A Novel Integrated Power Module with Solid-State …
11
Fig. 9 Schematic showing the device embedded in the resonant-cap cavity that forms resonant–cap
oscillator
components E z and H ϕ and the propagation vector k will be in the radial direction,
vide Fig. 9.
The E z component of electric field provides a total voltage of E z h between plates
(where h is the plate separation) while the H ϕ component provides a total radial
current of 2π rH ϕ (where r is the radius of the disc) that is directed outward from
one plate and inward into the other plate. In such a radial transmission line, the E z
and H ϕ field components are given by [21–23]:
E z = G 0 (kr)[Ae
jθ(kr)
+ Be
− jθ(kr)
]
(2)
H φ =
1
jωμ
∂ E z
∂r
=
G 1 (kr)
η
[Ae
jψ(kr)
− Be
− jψ(kr)
]
(3)
where
G 0 (x) =
J
2
0 (x) + N
2
0 (x)
(4a)
G 1 (x) =
J
2
1 (x) + N
2
1 (x)
(4b)
and
θ(x) = tan
−1
N 0 (x)
J 0 (x)
ψ(x) = tan
−1
J 1 (x)
−N 1 (x)
(5)
11
Fig. 9 Schematic showing the device embedded in the resonant-cap cavity that forms resonant–cap
oscillator
components E z and H ϕ and the propagation vector k will be in the radial direction,
vide Fig. 9.
The E z component of electric field provides a total voltage of E z h between plates
(where h is the plate separation) while the H ϕ component provides a total radial
current of 2π rH ϕ (where r is the radius of the disc) that is directed outward from
one plate and inward into the other plate. In such a radial transmission line, the E z
and H ϕ field components are given by [21–23]:
E z = G 0 (kr)[Ae
jθ(kr)
+ Be
− jθ(kr)
]
(2)
H φ =
1
jωμ
∂ E z
∂r
=
G 1 (kr)
η
[Ae
jψ(kr)
− Be
− jψ(kr)
]
(3)
where
G 0 (x) =
J
2
0 (x) + N
2
0 (x)
(4a)
G 1 (x) =
J
2
1 (x) + N
2
1 (x)
(4b)
and
θ(x) = tan
−1
N 0 (x)
J 0 (x)
ψ(x) = tan
−1
J 1 (x)
−N 1 (x)
(5)