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Chapter 2 Miniaturized Antennas with Wave Resonances

2.1 Spiraled Printed Inverted-F Antenna

2.1.2 Equivalent Circuit Analysis

In this section, the effect of the spiral is discussed and the circuit model is also developed for analyzing. And in Figure 2.2(a), there is a typical inverted-F antenna implemented on a printed circuit board. For this inverted-F antenna, the microstrip feed line is connected to a horizontal metal line with one end short-circuited to the ground and the other end open-circuited. The metal line and the ground plane form a quasi transmission line. It is easy to derive that as the total length of this quasi transmission line equals a quarter of wavelength, the input reactance vanishes due to the resonance of the inductor-like short-circuited line and the capacitor-like open-circuited line. The corresponding return loss simulated by the commercial EM simulator IE3D [50] is presented as the curve a in Figure 2.3(a). Here, the length of the horizontal metal line is designed as a quarter wavelength of the fundamental frequency 2.45 GHz, so that a deep resonance occurs at that frequency with return loss larger than 20 dB. It is noticed that another resonance presents at the frequency around 7.35 GHz, which is the triple of the fundamental frequency.

In order to demonstrate how the spiral works, a number of spiraled inverted-F antennas were also simulated. A set of spiraled inverted-F antennas (as Figure 2.2(a)-(d).) with the total length of the metal line kept similar and spiraled gradually were designed. The total length of the strip from short point to open end in Figure 2.2(a) is 25.5 mm. The fundamental resonant frequency of these antennas should remain about the same, which can be verified from the simulated return losses shown in the curves a-d of Figure 2.3(a). As a matter of fact, the return losses of the four antennas are all better than 15 dB, except for the variation of the bandwidth.

However, it is also found that the frequency of the second resonance becomes lower as the antenna tail is spiraled more. The second resonant frequency shrinks to about 71% (from 7.35 to 5.25 GHz) when the antenna structure is changed from the conventional PIFA of Figure 2.2(a) to the spiraled one of Figure 2.2(d).

(a) (b)

(c) (d)

Figure 2.2 Four printed inverted-F antennas with different spiraled tails. The tail lengths are kept the same for the four antennas.

1 2 3 4 5 6 7 8 9

Return Loss (dB)

25 20 15 10 5 0

a c b

d

Frequency (GHz)

0

(a)

2.2 2.3 2.4 2.5 2.6 2.7

Frequency (GHz) 50

60 70 80 90 100

Antenna Efficiency (%)

ab c d

(b)

Figure 2.3 (a)Simulated return losses, as functions of frequency, for the antennas shown in Figure 2.2.

(b)Simulated radiation efficiency, as functions of frequency, for the antennas shown in Figure 2.2.

The miniature antenna always encounters the problem of the efficiency, especially for the lower operation band. The simulation of antenna efficiency around 2.45GHz is shown in Figure 2.3(b). It can be found that the efficiency is almost the same (about 70%) for the four antennas shown in Figure 2.2. The degradation of efficiency is under 5% in the required bandwidth. It means that the additional loss induced in this miniaturized antenna design is negligible. The invariance of the efficiency may be due to that a large ground plane with length larger than a quarter wavelength is used.

(Note that the ground plane is a part of the antenna, on which the induced current contributes to the radiation performance of the antenna.) However, the bandwidth of the 2.45GHz band shown in Figure 2.3(a) becomes narrower with the smaller antenna size. This can be attributed to the increasing of antenna quality factor due to the antenna size. The efficiency of the well matched spiraled inverted-F antenna around 5.2GHz is about 50%, which is lower than that (70%) of a typical PIFA designed at the same frequency. In the 5GHz band, the proposed antenna operates at the high order mode with three quarter wavelength resonance. The current flows in the spiral with different directions, thus reducing the radiation efficiency of the antenna.

For conceptually understanding the frequency reduction effect of the second resonance, a brief equivalent circuit model for the spiraled PIFA is proposed as shown in Figure 2.4(a), where the PIFA is modeled as a short-circuited transmission line of length θ2 in shunt with a transmission line of length θ1

loaded by an effective radiation

resistance Ra. An inductor L is inserted in the end of the open-circuited transmission line in order to take account of the spiraling effect of the antenna tail and the parasitic inductance of the transmission line. In addition, a parasitic capacitor Cs shunt to respectively, of the transmission line. The admittance YL can be written as:



The input reflection coefficient Γ, or the return loss, can thus be calculated from

0

0 in in

Y Y

Y Y

Γ = −

+

. (2-3)

Feed

R

a

L

C

s

Z

o

Θ Θ Θ

1

Z

o

, Θ Θ Θ Θ

2

Y

2

Y

1

Y

L

(a)

S11(dB)

1 2 3 4 5 6 7 8 9

Frequency (GHz) -25

-20 -15 -10 -5 0

b a c

d

(b)

Figure 2.4 (a)Equivalent transmission line model for the spiraled printed inverted-F antenna.

(b)Simulated return losses of the equivalent model with Zo = 180 Ω, θ1 = 57.4o, θ2 = 18.3o, Cs = 0.13 pF, Ra = 150 Ω and L = 3.7, 6, 8, 12nH.

Figure 2.4(b) illustrates the calculated return losses, functions of frequency, for the

equivalent circuit model of the spiraled antenna. The characteristic impedance Z

o

is

180 Ω, which is about the EM-simulation value of the characteristic impedance for

the antenna’s quasi transmission line portion. The electrical length is set as θ

1

= 57.4

o

and θ

2

= 19

o

at 2.45GHz. The total electrical length is around quarter wavelength at

2.45GHz. Consider the small parasitic capacitor C

s

to be 0.19pF as fringe field. The

effective radiation resistance R

a

is around 150 Ω. The inductor L is related to the

spiraled strip, which is the dominant factor of the model. From the intuition, its

value should increase as the strip is spiraled more. However, since the inductance

caused from the spiraling is distributed in the structure, it is hard to extract from the EM simulation. In this study, this inductor was chosen as 3.7, 6, 8, and 12 nH for the antennas (a) to (d) in Figure 2.2, respectively, so as to fit the EM-simulation results (Figure 2.3 (a)) of the antennas.

One can observe from Figure 2.4(b) that in the frequency span, two resonances are generated by each circuit. The higher resonant frequency at 7.35 GHz moves towards the lower frequencies of 6.5, 6, and 5.25 GHz, although, at the same time, the lower resonant frequency is remained around 2.45 GHz. Finally the specified dual-band operation is achieved by only one resonator. The results resemble those of the spiral antennas quite well, meaning that the equivalent circuit model including the value-changing inductor does explain the frequency characteristics of the proposed dual-band antennas.