7.2 Analytical consideration of the radiation loss and a model for the free space radiation from the enclosure slot

Analogous to patch antennas, the radiated field of the parallel-plate structure is
conveniently calculated by the use of the equivalence source method
[102], [104], [105], [106],
described in Chapter 6. This method has been utilized by
Leone [59] to calculate the free space radiation for parallel rectangular
power planes with four open edges. Since the radiation loss of power planes with a very
small plane separation is low compared to the conduction and the dielectric losses,
[59] neglected the radiation loss. However, that is not sufficient in the
case of power planes with higher plane separation and especially not for an enclosure,
where the plane separation is much higher and the radiation loss becomes the dominant
loss mechanism. [45] considered the radiation loss in the cavity field
calculation with a quality factor which was obtained by a far field calculation of the
lossless cavity model. However, this approach fails, because the radiation from the
lossless model is much higher than that of a model which would correctly consider the
radiation loss. Thus, the radiation loss obtained from the lossless model is too high,
which explains the deviations of the calculation from the measurement results in
[45]. Therefore, the domain separation method of
Chapter 6 is utilized here to consider the radiation loss
at the slot of the enclosure. A radiation loss admittance matrix from ports at the slot
surface is obtained from a far field calculation without the cavity model. This loss
admittance matrix is therefore independent of the cavity model and considers the
radiation loss correctly for each voltage distribution along the slot surface. In a
second step the admittance matrix is introduced into the cavity model and the common
calculation yields the internal enclosure field and the slot field distribution under
consideration of the radiation loss. The radiated far field is calculated from the slot
field distribution utilizing a far field approximation approach. This provides an
analytical model for efficient predesign investigations about the field distribution
inside the enclosure, at the enclosure slot, and in the far field region.

- 7.2.1 Calculation of the far field from the slot field distribution
- 7.2.2 Derivation of an admittance matrix for the consideration of the radiation loss at the cavity field simulation
- 7.2.3 Introduction of the radiation loss admittance matrix into the cavity model matrix
- 7.2.4 Summary of the equations for the introduction of the radiation loss into the cavity model and the far field calculation