Chapter 3 Miniaturized Antennas with Circuit Resonances
3.1 Short Slot Radiator Utilizing a Right/Left-Handed Transmission Line Feed 39
Rather than employing CRLH or simply LH TL as mentioned in Chapter 1, a novel planar antenna utilizing cascaded right/left-handed transmission lines is proposed as sketched in Figure 3.1. The design concept is inspired from metamaterial antennas. Two cascaded transmission lines of equal amount of electrical length with opposite polarities, i.e. a section of RH TL and a section of LH TL, can also result in phase of zero degree as shown in Figure 3.2. With using the equivalent transmission line circuits, one can realize compact antennas consisting of printed inductors (L) and capacitors (C) on a printed circuit board without via. The physical dimensions of the antenna are decided by the values of the inductances and capacitances. The layout planning has significant influences on the implementation of such radiating structures.
Figure 3.1 Geometry of the proposed planar antenna.
Figure 3.2 Cascaded right/left-handed transmission lines.
3.1.1 Equivalent Transmission Line Model
The design starts with cascading a section of RH TL and a section of LH TL. The former one has a positive electrical length indicating phase delay whereas the latter one has a negative electrical length indicating phase advance. One port is pen-circuited as illustrated in Figure 3.2. The input impedance (Zin) possesses zero imaginary part, which is one of basic requirements for a resonant antenna. By employing the equivalent circuit model for a TL section, one can realize it with lumped circuits. With the specified characteristic impedance Z0, the operation frequency f0, and the electrical length θ, it is well-known that a certain length of transmission line can be modeled by either π or T equivalent circuit. Figure 3.3 shows the circuit models with
1 0
2 0
1 0
2 0
Y Y (csc cot )
Y Y csc
Z Z (csc cot )
Z Z csc
T T
j j j
j
π π
θ θ
θ
θ θ
θ
= −
= −
= −
= −
(3-1)
where Y0=1/Z0. These formulas can be easily derived by comparing the ABCD matrix for TL section with the ABCD matrix for π and T circuits at the design frequency. The susceptances of Yπ1, Yπ2 and the reactances of ZT1, ZT2, as functions of the electrical length θ, for the normalized component values with Y0=1 and Z0=1 are sketched in Figure 3.4. The upper half plane in Figure 3.4(a) and the lower plane in Figure 3.4(b) indicate capacitive elements whereas the lower half plane in Figure 3.4(a) and the upper plane in Figure 3.4(b) indicate inductive elements.
Figure 3.3 (a)π and (b)T equivalent circuit for a reciprocal two-port network.
Figure 3.4 (a)Susceptances of Yπ1, Yπ2 and (b)reactances of ZT1, ZT2, as functions of the electrical length θ, for the equivalent circuits of Figure 3.3 Y0 = 1 and Z0 = 1.
Figure 3.5 Cascaded circuit structure consisting of a π model for RH TL and a T model for LH TL.
The last series capacitor of the T circuit has been removed since it is connected to the open-circuit end.
3.1.2 Antenna Synthesis and Radiation Mechanism
Following the previous section, formulas for the inductors (L) and capacitors (C) of the equivalent transmission line model are listed in Table 3-1, where ω0 = 2πf0. The notation LLπ, for example, represents the value of the inductor of the π model for LH TL. Since each TL segment in Figure 3.2 can employ either π or T circuit, there are four combinations in total. A π circuit for RH TL and a T circuit for LH TL are chosen and connected with an open-circuit at the unconnected port of the LH TL. This can results in a via-free layout which does not require an extra fabrication process. The last series capacitor of the T circuit can be removed since it is connected to the open-circuit end. As shown in Figure 3.5, it turns out the circuit for designing the proposed antenna with C1 = C2 = CRπ, L1 = LRπ, C3 = CLT, and L2 = LLT.
In order to have a compact structure, the design of the circuit parameters was considered. Referring to Figure 3.4, choosing θ close to either 0 or 180 degrees leads to very large L or C value. Therefore, θ is chosen to be 90 degrees so as to keep a small circuit area. In addition, since many published antennas using metamaterial concepts, mentioned in Chapter 3.1.1, possess patch or patch-like radiation patterns, this study goes with introducing relatively larger capacitors rather than larger inductors. In case of avoiding large inductors and mainly having patches in the physical structure, a relatively small Z0 is preferred. Based on these conditions, several layout types were developed and compared to find the optimal topology.
