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So, I am a young researcher in physics and use RF components like splitters, mixers, couplers, amplifiers, etc. These are not high voltage amplitudes at all - at most a few volts - often hundreds of MHz, or GHz. My basic question is, under what circumstances can RF waves go somewhere that is damaging? Is this just component-dependent, whether the component is suited to deal with a wave in the reverse direction, or basically a function of whether the reflected wave has a significant amplitude? Besides reflection, if you mess up impedance matching, can you damage the component that the wave is moving into by transmission (e.g. an oscilloscope)? I would love a standardized source for best practices for safety and to avoid damaging components - it's possible that this would be in a thorough explanation of impedance matching, if anyone has one. I imagine this source may need to be from recent decades, e.g. in my experience it would be very hard to do something silly enough to destroy a power supply because they are built with very robust safeguards now, probably same for an oscilloscope.

It's fine to for example let RF waves be generated into a hanging/unattached BNC cable, but when is it necessary to terminate while building/testing RF circuits? Are RF terminators more so used for protecting components, or cleaning up noise, or does it depend on context? I am pretty lazy about using them. As far as I know I've never actually damaged an RF component, but I do get paranoid. Is it a reasonable rule of thumb that if it's really important, it will be printed on the component (like 'input last' often is for amplifiers)? Also, what kind of impedance mismatches will lead to what kind of consequences? These questions are partially based in wanting a generalizable physical understanding but also partially asking what problems are practically most likely to come up over the course of one's life experience.

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Your question is highly packed. So the first thing is can you damage thing by plugging them in the wrong direction, the answer is, YES. But not everything can't be plugged both way. For instance, if you have an amplifier, and you plug the output on the wrong side, you can damage them and anything in their path significantly. You need to know a bit what you do. It also depends what power level your are thinking of using. If your are using -20dBm, I doubt that you'll blow any thing (unless you have a very sensible structure). On the other hand, if you work at +10dBm or more, you need to be really careful. If you can work at a lower power, you are less likely to make a costly mistake.

Regarding test equipment, generators are almost always able to take their reflection at lower power. If you look carefully, on every RF port of any good test equipment, you will have the maximum power that it can receive. So if you got a source that has a maximum output level 15dBm but can't receive more then 10dBm, you should be terminated when you go anywhere close to 10dBm.Most source at lower frequency won't have those issue. At higher frequency, double check the manual, or terminate it. For oscilloscope, if they don't have a 50 ohm termination, you should simply not use them at higher frequency. You won't measure the right signal anyway.

Where the issue with test equipment come to play a lot more is when several test equipment are plugged at the same time. Then unplugging something will create a somewhat perfect reflection and can double the power at some ports. It is not advisable to do it. In many case, it is harmless, but when you have sensitive device, it can make you cry! When you leave an unterminated cable, 100% of the power is reflected. So think about that!

Everything really comes to what is the power you are working with.

You mentioned power supply, just to be sure, most test equipment don't like DC at all. Ensured you protect them with DC block.

You didn't mention ESD, but ESD discharge, even those you can't feel can make permanent damage to an equipment or circuit.

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