In some crystal receiver designs and other good designs , it is seen that the antenna is first coupled via inductive coupling. How can this increase the signal strength for long distance signals ? Won't they be further weakened by going through the core and all ? If the weak currents flow through the coils, doesn't they get affected by the reactances and other factors before being amplified by the impedance matching/transformer principle ?
Two scenarios might fit this question
At 1 MHz, an unbalanced antenna would be a quarter wave long or 75 metres and clearly nobody except a researcher is going to go to that trouble. So, what you end up with is an antenna that is somewhat shorter than one-quarter of a wavelength.
At a quarter wavelength a monopole looks like 37 ohms resistive with no reactive component. As the antenna length drops the resistance drops rapidly towards a few ohms but the capacitive reactance increases significantly and, at about one-tenth of one-quarter of one wavelength, the impedance is about 1000 ohms reactive: -
So if you were tuning into 1 MHz and used a 7.5 metre height (aka length) monopole antenna you should be able to see from the above graph that the impedance is -j1000 ohms (Xc is 1000 ohms).
This impedance does what it says - it impedes so sometimes, it makes sense to counter this with an added series inductance of 1000 ohms to series resonate the antenna and allow it to deliver more power.
On the other hand, for an antenna that might be more or less quarter wave in length (maybe shortwave or low VHF), because the impedance of the antenna is 30 odd ohms resistive, connecting this to a high impedance tuning circuit is going to ruin the Q (and selectivity) and so it is usually preferred to connect the antenna to a "low tap" on the tuning coil. If it were connected at one tenth the number of turns above ground then this low impedance wouldn't unduly affect the tuning at the top of the coil. In other words it's an impedance transformer. Impedance at the top would be 100 times greater approximately.