How can a radiocontrolled watch receive waves of a couple of km long without a (large) antenna? Some watches has the ability to make contact with DCF77. The DCF77 is a German longwave time signal and standard-frequency radio station. The highly accurate 77.5 kHz (approximately 3871 metres wavelength) carrier signal is generated from local atomic clocks that are linked with the German master clocks. 
Now those watches are not bigger than a couple of centimeters but still are capable of receiving waves of 4 km long. How do they that?
https://en.wikipedia.org/wiki/DCF77
 A: Lenght of the antenna rod is not neccessary correlated with the wavelength
Would it be possible to make an antenna for 77,5 kHz much more shorter than those mentioned by you? Yes, it would be possible. But to make it somehow resonant with the wave generator one has to make the current very small. This is because the number if electrons one can accelerate in the antenna rod is limited and since we want to use a short rod and a low frequency we have to accelerate the electrons not all at the same time. Otherwise we get more a trapeziodal than a sinusoidal wave characteristic. The efficiency will be poor and the power of the antenna will be very low, but it is makeable. What we learn from this? The length of the rod is important for the efficiency but not neccessary for the wavelenght of the radio wave. The generator is responsible for the wave modulation and by this for the wavelength of the radio wave.
What are radio waves?
A radio waves is modulated electromagnetic radiation. A wave generator generates a swelling potential difference in the antenna rod and by this some electrons of the rod get periodically accelerated. Any acceleration of electrons induce a magnetic field which induces again an electric field. Some part of this fields could not get back into the rod and starts travelling into space. This is the more macroscopic view. More in detail we know, that accelerated electrons emit photons and the number of emitted photons is proportional to the swelling potential difference from the generator.
How has to be built a receiver?
First at all a receiver has to be adjusted to the frequency of the emitter. Otherwise the noise of all the EM sources (natural and human made) will not allow to filter out the information coded in a radio or cellular phone source. For an receiver antenna rod one can use rods of different length, the task for the engineers is it to build the right receiver electronics. What happens in detail? The EM radiation aka a lot of photons of very different wavelengths are bombing your antenna rod. By the help of the electronic the needed frequency from the accelerated - by the incoming photons - electrons is filtered out and now the coded information (added to the swelling stream if photons) has additional to be filtered out. Different lengths of the antenna rod makes it easier or more complicated to support this process, but the lenght can be very short. In principle, than longer the rod than more photons will accelerate electrons and than more power comes into the receiver electronics. Than shorter the rod or which ever form you use than better the receiver electronics has to be. That's all.
