Comparison between analytical and neural approaches for multibias small signal modeling of microwave-scaled FETs

MHz), therefore, the path A should be lengthen, namely, the

size of the antenna will be increased accordingly for GSM

(880–960 MHz) operation. Thus, by using a capacity load

(antenna 2), the dimension of the antenna is reduced by 28%.

The radiation patterns of the fabricated antenna were meas-

ured at 900, 1800, and 2450 MHz, which are shown in Figure 7.

It can be seen that the radiation patterns at the three resonant

frequencies showed omnidirectional patterns in H-plane. Figure

8 shows the measured maximum gain of the proposed antenna,

which were about 2.6 dBi over GSM900 band, 3.2 dBi over

DCS/PCS band, and 3.5 dBi over WLAN/WiMAX band.

4. CONCLUSIONS

A design of planar sleeve monopole antenna with a concav-

ity sleeve and a capacity load has been proposed. The broad-

band performance to meet the requirements of GSM, DCS,

PCS, WLAN (2400–2484 MHz), and WiMAX (2500–2690

MHz) bands are achieved. The dimension of the antenna is

reduced largely by using the capacity load. Because of to its

omnidirectional radiation pattern, the antenna has wide

and potential applications for wireless communication

applications.

REFERENCES

1. Y.X. Guo, M.Y. Chia, and Z.N. Chen, Miniature built-in quadband

antennas for mobile handsets, IEEE Antennas Wireless Propag Lett

2 (2004), 30–32.

2. I. Ang, Y.X. Guo, and Y.W. Chia, Compact internal quad-band

antenna for mobile phones, Microwave Opt Technol Lett 38

(2003), 217–223.

3. B.K. Yu, B. Jung, H.J. Lee, F.J. Harackiewicz, and B. Lee, A

folded and bent internal loop antenna for GSM/DCS/PCS operate

of mobile handset applications, Microwave Opt Lett 48 (2006),

463–467.

4. B.S. Yildirim, Low-profile and planar antenna suitable for WLAN/

Bluetooth and UWB applications, IEEE Antennas Wireless Propag

Lett 5 (2006), 438–441.

5. W.I. Kwak, S.O. Park, and J.S. Kim, A folded planar inverted-F

antenna for GSM/DCS/Bluetooth triple-band application, IEEE

Antennas Wireless Propag Lett 5 (2006), 18–21.

6. W.C. Lu, Broadband dual frequency cross shaped slot CPW-feed

monopole antenna for WLAN operation, Microwave Opt Technol

Lett 46 (2005), 353–355.

7. J. Jung, W. Choi, and J. Choi, A small wideband microstrip-fed

monopole antenna, IEEE Microwave Wireless Compon Lett 4

(2005), 703–705.

8. Z.N. Low, J.H. Cheong, and C.L. Law, Low cost PCB antenna for

UWB application, Antennas Wireless Propag Lett 4 (2005),

237–239.

9. Y.J. Cho, S.H. Hwang, and S.O. Park, Printed antenna with folded

non-uniform meanderline for 2.4/5 GHz WLAN bands, Electron

Lett 41 (2005), 786–788.

10. D.C. Chang, M.Y. Liu, and C.H. Lin, A CPW-fed U type monop-

ole antenna for UWB application, In: Proceedings of the IEEE AP-

S International Symposium Digest, Washington, DC, July 3–8,

Vol. 2A, 2005, pp. 512–515.

11. S.H. Hwang, J.I. Moon, W.I. Kwak, and S.O. Park, Printed com-

pact dual band antenna for 2.4 and 5 GHz ISM band applications,

Electron Lett 40 (2005), 786–788.

12. J. Liang, C.C. Chiau, X. Chen, and C.G. Parini, Study of aprinted

circular disc monopole antenna for UWB systems, IEEE Trans

Antennas Propag 53 (2005), 3500–3504.

VC 2010 Wiley Periodicals, Inc.

