原创 元件的非理想效应_3

3.电感[6]

3.1 电感的定义：

从这个定义出发，可以看出，电感定义为包围一段电流的磁通量。磁通量是磁场强度对面积的积分。

因此，我们用两个物理量来衡量电感，一个是电流，一个是磁通量。

如图所示的一段载有电流的导线，我们用磁通量作为物理单位，查一下环绕这段电流的磁通量，然后除以电流，就得到电感。所以，可以从两个方面考察电感，一个是从磁通量的角度，一个是从电流的角度。

（1）            Inductance: the number of field line loops around a conductor per amp of current through it.

如果有两条导线存在，另外一条导线的磁力线也会环绕第一条导线，这时，环绕在a导线的磁力线是A+A_B。为了考察磁力线到底是哪段导线产生的，我们定义自感和互感。

（2）            Self-inductance: the number of field line loops around the conductor per amp of current through the same conductor.

（3）            Mutual inductance: the number of field line loops around a conductor per amp of current through another conductor.

电流是不能孤立存在的，必须存在于一个闭合的环路中，这使我们想到，当我们谈一段导线的电感的时候，这个环路中其他部分的导线产生的磁力线或磁通量怎么办？是否也算在内？这就引出了Partial inductance的概念。

假定我们只考虑一小段导线，这段导线上通有电流（实际中不可能），这时，一定有磁力线环绕这段导线，用这些磁力线(以磁通量作为单位)除以电流，就得到了这一小段导线的电感。Partial inductance完全是一种数学上的构造，不能够测量，但是却很有用，特别是当我们不知道环路其他部分的形状的时候。

同样的，Partial inductance也有自感和互感。

（4）            Partial inductance: the number of field line loops around a section of a conductor when no other currents exist anywhere.

（5）            Partial self-inductance: the number of field line loops around a section of a conductor per amp of current in that section when no other currents exist anywhere.

（6）            Partial mutual inductance: the number of field line loops around a section of a conductor per amp of current in another section when no other currents exist anywhere.

More often than not, when referring to the inductance of a lead in a package, or a connector pin, or a surface trace, we are really referring to the partial self-inductance of this interconnect element.

如果我们要把环路的其他部分的电流的效应也计算在内，就得到了Effective/ net/total inductance。假定这个环路有lega和legb组成。Lega的磁力线包围自身和legb，legb的磁力线包围自身和lega，当根据定义计算lega的电感的时候，就必须要考legb的磁力线的效应。这时的电感就是Effective, net, or total inductance.

（7）            Effective, net, or total inductance: the total number of field line loops around a section of a conductor per amp of current in the entire loop, taking into account the presence of field line loops from current in every part of the loop.

正如前面提到的，实际中的电流必定存在于一个环路中，当这个环路通有电流I的时候，我们沿着环路，统计出全部的磁力线的数量(以磁通量作为单位)，根据电感的定义，就可以计算这个环路的电感了。

（8）            Loop inductance: the total number of field line loops around the complete current loop per amp of current.

（9）            Loop self-inductance: the total number of field line loops around the complete current loop per amp of current in the same loop.

（10）            Loop mutual inductance: the total number of field line loops around a complete current loop per amp of current in another loop.

这就是我们平时经常谈到的电感和环路的面积有很大关系，其实，我们考虑的是整个环路的电感。

It is sometimes stated that the loop self-inductance depends on the "area of the loop." While this is roughly true in general, it doesn't help feed our intuition much. As we have seen, it is not so much the area that is important, it is the total number of field line loops encircling each leg that is important.

（11）            Equivalent inductance: the single self-inductance corresponding to the series or parallel combination of multiple inductors including the effect of their mutual inductance.

[3]中对电感从数学上给出了更详细的讨论。一个结论是：电感和环路的形状有很大关系；减小电感的有效方法之一就是在参考平面上方布线，这样，环路的面积就是“走线的长度×介质厚度”。

了解了电感的概念，接下来我们讨论电感的非理想效应是怎样的？