Table 3-1 The formulas of L and C for a TL section.
To perform the antenna layout, the following design procedure is adopted. The first is to determine the operation frequency, the electrical length, and characteristic impedance of the RH and LH transmission lines. Here, the operation frequency is 2.45 GHz and the characteristic impedance (Z0) of the LH and RH TLs is set to be 25 Ohm.
The second is using the circuit model to determine the values of required inductors and capacitors. This can be done by applying Table I. It turns out that all the three capacitors have the same value of 2.6 pF and both of the inductors have the same value of 1.62 nH at 2.45GHz. The third, the most important step, is to realize these capacitors and inductors by using printed elements. The capacitors are patches against the ground with proper size to fit the value of capacitance. The equation of the parallel plate capacitor can be used to get the initial sizes of the patches. The inductors are implemented by metal traces or metal traces with slotted ground. The lengths of metal traces and the sizes of the slots are designed by EM simulator to fit the value of inductance. Finally, the obtained printed capacitors and inductors are connected properly according to the circuit model. The arrangement of these elements is important for antenna performance. The layout consideration becomes the point of this antenna design. For planning the layouts, full wave EM simulation is done by utilizing the commercial software, Ansoft HFSS. Three possible layouts are considered for comparison as follows. The layout is made on a two sided FR4 substrate with relative dielectric constant of 4.4 and thickness of 0.4 mm.
A compact antenna structure based on the circuit in Figure 3.5 is proposed as illustrated in Figure 3.6 with the corresponding elements marked. The solid lines are for the top metal layout and the dashed lines are for the bottom layout. The rectangular patches are obviously planned to realize the capacitors. The narrow short metal traces dominantly contribute as inductors. This layout arranges the C1, L1,C2, C3,and L2 in turn forms a closed loop and intend to create the longer slot on the ground plane. The geometry parameters are L = W = 11.5 mm, wC = 4 mm, l23 = 9.5 mm, g = 1.3 mm, lS1 = 7.2 mm, lS2 = 3.2 mm. Instead of a narrow short trace, the small inductor L2 is realized by a wide and longer metal trace. Besides, a slot of width of 0.5 mm under L1 is introduced and observed to provide a wide tuning range for the input resistance by changing the slot length lS2.
and Figure 3.7(b), which are made also on the same FR4 substrate. For the type A layout, the bottom pattern is a wide trace of 5.5 mm in width with, of course, a narrow trace for L2. The top pattern is a less wide trace of 3.5 mm in width also with a narrow trace of 2.5 mm in length for L1. The type B layout has quite similar dimension with the type A layout but its wide traces go along an edge of the ground plane. The trace for L2 is directly connected to the ground plane. The dimension along the y axis of the straight type A antenna is 18.5 mm and the dimension along the x axis of the straight type B antenna is 18 mm. It can be roughly interpreted that the proposed layout is obtained by bending the straighter layout as the type A or B. It should be mentioned that all the three layouts have finite ground planes of 40 mm (y-direction) by 30 mm (x-direction) in size, extended in the negative y direction and partly ignored in the figures for simplicity of illustration.
Feed
Figure 3.6 Layout of the proposed antenna. The dashed lines are for the bottom metal layout and the solid lines are for the top metal layout.
(a) (b)
C3
C2
L1
C1 L2
C1 C2 C3
L1
L2
Figure 3.7 Layouts of (a) straight type A antenna and (b) straight type B antenna. The dashed lines are for the bottom metal layout and the solid lines are for the top metal layout.
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 0
50 100 150 200 250 300
InputResistance(Ohm)
Frequency (GHz)
Prop o se d
T yp e A
T yp e B
(a)
(b)
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 -300
-250 -200 -150 -100 -50 0 50 100 150 200 250 300
InputReactance(Ohm)
Frequency (GHz)
Propose d
T yp e A
T yp e B
Figure 3.8 Simulated (a)input resistance and (b)reactance for the proposed, type A, and type B antennas.