COMPARISON BETWEEN ANALYTICALAND NEURAL APPROACHES FORMULTIBIAS SMALL SIGNAL MODELINGOF MICROWAVE-SCALED FETS

Zlatica Marinkovic,1 Giovanni Crupi,2 Alina Caddemi,2

and Vera Markovic11 Faculty of Electronic Engineering, University of Nis, AleksandraMedvedeva 14, 18000 Nis, Serbia; Corresponding author:[email protected] Dipartimento di Fisica della Materia e Ingegneria Elettronica,University of Messina, Salita Sperone 31, 98166 Messina, Italy

Received 24 December 2009

ABSTRACT: Small signal models of microwave field-effect transistors

(FETs) can be obtained by using different modeling techniques. Thisarticle considers two techniques: an analytical approach based onequivalent circuit representation and an optimization approach based on

artificial neural networks. Both of the approaches are applied to extractmultibias models of scaled microwave FETs. A comprehensive

comparison of both techniques considering different modeling aspects isgiven. VC 2010 Wiley Periodicals, Inc. Microwave Opt Technol Lett

52:2238–2244, 2010; Published online in Wiley InterScience (www.

interscience.wiley.com). DOI 10.1002/mop.25432

Key words: analytical extraction; artificial neural networks; FET;scattering parameters; small signal model

1. INTRODUCTION

Accurate and reliable modeling of microwave transistors is a

key issue in the computer-aided design of microwave circuits.

This article refers to small signal modeling which is the first

step in characterization of a microwave transistor and helpful to

be performed before further building of the device noise and

large signal models. Since nowadays, the most popular devices

of the microwave FET family are high electron mobility transis-

tors (HEMTs), this article is dealing with small signal modeling

of these transistors; more precisely, the attention will be paid to

GaAs HEMTs. In literature, there are number of papers referring

to different small signal modeling techniques for microwave

FETs [1–10]. Most of them are the models based on a device

equivalent circuit representation [1–6]. In the last decade, the

models based on artificial neural networks (ANNs) have

appeared as a successful alternative to standard modeling

approaches [7–12]. The aim of this article is to contrast two ear-

lier proposed modeling techniques: analytical approach based on

equivalent circuit [4] and optimization approach based on ANNs

[10] and to compare them from the different aspects such as

model validity, complexity of the modeling procedure, as well

as modeling efficiency and accuracy. It should be noted that

both of the techniques are exploited to extract multibias small

signal models of scaled devices. They have been applied to on

wafer AlGaAs/GaAs HEMTs with different gate width: 100,

200, and 300 lm. This article is organized as follows: the com-

pared analytical and neural approaches are briefly described in

Section 2. The modeling results are presented and discussed in

Section 3. The final concluding remarks are given in Section 4.

2. MODELING APPROACHES

This section consists of two parts. The former is devoted for

presenting the analytical technique, while the latter is focused

on illustrating the neural technique. Particular attention is given

to illustrate the advantages and disadvantages of both the

approaches.

2238 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 52, No. 10, October 2010 DOI 10.1002/mop

2.1. Analytical TechniqueThe analyzed analytical approach is based on the circuit topol-

ogy shown in Figure 1 [4]. This equivalent circuit is composed

of eight extrinsic elements (Cpg, Cpd, Lg, Ls, Ld, Rg, Rs, and Rd)

and eight intrinsic elements (Cgs, Rgs, Cgd, Rgd, gm, s, Rds, and

Cds). The extrinsic capacitances Cpg and Cpd are divided in two

parts to account for distributed phenomena, which become more

pronounced by increasing the operating frequency. The extrinsic

circuit elements, which are assumed to be bias independent, are

analytically extracted from the scattering (S) parameters under

‘‘cold’’ pinch-off condition (i.e., Vds ¼ 0 V and Vgs ¼ �1.275

V). After removing their contributions from the data, the eight

intrinsic bias–dependent elements are straightforwardly calcu-

lated at each bias point from the four complex admittance (Y)parameters of the intrinsic device section.

