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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 21 — Oct. 10, 2011
  • pp: 20580–20585
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Photonic approach to microwave frequency measurement with digital circular-code results

Xihua Zou, Wei Pan, Bin Luo, Lianshan Yan, and Yushi Jiang  »View Author Affiliations


Optics Express, Vol. 19, Issue 21, pp. 20580-20585 (2011)
http://dx.doi.org/10.1364/OE.19.020580


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Abstract

A photonic approach to measuring microwave frequency with digital results is proposed and experimentally demonstrated. In the proposed approach, N photonic phase-shifted filters with a phase shift increment of π/N in the transmission responses are designed. The filters are then employed to process the single optical sideband generated by applying a microwave signal to a single sideband suppressed-carrier (SSB-SC) modulation module, to perform frequency-to-amplitude conversion and analog-to-digital conversion simultaneously. After the implementation of power detection and decision operation to the filtered optical sideband, an N-bit result in the form of the circular code is obtained, which indicates the frequency of the microwave signal. A proof-of-concept experiment is performed to verify the proposed approach and a 5-bit circular code is generated to indicate microwave frequency up to 40 GHz.

© 2011 OSA

1. Introduction

Microwave signal characterization is of critical importance in various fields such as electronic warfare receivers, radars, and next-generation wideband communications. As for microwave signal characterization, parameters of interest include frequency, amplitude, direction of arrival, modulation format, pulse descriptor word, and so on. Among these parameters, frequency is one of the most significant parameters to be measured [1

1. B. Boashash, “Estimating and interpreting the instantaneous frequency of a signal. I. Fundamentals,” Proc. IEEE 80(4), 520–538 (1992). [CrossRef]

,2

2. B. Boashash, “Estimating and interpreting the instantaneous frequency of a signal. II. Algorithms and applications,” Proc. IEEE 80(4), 540–568 (1992). [CrossRef]

]. A variety of techniques for frequency measurement have been proposed, which can be categorized by analog results or digital outputs. With the rapid development of digital signal processing, it is desirable to realize digital frequency measurement that shows a series of advantages such as robustness of digital signal processing, easy and simple storage of digital data, and compatibility to other digital setups [3

3. J. B. Y. Tsui, Digital techniques for wideband receivers (second version) (SciTech Publishing, Inc., Raleigh, 2004).

].

In both analog techniques and digital techniques aforementioned, a large instantaneous bandwidth for “wide-open” operation is highly required, for the bandwidth coverage for microwave/millimeter-wave signals ranges from 0 to 300 GHz in electronic warfare and radars [3

3. J. B. Y. Tsui, Digital techniques for wideband receivers (second version) (SciTech Publishing, Inc., Raleigh, 2004).

]. Conventional electronic methods cannot offer such a large instantaneous bandwidth, however, microwave photonics provides a promising way to solve this issue [4

4. R. A. Minasian, “Photonic signal processing of microwave signals,” IEEE Trans. Microw. Theory Tech. 54(2), 832–846 (2006). [CrossRef]

7

7. C. Wang and J. Yao, “Photonic generation of chirped millimeter-wave pulses based on nonlinear frequency-to-time mapping in a nonlinearly chirped fiber Bragg grating,” IEEE Trans. Microw. Theory Tech. 56(2), 542–553 (2008). [CrossRef]

] due to the inherent feature of photonics in large instantaneous bandwidth. Recently, various photonic approaches have been proposed to measure the frequency of microwave signals. Microwave frequency can be discriminated from two frequency-dependent microwave power functions [8

8. L. V. T. Nguyen and D. B. Hunter, “A photonic technique for microwave frequency measurement,” IEEE Photon. Technol. Lett. 18(10), 1188–1190 (2006). [CrossRef]

12

12. Y. Wang, J. Ni, H. Chi, X. Zhang, S. Zheng, and X. Jin, “Photonic instantaneous microwave frequency measurement based on two different phase modulation to intensity modulation conversions,” Opt. Commun. 284(16-17), 3928–3932 (2011). [CrossRef]

