Talk:Cavity perturbation theory

[Untitled]
A comment on chapter "Shape perturbation" and more specifically the figure "Cavity shape perturbation"

The shape perturbation volume, dV or rather ΔV, is shown as an externally added volume. I.e. the perturbed cavity is larger than the unperturbed cavity. This is problematic because of two reasons: - First, the fields in the perturbed region dV are either not known or identically zero as this volume is outside the original boundary conditions. Of course, the perturbation shall be small so the fields just outside the original region can probably be extrapolated from the fields just inside the boundary of the unperturbed cavity but you need to know what you are doing. - Second, it gives you the impression that an external volume element dV, as depicted, is a positive volume element. Hence, a volume perturbation by inserting for example a tuning screw, i.e. removing some volume from the cavity, should be interpreted as a negative volume. Going back to reference [3] (Pozar, Microwave Engineering), we see that this interpretation is wrong. Pozar depicts the shape perturbation as a reduction in size (page 309, figure 6.25). In example 6.8 on page 311 we can see that the removed volume is treated as a positive volume element. In other words we integrate the fields over the removed volume with signs as given in equation 6.107.

You could maybe argue that we are basically integrating inductive and electrical stored energy so each of these integrals must always be positive. However, it is possible to use perturbation theory both for reducing and expanding the cavity (if extrapolating the fields) and then we need to know if expansion or reduction is to be considered as positive dV. We cannot get around this. It needs to be defined. In fact I think even Pozar's figure is a little bit problematic as the normal vector n^ is going outwards from boundary. This would normally imply that a positive dV corresponds to an expansion of the integated region (cavity).

Please consider changing the figure so that it shows a volume removal (like inserting a metal object) instead of an expansion of the cavity (like Pozar's figure). Furthermore, the removed volume should be marked ΔV, not dV. Some words, or an example, to reduce the risk of confusion regarding sign of volume element dV in the integral could be good as well.

Bofz (talk) 11:02, 1 October 2018 (UTC)

Some issues I think
I am not sure if this formulation is correct. I think there should be a minus sign in front of the H, as Waldron discusses. Lalanne (ref. 4) also has this. Also, this formulation seems to be for non-dispersive media only. Ref. 4 also discusses the case for dispersive media. 2604:3D08:2482:4220:44B9:3355:1B4E:BD47 (talk) 13:55, 7 October 2022 (UTC)