It should be pointed out that the analytical approach allows

obtaining an equivalent circuit representation, which offers sev-

eral advantages:

1. A deep analysis of the microwave performance of the

transistor, as the circuit elements can be clearly linked to

the physical device structure.

2. A quick estimation of the dependence of the microwave

performance on the device geometrical dimensions, by

adopting the conventional scaling rules of the circuit

elements.

3. A compact representation, as the equivalent circuit is a

very compact model because of the frequency independ-

ence of the circuit elements.

4. A trustworthy extrapolation of the small signal perform-

ance at frequencies beyond the frequency range of the

measurements, thanks to reliable commercial microwave

circuit simulators.

Furthermore, the analytical methods allow avoiding the draw-

backs of complex optimization algorithms. As a matter of fact,

the optimization results may depend on many factors such as

the starting parameter values, local minima, and optimization

method itself and, in addition, the optimization approaches may

lead to models which are physically meaningless.

2.2. Neural TechniqueANNs have appeared as a very powerful modeling tool for a

range of problems in the field of microwaves, thanking to their

ability to learn from the presented data and to generalize (to

give correct output for the input values not presented to an

ANN during its learning process) [11]. Among other applica-

tions, the ANNs have been applied for modeling of microwave

transistors (small and large signal modeling as well as noise

modeling). Here, the small signal scalable bias-dependent mod-

eling purely based on ANNs is considered, Figure 2. It is an

improvement of the model proposed in Ref. 10. To ensure high

modeling accuracy, the S-parameters are modeled by separate

ANNs. The ANNs used for this purpose are multilayer percep-

tron ANNs consisting of layers of neurons (network basic units).

The neurons are grouped into layers: an input layer, an output

layer, as well as one or more hidden layers. There are no con-

nections among the neurons in a layer, but each neuron from a

layer is connected to all neurons from the next layer. Thresholds

of the neuron activation functions and the neuron connection

weights are parameters which have to be optimized during the

process of network learning (known as training) to make the

network outputs simulate the target values accurately.

Inputs of the considered model, i.e., inputs of each ANN are:

the device gate width, gate-to-source voltage, drain-to-source

voltage, and frequency. The model outputs are real and imagi-

nary parts of all four S-parameters (eight outputs in total).

Model development starts by S-parameter measurements for a

certain number of combinations of four input parameters. These

measured data are further used as the target data for the ANN

training. As far as the training of an ANN is considered, as the

number of neurons in hidden layers cannot be determined a pri-

ori, ANNs with different number of hidden neurons are trained,

the modeling accuracy is tested, and the ANN giving the best

modeling results is chosen as the final one. If the training is

properly done, the trained ANN is able to predict accurate out-

puts for all combinations of the input parameters lying in the

same ranges as the input values used for the training. Each

ANN can be represented by a set of mathematical expressions;

therefore, the set of the expressions corresponding to the trained

ANNs constituting the proposed model can be used in standard

microwave simulators for determining the S-parameters of the

modeled devices in a wide range of the input parameters.

The advantages of the ANN model are the following:

1. A single model for all three modeled devices (closed form

mathematical expressions);

2. The model allows high accuracy prediction of S-parame-

ters; it is a black-box type model trained using measured

data; therefore, all effects contributing to the device

behavior are included in the model;

3. The measured data are necessary for the model develop-

ment only; once the model is developed, the S-parameters

of the modeled devices are obtained simply by calculating

response of the ANNs; and

4. The model development is independent of frequency

range; the frequency range of the model is determined by

the frequency range of the data supplied for ANN training

purpose.

3. RESULTS AND COMPARISON

Both of the modeling approaches described in the previous sec-

tion were applied to on-wafer AlGaAs/GaAs HEMTs with dif-

ferent gate width 100, 200, and 300 lm. The models were

Figure 1 Small signal equivalent circuit for FET

Figure 2 Neural model

DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 52, No. 10, October 2010 2239

developed from the S-parameters of these devices measured

with an Agilent E8364A precision network analyzer. For each

device, the measurements were done in 101 points over the fre-

quency range extending from 0.5 up to 50 GHz at 546 different

bias points (0 V < Vds < 2.5 V with 100-mV step and 1.5 V <Vgs < 0 V with 75-mV step).

