做PCB設計過程中，在走線之前，一般我們會對自己要進行設計的項目進行疊層，根據厚度、基材、層數等信息進行計算阻抗，計算完後一般可得到如下圖示內容。
圖1 疊層信息圖示
從上圖可以看出，設計上面的單端網絡一般都是50歐姆來管控，那很多人就會問，為什麼要求按照50歐姆來管控而不是25歐姆或者80歐姆？首先，默認選擇用50歐姆，而且業內大家都接受這個值，一般來說，肯定是由某個公認的機構制訂了某個標準，大家是按標準進行設計的。電子技術有很大一部分是來源於軍隊，首先技術是使用於軍用，慢慢的由軍用轉為民用。在微波應用的初期，二次世界大戰期間，阻抗的選擇完全依賴於使用的需要，沒有一個標準值。隨著技術的進步，需要給出阻抗標準，以便在經濟性和方便性上取得平衡。在美國，最多使用的導管是由現有的標尺竿和水管連接成的，51.5歐姆十分常見，但看到和用到的適配器、轉換器又是50-51.5歐姆；為聯合陸軍和海軍解決這些問題，一個名為JAN的組織成立了（後來的DESC組織），由MIL特別發展的，綜合考慮後最終選擇了50歐姆，由此相關的導管被製造出來，並由此轉化為各種線纜的標準。此時歐洲標準是60歐姆，不久以後，在象Hewlett-Packard這樣在業界佔統治地位的公司的影響下，歐洲人也被迫改變了，所以50歐姆最終成為業界的一個標準沿襲下來，也就變成約定俗成了，而和各種線纜連接的PCB，為了阻抗的匹配，最終也是按照50歐姆阻抗標準來要求了。其次，一般標準的制定是會基於PCB生產工藝和設計性能、可行性的綜合考量。從PCB生產加工工藝角度出發，以現有的大部分PCB生產廠商的設備考慮，生產50歐姆阻抗的PCB是比較容易實現的。從阻抗計算過程可知，過低的阻抗需要較寬的線寬以及薄介質或較大的介電常數，這對於目前高密板來說空間上比較難滿足；過高的阻抗又需要較細的線寬及較厚的介質或較小的介電常數，不利於EMI及串擾的抑制，同時對於多層板及從量產的角度來講加工的可靠性會比較差。控制50歐姆阻抗在使用常用板材（FR4等）、常用芯板的環境下，生產常用的板厚的產品（如1mm、1.2mm等），可設計常見的線寬（4~10mil），這樣板廠加工起來是非常方便的，對其加工使用的設備要求也不是很高。從PCB設計方面考慮，50歐姆也是綜合考慮之後選擇。從PCB走線的性能來說，一般阻抗低比較好，對一個給定線寬的傳輸線，和平面距離越近，相應的EMI會減小，串擾也會因此減小。但從信號全路徑的角度看，還需要考慮最關鍵的一個因素，那就是晶片的驅動能力，在早期大多數晶片驅動不了阻抗小於50歐姆的傳輸線，而更高阻抗的傳輸線由於實現起來不便，所以折中採用50歐姆阻抗。所以一般選擇50歐姆作為常規時單端信號控制阻抗的默認值。有對英文感興趣的朋友可以閱讀下面的文章，來自全球信號完整性的大牛講師Howard Johnson的網站www.sigcon.com，他從理論分析了為什麼電路板的傳輸線使用50歐姆，而不是60或70歐姆。
Q: Why do most engineers use 50-Ω pc-board transmission lines (sometimes to the extent of this value becoming a default for pc-board layout)? Why not 60- or 70-Ω?-Tim Canales
A: Given a fixed trace width, three factors heavily influence pc-board-trace impedance decisions. First, the near-field EMI from a pc-board trace is proportional to the height of the trace above the nearest reference plane; less height means less radiation. Second, crosstalk varies dramatically with trace height; cutting the height in half reduces crosstalk by a factor of almost four. Third, lower heights generate lower impedances, which are less susceptible to capacitive loading.
All three factors reward designers who place their traces as close as possible to the nearest reference plane. What stops you from pressing the trace height all the way down to zero is the fact that most chips cannot comfortably drive impedances less than about 50 Ω. (Exceptions to this rule include Rambus, which drives 27 Ω, and the old National BTL family, which drives 17 Ω).
It is not always best to use 50 Ω. For example, an old NMOS 8080 processor operating at 100 kHz doesn't have EMI, crosstalk, or capacitive-loading problems, and it can't drive 50 Ω anyway. For this processor, because very high-impedance lines minimize the operating power, you should use the thinnest, highest-impedance lines you can make.
Purely mechanical considerations also apply. For example, in dense, multilayer boards with highly compressed interlayer spaces, the tiny lithography that 70-Ω traces require becomes difficult to fabricate. In such cases, you might have to go with 50-Ω traces, which permit a wider trace width, to get a manufacturable board.
What about coaxial-cable impedances? In the RF world, the considerations are unlike the pc-board problem, yet the RF industry has converged on a similar range of impedances for coaxial cables. According to IEC publication 78 (1967), 75 Ω is a popular coaxial impedance standard because you can easily match it to several popular antenna configurations. It also defines a solid polyethylene-based 50-Ω cable because, given a fixed outer-shield diameter and a fixed dielectric constant of about 2.2 (the value for solid polyethylene), 50-Ω minimizes the skin-effect losses.
