Abstract

A broadband linearization scheme for time-stretch analog-to-digital converters (TS-ADCs) is proposed based on an asymmetrical dual-parallel Mach-Zehnder modulator and a balanced detector. The theoretical and simulation results indicate that, compared with the differential and arcsine operation method generally employed in TS-ADCs, the proposed scheme has a superior performance on enhancing the spur-free dynamic range and suppressing the even-order distortions and the third-order spurs even under a large modulation depth. Additionally, the proposed scheme realizes online linearization. Therefore, it has the potential to enhance the dynamic range of a broadband TS-ADC in real time.

© 2016 Optical Society of America

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References

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2014 (2)

Z. Y. Zhang, H. P. Li, S. J. Zhang, and Y. Liu, “Analog-to-digital converters using photonic technology,” Chin. Sci. Bull. 59(22), 2666–2671 (2014).
[Crossref]

B. Xu, W. Lv, J. Ye, J. Zhou, X. Jin, X. Zhang, H. Chi, and S. Zheng, “Spurious-free dynamic range improvement in a photonic time-stretched analog-to-digital converter based on third-order predistrotion,” Photonics Res. 2(5), 97–101 (2014).
[Crossref]

2013 (2)

2012 (1)

C. M. Gee, G. Sefler, P. T. S. DeVore, and G. C. Valley, “Spurious-free dynamic range of a high-resolution photonic time-stretch analog-to-digital converter system,” Microw. Opt. Technol. Lett. 54(11), 2558–2563 (2012).
[Crossref]

2011 (1)

2010 (1)

S. Li, X. Zheng, H. Zhang, and B. Zhou, “Highly linear radio-over-fiber system incorporating a single-drive dual-parallel mach-zehnder modulator,” IEEE Photonics Technol. Lett. 22(24), 1775–1777 (2010).
[Crossref]

2009 (1)

A. Ferreira, T. Silveira, D. Fonseca, R. Ribeiro, and P. Monteiro, “Highly linear integrated optical transmitter for subcarrier multiplexed systems,” IEEE Photonics Technol. Lett. 21(7), 438–440 (2009).
[Crossref]

2007 (4)

2003 (1)

2001 (1)

P. W. Juodawlkis, J. C. Twichell, G. E. Betts, J. J. Hargreaves, R. D. Younger, J. L. Wasserman, F. J. O’Donnell, K. G. Ray, and R. C. Williamson, “Optically sampled analog-to-digital converters,” IEEE Trans. Microw. Theory Tech. 49(10), 1840–1853 (2001).
[Crossref]

2000 (1)

J. C. Twichell and R. Helkey, “Phase-encoded optical smapling for analog-to-digital converters,” IEEE Photonics Technol. Lett. 12(9), 1237–1239 (2000).
[Crossref]

1999 (1)

R. H. Walden, “Analog-to-digital converter survey and analysis,” IEEE. J. Sel. Areas Commun. 17(4), 539–550 (1999).
[Crossref]

1998 (1)

A. S. Bhushan, F. Coppinger, and B. Jalali, “Time-stretched analogue-to-digital convertion,” Electron. Lett. 34(11), 1081–1083 (1998).
[Crossref]

1995 (1)

J. A. Wepman, “Analog-to-digital converters and their applications in radio receivers,” IEEE Commun. Mag. 33(5), 39–45 (1995).
[Crossref]

Betts, G. E.

P. W. Juodawlkis, J. C. Twichell, G. E. Betts, J. J. Hargreaves, R. D. Younger, J. L. Wasserman, F. J. O’Donnell, K. G. Ray, and R. C. Williamson, “Optically sampled analog-to-digital converters,” IEEE Trans. Microw. Theory Tech. 49(10), 1840–1853 (2001).
[Crossref]

Bhushan, A. S.

A. S. Bhushan, F. Coppinger, and B. Jalali, “Time-stretched analogue-to-digital convertion,” Electron. Lett. 34(11), 1081–1083 (1998).
[Crossref]

Capmany, J.

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

Chi, H.

B. Xu, W. Lv, J. Ye, J. Zhou, X. Jin, X. Zhang, H. Chi, and S. Zheng, “Spurious-free dynamic range improvement in a photonic time-stretched analog-to-digital converter based on third-order predistrotion,” Photonics Res. 2(5), 97–101 (2014).
[Crossref]

Coppinger, F.

