GHz. The slightly different results of the simulations and mea-surement may be due to the fabrication tolerances. In addition, theproposed dual-band bandpass filter can generate two transmissionzeros, which provide a better cut-off rate in the stopband and givemuch improved selectivity.

4. CONCLUSION

A compact dual-band BPF using meandering SIRs has been pro-posed, which has good dual-passband performance at 2.4/5.25GHz. The dual-passband characteristics are generated by properlycontrolling the impedance ratio of SIRs. The bandwidth of eachpassband could be controlled independently by tuning the couplinggap and the spur-line length. The circuit size is reduced about 50%compared with the conventional BPF with the same specifications.Finally, the simulated results are verified by our experiment of thefabricated dual-band BPF.

ACKNOWLEDGMENT

This work is partially supported by the Science Funds of ChinaU0635004 and No. 60571056, and the Science Funds of Guang-dong 07118061.

REFERENCES

1. S. Wu and B. Razavi, A 900-MHz/1.8-GHz CMOS receiver for dual-band applications, IEEE J Solid-State Circ 33 (1998), 2178–2185.

2. J. Ryynanen, K. Kivekas, J. Jussila, A. Parssinen, and K.A.I. Halonen,A dual-band RF front-end for WCDMA and GSM applications, IEEE JSolid-State Circ 36 (2001), 1198–1204.

3. L.C. Tsai and C.W. Huse, Dual-band bandpass filters using equallengthcoupled-serial-shunted lines and Z-transform techniques, IEEE TransMicrowave Theory Tech 52 (2004), 1111–1117.

4. C.-Y. Chen and C.-Y. Hsu, A simple and effective method for micros-trip dual-band filters design, IEEE Microwave Wireless Compon Lett16 (2006), 246–248.

5. C.Y. Chen, C.Y. Hsu, and H.R. Chuang, Design of miniature planardual-band filter using dual-feeding structures and embedded resonators,IEEE Microwave Wireless Compon Lett 16 (2006), 669–671.

6. M. Makimoto and S. Yamashita, Bandpass filters using parallelcoupledstripline stepped impedance resonators, IEEE Trans MicrowaveTheory Tech 28 (1980), 1413–1417.

7. T.H. Huang, H.J. Chen, C.S. Chang, L.S. Chen, Y.H. Wang, and M.P.Houng, A novel compact ring dual-mode filter with adjustable second-passband for dual-band applications, IEEE Microwave Wireless Com-pon Lett 16 (2006), 360–362.

8. M.H. Weng, H.W. Wu, and Y.K. Su, Compact and low loss dual-bandbandpass filter using pseudo-interdigital stepped impedance resonatorsfor WLANs, IEEE Microwave Wireless Compon Lett 17 (2007), 187–189.

9. Y.P. Zhang and M. Sun, Dual-band microstrip bandpass filter usingstepped-impedance resonators with new coupling schemes, IEEE TransMicrowave Theory Tech 54 (2006), 3779–3785.

© 2008 Wiley Periodicals, Inc.

FOURIER-TRANSFORM PHASECOMPARATOR FOR THEMEASUREMENT OF EXTRINSIC FABRY-PEROT INTERFEROMETRIC SENSORS

Yi JiangDepartment of Optical Engineering, Beijing Institute of Technology,Beijing 100081, China; Corresponding author: bitjy@bit.edu.cn

Received 27 January 2008

ABSTRACT: A Fourier-transform phase comparator is developed tomeasure fiber optic extrinsic Fabry-Perot interferometric sensors. Thephase comparator is realized by comparing the phases of two white-light spectra, which are obtained by scanning the wavelength of thelight source. The changes of a cavity length, which are concerned inmost applications, can be interrogated. A linear output is obtained, anda measurement resolution of 15 pm is experimentally achieved, which isvery close to the theoretical value. The technique has high resolutionand a large dynamic measurement range. In addition, the measurementis not affected by various imperfections of the sensor, light source spec-trum profile, and the loss of leading fiber and connectors. © 2008 WileyPeriodicals, Inc. Microwave Opt Technol Lett 50: 2621–2625, 2008;Published online in Wiley InterScience (www.interscience.wiley.com).DOI 10.1002/mop.23719

Key words: extrinsic fabry-perot interferometer; Fourier transform;white-light interferometry

