Now, let us consider the reflector elements on each wall. After the spacing between the wall and the driving element has been determined, the dimensions of the wall are obtained. As shown in Fig. 4.4, the circumference of the rectangular loop is about one wavelength of the operating frequency; moreover, the length of the rectangular loop must longer than the width due to the requirement of response on the vertically polarized electromagnetic waves. The length and width of the center loop, (L
lp1
, Wlp1
), are 36 mm and 18 mm, respectively. Then, the length and width of the side loops, (Llp2
, Wlp2
), are 18 mm and 7mm, respectively. The center larger loop operates at 2.45 GHz, and the two side loops are responsible for 5.25 GHz. The current distribution on those reflectors changes with the switch states, so their frequency responses are quite different. Besides, there is a small spacing between the vertical line and horizontal line. This results from the unwanted interaction between them when they are connected together. It will be discussed later. The points, a and b, connect the center point of the horizontal line and the end point of the vertical line with a switch mounted on the backside of the wall.38
(a) (b)
(c) (d)
(e) (f)
Fig. 4.5. The induced current distribution on the reflecting loops (a) at 2.45 GHz. (b) at 5.25 GHz. (c) at 2.45 GHz (d) at 5.25 GHz when the switch is impassable. (e) at 2.45 GHz (f) at 5.25 GHz when the switch is passable.
In the beginning, consider about a single center large rectangular loop and two side rectangular loops without the transmission lines. As shown in Fig. 4.5(a), due to the symmetry of the center loop and about one-wavelength circumference of the loop, resonant current nulls appear at the top and bottom center of the loop, and the peak
39
Port 1Port 2
Reflecting structure
k
E
PEC Port 1
Port 2
Reflecting structure
k
E
Port 1Port 2
Reflecting structure
k
E
PEC
Fig. 4.6. The simulation model for designing dual-band switchable FSS structures.
current shows at the center of the arms at both side. Then, the re-radiated fields excited from the resonant current would cancel the incoming waves at the backside of the reflector while generate a wave propagating toward the opposite direction. Hence, the reflector reflects the incident waves. For 5.25 GHz, as shown in Fig. 4.5(b), the operating principle is the same as mentioned.
Next, let us think that two control lines exist in our schematics. Consider the control line for 2.45 GHz first. As shown in Fig. 4.5(c), a short control line connects the bottom middle point of the center loop. When the vertically polarized waves are incident, an open-circuit condition shows at the end of the line if the switch is impassible. In comparison with the wavelength of 2.45 GHz, its length is quite short. As a result, a nearly open-circuit condition appears at the bottom center point of the loop, which keeps the resonant current distribution. Hence, the center loop can reflect the vertically polarized incident waves as the one without the control line. For 5.25 GHz, due to the goal that reflectors for both frequencies can be controlled simultaneously, an open-circuit should exist at both ends of the horizontal control line when the switch is impassible. Due to symmetry of the line, open-circuit would appear at the middle point of the line. A one-wavelength of 5.25 GHz transmission line is needed here. According to the transmission line theory [25], through the half-wavelength transmission line from the midpoint of the
40
the center loop (b) two side loops.line to one of the ends, the induced current can be remained, as shown in Fig. 4.5(d), so the property of reflection at 5.25 GHz can exist.
On the other hand, when the switch is passable, a short-circuit condition exists at the end of the vertical control line and the midpoint of the horizontal control line. Therefore, a nearly short-circuit condition shows at the bottom center point of the center loop, and it shows at both ends of the horizontal line by a half-wavelength of 5.25 GHz transmission line. Therefore, the current distributions are destroyed, as shown in Fig. 4.5(e)(f). The levels of the induced current become weak so that the re-radiated field from them can be ignored. As a result, the incoming waves can pass through the FSS structures.
41
Fig. 4.8. The transmission coefficient curves of the reflectors for various thickness of (a) the center loop (b) two side loops.
The full-wave electromagnetic software Ansoft HFSS [26] was employed to analyze this switching reflector structures. The simulated method is shown in Fig. 4.6. Two ports excite the vertical polarized electromagnetic waves which are incident to the reflectors at the center. The boundary conditions around the structure are the perfect conducting surface under the reflector to be the ground and the radiation boundary at the other three surfaces to make it close to the conditions of the final proposed antenna. First, we define the transmission coefficient (S
21
) of the situation of no any reflector at the center as the reference. Then, we simulate the transmission coefficient with reflectors and subtract the reference from it to get the transmission coefficients of reflectors. There are some42
Fig. 4.9. The transmission coefficient curves of the reflectors for various horizontal position respect to the center point of the wall of two side loops.
1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6
Fig. 4.10. The transmission coefficient of the proposed reflector in ON-state and Off-state.
parameters except the dimensions of the loops can affect the operating frequencies and the bandwidth. As shown in Fig. 4.7, the heights, H
lp1
of the center loop and Hlp2
of the two side loops, vary with Tlp1
= 1 mm and Tlp2
= 2 mm. The resonance frequencies increase with increment of heights of the loops. Because the operating frequencies are 2.45 GHz and 5.25 GHz, Hlp1
and Hlp2
are chosen from 2 mm to 5mm and from 3mm to 9mm, respectively. In Fig. 4.8, the influences of the thickness of the loops are shown. For 2.45 GHz, Tlp1
does not affect the resonant frequency but the bandwidth in Fig. 4.8(a).Nevertheless, the influence of T