A. S. Bhushan, F. Coppinger, and B. Jalali, “Time-stretched analogue-to-digital convertion,” Electron. Lett. 34(11), 1081–1083 (1998).
[Crossref]

DeVore, P. T. S.

C. M. Gee, G. Sefler, P. T. S. DeVore, and G. C. Valley, “Spurious-free dynamic range of a high-resolution photonic time-stretch analog-to-digital converter system,” Microw. Opt. Technol. Lett. 54(11), 2558–2563 (2012).
[Crossref]

A. M. Fard, P. T. S. DeVore, D. R. Solli, and B. Jalali, “Impact of optical nonlinearity on performance of photonic time-stretch analog-to-digital converter,” J. Lightwave Technol. 29(13), 2025–2030 (2011).
[Crossref]

Fard, A. M.

A. M. Fard, S. Gupta, and B. Jalali, “Photonic time-stretch digitizer and its extension to real-time spectroscopy and imaging,” Laser Photonics Rev. 7(2), 207–263 (2013).
[Crossref]

A. M. Fard, P. T. S. DeVore, D. R. Solli, and B. Jalali, “Impact of optical nonlinearity on performance of photonic time-stretch analog-to-digital converter,” J. Lightwave Technol. 29(13), 2025–2030 (2011).
[Crossref]

Ferreira, A.

A. Ferreira, T. Silveira, D. Fonseca, R. Ribeiro, and P. Monteiro, “Highly linear integrated optical transmitter for subcarrier multiplexed systems,” IEEE Photonics Technol. Lett. 21(7), 438–440 (2009).
[Crossref]

Fonseca, D.

A. Ferreira, T. Silveira, D. Fonseca, R. Ribeiro, and P. Monteiro, “Highly linear integrated optical transmitter for subcarrier multiplexed systems,” IEEE Photonics Technol. Lett. 21(7), 438–440 (2009).
[Crossref]

Galt, S.

J. Stigwall and S. Galt, “Signal reconstruction by phase retrieval and optical backpropagation in phase-diverse photonic time-stretch systems,” J. Lightwave Technol. 25(10), 3017–3027 (2007).
[Crossref]

S. Gupta, B. Jalali, J. Stigwall, and S. Galt, “Demonstration of distortion suppression in photonic time-stretch ADC using back propagation method,” in Proceedings of IEEE International Topical Meeting on Microwave Photonics (IEEE, 2007), pp. 141–144.
[Crossref]

Gee, C. M.

C. M. Gee, G. Sefler, P. T. S. DeVore, and G. C. Valley, “Spurious-free dynamic range of a high-resolution photonic time-stretch analog-to-digital converter system,” Microw. Opt. Technol. Lett. 54(11), 2558–2563 (2012).
[Crossref]

Gu, W.

Gupta, S.

A. M. Fard, S. Gupta, and B. Jalali, “Photonic time-stretch digitizer and its extension to real-time spectroscopy and imaging,” Laser Photonics Rev. 7(2), 207–263 (2013).
[Crossref]

S. Gupta, G. C. Valley, and B. Jalali, “Distortion cancellation in time-stretch analog-to-digital converter,” J. Lightwave Technol. 25(12), 3716–3721 (2007).
[Crossref]

S. Gupta and B. Jalali, “2nd order distortion cancellation in photonic time stretch analog-to-digital converter,” in Proceedings of IEEE International Microwave Symposium digest (IEEE, 2007), pp. 229–232.
[Crossref]

S. Gupta, B. Jalali, J. Stigwall, and S. Galt, “Demonstration of distortion suppression in photonic time-stretch ADC using back propagation method,” in Proceedings of IEEE International Topical Meeting on Microwave Photonics (IEEE, 2007), pp. 141–144.
[Crossref]

Han, Y.

Hargreaves, J. J.

P. W. Juodawlkis, J. C. Twichell, G. E. Betts, J. J. Hargreaves, R. D. Younger, J. L. Wasserman, F. J. O’Donnell, K. G. Ray, and R. C. Williamson, “Optically sampled analog-to-digital converters,” IEEE Trans. Microw. Theory Tech. 49(10), 1840–1853 (2001).
[Crossref]

Helkey, R.

J. C. Twichell and R. Helkey, “Phase-encoded optical smapling for analog-to-digital converters,” IEEE Photonics Technol. Lett. 12(9), 1237–1239 (2000).
[Crossref]

Jalali, B.

