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Antennas and RF Components Using Dispersion Engineered Coupled
Microstrip Transmission Lines
John L. Volakis, Kubilay Sertel
ElectroScience Laboratory, The Ohio State University, 1320
Kinnear Rd, Columbus, OH 43212, USA,
[email protected] , [email protected]
Abstract We present a small printed antenna design based on the
emulation of degenerate band edge dispersion using a simple printed
partially coupled transmission line pair unit cell geometry. The
same topology, when printed on ferromagnetic substrates, is shown
to emulate the stationary inflection point in the dispersion that
supports frozen modes. Furthermore, we present a thee-way partially
coupled topology that supports stationary inflection points for
both propagation directions in its dispersion.
1. Introduction Controllable dispersion characteristics of
periodic assemblies, engineered from dielectric and metallic
textures, have enabled fundamental improvements on conventional
microwave components and antennas. Several research groups
published significant developments in negative index/left-handed
metamaterials in parallel. For example; negative index transmission
line concepts led to the development of very short delay lines,
baluns, couplers, and miniature printed antennas (see Chapter 2 in
[1]), Likewise, the mushroom structure [2] lead to one and two
dimensional left-right handed geometries leading to steerable
traveling wave antennas as well as improved couplers and small
antennas [3]. Extraordinary refraction, sub-wavelength image
resolution and electromagnetic cloaking are among the more talked
about aspects of negative index metamaterials [4]. In particular,
small antenna demonstrations [1,3,4,5] based on zeroth order
resonances (achievable through the negative index) has sparked
renewed interest in realizing miniature antennas. Coincidentally,
these came at a time when
wireless-data-capacity/device-weight-and-cost is becoming one of
the bottlenecks in mobile communication systems. Thus, such
demonstrations are seen as potentially revolutionary. On the other
hand, the Chu-Harrington limits on antenna gain-bandwidth-product
fundamentally restrict the desired performance. Hence, any small
antenna must be put in the perspective of Chu limits when assessing
its performance. Although the small metamaterial antennas may
provide much larger operation bandwidths, their efficiencies are
typically very poor, thus their performance often cannot reach the
optimum Chu-Harrington curve. Periodic assemblies with
ferromagnetic and anisotropic materials have been shown to support
a diverse mode structure with extraordinary wave dispersion [6,7].
In addition to band-gap characteristics of ordinary photonic
crystals, anisotropic crystals may be tuned to have various and
edge characteristics as shown in Fig. 1. If ferromagnetic layers
are also included (magnetic photonic crystals-MPCs), a stationary
inflection point (SIP) can be realized in the dispersion. These
phenomena were recently studied in [6-8] from a theoretical and
engineering perspective. A key observation was the directionality
and high directivity antennas operating at the DBE and MPC modes.
It was also demonstrated that these antennas can achieve optimum
gain-bandwidth performance as compared to the Chu-Harrington
limits.
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k (Bloch Wave Number)
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k (Bloch Wave Number)
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k (Bloch Wave Number)
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k (Bloch Wave Number)
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k (Bloch Wave Number)
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k (Bloch Wave Number)
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k (Bloch Wave Number)
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k (Bloch Wave Number)
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k (Bloch Wave Number)
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k (Bloch Wave Number)
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•B : Isotropic Dielectricse.g. free spaceA A B
Φ1Φ2
A A B
Φ1Φ2Photonic Crystals Degenerate Band Edge Crystals
Regular Band Edge Degenerate Band Edge
•Isotropic Dielectrics
•A : Anisotropic Dielectrics
Split Band Edge
A A F
Φ1Φ2
A A F
Φ1Φ2Magnetic Photonic Crystals
•A : Anisotropic Dielectrics
•F : Ferromagnetic Material
Stationary Inflection Point Figure 1: Various dispersion
characteristics of volumetric anisotropic assemblies.
