Space-Filling Curve
High-Impedance Ground
Planes
b96901128 王郁翔
Outline

1. Space-Filling Curve

2. Resonance Property

3. High-Impedance Surfaces
Outline

4. Applications
Thin Absorbing Screens
Antenna Application
DNG bulk media

5. Conclusions
Space-Filling Curve
A problem in mathematical analysis.
 Continuous mapping from line to plane
for infinite iteration order.

Why use space-filling curve?

This resonance structure is compacted
within a small
footprint.(microminiaturization)

The 2D structure is easy to fabricate.
Resonances Simulation

Use method-of-moments(MoM) code to
simulate.

Footprint = 30mm*30mm
Resonance Property

The footprint is electrically small.
However, the bandwidth is narrow.
High Impedance Surfaces

Reflection coefficient about +1

Artificial magnetic conductor

Utilizing resonance inclusions on a
nonconducting host substrate layer in
parallel with a conducting ground plane.
High Impedance Surfaces
Simulation of Peano Surface

Periodic MoM code

Measure reflection coefficient to
frequency.

Condition:
Normal incident plane wave.
Infinite extent of ground plane and Peano surface of order 2.
Perfect metal and dielectric(air).
Simulation of Peano Surface
Wire width = 0.5mm
footprint = 30mm*30mm
distance from ground = 15mm
separation = 3.75mm
Simulation of Peano Surface

Footprint and height are relatively small
compare to wavelength.(0.153,0.063)
(0.076,0.031)

Bandwidth: ±90°
Simulation of Peano Surface
Change height and separation.
 y-polarized is less pronounced.

Simulation of Hilbert Surface
Hilbert curve of order 3.
Footprint = 30mm*30mm Separation = 4.285mm
Height = 15mm
 Incident angle from 0 to 60.

Experiment Results
Fabricate curve on 1.575-mm FR-4
substrate with dielectric constant 4.4 and
loss tangent 0.02.
 Scaled to match the frequency of WR-430
waveguide.(1.7~2.6 GHz)

Experiment Results

Simulate by finite-element method and
the measure data.
Varying Loss Tangent

MoM-based IE3D simulation on Peano of
order 2 and Hilbert of order 3 for xpolarized wave.
Thin Absorbing Screens

Frequency-selective surfaces.

Thin absorber, application in absorbing
material and low observables.

Much smaller than Salisbury screen.
Antenna Application

Put a small dipole antenna above Hilbert
surface.

Image current enhanced radiation.

High-performance, low-profile, conformal,
flush-mounted antenna.
Antenna Simulation

MoM software package IE3D and NEC-4
based Code GNEC.

Simulate impedance to frequency.

Additional height 15mm
11*11 Hilbert curves
copper with conductivity 5.813*107S/m
Efficiency and Directivity

IE3D simulation code
DNG Bulk Media
Embedding many identical space-filling
curve inclusions within a host medium.
 Simulate electric and magnetic dipole
moments to frequency, then use the
Maxwell-Garnett mixing formula to
analyze this polarizability tensor to obtain
effective permittivity and permeability.

Permittivity and Permeability

MoM based code.
y-polarized
Hilbert curve of order 3
wire radius = 0.125mm
Maxwell-Garnett formula
SNG media by Peano

Peano curve inclusions also has negative
permittivity and permeability, but in
different frequency.

Multifunction media
Conclusions

There are two main problems have to
solve.

1.narrow bandwidth

2.dependence of the response of space-
filling curve on the polarization.