1. INTRODUCTION

Fiber optic extrinsic Fabry-Perot interferometric (EFPI) sensorshave been intensively studied because of their many advantages,including small size, high resolution, low cost, ease of fabrication,etc [1]. White-light interferometry (WLI)-based interrogation tech-nique for EFPI sensors possesses an ability to provide absolutemeasurements, a large dynamic measurement range, immunity tooptical power fluctuation, and high resolution. Spectral-domainWLI is a recently developed technique to interrogate the cavitylength of an EFPI. Several methods have been used to obtain thespectrum of an EFPI: detecting the back-reflected light with anoptical spectrum analyzer (OSA) [2], scanning the EFPI with aswept laser [3, 4], and scanning the EFPI with a fiber Fabry-Perottunable filter (FFP-TF) [5, 6]. Several demodulation methods forretrieval of the cavity length from an optical spectrum have beenproposed. The simple method of retrieving the cavity length is byusing the peak-to-peak method to measure the wavelength spacingbetween two apexes in the spectrum, where there is a 2� phaseshift [7]. The difficulty of this method is determining the peakpositions in a white-light spectrum, because the waveform is inquasi-sine distribution, and there is great uncertainty in determin-ing the peak position. The second method is linear or quadratureoperation by keeping a �/2 phase shift between the two interfero-metric beams [6]. Although the method has high resolution, thelimited measuring range and ease of being affected by environ-

2 3 4 5 6-60

-50

-40

-30

-20

-10

0

Frequency (GHz)

Ma

gnitu

de

(dB

)

Simulation

Measurement

S21

S11

Figure 6 Simulated and measured results of proposed dual-band filter.[Color figure can be viewed in the online issue, which is available atwww.interscience.wiley.com]

DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 50, No. 10, October 2008 2621

ment and various imperfections of the sensor limit its applicationin practical engineering. The third popular method is determiningthe peak position of the main frequency component when thewhite-light optical spectrum is Fourier-transformed, and the cavitylength can be calculated by using the frequency position of themain component [5]. However the resolution is much lower thanother competitors, because the position of the main frequencycomponent is insensitive to the change of the cavity length.

Generally, we are not concerned with the absolute cavity lengthof an EFPI sensor. What we are interested in are the changes of thecavity length. For example, the initial strain is regarded as zerowhen an EFPI sensor is installed on a structure, and there is aninitial cavity length. When the EFPI sensor is under loading, andthe cavity length is changed, the strain is only reflected by thechange of the cavity length, so it is also important to measure thechanges of a cavity length. In this article, a Fourier-transformphase comparator is developed to measure the change of a cavitylength, which keeps the properties of immunity to optical powerfluctuations, large dynamic measurement range, and high resolu-tion.

2. MEASUREMENT PRINCIPLE

The spectral fringe amplitude of an EFPI for a WLI may beexpressed as [4]

g1��� � a1��� � b1���cos�4�

�d � �0� (1)

where d is the initial cavity length and 2d is the actual pathdifference, a1(�) is the background introduced by the spectralprofile of the light source, b1(�) is the contrast, which is influencedby the cavity length and the reflection of the fiber ends, and �0 isthe initial phase shift, which is introduced by the second reflectorin an EFPI. When the cavity length is changed on account of theload or temperature, the spectrum fringe becomes

g2��� � a2��� � b2���cos�4�

��d � �d� � �0� (2)

where a2(�) and b2(�) have same meaning as a1(�) and b1(�) inEq. (1). Because the cavity length is variable, and the spectrum ofthe light source and the loss of the leading fiber are all variable,a1(�) and b1(�) cannot be regarded as a fixed value. �d is thechange of the cavity length, which is interrogated in this article.

We may rewrite Eqs. (1) and (2) in the following form

g1��� � a1��� �1

2b1���exp� j�4�

�d � �0��

�1

2b1���exp� � j�4�

�d � �0�� (3)

g2��� � a2��� �1

2b2���exp� j�4�

��d � �d� � �0��

�1

2b2���exp� � j�4�

��d � �d� � �0�� (4)

Next, we compute the Fourier transform of Eqs. (3) and (4), andhave

G1� f � � A1� f � � B1� f � f1� � B1*� f � f1� (5)

G2� f � � A2� f � � B2� f � f2� � B2*� f � f2� (6)

where * denotes a complex conjugate, the uppercase letters denotethe Fourier spectrum. f1 and f2 are the carrier frequencies. f1 isdominated by the cavity length d, f2 is dominated by d � �d. Fora cavity length of d, the carrier frequency f can be obtained fromthe equation

f �2d

�2 (7)

