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Audio Engineering Society Convention Paper
音频工程学会大会论文

Presented at the Convention
大会上发言
2016 September 29 - October 2, Los Angeles, CA, USA
2016年9月29日至10月2日,美国加利福尼亚州洛杉矶市

This paper was peer-reviewed as a complete manuscript for presentation at this convention. This paper is available in the AES
这篇论文的完整手稿已通过同行评审,将在本次大会上发表。本文可在 AES
E-Library (http://www.aes.org/e-lib) all rights reserved. Reproduction of this paper, or any portion thereof, is not permitted without direct permission from the Journal of the Audio Engineering Society.
电子图书馆 ( http://www.aes.org/e-lib) 保留所有权利。未经《音频工程学会杂志》直接许可,不得复制本文或其中任何部分。

Force Factor Modulation in Electro Dynamic Loudspeakers
电子动态扬声器中的力因子调制

Lars Risbo , Finn T. Agerkvist , Carsten Tinggaard , Morten Halvorsen , and Bruno Putzeys
Lars Risbo , Finn T. Agerkvist , Carsten Tinggaard , Morten Halvorsen , and Bruno Putzeys
Purifi, Denmark/Belgium
普里菲,丹麦/比利时
Acoustic Technology, DTU-Elektro, Technical University of Denmark, DK-2800 Lyngby, Denmark
声学技术,丹麦技术大学 DTU-Elektro, DK-2800 Lyngby, 丹麦
PointSource Acoustics, Roskilde, Denmark
PointSource Acoustics,丹麦罗斯基勒

Correspondence should be addressed to Lars Risbo (lars@purifi. dk)
通讯作者:Lars Risbo (lars@purifi. dk)

Abstract 摘要

The relationship between the non-linear phenomenon of 'reluctance force' and the position dependency of the voice coil inductance was established in 1949 by Cunningham, who called it 'magnetic attraction force'.
1949 年,坎宁安确定了 "磁阻力 "这一非线性现象与音圈电感位置相关性之间的关系,并将其称为 "磁吸引力"。

This paper revisits Cunningham's analysis and expands it into a generalised form that includes the frequency dependency and applies to coils with non-inductive (lossy) blocked impedance.
本文重温了坎宁安的分析,并将其扩展为一种包含频率相关性的通用形式,适用于具有非电感(有损)阻塞阻抗的线圈。

The paper also demonstrates that Cunningham's force can be explained physically as a modulation of the force factor which again is directly linked to modulation of the flux of the coil.
论文还证明,坎宁安力可以物理解释为力因子的调制,而力因子的调制又与线圈磁通量的调制直接相关。

A verification based on both experiments and simulations is presented along discussions of the impact of force factor modulation for various motor topologies. Finally, it is shown that the popular
报告基于实验和模拟进行了验证,并讨论了力因数调制对各种电机拓扑结构的影响。最后,还显示了流行的

This paper revisits Cunningham's analysis and expands it into a generalised form that includes the frequency dependency and applies to coils with non-inductive (lossy) blocked impedance.
本文重温了坎宁安的分析,并将其扩展为一种包含频率相关性的通用形式,适用于具有非电感(有损)阻塞阻抗的线圈。

The paper also demonstrates that Cunningham's force can be explained physically as a modulation of the force factor which again is directly linked to modulation of the flux of the coil.
论文还证明,坎宁安力可以物理解释为力因子的调制,而力因子的调制又与线圈磁通量的调制直接相关。

A verification based on both experiments and simulations is presented along discussions of the impact of force factor modulation for various motor topologies. Finally, it is shown that the popular coil impedance model does not correctly predict the force unless the new analysis is applied.
报告基于实验和模拟进行了验证,并讨论了力因数调制对各种电机拓扑结构的影响。最后表明,除非采用新的分析方法,否则常用的 线圈阻抗模型无法正确预测力。

1 Introduction 1 引言

The electro-dynamic loudspeaker recently celebrated its centenary and has not materially changed construction since the direct radiating speaker by Rice and Kellogg in 1923.
最近,电动扬声器迎来了它的百年诞辰,自 1923 年赖斯和凯洛格推出直接辐射扬声器以来,它的结构并没有实质性的改变。