As far as the analytical model is concerned, the details about

model development as well as values of the equivalent circuit

elements are given in Ref. 4. At this point, it should be noted

that all measurement data were used for model development.

For the neural model development, two subsets of the meas-

ured data set were used. The data set used for the training of the

ANNs corresponds to 42 bias points (Vgs ¼ {�1.35 V, �1.05

V, �0.75 V, �0.45 V, �0.15 V, 0 V} and Vds ¼ {0 V, 0.2 V,

0.8 V, 1.2 V, 1.8 V, 2.1 V, 2.5 V}). The other dataset (the test

set) was used for the model generalization test; it corresponds to

34 bias points (Vgs ¼ {�1.5 V, �1.2 V, �0.9 V, �0.6 V, �0.3

V, 0 V} and Vds ¼ {0 V, 0.5 V, 1 V, 1.5 V, 2 V, 2.5 V}), with

excluded data corresponding to bias points included in the train-

ing set: (0 V, 0 V), (0 V, 2.5 V), (�1.5 V, 0 V), and (�1.5 V,

2.5 V). The S-parameters were modeled by separate ANNs. For

the S11 and S22, a single ANN is used to model both real and

imaginary parts of each parameter. However, for the two other

parameters, S21 and S12, due to their more complicated behavior,

the real and imaginary parts of a parameter were modeled by

separate ANNs. Therefore, the model consists of two two-output

ANNs and four one-output ANNs. Each ANN was trained sepa-

rately. Among the trained ANNs with different number of the

hidden neurons, the ANN exhibiting the best modeling accuracy

was chosen for inclusion in the final model. It was found that

each of the chosen ANNs has two hidden layers with 25 neurons

per layer, except the ANN modeling imaginary part of S12,which has 21 neuron in the first hidden layer and 20 neurons in

the second hidden layer. The mathematical expressions describ-

ing these ANNs were implemented in a microwave simulator

and the simulation results were compared with the measured

results as well as with the results obtained by the developed an-

alytical model.

For the purpose of comparing simulated and the measured S-parameters at each particular bias point, the percentage errors Eij

were calculated as follows:

TABLE 1 Percentage Errors Between Simulated andMeasured S-Parameters at Vgs 5 20.6 V and Vds 5 2 V

Device 100 lm 200 lm 300 lm

Analytical model

E11 (%) 10.1 7.5 5.0

E21 (%) 10.1 7.7 10.7

E12 (%) 8.9 6.1 7.8

E22 (%) 5.4 5.6 3.5

ETOT (%) 8.6 6.7 6.8

Neural model

E11 (%) 1.8 2.2 1.7

E21 (%) 4.3 6.0 6.3

E12 (%) 9.5 6.0 9.4

E22 (%) 1.7 2.0 1.8

ETOT (%) 4.3 4.1 4.8

Figure 3 Analytical model (lines) versus measured values (symbols) at Vgs ¼ �0.6 V and Vds ¼ 2 V: (a) S11, (b) S21, (c) S12, and (d) S22

2240 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 52, No. 10, October 2010 DOI 10.1002/mop

Eij½%� ¼ 1

Nf

X100

SijMEASUREDðf Þ � SijSIMULATEDðf ÞSijMEASUREDðf Þ

����

���� (1)

where Nf represents the number of frequency points per a bias

point, which is 101 in the present case.

The total percentage error ETOT between model simulations

and measurements was obtained by averaging the evaluated

errors of the four S-parameters:

ETOT ¼ ðE11 þ E21 þ E12 þ E22Þ=4 (2)

In Table 1, there are the percentage errors calculated for

each of three HEMT devices at the bias point Vgs ¼ �0.6 V

and Vds ¼ 2 V. In addition, real and imaginary parts of the S-pa-rameters simulated by the analytical and neural models are

given in Figures 3 and 4, respectively, and compared with the

measured values. It can be observed that good agreement

between the simulated and measured data was achieved by both

of the models. However, in the case of the neural model, the

errors are lower or at least comparable to the errors correspond-

ing to the analytical model. Moreover, it should be noted that

this bias point was not included in the training of the neural

model ANNs, which indicates that the neural model shows very

good generalization.

