A Matching Technique for Dual-Band Composite Right ... - CiteSeerX
A Matching Technique for Dual-Band Composite Right/Left Handed (CRLH) Transmission Line Resonator Antennas S. Otto1, A. Rennings1, C. Caloz2, P. Waldow1 1
Department of Engineering Duisburg-Essen University, Bismarckstr. 81, D-47048 Duisburg, Phone: +49 203 379 1058, [email protected] 2 École Polytechnique de Montréal , 3333, ch. Queen Mary, Montréal (Québec), Canada impedance for the two operating frequencies. Qualitative (same mode pair) as well as quantitative (same CRLH line impedances) design will ensure fully equivalent dual frequency operation.
Abstract — Recently, a novel dual-band Composite Right/Left Handed (CRLH) resonator antenna was introduced. The two operation frequencies f−1 and f+1 of this antenna correspond to a pair of negative and positive resonance frequencies (-n,+n) associated with a left-handed (LH) and right-handed (RH) resonances of the CRLH structure, respectively. Although these resonances exhibit identical field distributions, because they have the same electrical length |βl|=|±nλg|, they can have significantly different input impedances in general, so that simultaneous good matching at both frequencies can be difficult. This paper provides a rigorous technique for this simultaneous matching of both frequencies to obtain an efficient dualband antenna. Furthermore, introducing a dual-band CRLH λ/4 resonator antenna, a more size effective antenna is obtained along with the suppression of undesired spurious modes.
2. THEORY 2.1. Resonant Modes The upper right corner of Fig. 1 shows the lumped element unit cell model of the CRLH-TL. An N-cell CRLH-TL resonator of physical length l=Np (p: length of the unit cell) has the following resonance condition: βn = nπ/l (n = 0, ±1, ±2, ±3, …, ±(N −1)) associated with the resonant frequencies [3]
nπ = cos −1 N
1. INTRODUCTION CRLH-TLs are artificially designed transmission lines. They have been used for various novel concepts of microwave devices [1]. A CRLH-TL is composed of cascaded CRLH unit cells. The lossless CRLH unit cell is modeled with its four lumped element circuit parameter as they are CR, LR, CL, LL. The series capacitance CL and shunt inductance LL account for the LH propagation (antiparallel group and phase velocity). This duality of the LH and RH propagation mechanism exhibits unusual phenomena. At lower frequencies the propagation is essential affected by the LH elements CL, LL, leading to backward propagation and a proportional relation of frequency and wavelength (f ~λ) on the transmission line. With increasing frequency the RH elements are dominating the wave propagation and the usual antiproportionality of frequency and wavelength is observed (f ~1/λ). This dispersion characteristic provides the same |β| for two different frequencies, one located in the LH frequency range with β < 0 and the other one in the RH frequency range with β > 0. Such a pair of propagation constants has been exploited in our open ended resonator antenna. In our previous work [2] the main focus has been on the two half-wavelength resonant modes and their qualitatively same voltage and current distribution. The highly dispersive transmission line impedance ZCRLH was not considered and therefore an additional matching circuit was needed to achieve simultaneous matching. The key idea to obtain equivalent dual band behavior is to have the same mode along with the same line
f se =
1 2π CL LR
,
(
)(
1 f 2 − f se2 f 2 − f sh2 1 − 2 f 2 f R2 f sh =
1 2π LLCR
and f R =
) ,
(1)
1 2π CR LR
An N-cell CRLH resonator supports the zeroth order resonance plus N-1 resonances in the RH range and N-1 resonances in the LH range. Every mode pair has the same voltage/current distribution on the open ended CRLH-TL. The voltage/current distributions at the terminals of the unit cells follow a sinusoidal half wavelength distribution, in the particular case of f−1 and f+1. The lower operating frequency f−1 is located in LH frequency region of the CRLH dispersion characteristics and the f+1 is located in the RH frequency region, respectively. 2.2. Line Impedance Based on the ABCD-matrix of the symmetrical unit cell depicted in the upper right corner of Fig. 1, the transmission line impedance ZCRLH (Bloch impedance [4]) for a lossless CRLH-TL is calculated: Z CRLH =