For a Fourier spectrum, the actual position of the carrier frequencyis the product of f divided by k, where k � fs/N, fs is samplingfrequency, and N is the sampled data amount. If the cavity lengthis significantly large, the carrier frequencies f1 and f2 become muchlarger than the spread of the spectra caused by the variation ofa1(�), a2(�), b1(�), and b2(�), so the three spectra in Eqs. (5) and(6) are separated by the carrier frequency. We select one spectrumB1� f � f1� from Eq. (5) and B2� f � f2� from Eq. (6) by aband-pass filter, respectively. Then we compute the inverse Fou-rier transform of B1� f � f1� and B2� f � f2� , and obtain theanalytic signals

h1��� �1

2c1b1���exp� j�4�

�d � �0�� (8)

h2��� �1

2c2b2���exp� j�4�

��d � �d� � �0�� (9)

where c1 and c2 are the additional multiplying factors introducedduring Fourier transform. Then we calculate a complex logarithmas below

h3��� � ln�h1��� � h2*���� � ln�c1c2

4b1���b2���� � j

4�

��d

� ���� � j���� (10)

where

���� � ln�c1c2

4b1���b2����

���� �4�

��d (11)

Now we have the phase �(�) in the imaginary part, which isseparated from the unwanted background a1(�) and a2(�), ampli-tude variation b1(�) and b2(�), and initial phase �0. The imaginarypart of Eq. (10) gives the principle value of the phase change withmodulo 2�, and the phase �(�) is wrapped into the range [��,��]. So, there are discontinuities with 2� phase jumps in �(�).This wrapped phase is corrected by using a phase unwrappingalgorithm. Then, a measurement of a large phase change exceeding2� can be realized. However, when scanning the wavelength from�1 to �2, we obtain a phase change Dj(�), so the change of thecavity length is actually obtained from the equation

�d ��1�2

4���1 � �2������ (12)

2622 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 50, No. 10, October 2008 DOI 10.1002/mop

3. EXPERIMENTS

To verify the effectiveness of the Fourier-transform phase com-parator, we made an EFPI sensor with a cavity length of 1417 m.The experimental set-up is shown in Figure 1. A sawtooth wave istriggered by a computer to drive a fiber Fabry-Perot tunable filter(FFP-TF) (Micron Optics). The FFP-TF has a free spectrum range(FSR) of 65 nm, and finesses of 200, so the bandwidth of theFFP-TF is 0.325 nm. The wavelength-swept light is divided intotwo beams. One beam is injected into an EFPI, and the reflectedlight detected by PD1 is the white-light spectrum signal. Anotherbeam is injected into an etalon combined with a fiber Bragg grating(FBG), and the transmission light is detected by PD0. The etalonwith fixed wavelength has a FSR of 0.8 nm (100 GHz), and finesseof 14. The wavelength thermal stability of the etalon is better than0.7 GHz from 0 to 70°C, and the wavelength accuracy is betterthan 10 pm. The FBG with bandwidth of 0.7 nm is used to eraseone of the peaks in the spectrum of the etalon. Then the other peaksin the spectrum of the etalon with fixed wavelength can be iden-

tified by this mark. The fixed wavelengths of the etalon are used tocalibrate the output wavelength of the FFP-TF because of the largehysteresis caused by the piezoelectric transducer in the FFP-TF.After the spectra of EFPI and etalon are sampled into a computer,the wavelength calibration is first performed to change the spec-trum of EFPI from sampling sequence to wavelength sequence byusing the spectrum of etalon. Then a digital resample is performedto obtain the optical spectrum of the EFPI with wavelength spacingof 1 pm. Then we obtain the datum array, in which the wavelengthspacing between two adjacent points is 1 pm. This technique hasbeen described in detail in our other literature [8].

The EFPI was mounted on an one-dimensional translationstage, with a resolution of 2 m. The cavity length can be adjustedover a large spatial range by moving the stage manually. At theinitial cavity length (1417 m), a white-light spectrum fringe wasobtained by scanning the FFP-TF. This signal was used as g1(�) inEq. (1). Then the cavity was elongated by 300 m, and thewhite-light spectrum fringe was used as g2(�) in Eq. (2). The twospectrum signals are shown in Figure 2, where the x-coordinate isthe array index, and the sampling interval is 1 pm, covering awavelength range from 1525.5 to 1564.5 nm. So the x-coordinatein Figure 2 is actually the wavelength with a wavelength spacingof 1 pm. The Fourier spectra of the two signals are shown in Figure3. In each Fourier spectrum, one main component was selected bya band-pass filter. The main component was inverse Fourier trans-formed. Thus we obtained two analytic signals shown as in Figure4. By using Eqs. (10) and (12), we obtained the change of thephase difference between the two signals caused by scanning thewavelength, as shown in Figure 5. Then the change of the cavitylength was calculated to be 299.98 m, in this example, by usingthe proposed phase comparator. This technique has a distinct meritthat the instrumentation factors, including various imperfections of