2. Realizing DBE and MPC modes via Coupled Transmission Lines As
the realization of DBE and MPC assemblies are rather complex, it is
important to realize the same modes on uniform substrates. To do
so, we pursued careful understanding of propagation of the MPC/DBE
modes within the assembly (see Fig. 2a). It can be stated that the
wave slowdown within the crystal is highly correlated to coupling
between the Ex and Ey field polarizations. Dispersion of
electromagnetic wave propagation in the material assembly, shown in
Fig. 2a,b can therefore be replicated for the voltage waves in the
transmission line circuit shown in Fig. 2c. Emulation of wave
dispersion in DBE crystal using simple coupled transmission lines
allows for a much faster and cheaper investigation of the
properties of such structures. Furthermore, various RF components
and printed antennas based on the DBE and MPC dispersion can be
readily realized using the widely used RF circuit manufacturing
techniques.
Coupled
Uncoupled
subε
Uncoupled
(0)⎡ ⎤⎢ ⎥= ⎢ ⎥⎢ ⎥⎣ ⎦
eq
45 0 0ε 0 17.78 0
0 0 45
(a) (b) (c)
( )⎡ ⎤⎢ ⎥ϕ = ⎢ ⎥⎢ ⎥⎣ ⎦
eq
38.1944 11.7876 0ε 11.7876 24.5833 0
0 0 45
k (Bloch Wave Number)
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k (Bloch Wave Number)
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Figure 2: Emulation of DBE dispersion in printed microstrip
TRLs. (a) 3-unit cell volumetric DBE crystal, (b) DBE dispersion of
the volumetric crystal, (c) Printed partially coupled microstrip
TRL equivalent of the volumetric DBE unit cell. This simple
partially coupled TRL geometries call for standard transmission
line models (see Fig. 3) [9]. Coupling can then be realized using
surface mount lumped capacitors and inductors.
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Coupled
UncoupledUncoupled
L1C1
0
L2C2
0
L3 LM
L3 LM
C3
0
C3
0
CMLM
(V1 I1)
(V2 I2)
(V3 I3)
(V4 I4)
Inductive coupling
Capacitive coupling
Coupled
UncoupledUncoupled
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UncoupledUncoupled
L1C1
0
L2C2
0
L3 LM
L3 LM
C3
0
C3
0
CMLM
(V1 I1)
(V2 I2)
(V3 I3)
(V4 I4)
Inductive coupling
Capacitive coupling
K – Bloch Wave Number
Freq
uenc
y (G
Hz)
(a)
(b) (c) Figure 3: (a) DBE-TRL unit cell geometry indication the
lumped element equivalences, (b) Simple lumped circuit element
model of the DBE-TRL unit cell, (c) Design of the dispersion
diagram to minimize the K=π frequency.
Recently, we incorporated measurements of an example showing
that these coupled transmission lines due result in optimum
gain-bandwidth antennas [9].
±180°
-150°
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-90°
-60°
-30°
0°
30°
60°
90°
120°
150°
5
2.5
0
-2.5
SimulationExperiment
1.35 1.4 1.45 1.5 1.55-20
-15
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-5
0
Measured S11
3.0%
1.451.35 1.551.501.40Frequency (GHz)
0
-5
-10
-20
-15|S 1
1| (d
B)
4.5 dB Gain at 1.48 GHz
Measured Return LossMeasured Radiation Pattern
Figure 5: DBE-TRL loop antenna, (a) Top view of the
metallization, (b) bottom view of the ground plane, (c) side view
of the realized antenna, (d) measure return loss, (d) measured
radiation pattern.
5. Printed TRLs on Ferromagnetic Substrates
So far, the TRLs have allowed for a DBE mode realization.
However, of interest is the emulation of dispersion diagrams with
SIP and multiple DBE/MPC modes. A straightforward way to realize
the frozen mode is to replace the TRL substrate with a ferrite
layer [10]. Doing so gives the results in Fig. 6. Another approach
to realizing the MPC mode and even multiple modes is to print
several coupled TRLs on a simple substrate. This is depicted in
Fig. 7.
