Electronic – How much power does a receiver antenna obtain from a radio station

How can I calculate a rough estimate of the radiated power, or at least a maximum value, of the radiated power if I know how much electric power I put in (assume an RLC circuit)?

If you use a resonant RLC circuit (basically a magnetic loop antenna) and you believe you know the value of R, you might still not get an accurate answer. This is because R is really hard to compute. It is it hard to compute because the electric and magnetic fields in the close vicinity of the loop antenna may be producing eddy currents and dielectric heating in things that are reasonably close by. How would you account for such things? It's still going to look like a real power loss and you just can't tell one power from another.

^{simulate this circuit – Schematic created using CircuitLab}

In the close vicinity of the loop (or in fact any antenna used for EM transmission), the localized electric and magnetic fields are not sufficiently aligned to form an EM wave and those losses (I mentioned above) are just straight forward local power losses and nothing to do with the emission of an EM wave.

The classic radar range equation can be used to solve this problem. Just google "radar range equation" if you are not familiar with it (although you should be if you are asking this question). All of the information given in your question can be used to deduce the variables in the range equation, one of which is your unknown, the peak power. Once the peak power is known the average power can be calculated from it, the pulse repetition rate and the pulse width.