Figure 1 Schematic diagram of the experimental set-up

Figure 2 Two spectrum signals at different cavity lengths: (a) thespectrum at initial cavity length, (b) the spectrum when the EFPI iselongated. The wavelength spacing between two adjacent points is 1 pm,and wavelength range covers from 1524.6 to 1565.4 nm. The spectrumwhen the EFPI is elongated. [Color figure can be viewed in the onlineissue, which is available at www.interscience.wiley.com]

Figure 3 The Fourier spectra of the two signals: (a) at initial cavitylength, (b) at a cavity length when the EFPI is elongated

DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 50, No. 10, October 2008 2623

the sensor, light source spectrum profile, and the loss of the leadingfiber and connectors, have no impact on the result. All these factorsare described as a1(�), a2(�), b1(�), b2(�), and �0 in Eqs. (1) and(2), and they are all to be removed during the demodulationprocess. This merit was verified by an experiment in which thedemodulated result had no change even if the light source wasreplaced with another one when obtaining g2(�).

During another experiment, in which the cavity length was2500 m, the cavity length was reduced by 30 m from the initialvalue. Then the cavity length was increased by 60 m in six stepsby adjusting the translation stage. At each step, 100 measurementswere performed at a sampling rate of 0.3 Hz. The total change ofthe cavity length was 60 m, and the measured results are shownin Figure 6, in which the change of the cavity length is quite in

agreement with the actual value.To evaluate the resolution of the measurement, 1000 measure-

ments were carried out over duration of 50 min at the last stepwhen the change of the cavity length was varied from �30 to 30m. As shown in Figure 7(a), the variation was limited to 0.3m, and the standard deviation was calculated to be 0.1 m. Weowe the large variation in experimental results to the environmen-tal mechanical vibration (such as vibration, air flow, acoustic,temperature etc.) and hysteresis of the PZT in an FFP-TF. Thevariation can be decreased greatly by doing an average calculation.In Figure 7(a), the data are divided into 10 sections, and eachsection has 100 data. The data in each section are averaged and theaveraged datum is used as the result of one measurement. We canobtain 10 data in all from Figure 7(a), as shown in Figure 7(b). The

Figure 4 The Filtered signals, (a) at initial cavity length, (b) at a cavitylength when the EFPI is elongated by 300 m. [Color figure can be viewedin the online issue, which is available at www.interscience.wiley.com]

Figure 5 The phase change caused by scanning the wavelength. [Colorfigure can be viewed in the online issue, which is available at www.interscience.wiley.com]

Figure 6 Result of the evaluation of the sensor’s cavity length at sevenlevels. [Color figure can be viewed in the online issue, which is availableat www.interscience.wiley.com]

Figure 7 The change of a cavity length over a period of 50 min, (a) acontinuous measurement of 1000 times, (b) the averaged results. [Colorfigure can be viewed in the online issue, which is available at www.interscience.wiley.com]

2624 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 50, No. 10, October 2008 DOI 10.1002/mop

variation now is calculated to be only 0.025 m, and the stan-dard deviation is 0.013 m. Considering the temperature changeduring 50-min measurement, the variation is only 15 nm.

This variation is very close to the theoretical value. For a cavitylength of 2500 m, the wavelength spacing between two apexes at1550 nm is 480 pm, where there is 2� phase shift. Because theaccuracy of the calibration wavelength of the etalon is better than 10pm, the measurement accuracy of the wavelength is assumed to bebetter than 10 pm, and it reflects a largest phase variation of 2�

480� 10 . So, in principle, the variation of a cavity length should be

16.1 nm (obtained from �d ��

4�� � ), which is very close to

the experimental result. If the length of the sensor head (not the cavitylength) is 15 mm, i.e., the distance spacing between the two fixedpoints is 15 mm when the EFPI is installed on a structure, 15-nmchange of the cavity length corresponds to a strain of 1 �, which isacceptable in most engineering applications.

4. CONCLUSIONS

In conclusion, a novel signal processing algorithm for an EFPIsensor is presented and experimentally verified. A Fourier-trans-form phase comparator is developed to measure the change of acavity length. A spectrum signal is sampled at initial cavity lengthfirst, and another spectrum signal is sampled to compare the phasewith the initial one. The changes of the cavity length, which areconcerned in most applications, can be calculated by using thepresented technique. A linear output is obtained, and a measure-ment resolution of 15 pm is experimentally achieved, which is veryclose to the theoretical value. A distinct merit of this technique isthat the measurement is not affected by various imperfections ofthe sensor, light source spectrum profile, and the loss of the leadingfiber and connector.