] or two responses of microwave photonic filters [13

13. J. Zhou, S. Aditya, P. P. Shum, and J. P. Yao, “Instantaneous microwave frequency measurement using a photonic microwave filter with an infinite impulse response,” IEEE Photon. Technol. Lett. 22(10), 682–684 (2010). [CrossRef]

16

16. J. Niu, S. N. Fu, K. Xu, J. Q. Zhou, S. Aditya, J. Wu, P. P. Shum, and J. T. Lin, “Instantaneous microwave frequency measurement based on amplified fiber-optic recirculating delay loop and broadband incoherent light source,” J. Lightwave Technol. 29(1), 78–84 (2011). [CrossRef]

]. By using optical channlization [17

17. S. T. Winnall, A. C. Lindsay, M. W. Austin, J. Canning, and A. Mitchell, “A microwave channelizer and spectroscope based on an integrated optical Bragg-grating Fabry-Perot and integrated hybrid Fresnel lens system,” IEEE Trans. Microw. Theory Tech. 54(2), 868–872 (2006). [CrossRef]

,18

18. X. Zou, W. Pan, B. Luo, and L. Yan, “Photonic approach for multiple-frequency-component measurement using spectrally sliced incoherent source,” Opt. Lett. 35(3), 438–440 (2010). [CrossRef] [PubMed]

], optical mixing [19

19. N. Sarkhosh, H. Emami, L. Bui, and A. Mitchell, “Reduced cost photonic instantaneous frequency measurement system,” IEEE Photon. Technol. Lett. 20(18), 1521–1523 (2008). [CrossRef]

21

21. M. V. Drummond, C. A. F. Marques, P. P. Monteiro, and R. N. Nogueira, “Photonic instantaneous microwave frequency measurement system based on signal remodulation,” IEEE Photon. Technol. Lett. 22(16), 1226–1228 (2010). [CrossRef]

], or optical comb/edge filters [22

22. H. Chi, X. Zou, and J. P. Yao, “An approach to the measurement of microwave frequency based on optical power monitoring,” IEEE Photon. Technol. Lett. 20(14), 1249–1251 (2008). [CrossRef]

25

25. X. Zou, W. Pan, B. Luo, and L. Yan, “Photonic instantaneous frequency measurement using a single laser source and two quadrature optical filters,” IEEE Photon. Technol. Lett. 23(1), 39–41 (2011). [CrossRef]

], frequency measurement could be realized as well. In most of these photonic approaches analog results are derived, however, digital results are preferred according to the advantages of digital signal processing.

In the paper, a photonic approach with digital results is proposed for microwave frequency measurement. By using an array of phase-shifted filters, a digital circular code is generated to indicate the microwave frequency.

2. Principle

The apparatus for the proposed measurement approach is shown in Fig. 1
Fig. 1 Apparatus of the proposed approach. (PD: photo-detector)
. An incoming microwave signal is applied to externally modulate the light wave from a CW laser. Under the condition of single sideband suppressed-carrier (SSB-SC) modulation, a single optical sideband is generated and is coupled into photonic phase-shifted filters and a reference branch. The phase-shifted filters, which are the key components of the apparatus, have isomorphic transmission responses with an identical free spectral range (FSR) but different phase shifts. To understand the operation of the proposed system, we start from the discussions on the transmission responses of the phase-shifted filters.

