Understanding " WARNING 53119: Possibly inaccurate active power (far field gain) when using equivalent sources in a coupled environment"
Altair EmployeeThe assumption with any equivalent impressed source (far field pattern, near field aperture and spherical mode source), is that the equivalent source is uncoupled from the environment. Meaning the impressed field of the equivalent source is not changed / influenced by geometry or other equivalent sources. This assumption also applies to equivalent receivers.
The total E-field and H-field in a coupled environment is calculated via complex vector addition of the impressed fields of each equivalent source and the field contribution from the rest of the model.
To show this consider a 7-element dipole array where the element radiation pattern is calculated for each dipole and an array pattern where the main beam is scanned to (theta, phi} = {90, 94} degrees., see Figure 1. The element pattern is calculated by exciting each dipole in the array with a voltage source with unit amplitude and zero phase. All the dipoles are loaded with 50Ohm
Figure 1: Element radiation patterns of dipoles 1 to 4 (clockwise from top left). The element patterns of dipoles 5,6 and 7 are mirror images of dipole patterns 3, 2 and 1.
In the equivalent source model, the element radiation patterns are used to reproduce the scanned array pattern. The scan pattern E-field matches exactly between the two models, see Figure 2, as the element pattern includes the coupling to the other dipoles.
Figure 2: E-field scan pattern comparison between the full and equivalent source representation
Given that the impressed field of an equivalent source is uncoupled from the environment and other equivalent sources, the source power of an equivalent source is calculated in isolation in the background medium (free space). Meaning no other structures or equivalent sources are considered.
If the physical sources, represented by equivalent sources, are not uncoupled from each other or from the environment, then generally the source power from the equivalent sources will be inconsistent with the total radiated power of the combined solution. To highlight this inconsistency Feko gives: "WARNING 53119: Possibly inaccurate active power (far field gain) when using equivalent sources in a coupled environment".
Far field directivity could also be inaccurate as the total radiation efficiency of the equivalent sources in the environment is also calculated without coupling.
The total field (near field and far field) of the equivalent impressed sources in the coupled environment is correct. The directivity can be recovered by integrating the far-field power density over a full sphere to obtain radiated power (P_radiated_FF). With P_radiated_FF you can scale the linear directivity (Directivity_eqv) obtained with the equivalent source solution by:
Directivity = Directivity_eqv*(P_source*eta)/P_radiated_FF
where P_source is the total active source power and eta is the radiation efficiency. Both these quantities are for the equivalent source model in the environment.
In a coupled environment the far-field gain of the equivalent source model can’t generally be recovered as the antenna source power (input reflection coefficient) of the physical model can change when it is placed in the environment.