Different layouts may cause different electric field and current distributions, thus affecting the radiation performance. Figure 3.8 shows the simulated input impedances of all the three antenna layouts. At the design frequency of 2.45 GHz, all of them possess an anti-resonance, (or a parallel resonance) as can be observed from Figure 3.8(b) where the curve for the input reactance have a zero crossing with a negative slope at that frequency. However, apparent differences of the real parts are observed.
The real part of antenna input impedance usually reflects the radiation performance for easy matching with good radiation efficiency. Thus the layout planning has
significant influences on providing efficient radiating structures while employing the cascaded right/left-handed transmission lines. It is observed that a second anti-resonance occurs around the harmonic frequency (4.5 GHz) for both the type A and B antennas with straight layout. This second anti-resonance also happens in the proposed antenna, however, at a lower frequency of 3.5 GHz. Since the design and analysis focus on the performance at the desired fundamental frequency, other resonances are not taken into account in this paper.
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 0
50 100 150 200 250 300
l S 2
InputResistance(Ohm)
Frequency (GHz) l
S2
(a)
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 -300
-250 -200 -150 -100 -50 0 50 100 150 200 250 300
l S 2
l S 2
InputReactance(Ohm)
Frequency (GHz)
(b)
Figure 3.9 Simulated (a) real part and (b)imaginary part of the input impedance, with changing the slot length lS2 under L1, for the proposed antenna. lS2 = 1.5, 3.0, 3.5, 4.5 mm.
The most difference between these three layouts is considered as the topology of the ground. The proposed antenna structure can be interpreted as closing the layout for L2 to the bottom side of C1. The surface electric current flow is guided roughly in a loop in the order of C1, L1, C2, C3, L2 and then back to C1. In contrast, the type A and B is extended straightly without closing the ground plane to the bottom side of C1. This difference causes the proposed layout introduces longer slot on the ground plane which may have significant influences on inducing radiating current on the ground efficiently. It is found that the slot length, lS2 of the proposed layout, can be used to reduce the input resistance of the antenna from hundreds of ohms to a few ohms with unapparent changing of resonant frequency shown in Figure 3.9. It proves the influence of the radiation from the proper slot on the ground plane. In addition, the proposed antenna can be easily matched.
Besides the consideration of the slot, the patches as capacitors which occupy the main area of the antenna are also studied. An individual patch of small size with respect to the wavelength can only generate negligible far field radiation since the equivalent surface magnetic current (MS) at the edges results in canceling each other at bore sight direction. A surface magnetic current MS is defined by
n E
Ms = × ˆ
(3-2) where E is the electric field, andnˆ
is the outward normal of the side walls for capacitor patches or the normal vector to the surface of the slots. The proposed layout (Figure 3.6) has a topology of patches at the top and slots at the bottom. The bottom pattern could be considered as the extended ground with two connected orthogonal slots. The capacitors confine electric energy and provide fringing fields at their edges. As seen in Figure 3.10(a), the simulated electric fields for C2 and C3 possess opposite polarities, i.e. the electric field vectors for C2 points upward if those for C3 points downward. The opposite polarities make the equivalent magnetic current flow from C2 goes counterclockwise while that from C3 goes clockwise, as indicated by the double-headed arrows of Figure 3.10(b). The radiation fields from the close and opposite directed pairs of the magnetic currents cancel with each other. Therefore, as a result, here are two edges at the top constructively contributing to radiation.These two edges provided by C2 and C3 at the top side operate as the radiating edges
the dimension from half wavelength to one-eleven wavelength. Moreover, there are two connected slots at the bottom side offering aperture electric field for constructing radiation. The contribution provided by C1 is not taken into account since its field strength is very weak. Regarding the type A, it plans three patches in a row with two short traces. The corresponding simulated electric fields and equivalent magnetic currents are shown in Figure 3.10(c) and (d), respectively. The magnetic currents provided by C1 cancel each other in the far field since they are close and opposite directed in pairs. The fringing field from C2 is too weak to contribute. Two remaining edges provide equivalent magnetic currents in the same direction. One is from the slot at the bottom side between C2 and C3. The other one is the upper edge of C3, which is close and parallel to the slot one. The type B has very similar field distribution with the type A.