Firstly, it is well known that the transmission response of a two-tap delay-line interferometer (i.e., a comb filter) can be expressed as F(f)=[1+cos(2πf/FSR+θ0)]/2, where f is the optical frequency, FSR is the free spectral range, and θ0 is the initial phase. As the frequency of the laser is set to be the reference value (i.e., f0) of the optical frequency coordinate, the transmission response can be rewritten as F(fm)=[1+cos(2πfm/FSR+θ0)]/2, where fm=ff0 is the microwave frequency to be measured and also the offset frequency from the optical carrier. A number of comb filters with discrete phase shifts following a linear distribution as Δθk=(k1)π/N are designed, to meet the requirement of the circular encoding. Namely, a phase shift increment of π/N is introduced to the transmission responses. Therefore, the transmission response of the k-th filter is derived as
Fk(fm)=1+cos[2πfm/FSR+θ0+(k1)π/N]2,1kN,
(1)
where k and N represent the order and the total number of the phase-shifted filters. At the output of each filter, the power of the single optical sideband filtered is detected by a power meter, so we have
Pk(fm)=P01+cos[2πfm/FSR+θ0+(k1)π/N]2,
(2)
where P0 is the power of the reference branch. It is clear from Eq. (2) that the frequency information is converted to an optical power. Via a comparison between the output power of the k-th filter and that of the reference branch, an optical power ratio can be derived as

Rk(fm)=1+cos[2πfm/FSR+θ0+(k1)π/N]2.
(3)

Based on the power ratio, an analog-to-digital conversion can be done. For the k-th filter, the output bit is labeled as “1” if the power ratio is not less than 0.5; otherwise, the bit is encoded as “0”. Therefore, we obtain an N-bit circular-code result which indicates the frequency value. An unambiguous measurement range of full FSR and a resolution of FSR/(2N) are realized. Note that the function of the phase-shifted filters is twofold, to perform frequency-to-amplitude conversion and analog-to-digital conversion.

A demonstration of the above principle is clearly shown in Fig. 2
Fig. 2 Demonstration of the transmission responses and the power ratios when N = 8.
when N = 8. From Eqs. (1) and (3), eight phase-shifted transmission responses or eight power ratios are present. The FSR is divided into sixteen sub-ranges, each of which corresponds to a resolution of FSR/16 in the frequency domain or to a relative phase shift of π/8 in the phase domain. Then 8-bit digits in the form of the circular code [25

25. X. Zou, W. Pan, B. Luo, and L. Yan, “Photonic instantaneous frequency measurement using a single laser source and two quadrature optical filters,” IEEE Photon. Technol. Lett. 23(1), 39–41 (2011). [CrossRef]

] are obtained for all sub-ranges as the threshold is specified as 0.5 for the decision operation.

3. Experiment and results

An experiment for obtaining digital measurement results is performed. To begin with, five phase-shifted filters are designed using a single high-birefringence (Hi-Bi) element. As shown in Fig. 3(a)
Fig. 3 (a) Design configuration for the phase-shifted filters and the distribution of (b) the detected optical powers and (c) the derived power ratios.
, a Hi-Bi element in conjunction with five branches is employed. When the optical sideband is linearly polarized at an angle of 45° with respect to one principal axis of the Hi-Bi element, identical FSRs are achieved for all five branches or filters, due to the use of the same differential group delay. On the other hand, at each branch an independent polarization controller is used to adjust the polarization angle and the initial phase of the optical sideband. Thus phase-shifted transmission responses are generated at the outputs of the five branches.

The SSB-SC modulation is implemented via the use of a carrier suppression setup in conjunction with an optical pass filter having a very narrow transition band. The optical filter removes the + 1st or the −1st sideband and a single optical sideband is generated after the external modulation [25

25. X. Zou, W. Pan, B. Luo, and L. Yan, “Photonic instantaneous frequency measurement using a single laser source and two quadrature optical filters,” IEEE Photon. Technol. Lett. 23(1), 39–41 (2011). [CrossRef]

]. A microwave signal with its frequency sweeping within the range of 14~40 GHz, is applied to the modulation module. Here the upper boundary is limited by the bandwidth of the modulator and the lower one is limited by the SSB-SC modulation. The optical powers detected at the outputs of the five branches and the reference branch, are depicted in Fig. 3(b).

4. Discussions

The encoding efficiency, the sensitivity, and the stability of the proposed approach and of the experiment are discussed here with more details.

