空間之間：理解高速數(shù)字電路的感應(yīng)系數(shù)

　　最左邊圓形的線圈，直徑為10英寸。最大自感應(yīng)系數(shù)為730nH。移動(dòng)到右邊，自感應(yīng)系數(shù)會(huì)逐漸變小直到達(dá)到最后螺旋狀的線圈時(shí)為190nH。

　　我提起這個(gè)簡(jiǎn)單的實(shí)驗(yàn)，因?yàn)槲医?jīng)常聽工程師說：“電路自感應(yīng)系數(shù)為1nH?！被蛘摺芭月冯娙萦?00pH的自感應(yīng)系數(shù)。這些話假定可以計(jì)算信號(hào)通道個(gè)別部分的離散感應(yīng)系數(shù)。

　　處理大組件時(shí)，這個(gè)假設(shè)是好的。根據(jù)電路分析的Kirchhoff定律，串聯(lián)的兩個(gè)導(dǎo)體的總感應(yīng)系數(shù)應(yīng)該等于它們各自感應(yīng)系數(shù)之和。

　　Kirchhoff分析的正確性有個(gè)重要前提，即在導(dǎo)體間沒有強(qiáng)烈的電磁場(chǎng)存在。高速數(shù)字電路將大量快速變化的電磁場(chǎng)注入導(dǎo)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(lǐng)域是無效的。

　　由于電場(chǎng)、寄生電容和磁場(chǎng)，高速電子學(xué)中用寄生電容補(bǔ)充Kirchhoff定律。

　　圖2舉例說明了兩個(gè)線圈周圍的磁場(chǎng)類型。線圈傳輸?shù)攘糠聪嚯娏?，類似圖1中的發(fā)夾結(jié)構(gòu)。假設(shè)電流I1通過一個(gè)線圈流出，在一個(gè)發(fā)夾中改變方向，流到另一個(gè)線圈形成電流I2。

　　如果從遠(yuǎn)距離觀察，電流I1產(chǎn)生的磁場(chǎng)幾乎抵消了I2所產(chǎn)生的大小相等方向相反的磁場(chǎng)。越接近線圈，抵消越明顯，總磁場(chǎng)強(qiáng)度越小。

　　感應(yīng)系數(shù)L的表現(xiàn)載流電路附近的總磁場(chǎng)強(qiáng)度E一樣。感應(yīng)系數(shù)和場(chǎng)強(qiáng)之間的精確表達(dá)式是：

　　如果線圈的間距影響了存儲(chǔ)的磁場(chǎng)強(qiáng)度，則間距也影響電路的感應(yīng)系數(shù)。

　　磁場(chǎng)的相互作用解釋了當(dāng)沒有指定完整信號(hào)的電流路徑的形狀和位置時(shí)，為什么不能對(duì)局部分布式電路計(jì)算感應(yīng)系數(shù)。它可能改變感應(yīng)系數(shù)。該路徑的每個(gè)部分都會(huì)影響感應(yīng)系數(shù)。

　　例如，通道的感應(yīng)系數(shù)依賴于附近兩部分連接的位置。旁路電容的感應(yīng)系數(shù)依賴于附近的參考面。

　　感應(yīng)系數(shù)不是獨(dú)立部件的特性。在分布式電路中，感應(yīng)系數(shù)是兩導(dǎo)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.

       英文原文地址：http://www.edn.com/article/CA6442436.html