamic coupling factor ([6] Klippel, W.: Dynamic Measurement of Non-Linear Parameters of Electrodynamical Loudspeakers and their Interpretation 88. Conv. Of the Audio Eng. Soc., March 1990, preprint 2903). To form the reference signal R (2 · f₁ + f₂), the signal f1 is additionally squared before multiplication. The output signal of the multiplier (71) is also subjected to linear filtering (74) with the transfer function X.

The reference signal R (f₁ + f₂) is linked in the correlator (79, 83) with the microphone signal, then the unbalanced control input (40) of the memoryless, non-linear two-port drive compensation N_B fed. In the same way, the reference signal R (2 · f₁ + f₂) is fed to the correlator (80, 84) and its output signal with the balanced control input (41) of the memoryless, non-linear two-port N_B the drive compensation connected. The characteristic curve is changed by both control signals so that the second and third order intermodulation products in the received measurement signal are reduced and the output signal of the integrators (83) and (84) runs towards zero. The sign of the correlation signal indicates over- or under-compensation by the equalizer network and leads to a reduction or Increasing the voltage in the subsequent hold circuits (48, 49, 50, 51, 52) of the memoryless non-linearity. After the individual assemblies of the adaptation system have been described, finally a functional representation of the overall system. With the start of the adaptation process, the main control system (89) connects the equalizer input (31) to the generating part (75), switches on the lowest excitation voltage via the voltage-controlled amplifier (91) and starts adapting the constants of the two-port N_D, N_S and determines the optimal voltage value in the hold circuit (48). At the same time, N_B changed the coefficients of the linear and quadratic branches and determined optimal voltages in the holding circuits (49, 50). When the system has settled, the main control system (89) switches the two higher coefficients of the Taylor expansion into N._B with the changeover switches (44, 45), increases the excitation voltage and determines the optimum value for the holding circuits (51, 52). The constant parameters in the two-port N_S and N_D, ie the values ​​in the holding circuits (48) are no longer changed. When the operating points have been passed through, the main control system switches off the generating part (75) and connects the equalizer input (31) to the general signal input (93).

The advantages achieved by the invention are, in particular, to implement simple equalizer networks which largely take into account the converter-specific features and require a minimal number of components. The problem of adapting the equalizer network to the converter was solved with the aid of a further circuit arrangement. The adaption system, which is activated at times, enables the optimum equalizer parameters to be determined and set independently. As a result, with the equalizer network coupled to the converter, both a desired change in the linear properties and a reduction in the non-linear distortions can be achieved over the entire modulation range of the converter.<tables id="tabl0001" num="0001"><img file="EP0508392A2_D0070.tif" /></tables><tables id="tabl0002" num="0002"><img file="EP0508392A2_D0071.tif" /></tables><tables id="tabl0003" num="0003"><img file="EP0508392A2_D0072.tif" /></tables><tables id="tabl0004" num="0004"><img file="EP0508392A2_D0073.tif" /></tables><tables id="tabl0005" num="0005"><img file="EP0508392A2_D0074.tif" /></tables>