To compare further the accuracy of the models, the percent-

age errors of the S-parameters were calculated for each of 546

bias points and the corresponding three-dimensional plots for

the 100-lm device are given in Figure 5 (analytical model) and

in Figure 6 (neural model). Comparing the plots, it can be con-

firmed that, generally, the neural model gives lower percentage

errors. Once again, it would be worthwhile to mention that in

the case of the neural model, although the measured data for

only 42 bias points were used for the model development, low

percentage errors can be observed not only for the bias points

used for the model development but also for the other bias

points. However, analyzing the plots in more details, one can

observe that there are certain bias points where the percentage

errors obtained by the neural model are greater than the ones

obtained by the analytical model (especially in the case of E21

at low Vds). These high percentage errors can be explained by

the following: in a case when a parameter modeled by an ANN

has a wide range of values, even though the ANN is very well

trained, for small values of the modeled parameter, it might hap-

pen that the amount of the deviation of the ANN output from

the target value can be comparable with the target value. In that

case, the error calculated relative to the target value is high.

Actually, this occurred in the case of the S21 which exhibits at

certain bias points (e.g., under pinch-off conditions) values

extremely small compared with its high values under typical

operating conditions. On the other side, the mentioned problem

usually does not appear in the cases when the values of the pa-

rameter modeled by an ANN are small for all input values, i.e.,

have no a wide range of change, as it is the case with the S12parameter, which is small for all bias points. This can be illus-

trated by the plots given in Figure 7 showing the S21 and S12 at

Figure 4 Neural model (lines) versus measured values (symbols) at Vgs ¼ �0.6 V and Vds ¼ 2 V: (a) S11, (b) S21, (c) S12, and (d) S22

DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 52, No. 10, October 2010 2241

two bias points: one referring to high gm condition (Vgs ¼ �0.6

V, Vds ¼ 2.5 V) and the other referring to pinch-off conditions

(Vgs ¼ �1.5 V, Vds ¼ 2.3 V). It should be noted that magnitude

of S21 at the bias point referring to high gm condition is scaled

by dividing by 10 to make the figure clearer. It can be observed

that at the pinch-off bias point, although the target (measured)

values of S12 and S21 are equal, in the case of the S12, there is a

good agreement between the simulated and measured data,

which is not the case with the S21. In contrast to the neural

approach, the analytical procedure allows obtaining small values

of E21 under all investigated bias points. This can be attributed

to the fact that the equivalent circuit is extracted analytically

from the measurements at each specific bias point without

accounting for the device behavior under the other bias condi-

tion, while the neural approach is strongly based on its general-

ization capability. The equivalent circuit allows reproducing

accurately such small values of S21 at low Vds, thanks to the

small transconductance obtained analytically from the small real

part of the intrinsic Y21.