B = C
Z (4 + ZY ) , 4Y
(2)
with Z=j(ωLR−1/ωCL) the series impedance and Y=j(ωCR−1/ωLL) the shunt admittance of the unit cell. The lumped element parameters used for the circuit simulations are: CL=1.4pF, LR =2.7nH and CR =2pF with the shunt inductance LL varied in three steps LL =1.6nH, 70
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LL =1.9nH and LL =2.1nH. The reason LL was chosen for the variation is the easily controllable inductance in the later design implementation in microstrip technology. In Fig. 1 the line impedance ZCRLH is plotted for the three different cases: I) LL =2.1nH with fsh < fse; II.) LL =1.9nH the balanced case with fsh = fse; III.) LL =2.1nH with fsh > fse. It can be observed that with increasing shunt inductance LL the CRLH-TL impedance in the LH frequency range increases as well. In the RH frequency range the opposite behavior of decreasing impedances with higher inductances is found. The line impedances for the balanced case are equivalent in the RH and LH region around the series resonator frequency fsh = fse. The shaded regions indicated the transmission band gaps and are associated with imaginary line impedance for the non-balanced cases in I.) and III.). 2CL
70 balanced case fse= fsh
50
LL
40
p
For the balanced case, plotted with solid lines, the input impedance is identical at both frequencies. The reason is the same TL impedance ZCRLH at both resonant frequencies. Three different port locations 1, 2 and 3 (Fig. 2) have been evaluated and plotted in the smith chart. A perfect agreement of the input impedance at the lower resonance f−1 and the upper resonance f+1 is found. With increasing distance from the center the input impedance enlarges which can be observed in Fig. 4 (c) for the balanced case. Therefore, the concept of the dualband half wavelength field distribution is totally supported by very simple circuit simulations and a consistent matching strategy to achieve dual-band matching can be proposed.
p
LL=1.6nH LL=1.9nH LL=2.1nH
30
LL / nH 1.6 1.9 2.1
20
) =2 .1 nH
f+1 / GHz 3.15 3.06 3.02
fsh / GHz 2.81 2.59 2.45
fse / GHz 2.59 2.59 2.59
f
sh
(L
f−1 / GHz 2.27 2.18 2.13
TABLE 1 SIMULATED RESONANCE FREQUENCIES OF THE RESONATOR LINE IN FIG. 2.
fsh(LL=1.6nH)
L
10
G
Fig. 3: CRLH unit cell model including losses for the circuit simulation.
CR
LL
R/2
LR/2
CR
LL
LR /2
LL
ZCRLH
Real{ZCRLH} / W
60
LR/2
2CL
LR /2
2CL 2CL
R/2
+j1.0
7
+j0.5
Fig. 1: Transmission line impedance (Bloch impedance) for an infinite CRLH transmission line.
-1
+j0.2
0.0
A 7-cell lumped circuit network, modeling a CRLH resonator, has been investigated. In order to account for losses mainly related to radiation, conductor losses and dielectric losses, a series resistor R=1Ω and a shunt conductor G=1/1MΩ have been introduced. The symmetrical unit cell model is depicted in Fig. 3. In Fig. 2 the overall configuration of 7 cascaded unit cells to form the open-ended resonator is shown. The circuit has been excited with a 50Ω port at the port position 3 as illustrated in Fig. 2. and the s11-parameter has been simulated. In Tab. 1 the f±1 resonance frequencies are listed for the three different inductance values. In Fig. 4 the s11-parameter is plotted for the (a) lower f−1 and (b) upper f+1 half-wavelength resonance frequency with LL varying. The input impedance at resonance is related to the TL impedance, so that the input impedance increases with higher ZCRLH values. port location
2
+j5.0
LL
5.0
2.3. Circuit Simulation
1
lower resonance: f
-j0.2
-j5.0
-j0.5 -j1.0
(a) +j1.0
s11 LL=1.6nH s11 LL=1.9nH s11 LL=2.1nH
+j0.5
+j0.2
+j5.0
LL 0.0
-j0.2
upper resonance: f+1
3
-j0.5
i=2
i=3
i=4
(b)
i=7
l
Fig. 2: Lumped circuit model of a 7-cell CRLH open-ended resonator. The symmetrical unit cell with its lumped element parameters of Fig. 3 is cascaded to form the resonator line.
