By varying the values of inductance (L) and capacitance (C) in the circuit, we can tune the circuit to receive a particular frequency. This may sound simplistic in reality, However, practical implementation, shows that a circuit tuned at a particular frequency receives a range of frequencies. This brings in another factor the range of operation for the antenna.
Most RF antennas operate upto a certain range of frequencies about the resonant frequency. This becomes a necessity, as the signal transmitted at a particular frequency would undergo several modifications, during its travel. This allows a range of frequencies to pass through, but outside the range the reactance rises to levels that are often too high for satisfactory operation. Other characteristics of the antenna may also suffer due to the increased range of frequencies hence the tank circuit filters the frequencies about the central operating frequency.
The impedance of an RF antenna stays same and does not change with its frequency. This causes an increase in the amount of reflected power. In case of a transmitting antenna, beyond a given level of reflected power, damage may occur to either the transmitter or the feeder. This would be a significant factor limiting the operating bandwidth of an antenna but not so much on the reception end.
As far as receiving is concerned the impedance changes of the antenna are not as critical as it will mean that the signal transfer from the antenna itself to the feeder is reduced and will cause the efficiency to fall.
In order to increase the bandwidth of an antenna there are a number of measures that can be taken for eg. using thicker conductors.