6.6. Induced Voltage and PowerΒΆ
A small air core loop of \(N\) turns with a cross sectional area \(A\) is placed in a uniform alternating magnetic field with the axis of the loop parallel to the field strength vector \(H\), then the induced emf will be:
If the aperture of the winding is filled with a long ferrite cylinder parallel to the loop, then the flux density of the loaded-loop will be increased by the factor of permeability of core \(\mu_r\). Therefore, induced voltage is given by
The strength of an electromagnetic field is usually expressed in terms of the electric field strength \(E\). Using the fundamental relation:
where \(H\) is in A/m, \(E\) is in V/m, and \(c\) velocity of electromagnetic waves in free space approximately \(3\times{10}^8\) m/s. Then, induced voltage can be written in terms of electric field strength [55]:
#Dunbar gave the formulation of induced voltage in the ferrite loaded receiving loop in free space
#In addition, an expression may be obtained for the induced voltage in a similar ferrite-cored receiving loop at a distance \(r\) from the transmitting loop, the loops being in the same plane to maximize the \(H_\theta\) component.
[Dunbar, 1972]
#Laurent and Carvalho gave an induced voltage formula of the ferrite loaded loop antennas [Laurent and Carvalho, 1962].
where
- \(E\) : electric field intensity vector
- \(c\) : speed of light
- \(A\) : cross section area of coil and rod
- \(d\) : diameter of coil and rod
- \(\mu_r\) : effective relative permeability of the rod
#An expression for the available power from the antenna is obtained [Pettengill, 1977]: