US 10,305,159 B2Granted

Apollonian-loaded split-ring resonator and method for designing the same

AssigneeThe United States of America as represented by the Secretary of the Air Force

InventorsPaul A. Sikora, Mark A. Southcott

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Abstract

The invention provides an apparatus comprising a wide bandwidth resonating structure based on a primary split ring resonator having a plurality of additional split ring resonators bounded by the primary split ring resonator. The invention provides a method for optimizing the placement and size of the additional split ring resonators to achieve the desired bandwidth for the overall resonator structure.

Claims8

Dependent claims

A resonator, comprising:

a primary conductor having a first end and a second end and being substantially annular shaped, disposed on a substrate;
a plurality of secondary conductors each having a first end and a second end and being substantially annular shaped, disposed on said substrate and bounded by said primary conductor;
a plurality of tertiary conductors each having a first end and a second end and being substantially annular in shape, disposed on said substrate and bounded by said primary conductor, wherein said tertiary conductors are determined in dimension according to an iterative computation of
d
=
a
+
b
+
c
±
2
2
⁢
ab
+
bc
+
ca
where
a is the normalized curvature (i.e., 1/radius) of a first reference conductor;
b is the normalized curvature (i.e., 1/radius) of a second reference conductor;
c is the normalized curvature (i.e., 1/radius) of a third reference conductor;
and
d is the normalized curvature of each of a tertiary conductor generated in a current iteration;
and
wherein said tertiary conductors are determined in location according to an iterative computation of:
d
⁡
(
X
4
+
Y
4
⁢
i
)
=
a
⁡
(
X
1
+
Y
1
⁢
i
)
+
b
⁡
(
X
3
+
Y
3
⁢
i
)
+
c
⁡
(
X
3
+
Y
3
⁢
i
)
±
2
2
⁢
⁢
a
⁡
(
X
1
+
Y
1
⁢
i
)
⁢
b
⁡
(
X
2
+
Y
2
⁢
i
)
+
b
⁡
(
X
2
+
Y
2
⁢
i
)
⁢
c
⁡
(
X
3
+
Y
3
⁢
i
)
+
c
⁡
(
X
3
+
Y
3
⁢
i
)
⁢
a
⁡
(
X
1
+
Y
1
⁢
i
)
where
X1+Y1i is the center point coordinate of said first reference conductor;
X2+Y2i is the center point coordinate of said second reference conductor;
X3+Y3i is the center point coordinate of said third reference conductor;
and
X4+Y4i are the center point coordinates of each of a tertiary conductor generated in a current iteration;
and
where each of said primary conductor, said secondary conductors and said tertiary conductors comprise a predetermined distance gap between said first end and said second end.

155 more elements

A method for designing a substantially planar resonator, comprising the steps of:

selecting a predetermined radius and cross-sectional width of a annularly shaped outer conductor;
selecting a predetermined radius, cross-sectional width, and location of a first pair of annularly shaped inner conductors such that they are bounded by said annularly shaped outer conductor and substantially tangent to each other and to said annularly shaped outer conductor;
and
iteratively generating, according to a predetermined function, successive annularly shaped inner conductors, each being bounded by said annularly shaped outer conductor and each being substantially tangent to at least two preexisting annularly shaped conductors.

1 more element

Dependencies are inferred from the claim text.

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Abstract