71
∞
-j5.0
-j1.0
i=1
∞
s11 LL=1.6nH s11 LL=1.9nH s11 LL=2.1nH
5.0
6 f /GHz
1.0
5
1.0
3 4 fse= fsh(LL=1.9nH)
0.5
2
0.5
1
0.2
0
0.2
0
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decreases for the upper resonance frequency with longer stubs. For ds=12.8mm (solid lines) a simultaneous matching for both frequencies is found. In Fig. 6 (c) it can be observed that a port shift in negative x-direction to the center of the next unit cell (position 2) results in a larger real part of the input impedance for both frequencies. Consequently, the matching strategy is as follows, first find line impedance to have both resonant circles almost congruent and second shift the port along the line to find the desired real input impedance.
+j1.0 +j0.5
+j0.2
3
2
5.0
1.0
0.0
0.5
0.2
+j5.0
-j0.2
1
∞
-j5.0
s11 port position 1 s11 port position 2 s11 port position 3
-j0.5
ds / mm 10.8 12.8 14.8
-j1.0
(c) Fig. 4: s11 is plotted with two parameters (LL and the port location) varied. In (a) and (b) the port is located at position 3, while the inductance LL varied. In (c) the port is shifted to location 2 and 1 with a constant inductance LL=1.9nH.
LL / nH 1.80 2.20 2.70
CR / pF 2.20 2.14 2.03
f−1 / GHz 2.32 2.19 2.06
f+1 / GHz 3.10 2.99 2.92
TABLE 2 PARAMETER EXTRACTION FOR THE CRLH UNIT CELL AND SIMULATED RESONANCE FREQUENCIES FOR THE 9-CELL OPEN-ENDED RESONATOR.
3. EM SIMULATION AND MEASUREMENTS
+j1.0
The results from the circuit simulation in 2.3 have been applied to optimize simultaneous matching for a proposed 9-cell resonator antenna. EM simulations with parameter variations corresponding the parameters in the circuit simulation in 2.3 have been performed. In Fig. 5 (a) the prototype of the proposed 9-cell resonator antenna is shown. It is composed of cascaded unit cell of Fig. 5 (b).
+j0.5
lower resonance: f -1
+j0.2
+j5.0
-j0.2
5.0
1.0
0.5
0.0
0.2
ds ∞
-j5.0
dss11 =10.8mm =12.8mm dss11 dss11 =14.8mm -j0.5 -j1.0
(a) +j1.0 +j0.5
upper resonance: f +1
(a)
+j0.2
+j5.0
2.30
6.30
unit cell
5.0
1.0
0.0
0.5
via hole
0.2
12.2
ds
ds
-j0.2
∞
-j5.0
dss11 =10.8mm =12.8mm dss11 dss11 =14.8mm
-j0.5
-j1.0
(b)
2.00
+j1.0
(b) Fig. 5: Picture of the λ/2 antenna prototype (a). The CRLH unit cell ms metallization layout with its physical dimensions (b). The width of the interdigital fingers is 0.3mm with a gap of 0.2mm between the fingers.
+j0.5
+j0.2
5.0
1.0
0.5
0.2
0.0
3.1. Matching Optimization
+j5.0
1
Extensive EM simulations using Ansoft Designer (MoM) have been performed. The model of the prototype shown in Fig. 5 (a) has been simulated with the stub length (Fig. 5 (b)) and the port location varied. The stub length variation ds has a main effect on the shunt inductance LL, which can be observed in Tab. 2. In Fig. 6 (a) and (b) s11 is plotted for the upper f+1 and lower f-1 resonance frequency. The real part of the input impedance increases for the lower resonance and
∞
2 -j0.2
-j5.0
-j0.5
s11 port position 1 s11 port position 2 -j1.0
(c) Fig. 6: s11 is plotted with two parameters varied. In (a) and (b) the port is located at position 1 while the stub length ds was varied. In (c) the port is shifted to location 2, with a constant stub length ds=12.8mm.
