S IMULATION FOR 1-D EBG S TRUCTURE

As the paragraph we mentioned previously, EBG surfaces are usually characterized through the evolution of the reflection phase over the frequency. To assess its reflection behavior, the structure is exposed to a plane wave, and the phase of the incident and the reflected waves are compared. In these cases, a single unit cell is modeled, and through the use of Periodic Boundary Conditions (PBCs) this cell is repeated infinitely.

By using Ansoft High Frequency Structure Simulator (HFSS) full-wave simulation software [29], simulation settings show in Fig. 2.6(a) (b). Fig. 2.6(a) is vertical top view of using four 1-D EBG unit cells toward -x direction, Fig. 2.6(b) is the side view of

A-A' cross-plane. The top side of Fig. 2.6 (a) is port1, and the bold line represent PEC plane, dotted line represent PMC plane. Because of the boundary conditions of PEC planes, the metal structures mirror and the unit cells repeat infinitely on the PEC sides.

Whereas the boundary conditions of PMC plane assure the TEM surface wave. These settings are designed to fulfill periodic structure and plane wave feeding. It is important that the simulated result of Fig. 2.6 is identical to the simulated result of one unit cell.

The reason for setting four unit cells instead of one is to confirm that the asymmetric unit cell can also be repeated periodically and infinitely by this EM simulation setting.

(a)

(b)

Figure 2.6: The settings of 1-D EBG structure simulation: (a) top view (b) A-A’ side view.

PEC  PEC 

PMC

PMC

E i

y E i x

L L

ground

x z

E i

PEC PEC

A A’

E r

PEC

In next chapter, we will design a GSM (824MHz- 960MHz) antenna as an application of 1-D EBG structure, so we choose 880MHz as the center frequency of the EBG structure in this section. The designed parameters of the unit cell is shown in Fig.2.7, where L1 = 13.25 mm, L2= 19 mm, H1 = 4 mm, W1 = 10 mm, W2 = 1 mm, and the used substrate is FR4 with relative dielectric constant 4.4 and thickness of 0.4mm.  

Figure 2.7: The parameter settings of the unit cell of 1-D EBG structure.

In general, when a plane wave incident into a PEC plane, the reflection phase will theoretically be 180 °, and when a plane wave incident into a PMC plane, the reflection phase will be 0 °. Fig. 2.8 shows the phase of S11 and frequency response of the proposed 1-D EBG structure. At resonant frequency 880 MHz, the reflection phase of A-A’ plane equals to 0 °. This confirms that the structure is an EBG structure, thus can be regarded as a PMC plane.

The usable bandwidth of an EBG, when operating as a PMC plane, has been considered to be the frequencies over which the phase of the reflection coefficient is bounded by 90 degrees. The resonant frequency (fc) and fractional bandwidth (Fb) of 1-D EBG structure is given by formula (2.1) and (2.2):

Ground

H1 via

z

x

L1

L1

L2

W1

W2

√

(2.2)

It is well known that this in-phase reflection bandwidth for a parallel LC circuit is proportional to L/C, while the resonance frequency is proportional to√ 1/LC . Therefore, the in-phase reflection bandwidth increases due to the reduced C. And the increase in L for a specific resonance frequency has the added advantage of increasing bandwidth as smaller capacitance would be needed to achieve the same resonant frequency.

Frequency (GHz)

0.6 0.7 0.8 0.9 1.0 1.1 1.2

Phase Angle of S11 (deg)

-180 -90 0 90 180

Figure 2.8: The reflection phase of 1-D EBG structure.

The resonant frequency of 1-D EBG structure can be designed by adjusting the length or width of the elements. Fig. 2.9 to Fig. 2.12 shows the changes in reflection phase while varying L1, H1, L2, and W2.

Fig. 2.9 shows that when L1 varies from 12.25 mm to 14.25 mm, the center frequency moves from 970 MHz to 810 MHz and the bandwidth is decreasing. The resonant frequency is shifted downwards with increasing L1, since the increasing L1 will increase coupling capacitance while it does not affect the value of inductance. The increasing coupling capacitor also reduces the bandwidth of 1-D EBG structure.  Fig.

