空間之間：理解高速數(shù)字電路的感應系數(shù)
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最左邊圓形的線圈，直徑為10英寸。最大自感應系數(shù)為730nH。移動到右邊，自感應系數(shù)會逐漸變小直到達到最后螺旋狀的線圈時為190nH。
我提起這個簡單的實驗，因為我經(jīng)常聽工程師說：“電路自感應系數(shù)為1nH。”或者“旁路電容有500pH的自感應系數(shù)。這些話假定可以計算信號通道個別部分的離散感應系數(shù)。
處理大組件時，這個假設是好的。根據(jù)電路分析的Kirchhoff定律，串聯(lián)的兩個導體的總感應系數(shù)應該等于它們各自感應系數(shù)之和。
Kirchhoff分析的正確性有個重要前提，即在導體間沒有強烈的電磁場存在。高速數(shù)字電路將大量快速變化的電磁場注入導體之間的空間。這些數(shù)字電路不滿足Kirchhoff的前提，因此，Kirchhoff定律在高速電路領域是無效的。
由于電場、寄生電容和磁場，高速電子學中用寄生電容補充Kirchhoff定律。
圖2舉例說明了兩個線圈周圍的磁場類型。線圈傳輸?shù)攘糠聪嚯娏鳎愃茍D1中的發(fā)夾結(jié)構(gòu)。假設電流I1通過一個線圈流出，在一個發(fā)夾中改變方向，流到另一個線圈形成電流I2。
如果從遠距離觀察，電流I1產(chǎn)生的磁場幾乎抵消了I2所產(chǎn)生的大小相等方向相反的磁場。越接近線圈，抵消越明顯，總磁場強度越小。
感應系數(shù)L的表現(xiàn)載流電路附近的總磁場強度E一樣。感應系數(shù)和場強之間的精確表達式是：
如果線圈的間距影響了存儲的磁場強度，則間距也影響電路的感應系數(shù)。
磁場的相互作用解釋了當沒有指定完整信號的電流路徑的形狀和位置時，為什么不能對局部分布式電路計算感應系數(shù)。它可能改變感應系數(shù)。該路徑的每個部分都會影響感應系數(shù)。
例如，通道的感應系數(shù)依賴于附近兩部分連接的位置。旁路電容的感應系數(shù)依賴于附近的參考面。
感應系數(shù)不是獨立部件的特性。在分布式電路中，感應系數(shù)是兩導體之間的空間特性。
英文原文：
In-between spaces: Understanding inductance in high-speed digital circuits
By Howard Johnson, PhD -- EDN, 5/24/2007
I measured the inductance of four loops of wire. Each loop comprises the same length of insulated #10 AWG solid-copper wire (Figure 1). During testing, I probe the wires at their endpoints (bottom of figure), holding the wires vertically above the tester and well away from all other metal objects.
The leftmost loop, the round one, has a diameter of 10 in. It gives the largest inductance at 730 nH. Moving to the right, the inductance drops in each case until you reach the final loop, the twisted wire, at 190 nH.
I mention this simple experiment because I have all too often heard engineers say: “My via has an inductance of 1 nH,” or “My bypass capacitor has an inductance of 500 pH.” Those statements assume that you can ascribe discrete inductances to individual portions of a signal path.
That assumption is a good one when dealing with macroscopic components. According to Kirchhoff’s laws for circuit analysis, the total inductance of two inductors in series should equal the sum of their independent inductances.
The correctness of Kirchhoff’s analysis hinges upon a crucial precondition, namely that no significant electromagnetic fields inhabit the spaces between conductors. High-speed digital currents infuse the spaces between conductors with massive, fast-changing electromagnetic fields. These digital circuits do not meet Kirchhoff’s precondition; therefore, Kirchhoff’s laws are invalid in the high-speed domain.
In hi
Figure 2 illustrates the pattern of magnetic fields surrounding two wires. The wires carry equal and opposite currents, much like the hairpin structures in Figure 1. Imagine current I1 going out on one wire, changing direction at a hairpin turn, and returning as I2 on the other wire.
If you observe from a remote distance, the magnetic fields that I1 generates nearly cancel the equal-but-opposite magnetic fields that I2 generates. The closer you bring the wires, the better the cancellation, and the smaller the overall magnetic-field energy.
Inductance L represents nothing more and nothing less than the total magnetic-field energy, E, surrounding a current-carrying circuit. The precise relation between inductance and field energy is:
If the spacing between wires affects the stored magnetic energy, then the spacing affects the circuit inductance, as well.
This interaction between magnetic fields explains why you cannot ascribe inductance to one part of a distributed circuit without also specifying the shape and location of the complete signal-current path. It might increase or decrease the inductance. All parts of the path influence the inductance.
For example, the inductance of a via depends on the location of nearby interplane connections. The inductance of a bypass capacitor depends on its proximity to the reference planes.
Inductance is not a property of an individual component. In distributed circuits, inductance is a property of the spaces between conductors.
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