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3.2 Measurement of the λ/2-Resonator Antenna Prototype
3.3. Simulation model of the λ/4 resonator antenna
The prototype in Fig. 5 (a) was measured and the simulated s11 along with the measured s11 is plotted in Fig. 7. The measured resonances are shifted by a nonnegligible frequency offset to lower frequencies. The reason has to be investigated in detail. Nevertheless, the concept itself is supported by the measurement and the measured resonant frequencies are f-1 and f+1. The radiation for the two modes is given in Fig. 8 and is in very good agreement with the simulated radiation. The measured gain is relative and has been normalized to match the maximum simulated gain for each frequency. The cross-polarization was 30dB below the copolarization level and is not plotted to maintain the shape of the graph. The E-field polarization is in x-direction corresponding to the non compensating current in xdirection on the structure. The aperture size relative to the radiated wavelength for the upper operating frequency is larger even though the same current distribution on the 9– cell antenna is present. This results in a higher directivity for the upper operating frequency.
This concept has been directly applied to obtain a λ/4 dual band resonator antenna (Fig. 9). Here, only the simulated s11 is presented and the same resonance behavior as for the λ/2 antenna has been achieved. An advantage of this proposed resonator is besides the size reduction of 50%, the suppression of undesired modes. The radiation is expected to differ from the initial λ/2 device. This will be investigated in our further work. 0
|s11| in dB
-5
|s11| in dB
-15
-25 -30 1.8
s11 MoM Simulation 2.0
2.2
2.4 2.6 f in GHz
2.8
3.0
3.2
Fig. 9: Simulated s11 for the proposed λ/4 dual frequency resonator antenna displayed in the inset.
-5
4. CONCLUSION AND OUTLOOK A novel concept of CRLH dual-band antennas has been discussed with the focus on the matching techniques. The main idea here is to exploit the same mode along with the same characteristic impedance on an open-ended resonator line to build dual-band antennas. As far as the matching to the 50 Ohm port impedance was concerned the line impedance was found to be crucial for the matching. Circuit and EM simulations have been performed for a 7-cell/9cell resonator line showing the effect of the line impedance on the input impedance at resonance. The optimized λ/2 resonator antenna was built and measured. Besides the deviation in the simulated and measured s11 (frequency offset) a good agreement of theory and measurement has been observed supporting the conceptual ideas. A new device of a λ/4 antenna has been proposed and the simulated s11-parameter has been presented. Simulation and measurement of the far-field characteristics will be evaluated in our upcoming work.
-10 -15 -20 s11 Measurement s11 MoM Simulation
-25
2.4 2.6 2.8 3.0 3.2 f in GHz Fig. 7: Comparison of the simulated and measured s11 for the EM optimized antenna with the port located at position 1 and ds=12.8mm.
2.0
2.2
z
Normalized Gain in dB
feed
-10
-20
0
-30 1.8
via fence
10 5 0 -5 300 -10 -15 -20 -25 -30 270 -25 -20 -15 -10 240 -5 0 5 10
0
f+1
330
30
f-1
60
REFERENCES 90
120
Measurement Simulation 210
[1] C. Caloz and T. Itoh, "Novel microwave devices and structures based on the transmission line approach of metamaterials", IEEE-MTT Int'l Symp., vol. 1, pp. 195-198, Philadelphia, PA, June 2003. [2] S. Otto, A. Sanada, C. Caloz, and T. Itoh, "A dualfrequency composite right/left-handed half-wavelength resonator antenna", Asia-Pacific Microwave Conference, India, December 2004, accepted for presentation. [3] A. Sanada, C. Caloz, and T. Itoh, "Novel zeroth-order resonance in composite right/left-handed transmission line resonator," 2003 Asia-Pacific Microwave Conference Proceedings, pp.1588-1591, Nov. 2003. [4] Collin, Robert E., "Foundations for Microwave Engineering", 2nd ed. New York: McGraw-Hill, 1992
x
150 180
Fig. 8: Measured and simulated far-field co-polarization patterns in the E-plane (x-z) plane for the upper f+1 and lower resonance frequency f-1. (The measured data is relative and has been normalized to the maximum simulated gain)
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Department of Engineering Duisburg-Essen University, Bismarckstr. 81, D-47048 Duisburg, Phone: +49 203 379 1058, [email protected] 2 École Polytechnique de Montréal , 3333, ch. Queen Mary, Montréal (Québec), Canada impedance for the two operating frequencies. Qualitative (same mode pair) as well as quantitative (same CRLH line impedances) design will ensure fully equivalent dual frequency operation.