Production of loudspeakers today numbers in billions of units per year and thanks to digital audio storage and distribution the speaker is by orders of magnitude the most non-linear device in the audio chain.
如今,扬声器的年产量已达数十亿只,而由于数字音频的存储和传播,扬声器在数量级上已成为音频链中最非线性的设备。

Unfortunately, the in-depth understanding and modelling of speakers has progressed at a modest pace and leaves still much work to be done.
遗憾的是,对扬声器的深入了解和建模工作进展缓慢,仍有许多工作要做。

Production of loudspeakers today numbers in billions of units per year and thanks to digital audio storage and distribution the speaker is by orders of magnitude the most non-linear device in the audio chain.
如今,扬声器的年产量已达数十亿只,而由于数字音频的存储和传播,扬声器在数量级上已成为音频链中最非线性的设备。

Unfortunately, the in-depth understanding and modelling of speakers has progressed at a modest pace and leaves still much work to be done.
遗憾的是,对扬声器的深入了解和建模工作进展缓慢,仍有许多工作要做。
A major breakthrough was the work by Cunningham in 1949 [1] who analysed the inherently non-linear response of the motor due to magnetic effects with surprising depth of insight.
一个重大突破是坎宁安在 1949 年的研究[1],他以惊人的洞察力分析了电机因磁效应而产生的固有非线性响应。

Aside from the position dependent force factor due to the non-homogeneous field in the gap and the linearising effect of overhung coils, Cunningham analysed 'Distortion due to magnetic attraction forces'.
除了间隙中的非均匀磁场和悬空线圈的线性化效应导致的与位置相关的力因子外,坎宁安还分析了 "磁吸引力导致的变形"。

He showed that 'this effect is not dependent upon the presence of a permanent field' but instead that this force was given by [1] :
他指出,"这种效应并不取决于永久场的存在",相反,这种力是由 [1] 给出的:

Aside from the position dependent force factor due to the non-homogeneous field in the gap and the linearising effect of overhung coils, Cunningham analysed 'Distortion due to magnetic attraction forces'.
除了间隙中的非均匀磁场和悬空线圈的线性化效应导致的与位置相关的力因子外,坎宁安还分析了 "磁吸引力导致的变形"。

He showed that 'this effect is not dependent upon the presence of a permanent field' but instead that this force was given by [1] :
他指出,"这种效应并不取决于永久场的存在",相反,这种力是由 [1] 给出的:
where is the stored magnetic energy, is the coil current, is the position dependent inductance of the voice coil and is defined as the current dependent force factor. The force is proportional to the square of the current and the spatial gradient of the coil's inductance. The result is order distortion as well as force acting in the direction of highest inductance.
其中, 是存储的磁能, 是线圈电流, 是与音圈位置有关的电感, 是与电流有关的力因子。力与电流的平方和线圈电感的空间梯度成正比。其结果是 阶失真以及 作用于最高电感方向的力。
Cunningham considered only moving coil transducers, but we will show in the Appendix that the analysis is equally applicable to all 3 known motor type, namely 'moving coil', moving magnet' and 'moving iron'. All
坎宁安只考虑了动圈传感器,但我们将在附录中说明,该分析同样适用于所有三种已知电机类型,即 "动圈"、"动磁 "和 "动铁"。所有

three motor types produce a force in response to the coil current having a desired proportional component defined by a permanent force factor as well as an undesired quadratic response c.f. (1). We will follow the conventions of moving coil transducers and call the force factor
三种电机对线圈电流都会产生一个力,这个力有一个由永久力系数定义的理想比例分量,以及一个不理想的二次响应,即 c.f. (1)。我们将遵循动圈传感器的惯例,将力因数称为

三种电机对线圈电流都会产生一个力,这个力有一个由永久力系数定义的理想比例分量,以及一个不理想的二次响应,即 c.f. (1)。我们将遵循动圈传感器的惯例,将力因数称为 。这并不影响我们分析的一般性。
The flux in the coil is central to the analysis of the force as we will show and the term flux modulation due to the coil current is thus quite apt.
线圈中的磁通量是分析力的核心,我们将展示这一点,因此线圈电流引起的磁通量调制这一术语非常贴切。