4. CONCLUSIONS

The aim of the analysis given here was to compare two model-

ing techniques of multibias S-parameters of on-wafer-scaled

FET devices: an analytical approach based on equivalent circuit

and an optimization approach based on ANNs. Both of the tech-

niques were applied to modeling of three on-wafer-scaled GaAs

HEMT transistors. Analyzing the modeling results and compar-

ing them with the measurements, it can be concluded that both

the techniques provide highly accurate models. Both the models

are valid for all tested devices (different gate width) in a wide

range of operating conditions: different frequency and bias

point. The modeling accuracy is generally better in the case of

the neural model. As it is a black-box model trained from the

measured data, all effects contributing to the device behavior

are included in the model without requiring any physical

approximation. The power of the neural model is in the fact

that, unlike the analytical model which requires measurements

of the S-parameters and calculation of the equivalent circuit ele-

ments for each bias point, the neural model requires the meas-

ured S-parameters only for a certain number of bias points; once

the model is developed, the S-parameters of the modeled devices

for any operating bias point are obtained simply by calculating

response of the ANNs. On the other hand, the analytical model

is connected with the physical device structure, and thus the

extracted equivalent circuit offers several advantages such as

being a useful feedback for a quick and reliable optimization of

the device fabrication processing. Moreover, thanking to the

mentioned connection with the physical device structure, in

some particular bias points, the analytical approach allows

obtaining percentage errors which are smaller than the values

obtained by the neural approach whose accuracy depends on the

achieved generalization capability. The decision on which of the

two models to choose depends primary on a further application

Figure 5 Bias dependence of the percentage errors obtained by the analytical approach: (a) E11, (b) E21, (c) E12, and (d) E22

2242 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 52, No. 10, October 2010 DOI 10.1002/mop

of a model. If the further application requires knowledge of the

S-parameter values and of their behavior only, the neural model

can be adopted. However, if there is a necessity for a model

linked with device physics, then the analytical model seems to

be an appropriate solution.

ACKNOWLEDGMENTS

This work was supported by ‘‘IMT-ARSEL’’ project prot.

RBIP06R9X5 with financial support by Italian MIUR and ‘‘CMO-

GAN’’ project through the contribution of the Italian Ministero

degli Affari Esteri, Direzione Generale per la Promozione e la

Figure 6 Bias dependence of the percentage errors obtained by the neural approach: (a) E11, (b) E21, (c) E12, and (d) E22

Figure 7 Neural model (lines) versus measured data (symbols) at high gm (Vgs ¼ �0.6 V and Vds ¼ 2.5 V) and under pinch-off conditions

(Vgs ¼ �1.5 V and Vds ¼ 2.3 V): (a) S21 and (b) S12

DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 52, No. 10, October 2010 2243

Cooperazione Culturale. The work was also supported by the pro-

ject No. TR-11033 of the Serbian Ministry of Science and Techno-

logical Development.

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nini, A new millimeter wave small signal modeling approach for

pHEMTs accounting for the output conductance time delay, IEEE

Trans Microwave Theory Tech 56 (2008), 741-746.

6. G. Crupi, D.M.M.-P. Schreurs, and A. Caddemi, On the small sig-

nal modeling of advanced microwave FETs: A comparative study,

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7. P.M. Watson, M. Weatherspoon, L. Dunleavy, and G.L. Creech,

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using artificial neural networks, In: Proceedings of Gallium Arse-

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MD, 1998, pp. 95–98.

8. V. Markovic, O. Pronic, and Z. Marinkovic, Noise wave modeling

of microwave transistors based on neural networks, Microwave

Opt Technol Lett 41 (2004), 294-297.

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low-noise microwave transistors based on neural networks, Int J

RF Microwave CE 15 (2005), 567-577.

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able modeling of microwave FETs based on artificial neural net-

works, Microwave Opt Technol Lett 48 (2006), 1932-1936.

11. Q.J. Zhang and K.C. Gupta, Neural networks for RF and micro-

wave design, Artech House, Norwood, MA, 2000.

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VC 2010 Wiley Periodicals, Inc.

SMALL-SIZE INTERNAL EIGHT-BANDLTE/WWAN MOBILE PHONE ANTENNAWITH INTERNAL DISTRIBUTED LCMATCHING CIRCUIT

Kin-Lu Wong,1 Wei-Yu Chen,1 Chun-Yih Wu,2 and Wei-Yu Li21 Department of Electrical Engineering, National Sun Yat-SenUniversity, Kaohsiung 80424, Taiwan; Corresponding author:[email protected] Information and Communications Research Laboratories,Industrial Technology Research Institute, Hsinchu 31040, Taiwan