A. M. Fard, S. Gupta, and B. Jalali, “Photonic time-stretch digitizer and its extension to real-time spectroscopy and imaging,” Laser Photonics Rev. 7(2), 207–263 (2013).
[Crossref]

A. M. Fard, P. T. S. DeVore, D. R. Solli, and B. Jalali, “Impact of optical nonlinearity on performance of photonic time-stretch analog-to-digital converter,” J. Lightwave Technol. 29(13), 2025–2030 (2011).
[Crossref]

S. Gupta, G. C. Valley, and B. Jalali, “Distortion cancellation in time-stretch analog-to-digital converter,” J. Lightwave Technol. 25(12), 3716–3721 (2007).
[Crossref]

Y. Han and B. Jalali, “Photonic time-stretched analog-to-digital converter: fundamental concepts and practical considerations,” J. Lightwave Technol. 21(12), 3085–3103 (2003).
[Crossref]

A. S. Bhushan, F. Coppinger, and B. Jalali, “Time-stretched analogue-to-digital convertion,” Electron. Lett. 34(11), 1081–1083 (1998).
[Crossref]

S. Gupta, B. Jalali, J. Stigwall, and S. Galt, “Demonstration of distortion suppression in photonic time-stretch ADC using back propagation method,” in Proceedings of IEEE International Topical Meeting on Microwave Photonics (IEEE, 2007), pp. 141–144.
[Crossref]

S. Gupta and B. Jalali, “2nd order distortion cancellation in photonic time stretch analog-to-digital converter,” in Proceedings of IEEE International Microwave Symposium digest (IEEE, 2007), pp. 229–232.
[Crossref]

Jiang, T.

Jin, X.

B. Xu, W. Lv, J. Ye, J. Zhou, X. Jin, X. Zhang, H. Chi, and S. Zheng, “Spurious-free dynamic range improvement in a photonic time-stretched analog-to-digital converter based on third-order predistrotion,” Photonics Res. 2(5), 97–101 (2014).
[Crossref]

Juodawlkis, P. W.

P. W. Juodawlkis, J. C. Twichell, G. E. Betts, J. J. Hargreaves, R. D. Younger, J. L. Wasserman, F. J. O’Donnell, K. G. Ray, and R. C. Williamson, “Optically sampled analog-to-digital converters,” IEEE Trans. Microw. Theory Tech. 49(10), 1840–1853 (2001).
[Crossref]

Li, H. P.

Z. Y. Zhang, H. P. Li, S. J. Zhang, and Y. Liu, “Analog-to-digital converters using photonic technology,” Chin. Sci. Bull. 59(22), 2666–2671 (2014).
[Crossref]

Li, J.

Li, S.

S. Li, X. Zheng, H. Zhang, and B. Zhou, “Highly linear radio-over-fiber system incorporating a single-drive dual-parallel mach-zehnder modulator,” IEEE Photonics Technol. Lett. 22(24), 1775–1777 (2010).
[Crossref]

Liu, Y.

Z. Y. Zhang, H. P. Li, S. J. Zhang, and Y. Liu, “Analog-to-digital converters using photonic technology,” Chin. Sci. Bull. 59(22), 2666–2671 (2014).
[Crossref]

Lv, W.

B. Xu, W. Lv, J. Ye, J. Zhou, X. Jin, X. Zhang, H. Chi, and S. Zheng, “Spurious-free dynamic range improvement in a photonic time-stretched analog-to-digital converter based on third-order predistrotion,” Photonics Res. 2(5), 97–101 (2014).
[Crossref]

Monteiro, P.

A. Ferreira, T. Silveira, D. Fonseca, R. Ribeiro, and P. Monteiro, “Highly linear integrated optical transmitter for subcarrier multiplexed systems,” IEEE Photonics Technol. Lett. 21(7), 438–440 (2009).
[Crossref]

Novak, D.

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

O’Donnell, F. J.

P. W. Juodawlkis, J. C. Twichell, G. E. Betts, J. J. Hargreaves, R. D. Younger, J. L. Wasserman, F. J. O’Donnell, K. G. Ray, and R. C. Williamson, “Optically sampled analog-to-digital converters,” IEEE Trans. Microw. Theory Tech. 49(10), 1840–1853 (2001).
[Crossref]

Ray, K. G.