Still we prefer the term force factor modulation since the force factor is the most important characteristic of a black box model of a motor while the magnetic field making up the flux is a complex 3-dimensional internal characteristic.
但我们更倾向于使用力因数调制这一术语,因为力因数是电机黑盒模型的最重要特征,而构成磁通的磁场则是复杂的三维内部特征。

Moreover, the term 'flux modulation' is sometimes used to refer to a change in permeability due to saturation of the iron [2].
此外,"通量调制 "一词有时也用来指由于铁饱和而导致的渗透率变化[2]。

The brevity of Cunningham's analysis (basically just one short paragraph) may be the reason for today's apparent confusion where 'flux-modulation' and 'reluctance force' are often treated as separate phenomena (see e.g., [3]).
坎宁安的分析简明扼要(基本上只有一小段),这可能是今天 "磁通调制 "和 "磁阻力 "经常被视为不同现象的原因(见 [3])。

Still we prefer the term force factor modulation since the force factor is the most important characteristic of a black box model of a motor while the magnetic field making up the flux is a complex 3-dimensional internal characteristic.
但我们更倾向于使用力因数调制这一术语,因为力因数是电机黑盒模型的最重要特征,而构成磁通的磁场则是复杂的三维内部特征。

Moreover, the term 'flux modulation' is sometimes used to refer to a change in permeability due to saturation of the iron [2].
此外,"通量调制 "一词有时也用来指由于铁饱和而导致的渗透率变化[2]。

The brevity of Cunningham's analysis (basically just one short paragraph) may be the reason for today's apparent confusion where 'flux-modulation' and 'reluctance force' are often treated as separate phenomena (see e.g., [3]).
坎宁安的分析简明扼要(基本上只有一小段),这可能是今天 "磁通调制 "和 "磁阻力 "经常被视为不同现象的原因(见 [3])。
The drive towards speakers with long strokes, full audio range and high linearity in very small form factors makes Cunningham's analysis even more important today than in 1949 when low power amplifiers dictated the use of speakers with large diaphragms and low excursion.
与 1949 年相比,如今的扬声器更需要长冲程、全音域和高线性度,而当时的小功率放大器要求使用大振膜和低偏移的扬声器。

Force factor modulation is a much greater problem today.
如今,力因数调制是一个更大的问题。

Force factor modulation is a much greater problem today.
如今,力因数调制是一个更大的问题。

1.1 Paper Structure 1.1 纸张结构

A fundamental analysis of the physics of a generalised electro-magnetic machine that serves as a basis for this paper is given in the Appendix. Throughout the paper we assume the use of linear magnetic materials.
附录中给出了作为本文基础的通用电磁机器的基本物理分析。本文始终假定使用线性磁性材料。

Section 2 generalises Cunningham's work to cover lossy coils and to include the frequency dependent dynamics of the force. Section 3 tests the theory with both measurements and Finite Element Simulations.
第 2 节对坎宁安的工作进行了概括,以涵盖有损线圈,并包括力的频率相关动态。第 3 节通过测量和有限元模拟对理论进行检验。

Section 4 discusses the new results as applied to the popular lumped parameter models for the speaker-impedance.
第 4 节讨论了应用于流行的扬声器阻抗整块参数模型的新结果。

Section 2 generalises Cunningham's work to cover lossy coils and to include the frequency dependent dynamics of the force. Section 3 tests the theory with both measurements and Finite Element Simulations.
第 2 节对坎宁安的工作进行了概括,以涵盖有损线圈,并包括力的频率相关动态。第 3 节通过测量和有限元模拟对理论进行检验。

Section 4 discusses the new results as applied to the popular lumped parameter models for the speaker-impedance.
第 4 节讨论了应用于流行的扬声器阻抗整块参数模型的新结果。

