"LTE 868 MHz Antenna" Why does 868 MHz stand for? Are antennas specified for a certain frequency or is it necessary for something like input type? For example, I want to transmit a 40 MHz RF signal. Can I use an 868 MHz or 2.4 GHz antenna to transmit? Or am I supposed to make an antenna specified for that frequency band? What might happen if I use an 868 MHz antenna on a 2.4 GHz compatible device like a WiFi router? Lack of performance? Not working?
It's not so much that antennas are specified at certain frequencies (they usually are), but that they tend to work best over certain frequency ranges, determined by their physical shape and the materials they're made of. But -- it's complicated. People can spend entire engineering careers doing nothing but designing antennas.
"LTE 868 MHz Antenna" Why does 868 MHz stand for? Are antennas specified for a certain frequency or is it necessary for something like input type?
"Specified" means someone is promising something. A given antenna will tend to actually work for some range of frequencies.
To work well, an antenna must work over the range of frequencies that the equipment it's connected to must work (i.e., if you're only going to transmit Morse code at only 11MHz, then you can have a really narrow band antenna -- but if you're going to receive any signal between 50MHz and 200MHz without changing the antenna dimensions, or if you have a signal that actually spans that range, then you need a very broad band antenna).
For example, I want to transmit a 40mhz RF signal. Can I use an 868MHz or 2.4GHz antenna to transmit?
Well, you can, in much the same way that you can use a knitting needle or a wheel off of a car for the same task. But it probably won't work out well.
Or am I supposed to make an antenna specified for that frequency band?
"Supposed" and "specified" presumes that there's some Physics Police out there who will arrest you or hand you demerits for getting it wrong. I have no clue what people expect you to do -- but a given antenna will work best at a given frequency, and if you're designing a system then you generally need to design the antenna to match, or obtain one that's going to (usually by design) work the way you wish it to.
What might happen if I use an 868 MHz antenna on a 2.4GHz compatible device like a wifi router? Lack of performance? Not working?
In the case of a consumer-grade WiFi router, probably degraded performance, perhaps to the point of not working unless you're inches away. You probably wouldn't damage it if it has external antenna connections, because a responsibly-designed consumer device will embrace the possibility that someone is doing something dumb with it.
In the case of a professional device that's intended for 2.4GHz and that includes a transmitter (or a really crappy consumer device) the mismatch between the antenna and the transmitter may damage the transmitter, the receiver section (if there) and possibly whatever circuit switches between receive and transmit. The difference here is that a professional device presupposes a professional doing the installation. Most modern RF devices will have some sort of protection, but the more "pro" it gets the more "pro" you are expected to be.
Antennas are tuned for particular frequency bands. They won't be damaged by using other frequencies (in theory the transmitter could be damaged by a mismatched antenna, but most commercial transmitters are protected against mismatched (or missing) antennas.
If you use outside the designed frequency band your performance will deteriorate -- likely very significantly (e.g. 10, or 100x worse).
Antennas are attuned for one particular frequency, since they need to match the wave length of the radio signal. Wave length can be calculated as c/f where c is the speed of light and f is the frequency.
In you case
299 792 458 m/s /
There are various antenna types such as full wave, half wave, quarter wave, which in this case means they have the exact physical length
This is for the ideal center frequency of the antenna where it sends/receives optimally. From there, antennas can be broad or narrow, as in accepting a wide or narrow span above and below the center frequeny. The longer you stray from center, the worse it will perform.
If you for example have a radio transmitter for 40MHz but an antenna for 868MHz, it will not work at all, as the energy generated from the 40MHz transmitter will just reflect back into the radio electronics instead of getting sent out in the air. Leading to excess energy that has to go somewhere - in the best case the radio circuit can deal with this, in the worst case it will get fried. So apart from not working at all, you might even damage the electronics by using the wrong antenna.
Remember that every technical product is the result of a lot of compromises, or with a better word design decisions.
The engineer designing the antenna will work according to a specification that will outline the priorities for the design. It will include things like: frequency range, amplification, directivity, max ratings for voltage and power, price, size, SVR, weight, materials, temperature range, longevity, ...
This means that a very high amplification very directive antenna with a huge budget (think radio telescope) will look very different from a 5 cent radio transistor antenna.
Trying to use the antenna outside of, say the intended frequency range, then you are on your own. It might work very well, it probably will not be great, but it might be acceptable. The exact design of the antenna might give an experienced person clues to the performance but the proof is in the actual performance.
Transmitting a 40 MHz signal using a 868 MHz antenna will probably result in very poor amplification, meaning that most of the energy will be transformed to heat and very little inte actual radio waves. It might as well show very odd directionality perhaps sending most of then radio energy into only a small lobe. Same effect might happen with a 868 MHz antenna on a 2.4 GHz router -- most of the transmitter radio signal will turn into heat (or perhaps not, depends on the exact design of the antenna). And similarily for the receiving end, the antenna might be quite "deaf" at frequencies outside the intended range, or not. Mty guess is that it will not give a satisfying result.
Additionally, it might hurt the transmitter. Pumping energy inte a circuit and not letting it exit the intended way through the antenna may hurt components and you will see the magic smoke exiting from them. Admittedly, in low power situations and/or consumer electronics the circuits are probably protected so harm may not occur.
Antennas can be whatever size you like and any frequency you like. At a given frequency, for a monopole antenna, two things depend on the antenna size: input impedance and radiation pattern. Input impedance that is different from your feedline impedance will require some kind of matching network. But all of the power reaching your antenna will be radiated (except the power that is warming the roof of your car). An antenna that has a constant impedance from DC to gamma rays is the holy grail of antenna engineering. Not likely you will ever encounter such a device.
Antennas are generally limited by mechanical considerations. I no longer carry a 66 foot vertical monopole on my car. Also I no longer use a spring at the base of my car antenna due to bad impotence. A California Highway Patrol officer advised me that the maximum permissible height for an antenna was 13 feet above ground. But an antenna that high will not do well around trees and bushes. As said above, engineering is full of compromises.