Digital circular-code results with a code length of 2N are generated in the proposed approach and the experiment, which is regarded as a simple and minimum-error encoding way. On the one hand, compared with the Gray code or the natural binary code with a code length of 2N, the encoding efficiency here is lower. For instance, the number of effective bits for the 5-bit circular-code results in the experiment is 3.32. On the other hand, the circular code is much easier to be implemented for the digital frequency measurement since the phase-shifted filters with identical FSRs can be designed using the same Hi-Bi element. While for the Gray code or the natural binary code results, filters with several exactly multiplied FSRs are required, which are more practically difficult to develop.

The sensitivity and the dynamic range are mostly determined by the half-wave voltage of the employed electro-optic modulator (MPZ-LN). To ensure measurement errors to be less than 0.2 GHz, the minimum power of the microwave signal should be greater than –40.2 dBm while Vπ=7V. Meanwhile, the maximum power should be less than −5.6 dBm to make sure that the 2nd sidebands are too small to be detected by the optical power-meter. Thus the dynamic range of the frequency measurement is 34.6 dB.

The stability of the experiment setup would suffer from the drift of the phase shifts under the influence of environment. For simplicity, we investigate the influence of the temperature on the stability of the phase shifts. The discrete phase shifts are set by detecting the optical power at the output of each filter, when no external modulation is implemented. For instance, a maximum power or half maximum power corresponds to a phase shift of 0 or π/3, respectively. In order to avoid encoding errors, in the experiment setup a drift less than 0.01π should be ensured such that a temperature stability of ±2.6Kis required. This temperature stability can be achieved using a commercially available temperature controller. Also, the wavelength of the laser source can be synchronously tuned to compensate the drift of all the phase shifts using the feedback from temperature change, to enable a stable frequency measurement. In addition, the stability of the phase-shifted filters can be improved using other solutions, such as the use of a photonic-crystal fiber with low temperature-dependent birefringence coefficient or the use of the photonic integrated circuits or commercial tunable interferometers.

5. Summary

In conclusion, with the use of photonic phase-shifted filters, an approach having digital circular-code results has been proposed and verified for microwave frequency measurement. When the discrete phase shifts of the N transmission responses are specified as (k1)π/N, N-bit circular codes were generated. The measurement range and the resolution were FSR and FSR/(2N), respectively. An experiment with 5-bit circular-code outputs was implemented to measure the frequency up to 40 GHz. In addition, the stability, the sensitivity, and the encoding efficiency are discussed.

Acknowledgments

The work was supported by National Natural Science Foundation of China (61101053, 71090402/G01), “973” Project (2012CB315704), Research Fund for the Doctoral Program of Higher Education of China (20100184120007, Funding for Priority Areas), and Fundamental Research Funds for the Central Universities (SWJTU09CX033, SWJTU10ZT05).

References and links

1.

B. Boashash, “Estimating and interpreting the instantaneous frequency of a signal. I. Fundamentals,” Proc. IEEE 80(4), 520–538 (1992). [CrossRef]

2.

B. Boashash, “Estimating and interpreting the instantaneous frequency of a signal. II. Algorithms and applications,” Proc. IEEE 80(4), 540–568 (1992). [CrossRef]

3.

J. B. Y. Tsui, Digital techniques for wideband receivers (second version) (SciTech Publishing, Inc., Raleigh, 2004).

4.

R. A. Minasian, “Photonic signal processing of microwave signals,” IEEE Trans. Microw. Theory Tech. 54(2), 832–846 (2006). [CrossRef]

5.

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007). [CrossRef]

6.

G. C. Valley, “Photonic analog-to-digital converters,” Opt. Express 15(5), 1955–1982 (2007). [CrossRef] [PubMed]

7.

C. Wang and J. Yao, “Photonic generation of chirped millimeter-wave pulses based on nonlinear frequency-to-time mapping in a nonlinearly chirped fiber Bragg grating,” IEEE Trans. Microw. Theory Tech. 56(2), 542–553 (2008). [CrossRef]

8.