2 Generalisation of Cunninghams's 1949 Formula
2 坎宁安 1949 年公式的一般化

Equation (1) says that the force produced by the force factor modulation is the spatial gradient of the stored magnetic energy. This equation holds generally as shown by the analysis in the Appendix. Equally fundamental is that the stored magnetic energy due the coil current and its generated flux is:
公式 (1) 指出,力因数调制产生的力 是存储磁能的空间梯度。如附录中的分析所示,该等式一般成立。同样重要的是,线圈电流 及其产生的磁通量 所产生的存储磁能:
We will now use the generality of (1) and (2) to study the force when the coil is not a pure inductor but exhibits frequency dependent losses, e.g., from eddy currents. The impedance of speaker coils has been studied intensely in literature .
现在,我们将利用 (1) 和 (2) 的一般性来研究当线圈不是纯电感,而是表现出随频率变化的损耗(如涡流损耗)时的力。扬声器线圈的阻抗在文献 中得到了深入研究。
The first step is to combine (1) and (2) to express the force as a product of the current and the current dependent force factor (also found as (25) in the Appendix):
第一步是结合 (1) 和 (2),将力表示为电流 和取决于电流的力系数 的乘积(也可在附录中找到 (25)):
From Faraday's law, the current dependent flux can be found from the time integral of the induced voltage in the coil at a stationary (blocked) position :
根据法拉第定律,从静止(闭锁)位置线圈中感应电压的时间积分 可以求得与电流相关的磁通量
where is the voltage induced in the coil, i.e., the voltage on the coil minus the voltage across its DCresistance . We now move to the -domain (Laplace domain) where to express the flux and note that the flux and induced voltage are linear responses of the current (thanks to our assumption of linear magnetic media). In the Laplace domain the time integral is replaced by a division by :
其中 是线圈中的感应电压,即线圈上的电压减去其直流电阻上的电压 。现在我们转到 域(拉普拉斯域), 来表示磁通量 ,并注意到磁通量和感应电压是电流的线性响应(这得益于我们对线性磁介质的假设)。在拉普拉斯域,时间积分由除以 代替:
where is the blocked impedance of the coil and is the Laplace tranform of the current.
其中 是线圈的阻塞阻抗, 是电流的拉普拉斯变换。
It is now practical to define the generalised inductance :
现在可以定义广义电感
Combining (3), (5) and (6) reveals that the instantaneous force factor due to the current is the coil current filtered by a transfer function:
结合 (3)、(5) 和 (6),可以看出电流 产生的瞬时力因数是经过传递函数滤波的线圈电流:
where we defined the force factor transfer function . The current dependent instantaneous force factor is simply the coil current filtered by this transfer function.
其中,我们定义了力因数传递函数 。与电流相关的瞬时力因数 就是用该传递函数滤波后的线圈电流
We now have a generalisation of Cunningham's formula where the gradient of the inductance is generalised to a filter being the -gradient of the generalised inductance . The force factor transfer function represents a dynamic linear system with possible frequency dependent phase and magnitude response. It is noted that for a purely inductive coil (Cunningham's original work) we have that . In this special case, is simply a constant.
现在,我们对坎宁安公式进行了概括,将电感梯度概括为滤波器 ,即概括电感的 - 梯度 。力因数传递函数 代表一个动态线性系统,其相位和幅值响应可能与频率有关。我们注意到,对于纯电感线圈(坎宁安的原创作品), 。在这种特殊情况下, 只是一个常数。
The current dependent force factor is the instantaneous proportionality between the current dependent force component and the current. However, as shown in the Appendix and dictated by conservation of energy, the back EMF generated in the coil in response to motion of the coil is counter-intuitively twice the factor times the velocity c.f. (27).
电流相关力系数 是电流相关力分量 与电流之间的瞬时比例关系。然而,如附录所示,根据能量守恒原理,线圈运动时在线圈中产生的反向 EMF 是 系数的两倍乘以速度 c.f. (27)。
A further and very practical consequence of the analysis is that the dynamic force factor modulation effect can simply fully be characterised by measuring (or simulating) the position dependency of the blocked impedance . It is not necessary to measure (or simulate) the modulation of the exact magnetic field to know the impact on the force and back EMF.
该分析的另一个非常实用的结果是,只需测量(或模拟)阻塞阻抗 的位置依赖性,就可以完全确定动态力因数调制效应的特征。无需测量(或模拟)精确磁场的调制,就能知道对力和反向 EMF 的影响。
A generalisation of Cunningham was attempted in [7]. However, only the real part of the generalised inductance (corresponding to the imaginary part of the impedance) was taken into consideration.
[7] 尝试对 Cunningham 进行了概括。不过,当时只考虑了广义电感的实部(对应于阻抗的虚部)。