Abstract — Recently, a novel dual-band Composite Right/Left Handed (CRLH) resonator antenna was introduced. The two operation frequencies f−1 and f+1 of this antenna correspond to a pair of negative and positive resonance frequencies (-n,+n) associated with a left-handed (LH) and right-handed (RH) resonances of the CRLH structure, respectively. Although these resonances exhibit identical field distributions, because they have the same electrical length |βl|=|±nλg|, they can have significantly different input impedances in general, so that simultaneous good matching at both frequencies can be difficult. This paper provides a rigorous technique for this simultaneous matching of both frequencies to obtain an efficient dualband antenna. Furthermore, introducing a dual-band CRLH λ/4 resonator antenna, a more size effective antenna is obtained along with the suppression of undesired spurious modes.
2. THEORY 2.1. Resonant Modes The upper right corner of Fig. 1 shows the lumped element unit cell model of the CRLH-TL. An N-cell CRLH-TL resonator of physical length l=Np (p: length of the unit cell) has the following resonance condition: βn = nπ/l (n = 0, ±1, ±2, ±3, …, ±(N −1)) associated with the resonant frequencies [3]
nπ = cos −1 N
1. INTRODUCTION CRLH-TLs are artificially designed transmission lines. They have been used for various novel concepts of microwave devices [1]. A CRLH-TL is composed of cascaded CRLH unit cells. The lossless CRLH unit cell is modeled with its four lumped element circuit parameter as they are CR, LR, CL, LL. The series capacitance CL and shunt inductance LL account for the LH propagation (antiparallel group and phase velocity). This duality of the LH and RH propagation mechanism exhibits unusual phenomena. At lower frequencies the propagation is essential affected by the LH elements CL, LL, leading to backward propagation and a proportional relation of frequency and wavelength (f ~λ) on the transmission line. With increasing frequency the RH elements are dominating the wave propagation and the usual antiproportionality of frequency and wavelength is observed (f ~1/λ). This dispersion characteristic provides the same |β| for two different frequencies, one located in the LH frequency range with β < 0 and the other one in the RH frequency range with β > 0. Such a pair of propagation constants has been exploited in our open ended resonator antenna. In our previous work [2] the main focus has been on the two half-wavelength resonant modes and their qualitatively same voltage and current distribution. The highly dispersive transmission line impedance ZCRLH was not considered and therefore an additional matching circuit was needed to achieve simultaneous matching. The key idea to obtain equivalent dual band behavior is to have the same mode along with the same line
f se =
1 2π CL LR
,
(
)(
1 f 2 − f se2 f 2 − f sh2 1 − 2 f 2 f R2 f sh =
1 2π LLCR
and f R =
) ,
(1)
1 2π CR LR
An N-cell CRLH resonator supports the zeroth order resonance plus N-1 resonances in the RH range and N-1 resonances in the LH range. Every mode pair has the same voltage/current distribution on the open ended CRLH-TL. The voltage/current distributions at the terminals of the unit cells follow a sinusoidal half wavelength distribution, in the particular case of f−1 and f+1. The lower operating frequency f−1 is located in LH frequency region of the CRLH dispersion characteristics and the f+1 is located in the RH frequency region, respectively. 2.2. Line Impedance Based on the ABCD-matrix of the symmetrical unit cell depicted in the upper right corner of Fig. 1, the transmission line impedance ZCRLH (Bloch impedance [4]) for a lossless CRLH-TL is calculated: Z CRLH =
B = C
Z (4 + ZY ) , 4Y
(2)
