We accomplish the printed inverted-E antenna on the FR4 substrate, whose dielectric constant is 4.7, loss tangent is 0.02, and thickness is 0.8 mm. The ground size is 46.7 mm × 88.8 mm. The feeding line is 50Ω microstrip line. The EM numerical simulators used for this design are Zeland IE3D and Ansoft HFSS. Figure 3-3 shows the photography of the antenna with a size of
11 mm × 6.4 mm
. Figure 3-4 shows the simulated and measured return loss of the antenna. The 10dB bandwidth from 2.235 GHz to 2.57 GHz is 335 MHz. The measured result usually has 100 MHz downward offset to the simulated one. The result reveals that the antenna is suitable for 802.11b/g applications. Figure 3-5 shows the current density distribution of the antenna. The electrical length from the short point to the open end isλ / 4
. But because of the capacitive load, the physical length of the antenna is shorter thanλ / 4
of the EM wave propagating in the substrate. Figure 3-6 shows the measured radiation patterns of the antenna at 2.44 GHz. The maximum gain and average gain of X-Z, Y-Z and X-Y plane are listed below:X-Z plane Y-Z plane X-Y plane
Maximum Gain 0.19 dBi 2.08 dBi -1.02 dBi
Average Gain -0.97 dBi 0.04 dBi -1.84 dBi
Table 3-1: The maximum and average gain of the printed inverted-E antenna in the X-Z, Y-Z and X-Y plane at 2.44 GHz.
Y-Z plane has not only nearly 0 dBi average gain and 2.09 dBi maximum gain larger than the other two cuts but also an omni-directional radiation pattern, so Y-Z plane has the best radiation performance between the three orthogonal planes.
The printed inverted-E antenna is used for the PCMCIA (personal computer memory card international association) card. The card has a case to protect the circuits on the PCB. The case may influence the radiation performance of the antenna, so we also measure the printed inverted-E antenna with a case. The photography of the printed inverted-E antenna with a case is shown in Figure 3-7. In practice, there is still an insulating material cover above the antenna in the photography. The simulated and measured return loss is shown in Figure 3-8. The 10dB bandwidth from 2.38 GHz to 2.62 GHz is 240 MHz. We can find that the case makes the resonant frequency have additional downward offset of 40 MHz. Figure 3-9 shows the measured radiation patterns of the antenna with a case at 2.44 GHz. The maximum gain and average gain of X-Z, Y-Z and X-Y plane are listed below:
X-Z plane Y-Z plane X-Y plane
Maximum Gain -1.29 dBi 1.40 dBi 1.43 dBi
Average Gain -1.32 dBi -0.51 dBi -1.16 dBi
Table 3-2: The maximum and average gain of the printed inverted-E antenna with a case in the X-Z, Y-Z and X-Y plane at 5.77 GHz.
The case influences the radiation performance obviously. Note that the radiation patterns of Y-Z plane have several ripples because of the additional case. The gain and the radiation patterns of the X-Y plane with a case becomes better than that without a
case. The radiation patterns of the antenna with a case look like “pressed flat”. Figure 3-10 shows the measured gain as a function of the resonant frequency for the antenna without the case. The three curves imply a certain degree of each plane which has higher peak gain performance in the plane. Each curve of the three planes has little variation from 2.4 GHz to 2.4835 GHz.
3.3 Analysis
From Section 3.1, we know that the magnitude of parallel plate capacitance influences the resonant frequency of the antenna. So to change the parameter HC can vary the resonant frequency of the antenna. Figure 3-11 shows the relationship between HC and resonant frequency. When HC becomes shorter, the equivalent capacitive load becomes smaller so that the resonant frequency becomes higher. Although the increase of HC results in a lower resonant frequency or smaller antenna size, it is impossible to reduce the size without constraints. There are two reasons. One is that a larger capacitance demands a smaller inductance to resonate at the same frequency from (2-16). Smaller inductance means the shorter short-circuited transmission line or the wider width of the transmission line. It has some limitations to shorten or thin the transmission line so that the inductance has a minimum value in practical fabrication.
The other reason is Q-value of the antenna. From [15], the Q-value is defined as
2 f π
times the peak energy stored/average power radiated. Practically speaking, high Q means that the input impedance is very sensitive to the small changes in frequency.The Q definition of antenna is similar to the circuit theory. From [17], the Q of the parallel RLC resonant circuit can be expressed as
Q = ω
0RC
(3-3) whereω is the center resonant frequency of the resonator. So lager capacitance
0 induces higher Q and the bandwidth becomes narrower. The capacitive load of theprinted inverted-E antenna will cause the Q-value to rise rapidly and reduce the bandwidth of the antenna. Hence, the increasing Q with diminishing size implies a fundamental limitation on the usable bandwidth of the antenna. High Q and small bandwidth are specific limitations of small antennas.
We establish the equivalent circuit model for printed inverted-E antenna. First, we remove the capacitive load of the antenna. This structure is simulated by Zeland IE3D. The dash line of Figure 3-13 is the simulated return loss of the antenna without capacitive load. The antenna without capacitive load is actual a short printed inverted-F antenna whose resonant frequency is about 4.2 GHz. From Section 2.5, we know the equivalent circuit model of the printed inverted-F antenna is a RLC resonator. So, we use Microwave Office to simulate a RLC circuit as shown in Figure 3-12, and let the simulated return loss of the circuit fit the previously simulated return loss curve of the short printed inverted-F antenna as shown in Figure 3-13. The return loss of the antenna seems to have other resonant frequencies but the equivalent circuit does not. It is because that the non-dominant modes induce other resonant frequencies.
To fit the curve better, we can add other RLC resonators to represent the non-dominant modes but it will increase the complexity of the equivalent circuit.
To complete the equivalent circuit mode of the printed inverted-E antenna, we connect an additional capacitor to the RLC resonator and wish that can fit the previously simulated return loss curve of the printed-E antenna. But there is still impedance mismatching between two curves. In addition to the capacitor, we further shunt a resistance to the RLC resonator as shown in Figure 3-14. The fitted curve is shown in Figure 3-15. Obviously, the additional resistance behaves as the leakage current in the parallel plate capacitor. The wider bandwidth of the antenna is also cause by the non-dominant mode as well as the above discussion.
If we remove the capacitive load and only adjust the length of the open arm. We
should obtain a printed inverted-F antenna resonated in the same frequency as the printed inverted-E antenna. Figure 3-16 shows the return loss of the two antennas.
The printed inverted-F antenna is impedance mismatching even if it has the same resonant frequency. Furthermore, the open arm of the printed inverted-F antenna is almost twice as long as the one of the printed inverted-E antenna. So, the printed inverted-E antenna is a compact antenna for WLAM applications.
Figure 3-1: Geometry of the printed inverted-E antenna
CL
L l0
Figure 3-2: Equivalent capacitance of the decreased length equals the capacitive load
(a) Front side
(b) Back side Figure 3-3: Photography of the printed inverted-E antenna
Frequency (GHz)
2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0
S11 (dB)
-50 -40 -30 -20 -10 0
2.43 GHz 2.235 GHz 2.57 GHz
Figure 3-4: Simulated and measured return loss of the printed inverted-E antenna
(a) Front side (b) Back side Figure 3-5: Current density distribution of the inverted-E antenna
X-Z Plane
Figure 3-6: Measured radiation patterns of the printed inverted-E antenna at 2.44 GHz E-total
E-phi