This means that the force factor modulation caused by the position dependency of the resistive part of the coil impedance is ignored
这意味着线圈阻抗电阻部分的位置依赖性所引起的力因数调制被忽略了

This means that the force factor modulation caused by the position dependency of the resistive part of the coil impedance is ignored
这意味着线圈阻抗电阻部分的位置依赖性所引起的力因数调制被忽略了

2.1 Symptoms of BI-modulation
2.1 BI 调节的症状

. plus a contribution due to the force factor modulation of:
......,再加上由于受力系数调制而产生的贡献:
Fig. 1: Cross section of motor structure of the used 4" driver. The motor has rotation symmetry around the -axis indicated by a vertical line.
图 1:所用 4 英寸驱动器的电机结构截面图。电机围绕 轴对称旋转,垂直线表示该轴。
The force has both a DC component (caused by real part of ) and a harmonic component. The imaginary part of represents the position gradient of the coil losses (effective series resistance) and this also causes force factor modulation in the form of a harmonic but with no accompanying DC component. Force factor modulation by a low frequency tone will amplitude modulate (AM) a high frequency voice tone (a.k.a. IMD2).
力有直流分量(由 的实部引起)和 谐波分量。 的虚部表示线圈损耗(有效串联电阻)的位置梯度,这也会导致 谐波形式的力因数调制,但不伴有直流分量。低频音调的力因数调制将对高频语音音调(又称 IMD2)进行调幅(AM)。

AM modulation manifests itself as sidebands to the voice tone (at the sum and difference frequencies) at an amplitude relative to the voice tone of:
调幅调制表现为语音音调的边带(在总频和差频),幅度相对于语音音调为

AM modulation manifests itself as sidebands to the voice tone (at the sum and difference frequencies) at an amplitude relative to the voice tone of:
调幅调制表现为语音音调的边带(在总频和差频),幅度相对于语音音调为
,where is the amplitude of the bass tone current and is the linear force factor due to the permanent field.
其中 是低音电流的振幅, 是永久磁场的线性力系数。

3 Verification Using Finite Element Simulations and Measurements
3 利用有限元模拟和测量进行验证

The theoretical results in the previous sections were verified using both numerical simulations and measurements. A 4 ", driver with a motor c.f. Fig. 1 was simulated and built. It is a variant of the transducer used in earlier work [8].
通过数值模拟和测量验证了前几节的理论结果。我们模拟并制作了一个 4 英寸 驱动器,其电机功率如图 1 所示。它是早期研究 [8] 中使用的传感器的变体。

3.1 Finite-Element Simulations
3.1 有限元模拟

Infolytica's MagNet tool was used for a series of transient simulations of a voltage step on the coil for a range of blocked coil positions to
使用 Infolytica 的 MagNet 工具对 进行了一系列瞬态模拟,模拟了线圈上的电压阶跃,模拟了一系列闭锁线圈位置
图 2: 绘制与 作为参数。实线:测量值,虚线:MagNet 模拟。
图 2: 绘制与 作为参数。实线:测量值,虚线:MagNet 模拟。
in increments). The voltage, current and force acting on the voice coil were sampled at . An antialias filter was included in the simulation. The result was exported to Matlab for post-processing. The instantaneous force factor was found as the force divided by the current. Subtracting the initial value representing the linear force factor yields the dynamic (current-induced) force factor . Next the blocked impedance and (i.e., the current to force factor transfer function) were identified using FFT-based deconvolution.
增量)。作用在音圈上的电压、电流和力的采样时间为 。模拟中包含一个抗混叠滤波器。模拟结果输出到 Matlab 进行后处理。瞬时作用力系数是用作用力除以电流得出的。减去代表线性力因数的初始值,得到动态(电流引起的)力因数。接下来,使用基于 FFT 的解卷积法确定阻塞阻抗和(即电流到力因子的传递函数)。

