铁磁靶相对磁导率对背偏传感器输出的影响

作者：Yannick Vuillermet，
雷竞技竞猜下载Allegro微系统欧洲有限公司

介绍

本应用说明旨在描述目标相对磁导率对Allegro背偏磁传感器输出的影响。

传感器性能在很大程度上取决于目标机械几何结构。在速度应用的情况下，齿和谷的几何形状是关键的，但这些机械性能不是本应用说明的主题。这里，假设目标是为客户应用程序精心设计的。相反，本应雷竞技最新网址用说明侧重于目标铁磁性材料的特性，尤其是磁导率。

The practical goal of this application note is to define the minimum target material relative permeability to guarantee optimum sensor performance in the application. This application note applies to any applications using a back-biased sensor associated with a ferromagnetic target: speed sensors (cam, crank, transmission, etc.), position sensors (linear, angle, etc.), etc.

铁磁性材料特性

当一种材料在外磁场中（从永磁体、线圈中的电流、地磁场等）倾向于获得磁化时，就称之为铁磁性材料。在铁磁性材料中，材料的磁化强度与产生的内部磁场一致。与永磁体相反，铁磁性材料的剩磁强度在没有磁场的情况下非常小
外加电场。

Figure 1 is a simplified way of representing the above properties. In this figure, it is assumed that the material behavior is purely linear in low field and that there is no hysteresis (this is equivalent to no remanent magnetization here).小时是磁场，日本是磁极化，日本s是饱和时的极化，以及μ是磁导率。磁极化日本与磁化有关米with this relationship:

J=μ0×M(1)

The relative permeability is defined as the permeability of the material versus the permeability of free spaceμ₀:

AN296132方程 (2)

在下文中，假设材料仅在线性范围内使用。这一假设在Allegro传感器针对的大多数应用程序中都是完全有效的。在这种线性条件下，雷竞技最新网址μ – μ₀是斜坡J（小时）曲线，以及：

B=μ₀× μr × H(3)

因此,唯一的磁参数,垫ters for the target material is the relative permeability,微升. 基本上，磁导率表示材料被外部磁场磁化的能力。

**Figure 1: Simplified magnetic properties of a ferromagnetic material**

Figure 2 shows the measured data of steel1010, which is a classical material used in combination with Allegro sensors. It appears that the relative permeability of this material is always larger than 600 in the linear range of the material, that is to say, forH<1000 A/m。

This 1000 A/m field value in the material, equivalent to ~12.5 Oe (oersted)—and which looks very small—must not be compared to the magnetic field in air, for example, produced by the back-biased magnet. A magnet can easily produce B-field of a few hundred gauss in air. However, a ferromagnetic material placed in this large B-field will have a much smaller internal H-field. As an example, for a magnet producing a 600 G field in air, a ferromagnetic material which has a relative permeability of 300 will typically only see a 5 Oe (or ~400A/m) H-field, according to equations 3 and 4, and to a typical form factor of 0.4 (see next section). This behavior is due to the demagnetizing field or, otherwise said, from the field that the material generates on itself. In summary, it is important to keep in mind that a large field in air from the back-biased magnet (few hundred gauss) does not necessarily imply that the ferromagnetic material works in its nonlinear mode.

**图2:Steel1010极化和相对磁导率与磁场的关系（来源：ANSYS电磁套件17.1.0）**

This table gives the magnetic relative permeability of some common materials.

材料	磁相对磁导率
Air	1
Copper	1
钕磁铁	1.05
钢*	1至4000
Permalloy	8,000
μ-metal	>20,000

资料来源：https://en.wikipedia.org/wiki/Permeability_(electromagnetism)
*请注意，一些钢变体不是磁性的，例如，一些不锈钢。

渗透率与形状系数

铁磁性材料的磁化由两个主要参数驱动：磁导率和物体的形状（形状因子）。

下面通过一个非常简单的例子说明这两个参数是如何影响磁化的。

在椭球体物体的情况下，无论施加在物体上的均匀外磁场是什么，材料内部的磁化是均匀的。注意，这个椭球体可以看作是速度目标齿的一个非常粗略的近似值。

图3显示了放置在均匀场中的椭球体小时o沿着十以及均匀磁化日本.

在这种情况下，假设没有材料磁饱和，磁化强度由下式给出：

AN296132方程 (4)

In this equation,Nx公司是椭球体的形状因子十. 此参数取决于椭球体的形状，并且始终小于1。拉长的物体十direction will have a smallNx公司(for exampleNx公司= 0.1). 一个具体的例子是具有Nx公司= 1/3.

图4显示了一些形状因子的物体极化与相对渗透率的关系。显然，在外场方向拉长的物体更容易磁化。更有趣的是，我们可以注意到，在给定的渗透率水平以上，物体的偏振只取决于物体的形状。当1/(微升–1）相对于形状系数Nx变得可以忽略不计。

Figure 5 shows the same plot but with normalized polarization to better see the permeability level. It appears that, whatever the object shape, at least 95% of the maximum magnetization is reached as soon as the relative permeability is larger than 300.

这一数字将在下一段的实际应用中得到确认。

**Figure 4: Ellipsoid polarization versus relative permeability in a 1000 A/m field**

**Figure 5: Ellipsoid normalized magnetization versus relative permeability**

典型应用示例：带ATS699LSN速度传感器的Allegro 60X参考目标

现在，考虑一个典型的速度应用程序，使用ATS699LSN公司transmission part placed in front of the Allegro 60X reference target (Figure 6). ATS699LSN is a differential part which has three Hall plates (Left, Center, and Right) and two differential channels (Left-Center and Center-Right). The output of only one channel is considered in the following.

此零件的典型工作气隙为1 mm和2 mm，气隙由传感器的标记面和目标齿顶部之间的距离定义。

Figure 7 gives the normalized output of one channel when the target is passing in front of the sensor over one and half period. This graph shows that the differential field waveform is almost not dependent on the relative magnetic permeability. It can be observed that there is only a (small) difference between the waveforms when微升=10，位置约为3°。无论相对渗透率如何，0°附近的位置都具有类似的行为，因为这些位置对应于目标的一个谷。

Figure 8 and Figure 9 give the peak-to-peak differential field of the channel versus relative permeability at 1 mm and 2 mm air gap respectively. These figures confirm what was seen earlier: to guarantee optimum performances, the target material relative permeability should be at least 300. Any further increase of relative permeability has a marginal impact on the magnetic signal measured by the sensor.

If the ferromagnetic target material has a relative permeability smaller than 300, it does not mean that the back-bias arrangement will not work. It will only work with degraded performance
与渗透率大的靶相比。例如，可以减小应用的最大工作气隙。

**Figure 9: Peak to peak field versus relative permeability at 2 mm air gap**

结论

最后，这个申请说明给出了一个简单的答案，“我的目标材料是否适合反偏差申请？“：为了获得最佳性能，目标材料的相对磁导率必须至少为300（H场<2000 A/m）。

然而，这是一个必要条件，但不是充分条件；具有适当的目标机械设计也是实现应用所需性能的强制性条件。

Allegro工程师可以帮助评估目标的材料是否适用于后偏安排。如果材料具有较低的相对渗透率，Allegro还可以提供支持来估计对应用程序性能的影响。