Reciprocity Theorem Essay

900 Words2 Pages

RECIPROCITY THEOREM

If voltage is applied to terminals of an antenna A and the current is measured at another antenna B, then an equal current (bot amplitude and phase) will appear at terminals of antenna A if same voltage is applied to antenna B.
Application of reciprocity theorem
Equality of Directional Patterns
Statement: 'The directional pattern of an antenna as a receiving antenna is identical to that when used as a transmitting antenna."

Proof: The above mentioned antenna theorem is the outcome of the application of the reciprocity theorem used in the linear and bilateral networks. Basically a directional pattern of a transmitting antenna is represented as a polar characteristic because it indicates the strength (amplitude) of the
radiated …show more content…

This current is the measure of the electric field at different positions of the dipole antenna. Now using the concept of the reciprocity theorem, the positions of the voltage excitation and the current measurement are interchanged. Now the same voltage V is applied to the terminals of the small dipole antenna which is moved along the surface of the sphere and the current I is measured in the test antenna located at the centre. Thus the receiving pattern for the test antenna can be obtained. But according to the reciprocity theorem, for every location of the dipole antenna, the ratio of V to I is same as before obtained for the test antenna as a transmitting antenna. Thus the radiation pattern i.e. directional pattern of a receiving antenna is identical to that of the transmitting antenna. Instead of the circular polarization, if the linear polarization is considered, then under such condition, the small dipole exploring antenna is oriented in such a way that direction is perpendicular to the radius vector and parallel to the electric …show more content…

Hence from equation (4) it is clear that the receiving antenna impedance is equal to the transmitting antenna impedance.
In the discussion of the impedance measurement of an antenna, we consider two antennas which are widely separated. But we can use the same concept for several antennas assuming all are widely separated from the antenna whose impedance is to be measured. Now assume that the other antennas are placed very close to the antenna being considered for impedance measurement. Under such condition, the mutual impedance cannot be ignored as it is comparable with the self impedance. Thus the receiving impedance will be the addition of the antenna self impedance and the impedance due to the presence of other antennas. But even under such condition, the transmitting impedance is equal to the receiving impedance if for the transmitting condition, other antennas are connected to the impedances equal to the impedances of the generators that used to excite

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