3.2 Comparing Measurements and Simulations of the Blocked Impedance
3.2 比较阻塞阻抗的测量值和模拟值

A precision positioning stage [8] was used to position and hold the coil in the motor structure without membrane or suspension. A periodic noiselike stimulus was applied and current and voltage recorded with a sound card at a sampling rate. Impedance vs. frequency curves were estimated using a synchronous FFT. The measurement was repeated for a range of positions (from to in increments). The generalised inductance c.f. to (6) was calculated for both the measurements and MagNet simulation results and plotted for comparison in Fig. (2). A convincing match is seen in general. At the lowest frequency ) the MagNet result underestimates inductance due to the limited length of the transient simulation. A mechanical resonance around affects the measured result at .
使用精密定位台[8]将线圈定位并固定在电机结构中,无需薄膜或悬挂物。使用声卡以 采样率记录电流和电压。使用同步 FFT 估算阻抗与频率的关系曲线。测量在一定范围内重复进行(从 ,以 为增量)。根据测量结果和 MagNet 模拟结果计算出广义电感 c.f. (6),并绘制成图 (2) 进行比较。总体而言,两者的吻合程度令人信服。在最低频率 ) 时,由于瞬态模拟长度有限,MagNet 的结果低估了电感值。 附近的机械共振影响了 的测量结果。

3.3 数值验证 使用 MagNet 模拟
3.3 数值验证 使用 MagNet 模拟

positions. From the interpolated , the generalised inductance was found using (6). This was then used to calculate the complex from (7). Fig 3 shows a convincing match between the force factor transfer function and the one obtained from the simulated actual force, both in magnitude and phase and across all positions. This strongly supports the theoretical result of (7). Some discrepancy is observed at higher frequencies around . This is because the resolution of the simulated data set is insufficient to reconstruct the sharp minimum of the inductance caused by the copper cap. At this minimum the gradient of the inductance v.s. position changes polarity. The peaks near the rest position towards and droops at both positive and negative position. Some asymmetry is noted: force factor modulation is greater at negative positions (coil inside the motor) than positive positions. This agrees with earlier findings [8].
位置。根据内插值,利用 (6) 计算出广义电感。然后根据 (7) 计算出复数。图 3 显示,力因数传递函数与模拟实际力得到的传递函数在幅度和相位上以及在所有位置上都非常吻合。这有力地证明了 (7) 的理论结果。在频率较高的 .这是因为模拟数据集的分辨率不足以重建由铜帽引起的电感的急剧最小值。在这个最小值处,电感随位置变化的梯度极性发生了变化。在静止位置附近达到峰值,而在正负位置则有所下降。我们注意到了一些不对称现象:负位置(线圈在电机内部)的力因子调制大于正位置。这与早先的研究结果一致[8]。
The rest position peaks at at . At this frequency a drive current of peak (e.g. when the driver is driven hard in a small box) gives an amplitude of which is about of the permanent of . Such error is comparable to or even greater than the typical position dependent variation of the permanent
静止位置 的峰值为 ,频率为 。在此频率下,峰值为 的驱动电流(例如在小盒子中大力驱动驱动器时)会产生 振幅,该振幅约为 的永久 。这种误差与永久磁场的典型位置变化相当,甚至更大。

3.4 Measurement of the DC Force
3.4 直流电力的测量

Force factor modulation produces a DC force in proportion to the real value of when the coil is driven by a sinusoidal current c.f. (8), i.e., AC current causes a DC force. One would readily assume this DC force always to point inwards [2] since the inductance grows when the coil is pushed into the motor.
当线圈由正弦电流驱动时,力因数调制会产生与 实际值成正比的直流力,即交流电流会产生直流力。由于线圈被推入电机时电感量会增加,因此人们很容易认为这个直流电总是向内的[2]。

A surprise prediction of our analysis is that at high frequencies a shorting device (e.g. a copper cap or shorting ring) can modify the inductance gradient to such an extent that the sign changes. When that happens the DC force propels the cone outwards. Fig.
我们分析得出的一个惊人预测是,在高频率下,短路装置(如铜帽或短路环)会改变电感梯度,以至于符号发生变化。当发生这种情况时,直流力会将锥体向外推动。图

4 shows the real and imaginary parts of
4 显示了

A surprise prediction of our analysis is that at high frequencies a shorting device (e.g. a copper cap or shorting ring) can modify the inductance gradient to such an extent that the sign changes. When that happens the DC force propels the cone outwards. Fig.
我们分析得出的一个惊人预测是,在高频率下,短路装置(如铜帽或短路环)会改变电感梯度,以至于符号发生变化。当发生这种情况时,直流力会将锥体向外推动。图