L. V. T. Nguyen and D. B. Hunter, “A photonic technique for microwave frequency measurement,” IEEE Photon. Technol. Lett. 18(10), 1188–1190 (2006). [CrossRef]

9.

X. Zou and J. P. Yao, “An optical approach to microwave frequency measurement with adjustable measurement range and resolution,” IEEE Photon. Technol. Lett. 20(23), 1989–1991 (2008). [CrossRef]

10.

M. Attygalle and D. B. Hunter, “Improved photonic technique for radio-frequency measurement,” IEEE Photon. Technol. Lett. 21(4), 206–208 (2009). [CrossRef]

11.

B. Vidal, “Photonic-based instantaneous microwave frequency measurement with extended range,” Opt. Commun. 284(16-17), 3996–3999 (2011). [CrossRef]

12.

Y. Wang, J. Ni, H. Chi, X. Zhang, S. Zheng, and X. Jin, “Photonic instantaneous microwave frequency measurement based on two different phase modulation to intensity modulation conversions,” Opt. Commun. 284(16-17), 3928–3932 (2011). [CrossRef]

13.

J. Zhou, S. Aditya, P. P. Shum, and J. P. Yao, “Instantaneous microwave frequency measurement using a photonic microwave filter with an infinite impulse response,” IEEE Photon. Technol. Lett. 22(10), 682–684 (2010). [CrossRef]

14.

S. Pan and J. P. Yao, “Instantaneous microwave frequency measurement using a photonic microwave filter pair,” IEEE Photon. Technol. Lett. 22(19), 1437–1439 (2010). [CrossRef]

15.

S. Fu, J. Zhou, P. P. Shum, and K. Lee, “Instantaneous microwave frequency measurement using programmable differential group delay (DGD) modules,” IEEE Photon. J. 2, 967–973 (2010).

16.

J. Niu, S. N. Fu, K. Xu, J. Q. Zhou, S. Aditya, J. Wu, P. P. Shum, and J. T. Lin, “Instantaneous microwave frequency measurement based on amplified fiber-optic recirculating delay loop and broadband incoherent light source,” J. Lightwave Technol. 29(1), 78–84 (2011). [CrossRef]

17.

S. T. Winnall, A. C. Lindsay, M. W. Austin, J. Canning, and A. Mitchell, “A microwave channelizer and spectroscope based on an integrated optical Bragg-grating Fabry-Perot and integrated hybrid Fresnel lens system,” IEEE Trans. Microw. Theory Tech. 54(2), 868–872 (2006). [CrossRef]

18.

X. Zou, W. Pan, B. Luo, and L. Yan, “Photonic approach for multiple-frequency-component measurement using spectrally sliced incoherent source,” Opt. Lett. 35(3), 438–440 (2010). [CrossRef] [PubMed]

19.

N. Sarkhosh, H. Emami, L. Bui, and A. Mitchell, “Reduced cost photonic instantaneous frequency measurement system,” IEEE Photon. Technol. Lett. 20(18), 1521–1523 (2008). [CrossRef]

20.

L. A. Bui, M. D. Pelusi, T. D. Vo, N. Sarkhosh, H. Emami, B. J. Eggleton, and A. Mitchell, “Instantaneous frequency measurement system using optical mixing in highly nonlinear fiber,” Opt. Express 17(25), 22983–22991 (2009). [CrossRef] [PubMed]

21.

M. V. Drummond, C. A. F. Marques, P. P. Monteiro, and R. N. Nogueira, “Photonic instantaneous microwave frequency measurement system based on signal remodulation,” IEEE Photon. Technol. Lett. 22(16), 1226–1228 (2010). [CrossRef]

22.

H. Chi, X. Zou, and J. P. Yao, “An approach to the measurement of microwave frequency based on optical power monitoring,” IEEE Photon. Technol. Lett. 20(14), 1249–1251 (2008). [CrossRef]

23.