You can prove the optimality of 50-Ω coaxial cable yourself from basic physical principles. The skin-effect loss, L, (in decibels per unit length) of the cable is proportional to the total skin-effect resistance, R, (per unit length) divided by the characteristic impedance, Z0, of the cable. The total skin-effect resistance, R, is the sum of the shield resistance and center conductor resistances. The series skin-effect resistance of the coaxial shield, at high frequencies, varies inversely with its diameter d2 . The series skin-effect resistance of the coaxial inner conductor, at high frequencies, varies inversely with its diameter d1 . The total series resistance, R, therefore varies proportionally to (1/d2 +1/d1). Combining these facts and given fixed values of d2 and the relative electric permittivity of the dielectric insulation, εR, you can minimize the skin-effect loss, L, starting with the following equation:
[1]
In any elementary textbook on electromagnetic fields and waves, you can find the following formula for Z0 as a function of d2, d1, and εR:
[2]
Substituting Equation [2] into Equation [1] , multiplying numerator and denominator by d2, and rearranging terms:
[3]
Equation [3] separates out the constant terms (εR½/60)×(1/d2)) from the operative terms ((1+d2/d1)/ln(d2/d1)) that control the position of the minimum. Close examination of Equation 3 reveals that the position of the minima is a function only of the ratio d2/d1 and not of either εR or the absolute diameter d2.
A plot of the operative terms as a function of the argument d2/d1 shows a minimum at d2/d1 =3.5911. Assuming a solid polyethylene insulation with a dielectric constant of 2.25 corresponding to a relative speed of 66% of the speed of light, the value d2/d1 =3.5911, when plugged into Equation 2, produces a characteristic impedance of 51.1 Ω. A long time ago, radio engineers decided to simply round off this optimal value of coaxial-cable impedance to a more convenient value of 50 Ω. It turns out that the minimum in L is fairly broad and flat, so as long as you stay near 50 Ω, it doesn't much matter which impedance value you use. For example, if you produce a 75-Ω cable with the same outer-shield diameter and dielectric, the skin-effect loss increases by only about 12 percent. Different dielectrics each posses their own slightly different optimal impedance.
另外Belden公司的官網也由著名的專欄作者Steve Lampen撰寫了一篇「
50 Ohms: The Forgotten Impedance」If you play with coax, short for coaxial cable, you probably know this it is available in a number of different impedances. The most common is 75 ohm, like video cable or antenna cable, but in fact our products range from 32 ohms up to 124 ohms.
Why all these different numbers? It's not an accident of course, and there is a reason for each one. Today, we're going to take a quick look at 50 ohm coax cable.
Belden makes hundreds of 50 ohm cables, including a whole line of ultra-low loss versions (Belden 7805 to Belden 7977). The two largest versions (Belden 7976 and 7977) are shown in the photograph below. They are HUGE. The 7977 has a diameter of .600" six-tenths of an inch! This is the largest coax cable that we make.
But first of all, why 50, or any other number? The answer can be shown in the graph below. This was produced by two researchers, Lloyd Espenscheid and Herman Affel, working for Bell Labs in 1929.
They were going to send RF signals (4 MHz) for hundred of miles carrying a thousand telephone calls. They needed a cable that would carry high voltage and high power. In the graph below, you can see the ideal rating for each. For high voltage, the perfect impedance is 60 ohms. For high power, the perfect impedance is 30 ohms.
This means, clearly, that there is NO perfect impedance to do both. What they ended up with was a compromise number, and that number was 50 ohms.
You will note that 50 ohms is closer to 60 than it is to 30, and that is because voltage is the factor that will kill your cable. Just ask any transmitter engineer. They talk about VSWR, voltage standing wave ratio, all the time. If their coax blows up, it is voltage that is the culprit.
So why not 60 ohms? Just look at the power handling at 60 ohms - below 50%. It is horrible! At the compromise value of 50 ohms, the power has improved a little. So 50 ohm cables are intended to be used to carry power and voltage, like the output of a transmitter. If you have a small signal, like video, or receive antenna signals, the graph above shows that the lowest loss or attenuation is 75 ohms.
Still, I get a lot of feedback from people who use 50 ohms for small signals; you can see above that they are taking a 2-3 dB hit in attenuation. Excuses I hear are 「It's too late to change now!」 or 「That's the impedance of the box itself.」 This is especially true of most test gear, which is universally 50 ohms. You have to buy a matching network to use it at 75 ohms or any other impedance. But there are lots of applications where 50 ohms is the best choice.
Belden 7977 mentioned above, can carry more than 5 kW at 30 MHz and more than 600 watts at 6 GHz. So even a cable this small could be used for TV or FM low power, boosters, translators, two-way radios, life-safety such as police/fire, RPU, many ham frequencies, microwave transmitters up to 6 GHz, and probably hundreds of other applications where signal are being delivered with high voltage and high power.
硬禾小幫手 -硬體工程師的設計助手