Abstract

We propose and demonstrate a novel switchable microwave photonic filter based on phase modulation. Both a microwave high Q bandpass filter and a microwave notch filter with flat passband are achieved respectively. And the switchability between them by tuning the two tunable optical bandpass filters is demonstrated. We also present a theoretical model and analytical expression for the proposed scheme. A frequency response of a high Q bandpass filter with a Q factor of 327 and a rejection ratio of exceeding 42 dB, and a frequency response of a notch filter with flat passband with a rejection ratio exceeding 34 dB are experimentally obtained. The operation frequency of microwave photonic filter is around 20 GHz.

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  1. R. A. Minasian, “Photonic Signal Processing of Microwave Signals,” IEEE Trans. Microw. Theory Tech. 54(2), 832–846 (2006).
    [CrossRef]
  2. J. Capmany, B. Ortega, D. Pastor, and S. Sales, “Discrete-Time Optical Processing of Microwave Signals,” J. Lightwave Technol. 23(2), 702–723 (2005).
    [CrossRef]
  3. J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007).
    [CrossRef]
  4. J. Yao, “Microwave Photonics,” J. Lightwave Technol. 27(3), 314–335 (2009).
    [CrossRef]
  5. J. Wang, F. Zeng, and J. Yao, “All-Optical Microwave Bandpass Filter With Negative Coefficients Based on PM-IM Conversion,” IEEE Photon. Technol. Lett. 17(10), 2176–2178 (2005).
    [CrossRef]
  6. Y. Yan, S. R. Blais, and J. Yao, “Tunable Photonic Microwave Bandpass Filter With Negative Coefficients Implemented Using an Optical Phase Modulator and Chirped Fiber Bragg Gratings,” J. Lightwave Technol. 25(11), 3283–3288 (2007).
    [CrossRef]
  7. F. Zeng and J. Yao, “Investigation of Phase-Modulator-Based All-Optical Bandpass Microwave Filter,” J. Lightwave Technol. 23(4), 1721–1728 (2005).
    [CrossRef]
  8. F. Zeng, J. Wang, and J. Yao, “All-optical microwave bandpass filter with negative coefficients based on a phase modulator and linearly chirped fiber Bragg gratings,” Opt. Lett. 30(17), 2203–2205 (2005).
    [CrossRef] [PubMed]
  9. F. Zeng and J. Yao, “All-optical bandpass microwave filter based on an electro-optic phase modulator,” Opt. Express 12(16), 3814–3819 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-16-3814 .
    [CrossRef] [PubMed]
  10. X. Yi and R. A. Minasian, “Novel Multitap, Flat-Top Microwave Photonic Filter Based on Sinusoidal Group Delay Gratings,” J. Lightwave Technol. 26(15), 2578–2583 (2008).
    [CrossRef]
  11. D. B. Hunter and R. A. Minasian, “Photonic Signal Processing of Microwave Signals Using an Active-Fiber Bragg-Grating-Pair Structure,” IEEE Trans. Microw. Theory Tech. 45(8), 1463–1466 (1997).
    [CrossRef]
  12. R. A. Minasian, K. E. Alameh, and E. H. W. Chan, “Photonics-Based Interference Mitigation Filters,” IEEE Trans. Microw. Theory Tech. 49(10), 1894–1899 (2001).
    [CrossRef]
  13. F. Zeng and J. Yao, “Frequency Domain Analysis of Fiber Bragg Grating Based phase Modulation to Intensity Modulation Conversion,” Proc. SPIE 5971, 594–601 (2005).
  14. F. Coppinger, S. Yegnanarayanan, P. D. Trinh, and B. Jalali, “All-Optical RF Filter Using Amplitude Inversion in a Semiconductor Optical Amplifier,” IEEE Trans. Microw. Theory Tech. 45(8), 1473–1477 (1997).
    [CrossRef]
  15. E. Xu, X. Zhang, L. Zhou, Y. Zhang, Y. Yu, X. Li, and D. Huang, “Ultrahigh-Q microwave photonic filter with Vernier effect and wavelength conversion in a cascaded pair of active loops,” Opt. Lett. 35(8), 1242–1244 (2010).
    [CrossRef] [PubMed]
  16. J. Capmany, B. Ortega, and D. Pastor, “A Tutorial on Microwave Photonic Filters,” J. Lightwave Technol. 24(1), 201–229 (2006).
    [CrossRef]
  17. J. Capmany, J. Cascón, J. L. Martín, S. Sales, D. Pastor, and J. Martí, “Synthesis of Fiber-Optic Delay Line Filters,” J. Lightwave Technol. 13(10), 2003–2012 (1995).
    [CrossRef]
  18. E. C. Heyde and R. A. Minasian, “A Solution to the Synthesis Problem of Recirculating Optical Delay Line Filters,” IEEE Photon. Technol. Lett. 6(7), 833–835 (1994).
    [CrossRef]
  19. E. H. W. Chan, K. E. Alameh, and R. A. Minasian, “Photonic Bandpass Filters With High Skirt Slectivity and Stopband Attenuatuon,” J. Lightwave Technol. 20(11), 1962–1967 (2002).
    [CrossRef]
  20. J. Capmany, J. Cascón, D. Pastor, and B. Ortega, “Reconfigurable Fiber-Optic Delay Line Filters Incorparating Electrooptic and Electroabsorption Modulators,” IEEE Photon. Technol. Lett. 11(9), 1174–1176 (1999).
    [CrossRef]
  21. E. H. W. Chan and R. A. Minasian, “Reflective Amplified Recirculating Delay Line Bandpass Filter,” J. Lightwave Technol. 25(6), 1441–1446 (2007).
    [CrossRef]