(a)
(b)
(c) (top)
(bottom)
(d) (top)
(bottom)
Figure 3.10 (a)Schematic for the electric field distribution at the PP cut for the proposed antenna. (b) Schematic of the equivalent magnetic current distribution for the proposed antenna. (c)Schematic of the electric field distribution at the AA cut for the type A antenna. (d)Schematic of the equivalent magnetic current distribution for the type A antenna.
3.1.3 Experimental Results
For experimental verification, both the type A and the proposed structure are fabricated and measured. These two printed antennas were implemented on an FR4 substrate with relative dielectric constant of 4.4 and thickness of 0.4 mm. The proposed antenna results in occupying an area of 11.5 mm by 11.5 mm with a connected ground size of 40 mm by 30 mm. The type A has the size of 5.5 mm by 18.5 mm with the same ground size as the proposed one. As the simulation result predicted, the input resistance of the type A antenna is about 150 Ω, which is relatively large for the 50-Ω system. Thus, an extra quarter-wavelength high impedance line is added between C1 and the 50-Ω microstrip feeding line for impedance transformation. Figure 3.11 shows the measured and simulated return losses, as functions of frequency, for the proposed antenna and the type A antenna.
Both of the measurement results shift a little in frequency from the desired 2.45 GHz.
The proposed antenna exhibits a resonant frequency at 2.23 GHz with the measured return loss of 23 dB, whereas the type A antenna is at 2.35 GHz with a return loss of 16 dB. The corresponding 10-dB return loss bandwidths are 4.5% and 5.3%, respectively. Figure 3.12 and Figure 3.13 show the measured radiation patterns for the proposed antenna and the type A antenna, respectively, in the three principal planes.
The peak gain is +0.16 dBi for the proposed antenna and is -0.54 dBi for the type A antenna.
1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
Frequency (GHz) Type A
25 20 15 10 5 0
Measurement HFSS Simulation Measurement HFSS Simulation
Return loss (dB)
Measurement HFSS Simulation Measurement HFSS Simulation
1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
Frequency (GHz) Proposed type
25 20 15 10 5 0
Measurement HFSS Simulation
Return loss (dB)
(a) (b)
Figure 3.11 Simulated and measured return loss for (a)the proposed antenna and (b)the type A antenna.
XY
Figure 3.12 Simulated and measured radiation patterns for the proposed antenna.
y
Figure 3.13 Simulated and measured radiation patterns for the type-A antenna.
To further understand the influence of the small patches on the radiation performance, two antennas, which have the same layout as the proposed antenna but with the printed capacitors in one antenna replaced by lumped capacitors (Figure 3.14 (a) and (b)), were designed and measured for comparison. Both antennas use same ground plane design with the same slots and equivalent capacitors and inductors. The measurement results and the photos of the antennas are shown in Figure 3.14. The input resistance of the antenna with lumped capacitor is a little less than the other at the center frequency, as can be observed from Figure 3.14(c) and (d). Also from Figure 3.14(e) and (f), it is seen that, the radiation patterns of the two antennas are quite similar, which means that the capacitor patches do not contribute significant radiation. Most of the radiation comes from the ground slots and the induced currents along the ground edges. Nevertheless, it is still noticeable that the theta component of the electrical field of the antenna with patch capacitors is about 2 dB larger than that of the antenna with lumped capacitors.
Through careful design and layout planning, the proposed antenna physically formed by small patches and slots can offer fairly good performance with a compact dimension of λ0 /11 square, where λ0 is the free space wavelength. Finally, due to the self-resonance of the antenna configuration, the resonant frequency of the proposed antenna is insensitive to the ground size, as can be observed from the measurement results shown in Figure 3.15. Here, three antennas with the ground sizes of 70 mm by 45 mm, 40 mm by 20 mm, and 27 mm by 25 mm using same antenna layout are measured and compared. It is seen that the resonant frequencies of the three antennas are almost the same. It proves that the ground size has negligible effect on the resonance of the proposed antenna structure. As a reference, three typical printed quarter-wavelength monopole antenna with different ground sizes have also been developed for comparison. The antennas have the same monopole strip size of 27 mm by 1.6 mm and with ground sizes of 70 mm by 45 mm, 40 mm by 20 mm, and 27 mm by 25 mm, respectively. Although not shown here, the center frequency of the monopole antenna varies with the change of the ground size from 2.35GHz to 1.99GHz. A 16.5% frequency offset is observed.
