- #1
FrankJ777
- 140
- 6
Hi all. I've been trying to study microwave and electromagnetic engineering . I'm not sure how I should interpret j in some of the field equations. For example, for the field equations for a rectangular waveguide resonant cavity are:
E[itex]_{y}[/itex] = E[itex]_{0}[/itex] sin[itex]\frac{\pi x }{a}[/itex] sin [itex]\frac{l \pi z}{a}[/itex]
H[itex]_{x}[/itex] = [itex]\frac{-j E_{0}}{Z_{TE}}[/itex] sin[itex]\frac{\pi x}{a}[/itex] cos [itex]\frac{l \pi z}{d}[/itex]
H[itex]_{z}[/itex] = [itex]\frac{j \pi E_{0}}{k \eta a}[/itex] cos[itex]\frac{\pi x}{a}[/itex] sin [itex]\frac{l \pi z}{d}[/itex]
What is the physical interpretation of j and -j in the H field in the x z direction? Does that indication that they are 90° out of phase of the E field? Does it indicate phase in the sense of time or space? Or should i think of them as derivatives of phasors? I know that the fields are derived from the more general phasor form of Maxwell's equations:
∇ × E = - jωμH
∇ × H = jωεE
for which jω = [itex]\frac{\partial E}{ \partial t }[/itex] and E is E[itex]_{0}[/itex] e[itex]^{j \omega t}[/itex]
which makes sense to me as I believe you can interpret jω as the sinusoidal frequency. But once the E and H fields have been derived as above it's no longer jω just j, so I've lost the sense of there meaning in the H fields. Could someone please explain how I should interpret them. Or anything else I seem to have screwed up in my thinking. Thanks a lot.
E[itex]_{y}[/itex] = E[itex]_{0}[/itex] sin[itex]\frac{\pi x }{a}[/itex] sin [itex]\frac{l \pi z}{a}[/itex]
H[itex]_{x}[/itex] = [itex]\frac{-j E_{0}}{Z_{TE}}[/itex] sin[itex]\frac{\pi x}{a}[/itex] cos [itex]\frac{l \pi z}{d}[/itex]
H[itex]_{z}[/itex] = [itex]\frac{j \pi E_{0}}{k \eta a}[/itex] cos[itex]\frac{\pi x}{a}[/itex] sin [itex]\frac{l \pi z}{d}[/itex]
What is the physical interpretation of j and -j in the H field in the x z direction? Does that indication that they are 90° out of phase of the E field? Does it indicate phase in the sense of time or space? Or should i think of them as derivatives of phasors? I know that the fields are derived from the more general phasor form of Maxwell's equations:
∇ × E = - jωμH
∇ × H = jωεE
for which jω = [itex]\frac{\partial E}{ \partial t }[/itex] and E is E[itex]_{0}[/itex] e[itex]^{j \omega t}[/itex]
which makes sense to me as I believe you can interpret jω as the sinusoidal frequency. But once the E and H fields have been derived as above it's no longer jω just j, so I've lost the sense of there meaning in the H fields. Could someone please explain how I should interpret them. Or anything else I seem to have screwed up in my thinking. Thanks a lot.