2010

2009

2008

2007

2006

R. A. Minasian, “Photonic Signal Processing of Microwave Signals,” IEEE Trans. Microw. Theory Tech. 54(2), 832–846 (2006).
[CrossRef]

J. Capmany, B. Ortega, and D. Pastor, “A Tutorial on Microwave Photonic Filters,” J. Lightwave Technol. 24(1), 201–229 (2006).
[CrossRef]

2005

2004

2002

2001

R. A. Minasian, K. E. Alameh, and E. H. W. Chan, “Photonics-Based Interference Mitigation Filters,” IEEE Trans. Microw. Theory Tech. 49(10), 1894–1899 (2001).
[CrossRef]

1999

J. Capmany, J. Cascón, D. Pastor, and B. Ortega, “Reconfigurable Fiber-Optic Delay Line Filters Incorparating Electrooptic and Electroabsorption Modulators,” IEEE Photon. Technol. Lett. 11(9), 1174–1176 (1999).
[CrossRef]

1997

F. Coppinger, S. Yegnanarayanan, P. D. Trinh, and B. Jalali, “All-Optical RF Filter Using Amplitude Inversion in a Semiconductor Optical Amplifier,” IEEE Trans. Microw. Theory Tech. 45(8), 1473–1477 (1997).
[CrossRef]

D. B. Hunter and R. A. Minasian, “Photonic Signal Processing of Microwave Signals Using an Active-Fiber Bragg-Grating-Pair Structure,” IEEE Trans. Microw. Theory Tech. 45(8), 1463–1466 (1997).
[CrossRef]

1995

J. Capmany, J. Cascón, J. L. Martín, S. Sales, D. Pastor, and J. Martí, “Synthesis of Fiber-Optic Delay Line Filters,” J. Lightwave Technol. 13(10), 2003–2012 (1995).
[CrossRef]

1994

E. C. Heyde and R. A. Minasian, “A Solution to the Synthesis Problem of Recirculating Optical Delay Line Filters,” IEEE Photon. Technol. Lett. 6(7), 833–835 (1994).
[CrossRef]

Alameh, K. E.

E. H. W. Chan, K. E. Alameh, and R. A. Minasian, “Photonic Bandpass Filters With High Skirt Slectivity and Stopband Attenuatuon,” J. Lightwave Technol. 20(11), 1962–1967 (2002).
[CrossRef]

R. A. Minasian, K. E. Alameh, and E. H. W. Chan, “Photonics-Based Interference Mitigation Filters,” IEEE Trans. Microw. Theory Tech. 49(10), 1894–1899 (2001).
[CrossRef]

Blais, S. R.

Capmany, J.

