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8.3 Design and practice of PSA

359

 

 

(a)

98 mm

L1

D1

2 mm

y

zx

98 mm

(b)

L2

2 mm

D2 y

z x

Figure 8.116 Circular loop antenna with extended line fed by (a) internal line and (b) external line ([103], copyright C 2006 IEEE).

8.3.2.4Loop antenna

A small circular loop antenna (CLA) operating at 911.25 MHz is designed for application to an RFID tag [103]. A one-wavelength and a half-wavelength CLA with a short stub are fabricated as shown in Figure 8.116, where (a) depicts an antenna with an internal stub, while (b) illustrates an antenna with an outer stub. The antenna dimensions are given in the figure. The stub increases the loop length so that the current path is increased and the diameter of the loop is reduced. The ratios of size reduction compared with a general CLA are 83% and 92%, respectively, for the one-wavelength CLA and the half-wavelength CLA. The return loss, 10 dB bandwidth, and gain are 11.9 dB, 12 MHz (1.3%), and 1.18 dBi, for the one wavelength CLA and 16.5 dB, 48 MHz (5%) and 0.58 dBi, respectively.

Another example is a square loop, but a part of the element is taken out, leaving three corners, as shown in Figure 8.117(a) [104]. Two elements are used to form a quasi-Yagi type antenna, with one element as a driver and another as a reflector, in order to produce a directional pattern as depicted in Figure 8.117(b), and consequent higher gain. The antenna is designed to install in a hand-held RFID reader as illustrated in Figure 8.117(c) for its operation in the near-field environment. The total dimensions of the antenna are 115 × 115 × 13.8 mm for operation of 433.92 MHz. The 10-dB bandwidth is 2.31 MHz (0.53%), covering the required bandwidth of 433.67–434.17 MHz for the ISO/IEC standards. When the reader is held by an operator, the radiation pattern deviates slightly

from the desired direction, the orientation of the reader, because the operators typically hold the reader at a slant. Then, the gain is 2.5 dBi at angle θ = 20(azimuth) at ϕ = 0(elevation), while 2.1 dBi at θ = 0.

The antenna radiates circular polarization and the bandwidth in terms of both

impedance and for axial ratio less than 3, is 0.58% (433.23–435.7 MHz) and 1.01% (430.5–434.9 MHz) at θ = 0and 20, respectively.

360

Design and practice of small antennas II

 

 

Feed

 

 

 

 

b: 115 mm (0.166λ)

c

c

a: 13.8 mm (0.02λ)

 

c: 115 mm (0.166λ)

 

 

 

 

 

 

 

 

 

Director

 

 

 

 

a

Feed

 

 

 

 

b

 

b

Driver

 

 

(a)

(b)

 

Director’s

direction

Desired direction

Antenna

(c)

Figure 8.117 A hand-held RFID device loaded with a two-wired broken square loop antenna ([104], copyright C 2010 IEEE).

L

L

2r2

 

 

s

2r1 V0

Figure 8.A1 A folded dipole [27b].

 

 

 

 

 

 

 

Ib(0)

 

 

 

 

(1–vi)Iu(0)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Vb

 

 

 

 

Vb

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Vu v

 

 

 

 

 

Ib(0)

iIu(0)

 

 

(a)

 

 

(a)

Figure 8.A2 Equivalent expression of a folded dipole: (a) balanced mode and (b) unbalanced mode [27b].

Appendix I

By folding an antenna structure, the input impedance depends on the ratio νi of the current distributions on the antenna elements. A folded antenna of length 2L is modeled as depicted in Figure 8A.1 [27b], in which current flows on each element having radius of r1 and r2 are denoted as I1 and I2, respectively, and the driven voltage is V0. This model is equivalently divided into two parts as shown in Figure 8A.2; one is a balanced

8.3 Design and practice of PSA

361

 

 

I2

I1

b

a

I3 I1 = I1 I2

Figure 8.A3 Current distributions at the feed point of the folded dipole connected with a coaxial cable [27b].