Received 25 December 2009

ABSTRACT: A coupled-fed planar inverted-F antenna (PIFA) to bemounted at the small no-ground portion of the system circuit board ofthe mobile phone with a low profile of 10 mm to the system ground

plane and a thin profile of 3 mm to the system circuit board ispresented. The proposed small-size PIFA is formed by a simple structure

of two radiating strips of different lengths, both capacitively fed by acoupling feed and short circuited to the system ground plane by ashorting strip. The coupling feed and shorting strip together function as

an internal distributed LC matching circuit, with the coupling feed as acapacitive element and the shorting strip as an inductive element. This

internal distributed LC matching circuit has an equivalent layout as theconventional external high-pass LC matching circuit with lumpedelements; both are effective in tuning the antenna’s lower band

bandwidth. In addition, the antenna with the proposed internaldistributed LC matching circuit, in this study, can lead to much widenedbandwidths in both the antenna’s lower and upper bands to cover the

698–960 and 1710–2690 MHz bands, respectively. That is, eight-bandLTE/WWAN operation can be achieved. Results of the proposed antenna

with the internal distributed LC matching circuit are presented. VC 2010

Wiley Periodicals, Inc. Microwave Opt Technol Lett 52:2244–2250,

2010; Published online in Wiley InterScience (www.interscience.

wiley.com). DOI 10.1002/mop.25431

Key words: mobile antennas; handset antennas; internal mobile phoneantennas; LTE/WWAN antennas

1. INTRODUCTION

Recently, it has been demonstrated that by using a coupling

feed, the type of planar inverted-F antenna (PIFA) with no back

ground plane for WWAN operation can have dual-resonance ex-

citation in the antenna’s lower band at about 900 MHz [1–6] or

excite its 1/8-wavelength resonant mode as the antenna’s lowest

resonant mode [7–9]. The former leads to a wide lower band to

cover the GSM850/900 operation (824–960 MHz) for the PIFA

without increasing its occupied volume, while the latter results

in a compact size for the PIFA to operate at about 900 MHz. In

the reported studies of such coupled-fed PIFAs [1–9], the design

considerations mainly focus on the coupling feed only; tuning

the shorting strip to incorporate with the coupling feed to

achieve much widened bandwidths of the PIFA is not included

in the study.

In this article, we propose that the coupling feed and the

shorting strip together can be considered as an internal distrib-

uted LC matching circuit for the coupled-fed PIFAs. That is, the

coupling feed can be treated as a capacitive element, while the

shorting strip is considered as an inductive element [10, 11].

More specifically, this internal distributed LC matching circuit

has an equivalent layout as the conventional external high-pass

LC matching circuit with lumped elements [12–15] (see Fig. 2),

which is effective in tuning the antenna’s lower band bandwidth.

In the internal distributed matching circuit, the equivalent capac-

itance and inductance in the matching circuit can be adjusted by

tuning the dimensions of the coupling feed and the shorting

strip. The obtained bandwidths of the proposed PIFA can then

be effectively widened.

By applying the design concept of the proposed internal dis-

tributed LC matching circuit to the PIFA with a simple structure

of two radiating strips of different lengths, large bandwidths in

both the antenna’s lower and upper bands are easily achieved.

The operating bands of 698–960 MHz (LTE700/GSM850/900)

and 1710–2690 MHz (GSM1800/1900/UMTS/LTE2300/2500)

have been obtained for the proposed PIFA with a thin profile of

3 mm and a low profile of 10 mm to be mounted at the small

no-ground portion of the system circuit board of the mobile

phone. Notice that the LTE operation [16, 17] in the 700 MHz

(698–787 MHz), 2300 MHz (2305–2400 MHz), and 2500 MHz

bands (2500–2690 MHz) is recently introduced, which can pro-

vide better mobile broadband and multimedia services than the

existing WWAN operation including the GSM (GSM850/900,

824–960 MHz and GSM1800/1900, 1710–1990 MHz) and

UMTS (1920–2170 MHz) [18]. This makes the eight-band LTE/

WWAN operation in the 698–960 and 1710–2690 MHz bands

2244 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 52, No. 10, October 2010 DOI 10.1002/mop