with Z=j(ωLR−1/ωCL) the series impedance and Y=j(ωCR−1/ωLL) the shunt admittance of the unit cell. The lumped element parameters used for the circuit simulations are: CL=1.4pF, LR =2.7nH and CR =2pF with the shunt inductance LL varied in three steps LL =1.6nH, 70
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LL =1.9nH and LL =2.1nH. The reason LL was chosen for the variation is the easily controllable inductance in the later design implementation in microstrip technology. In Fig. 1 the line impedance ZCRLH is plotted for the three different cases: I) LL =2.1nH with fsh < fse; II.) LL =1.9nH the balanced case with fsh = fse; III.) LL =2.1nH with fsh > fse. It can be observed that with increasing shunt inductance LL the CRLH-TL impedance in the LH frequency range increases as well. In the RH frequency range the opposite behavior of decreasing impedances with higher inductances is found. The line impedances for the balanced case are equivalent in the RH and LH region around the series resonator frequency fsh = fse. The shaded regions indicated the transmission band gaps and are associated with imaginary line impedance for the non-balanced cases in I.) and III.). 2CL
70 balanced case fse= fsh
50
LL
40
p
For the balanced case, plotted with solid lines, the input impedance is identical at both frequencies. The reason is the same TL impedance ZCRLH at both resonant frequencies. Three different port locations 1, 2 and 3 (Fig. 2) have been evaluated and plotted in the smith chart. A perfect agreement of the input impedance at the lower resonance f−1 and the upper resonance f+1 is found. With increasing distance from the center the input impedance enlarges which can be observed in Fig. 4 (c) for the balanced case. Therefore, the concept of the dualband half wavelength field distribution is totally supported by very simple circuit simulations and a consistent matching strategy to achieve dual-band matching can be proposed.
p
LL=1.6nH LL=1.9nH LL=2.1nH
30
LL / nH 1.6 1.9 2.1
20
) =2 .1 nH
f+1 / GHz 3.15 3.06 3.02
fsh / GHz 2.81 2.59 2.45
fse / GHz 2.59 2.59 2.59
f
sh
(L
f−1 / GHz 2.27 2.18 2.13
TABLE 1 SIMULATED RESONANCE FREQUENCIES OF THE RESONATOR LINE IN FIG. 2.
fsh(LL=1.6nH)
L
10
G
Fig. 3: CRLH unit cell model including losses for the circuit simulation.
CR
LL
R/2
LR/2
CR
LL
LR /2
LL
ZCRLH
Real{ZCRLH} / W
60
LR/2
2CL
LR /2
2CL 2CL
R/2
+j1.0
7
+j0.5
Fig. 1: Transmission line impedance (Bloch impedance) for an infinite CRLH transmission line.
-1
+j0.2
0.0
A 7-cell lumped circuit network, modeling a CRLH resonator, has been investigated. In order to account for losses mainly related to radiation, conductor losses and dielectric losses, a series resistor R=1Ω and a shunt conductor G=1/1MΩ have been introduced. The symmetrical unit cell model is depicted in Fig. 3. In Fig. 2 the overall configuration of 7 cascaded unit cells to form the open-ended resonator is shown. The circuit has been excited with a 50Ω port at the port position 3 as illustrated in Fig. 2. and the s11-parameter has been simulated. In Tab. 1 the f±1 resonance frequencies are listed for the three different inductance values. In Fig. 4 the s11-parameter is plotted for the (a) lower f−1 and (b) upper f+1 half-wavelength resonance frequency with LL varying. The input impedance at resonance is related to the TL impedance, so that the input impedance increases with higher ZCRLH values. port location
2
+j5.0
LL
5.0
2.3. Circuit Simulation
1
lower resonance: f
-j0.2
-j5.0
-j0.5 -j1.0
(a) +j1.0
s11 LL=1.6nH s11 LL=1.9nH s11 LL=2.1nH
+j0.5
+j0.2
+j5.0
LL 0.0
-j0.2
upper resonance: f+1
3
-j0.5
i=2
i=3
i=4
(b)
i=7
l
Fig. 2: Lumped circuit model of a 7-cell CRLH open-ended resonator. The symmetrical unit cell with its lumped element parameters of Fig. 3 is cascaded to form the resonator line.
