50 ohm is the most common impedance for RF connectors. So commonplace that it is not surprising. Why 50 ohm? 30 ohm okay? What about 100 ohm? Who set this standard? Today we will talk about the ins and outs of 50 ohm.
RF circuit design is a tangled process. This is especially true for someone with Difficult Choice Syndrome like me. One design performs better, one is smaller, and the other is less expensive. Are there any good, small and cheap designs out there? I think there should be, so I'm looking for the best solution every time. This constant entanglement process can be said to run through the entire development cycle of the project. 50 ohm is also a compromise that has come and gone. Where does this compromise come from? An eternal topic in RF circuit design is power and power consumption. How to transmit maximum power? How to minimize power consumption? No consumption exists only in the ideal, and consumption is the reality. 50 ohm is a value in the balance of maximum power and minimum loss.
Take our most commonly used coaxial cable as an example. Look at what kind of impedance value is 50 ohm?
The figure above is a schematic diagram of a coaxial line, which consists of an inner conductor and an outer conductor. Because the inner conductor and the outer conductor are coaxial, it is called a coaxial line. The main mode of coaxial transmission is the TEM mode. In addition to the frequency doubling of the TEM mode, the higher-order modes also have TE and TM modes caused by the cavity. The coaxial lines we use are all working in TEM mode, and the field distribution is shown in the following figure: the electric field is from the outer 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.
Stable working mode, super wide working bandwidth, super low transmission loss, coaxial cable has been loved by the majority of RF engineers since its invention. It is many times better than its old predecessor, Double Line. So beginning in the 1930s, RF engineers began searching for an optimal coaxial cable—the highest power and voltage transfer, and the lowest loss.
But the deeper the research, the more engineers discovered that this best seemed impossible. why?
First, the impedance corresponding to the largest power capacity is 30 ohm, and the impedance corresponding to the largest voltage is 60 ohm. The two are quite different. As shown below
More importantly, the minimum loss corresponds to a higher characteristic impedance of 77 ohm.
The three are very different. If you don't believe me, try impedance matching to see how much the echo changes? This has nothing to do with 50 ohm. The compromise is here. Engineers like to average. The arithmetic average of the maximum power impedance and the minimum loss impedance is 53.5 ohm. Is it close to 50? There is also a geometric mean of 48 ohm. That is to say, the impedance range of 48 ohm to 53 ohm is acceptable to RF engineers without affecting too much power capacity and signal loss. Therefore, the value of 50 ohm was born. It has gradually become a standard value for RF design. That's where 50 ohm comes in. Of course, in some specific occasions, 75 ohm and 30 ohm will also be used.
What are the benefits of setting this impedance standard?
In addition to the power and loss tradeoff mentioned above, more importantly, 50 ohm is a port standard for RF devices. A radio frequency system consists of many radio frequency modules, and when we design a single radio frequency module, we only need to set the port to 50 ohm, so that the port can be easily matched when the system is integrated.
Of course, this is only an ideal situation, and it is difficult for us to achieve full 50 ohm in actual circuit design. For example, our port return loss can sometimes only be 10dB. But remember, this 10dB echo is only for the port impedance of 50 ohm. If you change the impedance, the performance will change greatly. This 50 ohm port impedance is the impedance of our test line port, so before testing, we need to calibrate to ensure that the test line port is 50 ohm.
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