金属环境HF RFID线圈天线频移解析解

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ZHANG AND XIE: CLOSED-FORM SOLUTION OF FREQUENCY SHIFT FOR HF RFID COIL ANTENNA IN METALLIC ENVIRONMENTS 3929

Fig. 2. Equivalent circuit of a coil antenna including source circuit,

impedance matching circuit, and resonant circuit.

orientations, located in a point above the ground with complex

 and μ values different from those of the air. Instead of apply-

ing the conventional potential formulation, the theory is based

on the transverse electric and magnetic ﬁeld components par-

allel to the ground surface (transverse to the normal direction).

The Fourier transformed ﬁelds are seen to satisfy transmission-

line equations in the normal direction with vector voltage and

current-like quantities. The distributed parallel admittance and

series impedance quantities of the transmission line as well as

the characteristic impedance and reﬂection coefﬁcient of the

wave are seen to be dyadic, whereas the propagation factor

is a scalar. The inverse Fourier transform is written in such

a form that the image sources can be identiﬁed and found to

be located in complex space in order to be properly converg-

ing [29]–[31]. Moreover, the theory has been developed step

by step toward the most general volume current source case.

In this paper, the idea of MCRM is proposed based on the

exact image theory.

In this section, many symbols are used to accomplish the-

oretical analysis. Moreover, the symbols used to describe the

equivalent image model which is proposed based on image

theory have subscript “m.” Table I depicts main symbols used

for equations derivation and their notations.

Fig. 1 illustrates the HF RFID coil antenna with two typi-

cal metal plate conﬁgurations. Fig. 1(a) shows the coil antenna

with a side-placement metal plate. The metal plate is perpen-

dicular to the coil antenna, and the separation between the

metal plate and the lower edge of the coil antenna is indicated

by d.Fig.1(b) demonstrates the coil antenna with a back-

placement metal plate that is placed in parallel to the antenna,

and the separation between the antenna and the metal plate is

also indicated by d. The dimensions W ×W of metal plate are

much larger than coil antenna with radius a. The wire-radius

r is much less than the coil radius a.

A. Closed-Form Solution of Operating Frequency Shift

The equivalent circuit model of a coil antenna can be

depicted in Fig. 2. The equivalent circuit consists of source cir-

cuit, impedance matching circuit and resonant circuit. Source

circuit is composed of signal source V

and impedance of

signal source Z

, impedance matching circuit includes capac-

itances (C

, C

), and resonant circuit consists of capacitance

(a) (b)

Fig. 3. MCRM of the coil antenna with (a) side-placement metal plate and

(b) back-placement metal plate.

is too small to lower the quality factor Q of the coil antenna

without the metal plate, resistance R is introduced to broad-

band bandwidth (BW), which is inversely proportional to Q,

given by

Q =

R + R

(1)

BW =

(2)

where ω

is resonant angular frequency denoted by (3) for the

coil antenna without the metal plate. Moreover, the operating

frequency ω of HF RFID coil antenna is usually set to be

consistent with its resonant frequency to improve the coupling

characteristics. Then, the operating frequency will shift when

this coil antenna operates in the metallic environments

√

. (3)

To study the proximity effects of metallic environments on

the performance of HF RFID antenna, the equivalent model,

MCRM, can be designed based on image theory as shown in

Fig. 3. The MCRM of the coil antenna with side-placement

metal plate is shown in Fig. 3(a), which is composed of a coil

antenna and an image coil antenna. The separation between

the right edge of the coil antenna and the left edge of the

image coil antenna is indicated by 2d. The MCRM of the

coil antenna with back-placement metal plate is shown in

Fig. 3(b), which is also composed of a coil antenna and an

image coil antenna with separation 2d. The image coil antenna

has the same geometric dimensions and structure as the coil

antenna, including the same values of lumped components. In

the MCRM of coil antenna with side-placement metal plate,

the signal source of image coil antenna is in phase with that

of the coil antenna, while the signal source of the image coil

antenna is out of phase with that of coil antenna in the MCRM

of the coil antenna with back-placement metal plate based on

image theory.

The operating frequency of the coil antenna in metallic envi-

ronments can be predicted with the help of the equivalent

circuit extracted from the MCRM. Fig. 4 illustrates the equiva-

lent circuit extracted from the MCRM of the coil antenna with

back-placement metal plate, which is composed of a coil cir-

cuit and an image coil circuit. The values of components in the

image coil circuit can be equal to corresponding components

in the coil circuit. The mutual inductance between the coil

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