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2021-11-07

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Author：Downs

Many people who are new to impedance will have this question. Why do common single-ended traces in **PCB boards** are controlled by 50 ohms instead of 40 ohms or 60 ohms by default? This is a seemingly simple question that is not easy to answer. Before writing this article, we also looked up a lot of information, the most well-known of which is Howard Johnson, PhD’s reply on this question,

Why is it difficult to answer? The signal integrity problem itself is a question of trade-offs, so the most famous sentence in the industry is: "It depends..." This is a problem where there is no standard answer. Today, Mr. Expressway will briefly summarize this question by combining various answers, and here is also an introduction. I hope that more people can summarize more relevant factors from their own perspectives.

First of all, 50 ohms has a certain historical origin, which has to start with standard cables. We all know that a large part of modern electronic technology is derived from the military, and slowly converted from military use to civilian use. In the early days of microwave application, during the Second World War, the choice of impedance was completely dependent on the needs of use. With the advancement of technology, impedance standards need to be given in order to strike a balance between economy and convenience. In the United States, the most commonly used conduits are connected by existing rods and water pipes. 51.5 ohms is very common, but the adapters/converters that are seen and used are 50 ohms to 51.5 ohms; it is a solution for the joint army and navy. For these problems, an organization named JAN was established, which was later DESC, which was specially developed by MIL. After comprehensive consideration, 50 ohms was finally selected, and special conduits were manufactured and transformed into various cables. standard. At this time, the European standard was 60 ohms. Soon after, under the influence of companies that dominate the industry like Hewlett-Packard, Europeans were also forced to change, so 50 ohms eventually became a standard in the industry.

It has become a convention, and the PCB connected to various cables is ultimately required to comply with the 50 ohm impedance standard for impedance matching.

Secondly, from the perspective of achievable PCB circuit board production, 50 ohms is more convenient to achieve. From the foregoing impedance calculation formula, it can be seen that too low impedance requires a wider line width and a thin medium (or a larger dielectric constant), which is more difficult to meet in space for current high-density boards; too high impedance requires a higher Thin line width and thicker dielectric (or smaller dielectric constant) are not conducive to the suppression of EMI and crosstalk. At the same time, the reliability of processing for multi-layer boards and from the perspective of mass production will be relatively poor; and 50 Ohm's ordinary line width and dielectric thickness (4~6mil) in the environment of commonly used materials meet the design requirements (the impedance calculation in the figure below), and it is easy to process, and it is not surprising that it slowly becomes the default choice.

Third, from the perspective of loss, based on basic physics, it can be proved that the 50 ohm impedance skin effect loss is the smallest (taken from Howard Johnson, PhD's reply). Generally, the skin effect loss of the cable L (in decibels) is proportional to the total skin effect resistance R (unit length) divided by the characteristic impedance Z0. The total skin effect resistance R is the sum of the resistance of the shielding layer and the intermediate conductor. The skin effect resistance of the shielding layer is inversely proportional to its diameter d2 at high frequencies. The skin effect resistance of the inner conductor of a coaxial cable is inversely proportional to its diameter d1 at high frequencies. The total series resistance R is therefore proportional to (1/d2+1/d1). Combining these factors, given d2 and the corresponding dielectric constant Er of the isolation material, the following formula can be used to minimize the skin effect loss.

In any basic book on electromagnetic fields and microwaves, you can find that Z0 is a function of d2, d1, and Er.

Substitute formula 2 into formula 1, multiply the numerator and denominator by d2 at the same time, and get

Separate the constant term (/60)*(1/d2) from the formula 3, and the effective term ((1+d2/d1)/ln(d2/d1)) to determine the minimum point. Look carefully at the minimum point of formula 3 only controlled by d2/d1, and has nothing to do with Er and the fixed value d2. Take d2/d1 as a parameter and draw a graph for L. When d2/d1=3.5911, the minimum value is obtained. Assuming that the dielectric constant of solid polyethylene is 2.25 and d2/d1=3.5911, the characteristic impedance is 51.1 ohms. A long time ago, radio engineers, for convenience, approximated this value to 50 ohms as the optimal value for coaxial cables. This proves that around 50 ohms, L is the smallest.

Finally, from the perspective of electrical performance, the advantage of 50 ohms is also a compromise after comprehensive consideration. Purely from the performance of **PCB traces**, low impedance is better. For a transmission line with a given line width, the closer the distance from the plane is, the corresponding EMI will be reduced, crosstalk will also be reduced, and it is not easy to be subjected to capacitive loads. Influence. But from the perspective of the full path, the most critical factor needs to be considered, that is the drive capability of the chip. In the early days, most chips could not drive transmission lines with an impedance less than 50 ohms, and transmission lines with higher impedance were inconvenient to implement. 50 ohm impedance is used in the.

To sum up: 50 ohms as the default value of the **PCB industry** has its inherent advantages, and it is also a compromise solution after comprehensive consideration, but it does not mean that 50 ohms must be used. In many cases, it depends on matching with it. For example, 75 ohms is still the standard for remote communication. Some cables and antennas use 75 ohms. At this time, a matching PCB line impedance is required. In addition, there are some special chips that reduce the impedance of the transmission line by improving the chip's driving ability to better suppress EMI and crosstalk. For example, most Intel chips require impedance control at 37 ohms, 42 ohms or even lower. I won't repeat them here.