For RF users, 50 ohms is the most common impedance. It's so prevalent that it's unsurprising. What is the significance of 50 Ohms? Are 30 ohms ok? What about the resistance of 100 ohms? Who established this benchmark?

Today, we'll go over the fundamentals of 50 ohms.

After more than ten years of RF circuit design, I've finally discovered that it's a complicated process. This is especially relevant for someone like me who suffers from Difficult Choice Syndrome. One design is more efficient, but the other is smaller and less expensive. Is there anything out there that is decent, tiny, and inexpensive? I believe there should be, so I always look for the best option. This continual entanglement process can be considered to continue throughout the project's development cycle.

A twisted compromise is 50 ohms. What is the source of this compromise? Let's take a look at what we've got.

Power and power consumption are perennial topics in RF  circuit design. How can you get the most power out of your transmission? How can power consumption be reduced? Consumption is the reality, and no consumption exists solely in the ideal. 50 ohms is a good compromise between greatest power and least loss.

Take, for example, our most regularly used coaxial wire. Take a look at the impedance value of 50 ohms.

Figure. 1

A schematic illustration of a coaxial line, which consists of an inner conductor and an outer conductor, is shown above. It's referred to as a coaxial line since the inner and outer conductors are coaxial. The TEM mode is the most common coaxial transmission mode. The cavity also causes TE and TM modes in the higher-order modes, in addition to the frequency doubling of the TEM mode. The electric field is from the outside surface of the inner conductor to the inner surface of the outer conductor, and the magnetic field surrounds the inner conductor and is periodically distributed in the length direction, as illustrated in the following picture.

Figure. 2

Since its creation, coaxial cable has been favored by the majority of RF  engineers due to its stable operating mode, super-wide working bandwidth, and extremely low transmission loss. It outperforms its predecessor, Double Line, by a wide margin. So, starting in the 1930s, RF experts began looking for the best coaxial cable—one that could transport the most power and voltage with the least loss. However, the more engineers looked at it, the more they discovered that this solution seemed implausible. why?

First, the maximum power capacity corresponds to 30 ohms, whereas the largest voltage corresponds to 60 ohms. The two are diametrically opposed. As seen in the diagram below

Figure. 3

The minimum loss, moreover, corresponds to a higher characteristic impedance of 77 ohms.

Figure. 4

The three are diametrically opposed. Try impedance matching to see how much the echo changes if you don't believe me. This has nothing to do with the resistance of 50 ohms. The compromise has been reached. Engineers are fond of averages. 53.5 ohms is the arithmetic average of maximum power and minimum loss impedance. Is it close to 50 degrees? A geometric mean of 48 ohms is also present. That is to say, RF engineers can work with an impedance range of 48 ohms to 53 ohms without sacrificing too much power capacity or signal loss. As a result, the value of 50 ohms was created. For RF  design, it has increasingly become a standard value.

What are the benefits of setting this impedance standard?

More crucially, 50 ohms is a port standard for RF devices, in addition to the power and loss tradeoffs discussed above. A radio frequency system consists of multiple radio frequency modules, and while designing a single radio frequency module, we simply need to set the port to 50 ohms so that the port can be readily matched when the system is integrated and a single module will not be confused. They are invincible in the world, but they are rotten to the point of slag when they are all together.

Of course, this is an ideal circumstance, and achieving the full 50 ohms in practical circuit design is tough. For example, our port return loss might be as low as 10dB at times. But keep in mind that this 10dB echo is only for ports with a 50-ohm impedance. The performance will drastically vary if the impedance is changed. Because the impedance of our test line port is 50 ohms, we must calibrate before testing to guarantee that the test line port is 50 ohms.

There are several key parameter formulas to remember while working with coaxial wires.

1. Impedance formula

Figure. 5

where b is the radius of the outer conductor and an is the radius of the inner conductor

The inner and outer conductor radius ratio equivalent to 50 ohms for air coaxial cable is 2.302. Because this value will be used frequently, it is suggested that you remember it. The ratio between inner and outer conductor radius for 75 ohms is 3.5. This is more typically utilized in the design of filters.

The greater the impedance, the thicker the outside conductor, and the lower the impedance, the thicker the inner conductor. This is especially noticeable in the candied fruit's low pass. The thickness of the inner conductor is changed to obtain high and low impedance, as indicated in the diagram below.

Figure. 6

2. Cutoff frequency formula

Figure. 7

The lowest frequency of the higher-order mode operating in the coaxial line is this cutoff frequency. As previously stated, the coaxial line can only transmit the TEM mode over a very broad frequency range, and the cutoff frequency of the first higher-order mode, the TE11 mode, is inversely proportional to the inner and outer radius, as indicated in the calculation above. The relationship between D and d is set for a coaxial transmission line with a typical impedance of 50 ohms. The wider the diameter of the coaxial line, the lower the cutoff frequency, as can be seen intuitively. The lower the cutoff frequency, the higher the dielectric constant of the filling medium. This is especially crucial when choosing cables and connectors. Cable and connection cutoff frequencies are typically lower than this ideal cutoff frequency, typically about 90%.

The operating frequencies of popular   RF   connectors and cables are shown in the diagram below.

Figure. 8