ACKNOWLEDGMENT

This work was supported by Program for New Century ExcellentTalents in University (NCET) of China and BIT basic researchfoundation.

REFERENCES

1. K.A. Murphy, M.F. Gunther, A.M. Vengsarkar, et al., Quadraturephase-shift, extrinsic Fabry-Perot optical fiber sensors, Opt Lett 16(1991), 273–275.

2. A.C.L. Wang, P.A. Childs, and G.D. Peng, Simultaneous demodulationtechnique for a multiplexed fiber Fizeau interferometer and fiber Bragggrating sensor system, Opt Lett 31 (2006), 23–25.

3. Y.J. Rao, X.J. Wang, T. Zhu, and X. Zhou, Demodulation algorithm forspatial-frequency-division-multiplexed fiber-optic Fizeau strain sensornetworks, Opt Lett 31 (2006), 700–702.

4. M. Han, Y Zhang, F.B. Shen, G.R. Pickrell, and A.B. Wang, Signal-processing algorithm for white-light optical fiber extrinsic Fabry-Perotinterferometric sensors, Opt Lett 29 (2004), 1736–1738.

5. C. Boulet, M. Hathaway, and D.A. Jackson, Fiber-optic-based absolutedisplacement sensor at 1500 nm by means of a variant of channeledspectrum recovery, Opt Lett 29 (2004), 1602–1604.

6. B. Yu, A.B. Wang, G.R. Pickrell, and J. Xu, Tunable-optical-filter-basedwhite-light interferometry for sensing, Opt Lett 30 (2005), 1452–1454.

7. V. Bhatia, M.B. Sen, K.A. Murphy, and R.O. Claus, Wavelength-tracked white light interferometry for highlt sensitive strain and tem-perature measurements, Electron Lett 32 (1996), 247–249.

8. Y. Jiang, High-resolution interrogation technique for an EFPI by peak-to-peak method, Accepted for publication.

© 2008 Wiley Periodicals, Inc.

ANALYSIS OF SLOT-LOADED STACKEDDISK PATCH ANTENNA

J. A. Ansari,1 Prabhakar Singh,1 Satya Kesh Dubey,1

R. U. Khan,2 and Babau R. Vishvakarma2

1 Department of Electronics and Communication, University ofAllahabad, Allahabad, India2 Department of Electronics Engineering, I. T. BHU, Varanasi 221005,India; Corresponding author: jaansari@rediffmail.com

Received 1 February 2008

ABSTRACT: In the present article circular disk loaded with slot as wellas stacking with parasitic element is analyzed in which it is found thatbandwidth of the antenna improves by loading it with slot as well as para-sitic element. The resonance frequency and matching of the antenna de-pends on slot dimensions and substrate thickness (h1 and h2). The theoreti-cal results are compared with the simulated results using IE3D. © 2008Wiley Periodicals, Inc. Microwave Opt Technol Lett 50: 2625–2629, 2008;Published online in Wiley InterScience (www.interscience.wiley.com).DOI 10.1002/mop.23738

Key words: microstrip patch antenna; circular patch antenna; slotloaded disk antenna; stacked antenna

1. INTRODUCTION

Compared with the conventional microwave antenna, microstrippatch antenna shows better properties such as small volume, light-weight, low profile, low cost, and easy to conform with the shapebut the narrow bandwidth of this kind of antenna restricts its widerapplications [1]

A lot of method has been employed to improve the bandwidthsuch as using thick substrate, substrates of low relative permittivity[2], multilayer geometry [3], multiple resonators [4–7], and slot-loaded antenna geometry [8] etc.

In the present article circular microstrip antenna has beeninvestigated. The effect of slot cut in the circular disk is analyzedby considering duality relation between dipole and slot [9] andhence the effect of narrow slot on the performance of the antennais analyzed. Further a circular disk is stacked on slot-loaded diskto study the antenna performance by varying the slot length widthalong with the thickness between driven and parasitic patch andbetween ground and driven patch. Entire investigations are carriedout using equivalent circuit model the details of which are given infollowing sections.

2. THEORETICAL CONSIDERATIONS

2.1. Analysis of Slot-Loaded Disk Microstrip AntennaDisk microstrip antenna is considered as the parallel combinationof capacitance (CP ) inductance (LP ), and resistance (RP ), thevalues of which can be defined as [10]

CP �QT

2�Rfr, (1)

LP �R

2�frQT(2)

and

RP �h2E0

2Jn2�k��

2PT(3)

DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 50, No. 10, October 2008 2625