P. W. Juodawlkis, J. C. Twichell, G. E. Betts, J. J. Hargreaves, R. D. Younger, J. L. Wasserman, F. J. O’Donnell, K. G. Ray, and R. C. Williamson, “Optically sampled analog-to-digital converters,” IEEE Trans. Microw. Theory Tech. 49(10), 1840–1853 (2001).
[Crossref]

Ribeiro, R.

A. Ferreira, T. Silveira, D. Fonseca, R. Ribeiro, and P. Monteiro, “Highly linear integrated optical transmitter for subcarrier multiplexed systems,” IEEE Photonics Technol. Lett. 21(7), 438–440 (2009).
[Crossref]

Sefler, G.

C. M. Gee, G. Sefler, P. T. S. DeVore, and G. C. Valley, “Spurious-free dynamic range of a high-resolution photonic time-stretch analog-to-digital converter system,” Microw. Opt. Technol. Lett. 54(11), 2558–2563 (2012).
[Crossref]

Silveira, T.

A. Ferreira, T. Silveira, D. Fonseca, R. Ribeiro, and P. Monteiro, “Highly linear integrated optical transmitter for subcarrier multiplexed systems,” IEEE Photonics Technol. Lett. 21(7), 438–440 (2009).
[Crossref]

Solli, D. R.

Stigwall, J.

J. Stigwall and S. Galt, “Signal reconstruction by phase retrieval and optical backpropagation in phase-diverse photonic time-stretch systems,” J. Lightwave Technol. 25(10), 3017–3027 (2007).
[Crossref]

S. Gupta, B. Jalali, J. Stigwall, and S. Galt, “Demonstration of distortion suppression in photonic time-stretch ADC using back propagation method,” in Proceedings of IEEE International Topical Meeting on Microwave Photonics (IEEE, 2007), pp. 141–144.
[Crossref]

Twichell, J. C.

P. W. Juodawlkis, J. C. Twichell, G. E. Betts, J. J. Hargreaves, R. D. Younger, J. L. Wasserman, F. J. O’Donnell, K. G. Ray, and R. C. Williamson, “Optically sampled analog-to-digital converters,” IEEE Trans. Microw. Theory Tech. 49(10), 1840–1853 (2001).
[Crossref]

J. C. Twichell and R. Helkey, “Phase-encoded optical smapling for analog-to-digital converters,” IEEE Photonics Technol. Lett. 12(9), 1237–1239 (2000).
[Crossref]

Valley, G. C.

C. M. Gee, G. Sefler, P. T. S. DeVore, and G. C. Valley, “Spurious-free dynamic range of a high-resolution photonic time-stretch analog-to-digital converter system,” Microw. Opt. Technol. Lett. 54(11), 2558–2563 (2012).
[Crossref]

S. Gupta, G. C. Valley, and B. Jalali, “Distortion cancellation in time-stretch analog-to-digital converter,” J. Lightwave Technol. 25(12), 3716–3721 (2007).
[Crossref]

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

Walden, R. H.

R. H. Walden, “Analog-to-digital converter survey and analysis,” IEEE. J. Sel. Areas Commun. 17(4), 539–550 (1999).
[Crossref]

Wasserman, J. L.

P. W. Juodawlkis, J. C. Twichell, G. E. Betts, J. J. Hargreaves, R. D. Younger, J. L. Wasserman, F. J. O’Donnell, K. G. Ray, and R. C. Williamson, “Optically sampled analog-to-digital converters,” IEEE Trans. Microw. Theory Tech. 49(10), 1840–1853 (2001).
[Crossref]

Wepman, J. A.

J. A. Wepman, “Analog-to-digital converters and their applications in radio receivers,” IEEE Commun. Mag. 33(5), 39–45 (1995).
[Crossref]

Williamson, R. C.

P. W. Juodawlkis, J. C. Twichell, G. E. Betts, J. J. Hargreaves, R. D. Younger, J. L. Wasserman, F. J. O’Donnell, K. G. Ray, and R. C. Williamson, “Optically sampled analog-to-digital converters,” IEEE Trans. Microw. Theory Tech. 49(10), 1840–1853 (2001).
[Crossref]

Xie, Q.

Xu, B.

B. Xu, W. Lv, J. Ye, J. Zhou, X. Jin, X. Zhang, H. Chi, and S. Zheng, “Spurious-free dynamic range improvement in a photonic time-stretched analog-to-digital converter based on third-order predistrotion,” Photonics Res. 2(5), 97–101 (2014).
[Crossref]

Ye, J.