71
∞
-j5.0
-j1.0
i=1
∞
s11 LL=1.6nH s11 LL=1.9nH s11 LL=2.1nH
5.0
6 f /GHz
1.0
5
1.0
3 4 fse= fsh(LL=1.9nH)
0.5
2
0.5
1
0.2
0
0.2
0
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decreases for the upper resonance frequency with longer stubs. For ds=12.8mm (solid lines) a simultaneous matching for both frequencies is found. In Fig. 6 (c) it can be observed that a port shift in negative x-direction to the center of the next unit cell (position 2) results in a larger real part of the input impedance for both frequencies. Consequently, the matching strategy is as follows, first find line impedance to have both resonant circles almost congruent and second shift the port along the line to find the desired real input impedance.
+j1.0 +j0.5
+j0.2
3
2
5.0
1.0
0.0
0.5
0.2
+j5.0
-j0.2
1
∞
-j5.0
s11 port position 1 s11 port position 2 s11 port position 3
-j0.5
ds / mm 10.8 12.8 14.8
-j1.0
(c) Fig. 4: s11 is plotted with two parameters (LL and the port location) varied. In (a) and (b) the port is located at position 3, while the inductance LL varied. In (c) the port is shifted to location 2 and 1 with a constant inductance LL=1.9nH.
LL / nH 1.80 2.20 2.70
CR / pF 2.20 2.14 2.03
f−1 / GHz 2.32 2.19 2.06
f+1 / GHz 3.10 2.99 2.92
TABLE 2 PARAMETER EXTRACTION FOR THE CRLH UNIT CELL AND SIMULATED RESONANCE FREQUENCIES FOR THE 9-CELL OPEN-ENDED RESONATOR.
3. EM SIMULATION AND MEASUREMENTS
+j1.0
The results from the circuit simulation in 2.3 have been applied to optimize simultaneous matching for a proposed 9-cell resonator antenna. EM simulations with parameter variations corresponding the parameters in the circuit simulation in 2.3 have been performed. In Fig. 5 (a) the prototype of the proposed 9-cell resonator antenna is shown. It is composed of cascaded unit cell of Fig. 5 (b).
+j0.5
lower resonance: f -1
+j0.2
+j5.0
-j0.2
5.0
1.0
0.5
0.0
0.2
ds ∞
-j5.0
dss11 =10.8mm =12.8mm dss11 dss11 =14.8mm -j0.5 -j1.0
(a) +j1.0 +j0.5
upper resonance: f +1
(a)
+j0.2
+j5.0
2.30
6.30
unit cell
5.0
1.0
0.0
0.5
via hole
0.2
12.2
ds
ds
-j0.2
∞
-j5.0
dss11 =10.8mm =12.8mm dss11 dss11 =14.8mm
-j0.5
-j1.0
(b)
2.00
+j1.0
(b) Fig. 5: Picture of the λ/2 antenna prototype (a). The CRLH unit cell ms metallization layout with its physical dimensions (b). The width of the interdigital fingers is 0.3mm with a gap of 0.2mm between the fingers.
+j0.5
+j0.2
5.0
1.0
0.5
0.2
0.0
3.1. Matching Optimization
+j5.0
1
Extensive EM simulations using Ansoft Designer (MoM) have been performed. The model of the prototype shown in Fig. 5 (a) has been simulated with the stub length (Fig. 5 (b)) and the port location varied. The stub length variation ds has a main effect on the shunt inductance LL, which can be observed in Tab. 2. In Fig. 6 (a) and (b) s11 is plotted for the upper f+1 and lower f-1 resonance frequency. The real part of the input impedance increases for the lower resonance and
∞
2 -j0.2
-j5.0
-j0.5
s11 port position 1 s11 port position 2 -j1.0
(c) Fig. 6: s11 is plotted with two parameters varied. In (a) and (b) the port is located at position 1 while the stub length ds was varied. In (c) the port is shifted to location 2, with a constant stub length ds=12.8mm.