4 shows the real and imaginary parts of at the rest position for the test driver obtained from the MagNet simulations. The sign of the real part of changes around .
4 显示了从 MagNet 模拟中获得的测试驾驶员在静止位置 的实部和虚部。 的实部符号在 附近发生变化。
An experiment was done to measure the DC force caused by an AC current on the test driver (DUT)
测试驱动器(DUT)上的交流电流所产生的直流力进行了测量。
Fig. 3: The force factor modulation transfer function , Solid: from the simulated , Round markers: from the simulated force.
图 3:力因子调制传递函数 ,实线:来自模拟 ,圆标记:来自模拟力。
while minimizing excursion. terms generated by asymmetries in the permanent force factor and suspension compliance [2] might otherwise confound the test.
由永久力系数 和悬架顺应性 [2] 中的不对称产生的 项可能会对测试造成干扰。
For the high frequency test the moving mass naturally renders excursion negligible so the driver could simply be tested in free air.
在高频测试中,运动质量自然会使偏移忽略不计,因此只需在自由空气中对驱动器进行测试即可。

For the tests at low frequencies, AC cone movement was countered by another 4 " driver mounted in the same cabinet and driven with a signal of the same frequency but with a carefully adjusted phase and amplitude.
在低频测试中,交流振盆运动由安装在同一箱体中的另一个 4 英寸驱动器抵消,该驱动器由频率相同但相位和振幅经过仔细调整的信号驱动。

The cabinet was intentionally made slightly leaky so that again, long term DC excursion was controlled only by the free-air complince of the driver. For all experiments, the AC excursion remained below
箱体故意做成略微漏气的样子,这样,长期直流偏移也只能由驱动器的自由空气顺从性来控制。在所有实验中,交流偏移都低于

For the tests at low frequencies, AC cone movement was countered by another 4 " driver mounted in the same cabinet and driven with a signal of the same frequency but with a carefully adjusted phase and amplitude.
在低频测试中,交流振盆运动由安装在同一箱体中的另一个 4 英寸驱动器抵消,该驱动器由频率相同但相位和振幅经过仔细调整的信号驱动。

The cabinet was intentionally made slightly leaky so that again, long term DC excursion was controlled only by the free-air complince of the driver. For all experiments, the AC excursion remained below DC blocking capacitor was added in series with the voice coil.
箱体故意做成略微泄漏的样子,这样,长期直流偏移同样只能由驱动器的自由空气顺从性来控制。在所有实验中,交流偏移都低于直流偏移,音圈上串联了阻塞电容器。
Fig. 4: Real and Imaginary components of for from MagNet simulations of the 4 " test driver.
图 4: 的实部和虚部 ,来自 4 英寸测试驱动器的 MagNet 仿真。
Fig. 5: DC-excursion caused by a series of tone bursts of varying amplitude with a order low-pass filter applied. Solid=measured, Dash model fit.
图 5:在 低通滤波器的作用下,一系列不同振幅的 音脉冲串引起的直流激增。实线=测量值,虚线 模型拟合值。
Excursion was measured with a Keyence triangulating laser head and captured alongside coil current. DC free air compliance was estimated at by applying a 10 gram weight and recording displacement, permitting conversion between DC excursion and DC force.
用 Keyence 三角测量激光头测量偏移量,并捕捉线圈电流。直流自由空气顺应性是通过施加 10 克重物并记录位移来估算的, ,从而实现直流偏移和直流力之间的转换。
Fig. 5 shows the result for a series of tone bursts at different amplitudes. The recorded excursion was low-pass filtered at . For comparison the graph is overlaid with a plot of the predicted force multiplied by the estimated compliance. To be precise, the predicted force is the square of the current filtered by the same low-pass filter and scaled by a best fit constant which ideally equals . The experiment was repeated for and resulting in:
图 5 显示了一系列不同振幅的 音调脉冲串的结果。记录的偏移在 进行了低通滤波。为便于比较,图上叠加了预测力乘以估计顺应性的曲线图。准确地说,预测力是经相同低通滤波器滤波的电流的平方,并按最佳拟合常数 (理想情况下等于 )缩放。对 重复实验,结果如下:
frequency 频率 best fit  最合适 simulated