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

J. Capmany, B. Ortega, and D. Pastor, “A Tutorial on Microwave Photonic Filters,” J. Lightwave Technol. 24(1), 201–229 (2006).
[CrossRef]

J. Capmany, B. Ortega, D. Pastor, and S. Sales, “Discrete-Time Optical Processing of Microwave Signals,” J. Lightwave Technol. 23(2), 702–723 (2005).
[CrossRef]

J. Capmany, J. Cascón, D. Pastor, and B. Ortega, “Reconfigurable Fiber-Optic Delay Line Filters Incorparating Electrooptic and Electroabsorption Modulators,” IEEE Photon. Technol. Lett. 11(9), 1174–1176 (1999).
[CrossRef]

J. Capmany, J. Cascón, J. L. Martín, S. Sales, D. Pastor, and J. Martí, “Synthesis of Fiber-Optic Delay Line Filters,” J. Lightwave Technol. 13(10), 2003–2012 (1995).
[CrossRef]

Cascón, J.

J. Capmany, J. Cascón, D. Pastor, and B. Ortega, “Reconfigurable Fiber-Optic Delay Line Filters Incorparating Electrooptic and Electroabsorption Modulators,” IEEE Photon. Technol. Lett. 11(9), 1174–1176 (1999).
[CrossRef]

J. Capmany, J. Cascón, J. L. Martín, S. Sales, D. Pastor, and J. Martí, “Synthesis of Fiber-Optic Delay Line Filters,” J. Lightwave Technol. 13(10), 2003–2012 (1995).
[CrossRef]

Chan, E. H. W.

Coppinger, F.

F. Coppinger, S. Yegnanarayanan, P. D. Trinh, and B. Jalali, “All-Optical RF Filter Using Amplitude Inversion in a Semiconductor Optical Amplifier,” IEEE Trans. Microw. Theory Tech. 45(8), 1473–1477 (1997).
[CrossRef]

Heyde, E. C.

E. C. Heyde and R. A. Minasian, “A Solution to the Synthesis Problem of Recirculating Optical Delay Line Filters,” IEEE Photon. Technol. Lett. 6(7), 833–835 (1994).
[CrossRef]

Huang, D.

Hunter, D. B.

D. B. Hunter and R. A. Minasian, “Photonic Signal Processing of Microwave Signals Using an Active-Fiber Bragg-Grating-Pair Structure,” IEEE Trans. Microw. Theory Tech. 45(8), 1463–1466 (1997).
[CrossRef]

Jalali, B.

F. Coppinger, S. Yegnanarayanan, P. D. Trinh, and B. Jalali, “All-Optical RF Filter Using Amplitude Inversion in a Semiconductor Optical Amplifier,” IEEE Trans. Microw. Theory Tech. 45(8), 1473–1477 (1997).
[CrossRef]

Li, X.

Martí, J.

J. Capmany, J. Cascón, J. L. Martín, S. Sales, D. Pastor, and J. Martí, “Synthesis of Fiber-Optic Delay Line Filters,” J. Lightwave Technol. 13(10), 2003–2012 (1995).
[CrossRef]

Martín, J. L.

J. Capmany, J. Cascón, J. L. Martín, S. Sales, D. Pastor, and J. Martí, “Synthesis of Fiber-Optic Delay Line Filters,” J. Lightwave Technol. 13(10), 2003–2012 (1995).
[CrossRef]

Minasian, R. A.

X. Yi and R. A. Minasian, “Novel Multitap, Flat-Top Microwave Photonic Filter Based on Sinusoidal Group Delay Gratings,” J. Lightwave Technol. 26(15), 2578–2583 (2008).
[CrossRef]

E. H. W. Chan and R. A. Minasian, “Reflective Amplified Recirculating Delay Line Bandpass Filter,” J. Lightwave Technol. 25(6), 1441–1446 (2007).
[CrossRef]

R. A. Minasian, “Photonic Signal Processing of Microwave Signals,” IEEE Trans. Microw. Theory Tech. 54(2), 832–846 (2006).
[CrossRef]

E. H. W. Chan, K. E. Alameh, and R. A. Minasian, “Photonic Bandpass Filters With High Skirt Slectivity and Stopband Attenuatuon,” J. Lightwave Technol. 20(11), 1962–1967 (2002).
[CrossRef]

R. A. Minasian, K. E. Alameh, and E. H. W. Chan, “Photonics-Based Interference Mitigation Filters,” IEEE Trans. Microw. Theory Tech. 49(10), 1894–1899 (2001).
[CrossRef]

D. B. Hunter and R. A. Minasian, “Photonic Signal Processing of Microwave Signals Using an Active-Fiber Bragg-Grating-Pair Structure,” IEEE Trans. Microw. Theory Tech. 45(8), 1463–1466 (1997).
[CrossRef]

E. C. Heyde and R. A. Minasian, “A Solution to the Synthesis Problem of Recirculating Optical Delay Line Filters,” IEEE Photon. Technol. Lett. 6(7), 833–835 (1994).
[CrossRef]

Novak, D.