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3.2 Measurement of the λ/2-Resonator Antenna Prototype
3.3. Simulation model of the λ/4 resonator antenna
The prototype in Fig. 5 (a) was measured and the simulated s11 along with the measured s11 is plotted in Fig. 7. The measured resonances are shifted by a nonnegligible frequency offset to lower frequencies. The reason has to be investigated in detail. Nevertheless, the concept itself is supported by the measurement and the measured resonant frequencies are f-1 and f+1. The radiation for the two modes is given in Fig. 8 and is in very good agreement with the simulated radiation. The measured gain is relative and has been normalized to match the maximum simulated gain for each frequency. The cross-polarization was 30dB below the copolarization level and is not plotted to maintain the shape of the graph. The E-field polarization is in x-direction corresponding to the non compensating current in xdirection on the structure. The aperture size relative to the radiated wavelength for the upper operating frequency is larger even though the same current distribution on the 9– cell antenna is present. This results in a higher directivity for the upper operating frequency.
This concept has been directly applied to obtain a λ/4 dual band resonator antenna (Fig. 9). Here, only the simulated s11 is presented and the same resonance behavior as for the λ/2 antenna has been achieved. An advantage of this proposed resonator is besides the size reduction of 50%, the suppression of undesired modes. The radiation is expected to differ from the initial λ/2 device. This will be investigated in our further work. 0
|s11| in dB
-5
|s11| in dB
-15
-25 -30 1.8
s11 MoM Simulation 2.0
2.2
2.4 2.6 f in GHz
2.8
3.0
3.2
Fig. 9: Simulated s11 for the proposed λ/4 dual frequency resonator antenna displayed in the inset.
-5
4. CONCLUSION AND OUTLOOK A novel concept of CRLH dual-band antennas has been discussed with the focus on the matching techniques. The main idea here is to exploit the same mode along with the same characteristic impedance on an open-ended resonator line to build dual-band antennas. As far as the matching to the 50 Ohm port impedance was concerned the line impedance was found to be crucial for the matching. Circuit and EM simulations have been performed for a 7-cell/9cell resonator line showing the effect of the line impedance on the input impedance at resonance. The optimized λ/2 resonator antenna was built and measured. Besides the deviation in the simulated and measured s11 (frequency offset) a good agreement of theory and measurement has been observed supporting the conceptual ideas. A new device of a λ/4 antenna has been proposed and the simulated s11-parameter has been presented. Simulation and measurement of the far-field characteristics will be evaluated in our upcoming work.
-10 -15 -20 s11 Measurement s11 MoM Simulation
-25
2.4 2.6 2.8 3.0 3.2 f in GHz Fig. 7: Comparison of the simulated and measured s11 for the EM optimized antenna with the port located at position 1 and ds=12.8mm.
2.0
2.2
z
Normalized Gain in dB
feed
-10
-20
0
-30 1.8
via fence
10 5 0 -5 300 -10 -15 -20 -25 -30 270 -25 -20 -15 -10 240 -5 0 5 10
0
f+1
330
30
f-1
60
REFERENCES 90
120
Measurement Simulation 210
[1] C. Caloz and T. Itoh, "Novel microwave devices and structures based on the transmission line approach of metamaterials", IEEE-MTT Int'l Symp., vol. 1, pp. 195-198, Philadelphia, PA, June 2003. [2] S. Otto, A. Sanada, C. Caloz, and T. Itoh, "A dualfrequency composite right/left-handed half-wavelength resonator antenna", Asia-Pacific Microwave Conference, India, December 2004, accepted for presentation. [3] A. Sanada, C. Caloz, and T. Itoh, "Novel zeroth-order resonance in composite right/left-handed transmission line resonator," 2003 Asia-Pacific Microwave Conference Proceedings, pp.1588-1591, Nov. 2003. [4] Collin, Robert E., "Foundations for Microwave Engineering", 2nd ed. New York: McGraw-Hill, 1992
x
150 180
Fig. 8: Measured and simulated far-field co-polarization patterns in the E-plane (x-z) plane for the upper f+1 and lower resonance frequency f-1. (The measured data is relative and has been normalized to the maximum simulated gain)
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