2.10 shows that when H1 varies from 3 mm to 5 mm, the center frequency moves from 938 MHz to 838 MHz and the bandwidth is increasing. The resonant frequency is also shifted downwards with increasing H1, since the longer H1 contributes to larger inductance while it does not affect the value of coupling capacitance. The lager inductance causes larger bandwidth, but also need more designing space. Fig. 2.11 shows that when L2 varies from 17 mm to 21 mm, the center frequency moves from 860 MHz to 925 MHz and the bandwidth is increasing .The resonant frequency is shifted upwards with increasing L2, since the increasing L2 contributes to increasing value of inductance and decreasing value of coupling capacitance. Although longer L2 will increase the unit cell size, the bandwidth of 1-D EBG can be improved effectively. Fig.

2.12 shows that when W2 varies from 0.5 mm to 1.5 mm, the center frequency moves from 1100 MHz to 740 MHz and the bandwidth is decreasing. The resonant frequency is shifted downwards with increasing W2. The increasing W2 contributes to the increasing coupling capacitance while it does not affect the value of inductance. Also, lager coupling capacitance causes smaller bandwidth of 1-D EBG structure.

This simulation method yields good results when studying the theoretical behavior of the 1-D EBG surface, but does not assess real situations, in which the structure is always finite in size. For example, the characteristic properties of antennas are strongly influenced by the size of the ground plane, so it is therefore important to determine how the truncation of the infinite EBG cell distribution will affect the performance. The antenna applications of 1-D EBG structure will be proposed in Chapter 3 and Chapter 4.

Frequency (GHz)

0.6 0.7 0.8 0.9 1.0 1.1 1.2

Phase Angle of S11 (deg)

-180 Figure 2.9: The reflection phase of 1-D EBG structure with H1 = 4mm, L2 = 19mm, W2=1mm and

varied L1 from 12.25 mm to 14.25 mm.

Frequency (GHz)

0.6 0.7 0.8 0.9 1.0 1.1 1.2

Phase Angle of S11 (deg)

-180

Figure 2.10: The reflection phase of 1-D EBG structure with L1 = 13.25mm, L2 = 19mm, W2=1mm and varied H1 from 3 mm to 5 mm..

Frequency (GHz)

0.6 0.7 0.8 0.9 1.0 1.1 1.2

Phase Angle of S11 (deg)

-180

Figure 2.11: The reflection phase of 1-D EBG structure with H1 = 4mm, L1 = 13.25mm, W2=1mm and varied L2 from 17 mm to 21 mm.   

Frequency (GHz)

0.6 0.7 0.8 0.9 1.0 1.1 1.2

Phase Angle of S11 (deg)

-180

Figure 2.12: The reflection phase of 1-D EBG structure with H1 = 4mm, L1 = 13.25mm, L2=19mm and varied W2 from 0.5 mm to 1.5 mm.

Chapter 3 A H IGH E FFICIENCY G ROUND -P ROXIMITY

D IPOLE A NTENNA

The 1-D EBG structure has been characterized and designed in previous chapter, and now we shift our focus to 1-D EBG applications in antenna engineering. The important property of 1-D EBG structures is the phase response to the plane wave illumination, where the reflection phase changes from 180◦ to −180◦ as the frequency increases. In this chapter, we utilize this property to improve the radiation efficiency of a dipole antenna near a ground plane.

The proposed antenna is shown in Fig. 3.1, we applied the 1-D EBG structure to the ground-proximity dipole antenna, thus the impedance matching and antenna gain degrade problem can be improved. Hence, the dipole antenna can be placed close to the high impedance surface of 1-D EBG structure on the ground plane and maintained the antenna performance. The used 1-D EBG structure will be shown briefly in section 3.1, design considerations of the dipole antenna with 1-D EBG structure are described in section 3.2, and measured results are presented in section 3.3.

Figure 3.1: A high efficiency ground-proximity dipole antenna designed using 1-D EBG structure, and the total size of antenna is 10 mm 153 mm.

153mm

10mm

Ground size :200mm × 300mm feed dipole antenna

+

-x z