J. Dai, K. Xu, X. Sun, J. Niu, Q. Lv, J. Wu, X. Hong, W. Li, and J. Lin, “A simple photonic-assisted microwave frequency measurement system based on MZI with tunable measurement range and high resolution,” IEEE Photon. Technol. Lett. 22(15), 1162–1164 (2010). [CrossRef]

24.

Z. Li, B. Yang, H. Chi, X. Zhang, S. Zheng, and X. Jin, “Photonic instantaneous measurement of microwave frequency using fiber Bragg grating,” Opt. Commun. 283(3), 396–399 (2010). [CrossRef]

25.

X. Zou, W. Pan, B. Luo, and L. Yan, “Photonic instantaneous frequency measurement using a single laser source and two quadrature optical filters,” IEEE Photon. Technol. Lett. 23(1), 39–41 (2011). [CrossRef]

26.

R. van de Plassche, CMOS integrated analog-to-digital and digital-to- analog converters (2nd edition), (Boston, MA: Kluwer, 2003)

OCIS Codes
(230.0250) Optical devices : Optoelectronics
(350.4010) Other areas of optics : Microwaves
(060.5625) Fiber optics and optical communications : Radio frequency photonics
(230.7408) Optical devices : Wavelength filtering devices

ToC Category:
Optical Devices

History
Original Manuscript: July 28, 2011
Revised Manuscript: September 3, 2011
Manuscript Accepted: September 4, 2011
Published: October 3, 2011

Citation
Xihua Zou, Wei Pan, Bin Luo, Lianshan Yan, and Yushi Jiang, "Photonic approach to microwave frequency measurement with digital circular-code results," Opt. Express 19, 20580-20585 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-21-20580


