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Why the single-ended impedance on the PCB controls 50 ohms

Many people who are new to impedance will have this question. Why is the common single-ended wiring on the board required to be controlled by 50 ohms by default instead of 40 ohms or 60 ohms? This is a seemingly simple but difficult question to answer.

Why is it difficult to answer? The signal integrity problem itself is a question of trade-offs, so it is often said in the industry: "It depends..." This is a question where there is no standard answer. The benevolent sees the benevolent and the wise sees the wisdom. Today, China PCB manufacturer - SysPCB summarized the various answers to this question briefly, and here is also an introduction, hope more people can summarize more relevant factors from their own perspectives.

First of all, 50 ohms has a certain historical origin, and this 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 surveyor's pole and water pipes. 51.5 ohms is very common, but the adapters/converters used are 50 ohms to 51.5 ohms. To solve these problems for the joint army and navy, 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 from it. It is the standard of various cables. At this time, the European standard was 60 ohms. Soon after, under the influence of dominant companies 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 circuit board production, 50 ohms is more convenient to implement. From the 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 needs to be thinner the 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 ohms under the environment of commonly used materials, the ordinary line width and dielectric thickness (4~6mil) meet the design requirements (as shown in the Formula 1 below for impedance calculation), and are convenient for processing. It is not surprising that they gradually become the default choice.

Third, from the point of view of loss, according to basic physics, it can be proved that the skin effect loss of 50 ohm impedance is the smallest (taken from Howard Johnson, PhD's reply). Generally, the skin effect loss L (in decibels) of the cable 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 the 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 dielectric constant Er of the corresponding 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 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, for the convenience of use, radio engineers 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 to the plane, the corresponding EMI will be reduced, the crosstalk will also be reduced, and it is also less susceptible to capacitive loads. However, from the perspective of the full path, one of the most critical factors 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 of less than 50 ohms, and higher impedance transmission lines were inconvenient to implement, so 50 ohm impedance was used as a compromise.

To sum up: 50 ohms as the default value in the 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 the matching interface. For example, 75 ohms is still the standard for remote communication. Some cables and antennas use 75 ohms. At this time, 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.