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(a) (b) Figure 6: (a) Geometry of the MPC-TRL structure, (b)
resulting dispersion diagram displaying a SIP for s1=138 mil
0 π/4 π/2 3π/4 π 5π/4 3π/2 7π/4 2π1
1.5
2
2.5
3 ξ 109
K – Bloch Wavenumber
Freq
uenc
y (G
Hz)
Higher order K-ω curve
0 π/4 π/2 3π/4 π 5π/4 3π/2 7π/4 2π1
1.5
2
2.5
3 ξ 109
K – Bloch Wavenumber
Freq
uenc
y (G
Hz)
Higher order K-ω curve
Higher order K-ω Curve
0 π/4 π/2 3π/4 π 5π/4 3π/2 7π/4 2π1
1.5
2
2.5
3 ξ 109
K – Bloch Wavenumber
Freq
uenc
y (G
Hz)
Higher order K-ω curve
0 π/4 π/2 3π/4 π 5π/4 3π/2 7π/4 2π1
1.5
2
2.5
3 ξ 109
K – Bloch Wavenumber
Freq
uenc
y (G
Hz)
Higher order K-ω curve
Higher order K-ω Curve
π/2 3π/4 π 5π/4 3π/22.4
2.5
2.6
2.7 ξ 109
K – Bloch Wavenumber
Freq
uenc
y (G
Hz)
π/2 3π/4 π 5π/4 3π/22.4
2.5
2.6
2.7 ξ 109
K – Bloch Wavenumber
Freq
uenc
y (G
Hz)
Coupled
Uncoupled Uncoupled
Possible Realization
SIP SIP
(a) (b) (c)
Figure 7: (a) 6th order dispersion in three-way partially
coupled microstrip TRL geometry, (b) close-up view of the symmetric
SIPs, (c) possible realization of the SIP-TRL unit cell.
7. References
1. G.V. Eleftheriades and K.G. Balmain, editors, “Negative
Refraction Metamaterials”, Wiley 2005 2. C. Caloz and T. Itoh,
“Electromagnetic Metamaterials”, Wiley 2006 3. D. Sievenpiper, L.
Zhang, R.F.J. Broas, N.G. Alexopolous and E. Yablonovitch.
“High-Impedance Electromagnetic
Surfaces with a Forbidden Frequency Band,” IEEE Trans. On
Microwave Theory Tech., vol. 47, 11:2059-2074 Nov. 1999.
4. N. Engheta and R.W. Ziolkowski, “Electromagnetic
Metamaterials”, Wiley 2006. 5. A. Erentok and R. W. Ziolkowski, “An
efficient metamaterial–inspired electrically–small antenna,”
Microwave and
Optical Technology Letters, vol. 49, no. 6, pp. 1287–1290, June
2007. 6. A. Figotin and I. Vitebsky, “Nonreciprocal magnetic
photonic crystals,” Phys. Rev. E, vol. 63, pp. 066 609,1–20,
May 2001. 7. A. Figotin and I. Vitebskiy, “Gigantic transmission
band-edge resonance in periodic stacks of anisotropic layers,”
Phys. Rev. E, vol. 72-036619, pp. 1–12, Sep. 2005. 8. G. Mumcu,
K. Sertel, J. L. Volakis, I. Vitebskiy, and A. Figotin, “RF
propagation in finite thickness unidirectional
magnetic photonic crystals,” IEEE Trans. Antennas and Propagat.,
vol. 53, no. 12, pp. 4026–4034, Dec. 2005. 9. G. Mumcu, K. Sertel,
and J.L. Volakis, “Miniature antenna using printed coupled lines
emulating degenerate band
edge crystals”, 2008 URSI National Radio Science Meeting Student
Paper Competition, Jan. 3-6, 2008, Boulder, CO.
10. M.B. Stephanson, K. Sertel, and J.L. Volakis, “Frozen Modes
in Coupled Microstrip Lines Printed on Ferromagnetic Substrates”,
to appear in IEEE Mw. and Wrl. Comp. Lett.,