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References

  1. B. Boashash, “Estimating and interpreting the instantaneous frequency of a signal. I. Fundamentals,” Proc. IEEE80(4), 520–538 (1992). [CrossRef]
  2. B. Boashash, “Estimating and interpreting the instantaneous frequency of a signal. II. Algorithms and applications,” Proc. IEEE80(4), 540–568 (1992). [CrossRef]
  3. J. B. Y. Tsui, Digital techniques for wideband receivers (second version) (SciTech Publishing, Inc., Raleigh, 2004).
  4. R. A. Minasian, “Photonic signal processing of microwave signals,” IEEE Trans. Microw. Theory Tech.54(2), 832–846 (2006). [CrossRef]
  5. J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics1(6), 319–330 (2007). [CrossRef]
  6. G. C. Valley, “Photonic analog-to-digital converters,” Opt. Express15(5), 1955–1982 (2007). [CrossRef] [PubMed]
  7. C. Wang and J. Yao, “Photonic generation of chirped millimeter-wave pulses based on nonlinear frequency-to-time mapping in a nonlinearly chirped fiber Bragg grating,” IEEE Trans. Microw. Theory Tech.56(2), 542–553 (2008). [CrossRef]
  8. L. V. T. Nguyen and D. B. Hunter, “A photonic technique for microwave frequency measurement,” IEEE Photon. Technol. Lett.18(10), 1188–1190 (2006). [CrossRef]
  9. X. Zou and J. P. Yao, “An optical approach to microwave frequency measurement with adjustable measurement range and resolution,” IEEE Photon. Technol. Lett.20(23), 1989–1991 (2008). [CrossRef]
  10. M. Attygalle and D. B. Hunter, “Improved photonic technique for radio-frequency measurement,” IEEE Photon. Technol. Lett.21(4), 206–208 (2009). [CrossRef]
  11. B. Vidal, “Photonic-based instantaneous microwave frequency measurement with extended range,” Opt. Commun.284(16-17), 3996–3999 (2011). [CrossRef]
  12. Y. Wang, J. Ni, H. Chi, X. Zhang, S. Zheng, and X. Jin, “Photonic instantaneous microwave frequency measurement based on two different phase modulation to intensity modulation conversions,” Opt. Commun.284(16-17), 3928–3932 (2011). [CrossRef]
  13. J. Zhou, S. Aditya, P. P. Shum, and J. P. Yao, “Instantaneous microwave frequency measurement using a photonic microwave filter with an infinite impulse response,” IEEE Photon. Technol. Lett.22(10), 682–684 (2010). [CrossRef]
  14. S. Pan and J. P. Yao, “Instantaneous microwave frequency measurement using a photonic microwave filter pair,” IEEE Photon. Technol. Lett.22(19), 1437–1439 (2010). [CrossRef]
  15. S. Fu, J. Zhou, P. P. Shum, and K. Lee, “Instantaneous microwave frequency measurement using programmable differential group delay (DGD) modules,” IEEE Photon. J.2, 967–973 (2010).
  16. J. Niu, S. N. Fu, K. Xu, J. Q. Zhou, S. Aditya, J. Wu, P. P. Shum, and J. T. Lin, “Instantaneous microwave frequency measurement based on amplified fiber-optic recirculating delay loop and broadband incoherent light source,” J. Lightwave Technol.29(1), 78–84 (2011). [CrossRef]
  17. S. T. Winnall, A. C. Lindsay, M. W. Austin, J. Canning, and A. Mitchell, “A microwave channelizer and spectroscope based on an integrated optical Bragg-grating Fabry-Perot and integrated hybrid Fresnel lens system,” IEEE Trans. Microw. Theory Tech.54(2), 868–872 (2006). [CrossRef]
  18. X. Zou, W. Pan, B. Luo, and L. Yan, “Photonic approach for multiple-frequency-component measurement using spectrally sliced incoherent source,” Opt. Lett.35(3), 438–440 (2010). [CrossRef] [PubMed]
  19. N. Sarkhosh, H. Emami, L. Bui, and A. Mitchell, “Reduced cost photonic instantaneous frequency measurement system,” IEEE Photon. Technol. Lett.20(18), 1521–1523 (2008). [CrossRef]
  20. L. A. Bui, M. D. Pelusi, T. D. Vo, N. Sarkhosh, H. Emami, B. J. Eggleton, and A. Mitchell, “Instantaneous frequency measurement system using optical mixing in highly nonlinear fiber,” Opt. Express17(25), 22983–22991 (2009). [CrossRef] [PubMed]
  21. M. V. Drummond, C. A. F. Marques, P. P. Monteiro, and R. N. Nogueira, “Photonic instantaneous microwave frequency measurement system based on signal remodulation,” IEEE Photon. Technol. Lett.22(16), 1226–1228 (2010). [CrossRef]
  22. H. Chi, X. Zou, and J. P. Yao, “An approach to the measurement of microwave frequency based on optical power monitoring,” IEEE Photon. Technol. Lett.20(14), 1249–1251 (2008). [CrossRef]
  23. J. Dai, K. Xu, X. Sun, J. Niu, Q. Lv, J. Wu, X. Hong, W. Li, and J. Lin, “A simple photonic-assisted microwave frequency measurement system based on MZI with tunable measurement range and high resolution,” IEEE Photon. Technol. Lett.22(15), 1162–1164 (2010). [CrossRef]
  24. Z. Li, B. Yang, H. Chi, X. Zhang, S. Zheng, and X. Jin, “Photonic instantaneous measurement of microwave frequency using fiber Bragg grating,” Opt. Commun.283(3), 396–399 (2010). [CrossRef]
  25. X. Zou, W. Pan, B. Luo, and L. Yan, “Photonic instantaneous frequency measurement using a single laser source and two quadrature optical filters,” IEEE Photon. Technol. Lett.23(1), 39–41 (2011). [CrossRef]
  26. R. van de Plassche, CMOS integrated analog-to-digital and digital-to- analog converters (2nd edition), (Boston, MA: Kluwer, 2003)

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