mode shown in (a), on which the currents Ib(0) flow on both elements [I(0) : current at the driven terminals] and the driven voltage is Vb. The other part is an unbalanced mode shown in (b), on which current flow on one element is Iu1 = (1 – νi) I(0) and on other element is Iu2 = νi I(0), respectively, and the driven voltage is Vu. Relationships between these voltages are given by

2(1 νi )Vb + Vu = V0 ·

(A8.1)

2νi Vb + Vu = 0

 

From this

Vb = V0

/2

(A8.2)

 

·

Vu = νi V0

Then, input impedance Zin of the antenna is given by

Zin = V0/[νi Iu (0) + Ib(0)]

= 1/[(Zu i ) 1 + 2Zb 1]

(A8.3)

where Zu = Vu/Iu (0) and Zb = Vb/Ib.

When two elements have the same radius, νi = 1/2.

Appendix II

When a coaxial cable is directly connected to a folded dipole as shown in Figure 8A.3, current I1 flowing into the dipole from the inner conductor of the coax returns to the coax as the sum of the current I2, current at the opposite terminal of the dipole, and I3, current on the outer conductor of the coax, which is equal to the difference of currents I1 and I2 [27b]. This is equivalently rewritten as a model shown in Figure 8A.4(a). This model is further divided into two modes; A and B, respectively, as Figure 8A.4(b) and (c) show. In each mode, the following relationships exist, by

362

Design and practice of small antennas II

 

 

 

 

 

 

2L

 

 

 

 

 

 

 

 

 

 

 

 

V0

 

 

 

 

 

 

V0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2

 

 

 

 

d

i

 

 

 

 

 

 

d

 

 

2

 

 

 

 

i

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

V0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

b

 

 

 

 

 

 

 

 

 

 

 

 

b

 

 

 

 

 

 

 

bb

 

 

 

 

b

 

 

a

 

 

 

 

b

 

 

a

 

 

 

 

 

 

a

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I1 I2

 

 

 

 

 

 

I1 I2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I1 + I2

 

 

 

 

 

 

 

 

 

 

 

2

 

 

 

 

 

2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

=

 

 

 

 

 

 

 

 

 

 

+

 

 

 

 

 

 

2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I1

I2

 

 

 

 

 

 

 

 

 

 

 

 

 

I1 I2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

c

 

 

 

 

 

 

 

 

 

c

 

 

 

 

 

 

 

 

 

 

c

 

 

 

 

 

 

 

 

(a)

 

 

 

(b)

 

 

 

 

 

 

 

 

 

 

 

 

(c)

 

0

 

d

 

0

 

 

 

 

 

 

 

 

i

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(b, a)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

b

 

 

 

 

 

 

 

a

 

 

a

 

 

 

 

 

 

 

 

 

 

 

I1 I2

 

 

 

I1 I2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2

 

 

 

2

 

 

 

 

V0

 

 

 

 

 

 

V0

I1 + I2

 

 

 

 

I1 + I2

I1 I2

 

 

 

 

2

 

 

2

 

 

 

 

2

 

 

 

 

 

 

 

 

 

 

c

 

 

 

 

 

 

 

 

 

c

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(b)

 

 

 

(c)

Figure 8.A4 Current and voltage at the feed point of a folded dipole (a) original mode, (b) and (b ) A mode, and (c) and (c ) B mode [27b].

using Za and Zb, impedances of A mode and B mode, respectively, seen at the terminals b–d,

V0/2 = (I1

I2)/Za for A mode,

(A8.4)

V0 = (I1

·

+ I2)Zb/2 for B mode.

 

From these,

 

 

(I1 I2) = V0/(2Za )

(A8.5)

(I1 + I2) = V0/(Zb/2)·

When the length of antenna L is a half wavelength, that is, one side is a quarter wavelength, Za becomes infinite, then I1 = I2 = I, and (I1 + I2)/2 = I. This means that the current on the outer conductor of the coax (I1 I2) disappears, and the same current I flows in and out from the coax, implying that a balun is not required. This is the

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