B. Xu, W. Lv, J. Ye, J. Zhou, X. Jin, X. Zhang, H. Chi, and S. Zheng, “Spurious-free dynamic range improvement in a photonic time-stretched analog-to-digital converter based on third-order predistrotion,” Photonics Res. 2(5), 97–101 (2014).
[Crossref]

Younger, R. D.

P. W. Juodawlkis, J. C. Twichell, G. E. Betts, J. J. Hargreaves, R. D. Younger, J. L. Wasserman, F. J. O’Donnell, K. G. Ray, and R. C. Williamson, “Optically sampled analog-to-digital converters,” IEEE Trans. Microw. Theory Tech. 49(10), 1840–1853 (2001).
[Crossref]

Yu, S.

Zhang, H.

S. Li, X. Zheng, H. Zhang, and B. Zhou, “Highly linear radio-over-fiber system incorporating a single-drive dual-parallel mach-zehnder modulator,” IEEE Photonics Technol. Lett. 22(24), 1775–1777 (2010).
[Crossref]

Zhang, S. J.

Z. Y. Zhang, H. P. Li, S. J. Zhang, and Y. Liu, “Analog-to-digital converters using photonic technology,” Chin. Sci. Bull. 59(22), 2666–2671 (2014).
[Crossref]

Zhang, X.

B. Xu, W. Lv, J. Ye, J. Zhou, X. Jin, X. Zhang, H. Chi, and S. Zheng, “Spurious-free dynamic range improvement in a photonic time-stretched analog-to-digital converter based on third-order predistrotion,” Photonics Res. 2(5), 97–101 (2014).
[Crossref]

Zhang, Y. C.

Zhang, Z. Y.

Z. Y. Zhang, H. P. Li, S. J. Zhang, and Y. Liu, “Analog-to-digital converters using photonic technology,” Chin. Sci. Bull. 59(22), 2666–2671 (2014).
[Crossref]

Zheng, S.

B. Xu, W. Lv, J. Ye, J. Zhou, X. Jin, X. Zhang, H. Chi, and S. Zheng, “Spurious-free dynamic range improvement in a photonic time-stretched analog-to-digital converter based on third-order predistrotion,” Photonics Res. 2(5), 97–101 (2014).
[Crossref]

Zheng, X.

S. Li, X. Zheng, H. Zhang, and B. Zhou, “Highly linear radio-over-fiber system incorporating a single-drive dual-parallel mach-zehnder modulator,” IEEE Photonics Technol. Lett. 22(24), 1775–1777 (2010).
[Crossref]

Zhou, B.

S. Li, X. Zheng, H. Zhang, and B. Zhou, “Highly linear radio-over-fiber system incorporating a single-drive dual-parallel mach-zehnder modulator,” IEEE Photonics Technol. Lett. 22(24), 1775–1777 (2010).
[Crossref]

Zhou, J.

B. Xu, W. Lv, J. Ye, J. Zhou, X. Jin, X. Zhang, H. Chi, and S. Zheng, “Spurious-free dynamic range improvement in a photonic time-stretched analog-to-digital converter based on third-order predistrotion,” Photonics Res. 2(5), 97–101 (2014).
[Crossref]

Chin. Sci. Bull. (1)

Z. Y. Zhang, H. P. Li, S. J. Zhang, and Y. Liu, “Analog-to-digital converters using photonic technology,” Chin. Sci. Bull. 59(22), 2666–2671 (2014).
[Crossref]

Electron. Lett. (1)

A. S. Bhushan, F. Coppinger, and B. Jalali, “Time-stretched analogue-to-digital convertion,” Electron. Lett. 34(11), 1081–1083 (1998).
[Crossref]

IEEE Commun. Mag. (1)

J. A. Wepman, “Analog-to-digital converters and their applications in radio receivers,” IEEE Commun. Mag. 33(5), 39–45 (1995).
[Crossref]

IEEE Photonics Technol. Lett. (3)

J. C. Twichell and R. Helkey, “Phase-encoded optical smapling for analog-to-digital converters,” IEEE Photonics Technol. Lett. 12(9), 1237–1239 (2000).
[Crossref]

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Figures (6)