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

Ortega, B.

J. Capmany, B. Ortega, and D. Pastor, “A Tutorial on Microwave Photonic Filters,” J. Lightwave Technol. 24(1), 201–229 (2006).
[CrossRef]

J. Capmany, B. Ortega, D. Pastor, and S. Sales, “Discrete-Time Optical Processing of Microwave Signals,” J. Lightwave Technol. 23(2), 702–723 (2005).
[CrossRef]

J. Capmany, J. Cascón, D. Pastor, and B. Ortega, “Reconfigurable Fiber-Optic Delay Line Filters Incorparating Electrooptic and Electroabsorption Modulators,” IEEE Photon. Technol. Lett. 11(9), 1174–1176 (1999).
[CrossRef]

Pastor, D.

J. Capmany, B. Ortega, and D. Pastor, “A Tutorial on Microwave Photonic Filters,” J. Lightwave Technol. 24(1), 201–229 (2006).
[CrossRef]

J. Capmany, B. Ortega, D. Pastor, and S. Sales, “Discrete-Time Optical Processing of Microwave Signals,” J. Lightwave Technol. 23(2), 702–723 (2005).
[CrossRef]

J. Capmany, J. Cascón, D. Pastor, and B. Ortega, “Reconfigurable Fiber-Optic Delay Line Filters Incorparating Electrooptic and Electroabsorption Modulators,” IEEE Photon. Technol. Lett. 11(9), 1174–1176 (1999).
[CrossRef]

J. Capmany, J. Cascón, J. L. Martín, S. Sales, D. Pastor, and J. Martí, “Synthesis of Fiber-Optic Delay Line Filters,” J. Lightwave Technol. 13(10), 2003–2012 (1995).
[CrossRef]

Sales, S.

J. Capmany, B. Ortega, D. Pastor, and S. Sales, “Discrete-Time Optical Processing of Microwave Signals,” J. Lightwave Technol. 23(2), 702–723 (2005).
[CrossRef]

J. Capmany, J. Cascón, J. L. Martín, S. Sales, D. Pastor, and J. Martí, “Synthesis of Fiber-Optic Delay Line Filters,” J. Lightwave Technol. 13(10), 2003–2012 (1995).
[CrossRef]

Trinh, P. D.

F. Coppinger, S. Yegnanarayanan, P. D. Trinh, and B. Jalali, “All-Optical RF Filter Using Amplitude Inversion in a Semiconductor Optical Amplifier,” IEEE Trans. Microw. Theory Tech. 45(8), 1473–1477 (1997).
[CrossRef]

Wang, J.

J. Wang, F. Zeng, and J. Yao, “All-Optical Microwave Bandpass Filter With Negative Coefficients Based on PM-IM Conversion,” IEEE Photon. Technol. Lett. 17(10), 2176–2178 (2005).
[CrossRef]

F. Zeng, J. Wang, and J. Yao, “All-optical microwave bandpass filter with negative coefficients based on a phase modulator and linearly chirped fiber Bragg gratings,” Opt. Lett. 30(17), 2203–2205 (2005).
[CrossRef] [PubMed]

Xu, E.

Yan, Y.

Yao, J.

Yegnanarayanan, S.

F. Coppinger, S. Yegnanarayanan, P. D. Trinh, and B. Jalali, “All-Optical RF Filter Using Amplitude Inversion in a Semiconductor Optical Amplifier,” IEEE Trans. Microw. Theory Tech. 45(8), 1473–1477 (1997).
[CrossRef]

Yi, X.

Yu, Y.

Zeng, F.

Zhang, X.

Zhang, Y.

Zhou, L.

IEEE Photon. Technol. Lett.

J. Wang, F. Zeng, and J. Yao, “All-Optical Microwave Bandpass Filter With Negative Coefficients Based on PM-IM Conversion,” IEEE Photon. Technol. Lett. 17(10), 2176–2178 (2005).
[CrossRef]

E. C. Heyde and R. A. Minasian, “A Solution to the Synthesis Problem of Recirculating Optical Delay Line Filters,” IEEE Photon. Technol. Lett. 6(7), 833–835 (1994).
[CrossRef]

J. Capmany, J. Cascón, D. Pastor, and B. Ortega, “Reconfigurable Fiber-Optic Delay Line Filters Incorparating Electrooptic and Electroabsorption Modulators,” IEEE Photon. Technol. Lett. 11(9), 1174–1176 (1999).
[CrossRef]

IEEE Trans. Microw. Theory Tech.