XZ
Figure 3.14 (a)The realized proposed antenna layout with printed elements. (b)The realized proposed antenna layout with lumped capacitors. (c)The measured input impedance of the antenna with printed element. (d)The measured input impedance of the antenna with lumped capacitors. (e)The measured radiation pattern of the antenna with printed element in x-z plane. (f)The measured radiation pattern of the antenna with lumped capacitors in x-z plane.
Ground size:
70mm X 45mm
Ground size:
40mm X 20mm
Ground size:
27mm X2 5mm
Type_1 Type_2 Type_3
(a)
1 1.5 2 2.5 3 3.5 4 4.5 5
Frequency (GHz)
The Proposed Antenna Configuration
25 20 15 10 5 0
Return loss (dB)
Type_3 Type_1 Type_2 Type_3 Type_1 Type_2
(b)
Figure 3.15 (a)The proposed antenna configuration with different ground sizes. (b)The return loss of the proposed antenna configuration with different ground sizes.
3.1.4 Summary
A novel compact planar antenna is designed and verified experimentally. Fairly good measurement results are obtained. Layout planning plays a crucial role for radiating as discussed. Different layouts for the same circuit model can cause different performances. This paper shows the possibility to design compact antennas based on cascaded right/left-handed transmission lines. Through applying the equivalent transmission line model, the physical dimension can be compact with a size are small as λ0/11 square. In this paper, the proposed antenna avoids via and consists of only five lumped elements by the selection of the EQC model combination. The π and T models can offer exact formulas for L and C for almost all-range electrical length, θ, rather than CRLH TL of which formulas for the circuit elements are valid for very small θ with the same accuracy as sinθ approaches unity. (In fact, the CRLH TL method can be considered as a sub-category of the general π and T models.) Possible radiation mechanism, including the radiation from the capacitor patches and the slots, of the proposed antenna has also been proposed. After the experimental comparison as shown in Figure 3.14, it is found that the antenna is more like a slot radiator. Instead of only half-space patch-like radiation, the proposed antenna structure with more than two radiating edges gives a fairly omni-directional radiation pattern. The proposed design has several advantages, such as easily achieving resonance, simple structure, compact size without performance degradation, and stable frequency against different ground size. Additionally, although the equivalent circuit parameters in this paper are chosen for certain considerations, different electrical length, different characteristic
A novel compact planar antenna is designed and verified experimentally. Fairly good measurement results are obtained. Layout planning plays a crucial role for radiating as discussed. Different layouts for the same circuit model can cause different performances. This paper shows the possibility to design compact antennas based on cascaded right/left-handed transmission lines. Through applying the equivalent transmission line model, the physical dimension can be compact with a size are small as λ0/11 square. In this paper, the proposed antenna avoids via and consists of only five lumped elements by the selection of the EQC model combination. The π and T models can offer exact formulas for L and C for almost all-range electrical length, θ, rather than CRLH TL of which formulas for the circuit elements are valid for very small θ with the same accuracy as sinθ approaches unity. (In fact, the CRLH TL method can be considered as a sub-category of the general π and T models.) Possible radiation mechanism, including the radiation from the capacitor patches and the slots, of the proposed antenna has also been proposed. After the experimental comparison as shown in Figure 3.14, it is found that the antenna is more like a slot radiator. Instead of only half-space patch-like radiation, the proposed antenna structure with more than two radiating edges gives a fairly omni-directional radiation pattern. The proposed design has several advantages, such as easily achieving resonance, simple structure, compact size without performance degradation, and stable frequency against different ground size. Additionally, although the equivalent circuit parameters in this paper are chosen for certain considerations, different electrical length, different characteristic