Fig. 1
Fig. 1 Architecture of the proposed TS-ADC. MLL: mode-locked laser, DCF: dispersion compensation fiber, DPMZM: dual parallel Mach-Zehnder modulator, OC: optical circulator, PD: photodiode.
Fig. 2
Fig. 2 Architecture of the asymmetrical DPMZM employed in the proposed TS-ADC.
Fig. 3
Fig. 3 Output spectrum employing (a) the differential detection, (b) the differential scheme with assist of arcsine operation and (c) the proposed one.
Fig. 4
Fig. 4 Output spectrum employing (a) the differential detection, (b) the differential scheme with assist of arcsine operation and (c) the proposed one.
Fig. 5
Fig. 5 Output RF power vs input RF power in (a) the differential detection, (b) the differential scheme with assist of arcsine operation and (c) the proposed one.
Fig. 6
Fig. 6 ENOB under various deviations of sin2α and sin2β.

Tables (2)

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Table 1 Parameters of the optical source and the dispersion compensation fiber.

Tables Icon

Table 2 Comparison of C/IM3 in the differential detection scheme, the differential scheme with assist of arcsine operation and the proposed one under various modulation indexes.

Equations (21)

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E 1 ( ω )= E 0 2π T 0 2 exp( T 0 2 ω 2 2 )
E 2 ( ω )= E 1 ( ω )exp( j 2 β 2 L 1 ω 2 )
E 3 ( T )= 2 2 E 2 ( T ){ cosαcosβsin[ m 2 cos( ω RF t ) ]sinαsinβsin[ m 2γ cos( ω RF t ) ] }
E 3 ( T )= 2 2 E 3 ( T ) 1 2 E 2 ( T )
E 3+ ( T )=j[ 2 2 E 3 ( T )+ 1 2 E 2 ( T ) ]
E 4± ( ω )= E 3± ( ω )exp( j 2 β 2 L 2 ω 2 )
I ± (T)= 1 2 nc ε 0 A eff R PD E 4± (T) E 4± (T)
I( T )= I + ( T ) I ( T ) = I env ( T ){ [ 4cosαcosβ J 1 ( m 2 )4sinαsinβ J 1 ( m 2γ ) ]cos( φ DIP )cos( ω RF M t ) [ 4cosαcosβ J 3 ( m 2 )4sinαsinβ J 3 ( m 2γ ) ]cos( 9 φ DIP )cos( 3 ω RF M t ) +[ 4cosαcosβ J 5 ( m 2 )4sinαsinβ J 5 ( m 2γ ) ]cos( 25 φ DIP )cos( 5 ω RF M t )+ }
I env ( T )= 1 4 nc ε 0 A eff R PD E 0 2 1 1+ ( β 2 ( L 1 + L 2 ) T 0 2 ) 2 exp{ T 2 T 0 2 [ 1+ ( β 2 ( L 1 + L 2 ) T 0 2 ) 2 ] }
J n ( x )= m=0 ( 1 ) m m!( m+n )! ( x 2 ) 2m+n
m 3 4 2 ×3! ( cosαcosβ sinαsinβ γ 3 ) m 5 4 4 ×4! ( cosαcosβ sinαsinβ γ 5 ) + m 7 2× 4 6 ×5! ( cosαcosβ sinαsinβ γ 7 )+
tanαtanβ= γ 3
I( T )=Amcos( ω RF M T )+B m 5 cos( 3 ω RF M T )+C m 5 cos( 5 ω RF M T )
A= I env ( T )cosαcosβ( 1 γ 2 )cos( ω RF 2 φ DIP )
B= 1 4 4 ×4! I env ( T )cosαcosβ( 1 1 γ 2 )cos( 9 ω RF 2 φ DIP )
C= 1 4 4 ×5! I env ( T )cosαcosβ( 1 1 γ 2 )cos( 25 ω RF 2 φ DIP )
SFD R 3 = ( | A B | 1/2 A 2 R 2N ) 2/3
SFD R 3 = ( I env 2 R 2N ) 2/3 ( 4 × 4 4! ) 1/3 ( cos 2 α cos 2 β ) 2/3 | ( 1 γ 2 ) 5/3 ( 11/ γ 2 ) 1/3 |
SFD R 3 ( I env 2 R 2N ) 2/3 ( 4 × 4 4! ) 1/3 | ( 1 γ 2 ) 5/3 ( 1+ γ 3 ) 4/3 ( 11/ γ 2 ) 1/3 |
m 4 m 3 2× 4 3 + m 5 12× 4 5
cos 2 α( 1 γ 2 ) m 4 + cos 2 α( 1 1 γ 2 ) m 5 12× 4 5

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