D. B. Hunter and R. A. Minasian, “Photonic Signal Processing of Microwave Signals Using an Active-Fiber Bragg-Grating-Pair Structure,” IEEE Trans. Microw. Theory Tech. 45(8), 1463–1466 (1997).
[CrossRef]

R. A. Minasian, K. E. Alameh, and E. H. W. Chan, “Photonics-Based Interference Mitigation Filters,” IEEE Trans. Microw. Theory Tech. 49(10), 1894–1899 (2001).
[CrossRef]

F. Coppinger, S. Yegnanarayanan, P. D. Trinh, and B. Jalali, “All-Optical RF Filter Using Amplitude Inversion in a Semiconductor Optical Amplifier,” IEEE Trans. Microw. Theory Tech. 45(8), 1473–1477 (1997).
[CrossRef]

R. A. Minasian, “Photonic Signal Processing of Microwave Signals,” IEEE Trans. Microw. Theory Tech. 54(2), 832–846 (2006).
[CrossRef]

J. Lightwave Technol.

J. Capmany, B. Ortega, D. Pastor, and S. Sales, “Discrete-Time Optical Processing of Microwave Signals,” J. Lightwave Technol. 23(2), 702–723 (2005).
[CrossRef]

J. Yao, “Microwave Photonics,” J. Lightwave Technol. 27(3), 314–335 (2009).
[CrossRef]

Y. Yan, S. R. Blais, and J. Yao, “Tunable Photonic Microwave Bandpass Filter With Negative Coefficients Implemented Using an Optical Phase Modulator and Chirped Fiber Bragg Gratings,” J. Lightwave Technol. 25(11), 3283–3288 (2007).
[CrossRef]

F. Zeng and J. Yao, “Investigation of Phase-Modulator-Based All-Optical Bandpass Microwave Filter,” J. Lightwave Technol. 23(4), 1721–1728 (2005).
[CrossRef]

E. H. W. Chan, K. E. Alameh, and R. A. Minasian, “Photonic Bandpass Filters With High Skirt Slectivity and Stopband Attenuatuon,” J. Lightwave Technol. 20(11), 1962–1967 (2002).
[CrossRef]

J. Capmany, B. Ortega, and D. Pastor, “A Tutorial on Microwave Photonic Filters,” J. Lightwave Technol. 24(1), 201–229 (2006).
[CrossRef]

J. Capmany, J. Cascón, J. L. Martín, S. Sales, D. Pastor, and J. Martí, “Synthesis of Fiber-Optic Delay Line Filters,” J. Lightwave Technol. 13(10), 2003–2012 (1995).
[CrossRef]

E. H. W. Chan and R. A. Minasian, “Reflective Amplified Recirculating Delay Line Bandpass Filter,” J. Lightwave Technol. 25(6), 1441–1446 (2007).
[CrossRef]

X. Yi and R. A. Minasian, “Novel Multitap, Flat-Top Microwave Photonic Filter Based on Sinusoidal Group Delay Gratings,” J. Lightwave Technol. 26(15), 2578–2583 (2008).
[CrossRef]

Nat. Photonics

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

Opt. Express

Opt. Lett.

Proc. SPIE

F. Zeng and J. Yao, “Frequency Domain Analysis of Fiber Bragg Grating Based phase Modulation to Intensity Modulation Conversion,” Proc. SPIE 5971, 594–601 (2005).

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Figures (11)

Fig. 1
Fig. 1

Experimental setup of the proposed switchable microwave photonic filter.

Fig. 2
Fig. 2

When the TOBF is blue shift or red shift (a), the envelopes of converted intensity signals are out of phase (b).

Fig. 3
Fig. 3

The formation process of a bandpass filter.

Fig. 4
Fig. 4

The formation process of notch filter with flat passband .

Fig. 5
Fig. 5

The relationship between the two TOBFs and phase modulated signal (a), and the optical spectrum before PD (b).

Fig. 6
Fig. 6

The measured and predicted results.

Fig. 7
Fig. 7

The relationship between the two TOBFs and phase modulated signal (a) and the optical spectrum before PD (b).

Fig. 8
Fig. 8

The measured and predicted results.

Fig. 9
Fig. 9

PM-IM conversion under low frequency modulation

Fig. 10
Fig. 10

The response of a microwave photonic notch filter.

Fig. 11
Fig. 11

The Q N factor of notch filter versus the Q factor of bandpass filter.

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

E ( t ) = P 0 cos ( ω c t + Δ φ ) = P 0 cos [ ω c t + π V p p 2 V π cos ( ω m t ) ] ,
E ( t ) = P 0 n = J n ( π V p p 2 V π ) cos [ ( ω c + n ω m ) t + 1 2 n π ] ,
E ( t ) = P 0 { J 0 ( π V p p 2 V π ) cos ( ω c t ) + J 1 ( π V p p 2 V π ) cos [ ( ω c + ω m ) t + 1 2 π ] + J 1 ( π V p p 2 V π ) cos [ ( ω c ω m ) t 1 2 π ] } .
E 1 ( t ) = κ P 0 { α 20 J 0 ( π V p p 2 V π ) cos ( ω c t ) + α 21 J 1 ( π V p p 2 V π ) cos [ ( ω c + ω m ) t + 1 2 π ] + α 2 1 J 1 ( π V p p 2 V π ) cos [ ( ω c ω m ) t 1 2 π ] } ,
P ω m ( t ) = P 0 κ α 20 J 0 ( π V p p 2 V π ) J 1 ( π V p p 2 V π ) ( α 21 α 2 1 ) cos ( ω m t + π / 2 ) .
H 1 ( ω ) = P 0 κ α 20 J 0 ( π V p p 2 V π ) J 1 ( π V p p 2 V π ) ( α 21 α 2 1 ) e j π / 2 .
E 2 ( t ) = ( 1 κ ) ( κ ) n 1 ( G ) n P 0 { ( α 10 ) n α 20 J 0 ( π V p p 2 V π ) cos ( ω c t ) + ( α 11 ) n α 21 J 1 ( π V p p 2 V π ) cos [ ( ω c + ω m ) t + 1 2 π ] + ( α 1 1 ) n α 2 1 J 1 ( π V p p 2 V π ) cos [ ( ω c ω m ) t 1 2 π ] } ,
P ω m ( t ) = P 0 ( 1 κ ) 2 κ n 1 G n ( α 10 ) n α 20 J 0 ( π V p p 2 V π ) J 1 ( π V p p 2 V π ) · [ ( α 11 ) n α 21 ( α 1 1 ) n α 2 1 ] cos ( ω m t + π / 2 ) .
H 2 ( ω ) = n = 1 P 0 ( 1 κ ) 2 κ n 1 ( G ) n ( α 10 ) n α 20 · J 0 ( π V p p 2 V π ) J 1 ( π V p p 2 V π ) [ ( α 11 ) n α 21 ( α 1 1 ) n α 2 1 ] e j ( n ω T + π / 2 ) = P 0 ( 1 κ ) 2 J 0 ( π V p p 2 V π ) J 1 ( π V p p 2 V π ) α 10 α 20 G e j ( ω T + π / 2 ) · ( α 21 α 11 α 2 1 α 1 1 ) κ G α 10 α 11 α 1 1 ( α 21 α 2 1 ) e j ω T ( 1 κ G α 10 α 11 e j ω T ) ( 1 κ G α 10 α 1 1 e j ω T ) ,
H ( ω ) = · [ H 1 ( ω ) + H 2 ( ω ) ] = P 0 κ α 20 J 0 ( π V p p 2 V π ) J 1 ( π V p p 2 V π ) ( α 21 α 2 1 ) e j π / 2 + P 0 ( 1 κ ) 2 J 0 ( π V p p 2 V π ) J 1 ( π V p p 2 V π ) α 10 α 20 G e j ( ω T + π / 2 ) · ( α 21 α 11 α 2 1 α 1 1 ) κ G α 10 α 11 α 1 1 ( α 21 α 2 1 ) e j ω T ( 1 κ G α 10 α 11 e j ω T ) ( 1 κ G α 10 α 1 1 e j ω T ) ,
z p 1 = κ G α 10 α 11
z p 2 = κ G α 10 α 1 1 ,
Q N = F S R Δ f 3 d B ,

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