Abstract

The method of Mach-Zehnder electro-optical modulation is applied to Intra-Body Communication (IBC), where the modeling and characterization of this type of IBC are discussed. The mathematical model of the electrostatic coupling IBC based on Mach-Zehnder electro-optical modulation is developed. The main characteristics of this IBC form have been simulated within the frequency range of 200 kHz-40MHz and compared to in-vivo measurements, with close agreements. Results show that the proposed method will help achieving good temperature characteristics, small size, and lower power consumption IBC system.

© 2012 OSA

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References

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  1. T. G. Zimmerman, Personal Area Networks (PAN): Near-Field Intra-Body Communication, in Media Art and Science. Master Thesis: Massachusetts Institute of Technology (1995).
  2. M. S. Wegmueller, M. Oberle, N. Felber, N. Kuster, and W. Fichtner, “Signal Transmission by Galvanic Coupling Through the Human Body,” IEEE Trans. Instrum. Meas. 59(4), 963–969 (2010).
    [CrossRef]
  3. M. Shinagawa, M. Fukumoto, K. Ochiai, and H. Kyuragi, “A Near-Field-Sensing Transceiver for Intrabody Communication Based on the Electrooptic Effect,” IEEE Trans. Instrum. Meas. 53(6), 1533–1538 (2004).
    [CrossRef]
  4. M. S. Wegmueller, S. Huclova, J. Froehlich, M. Oberle, N. Felber, N. Kuster, and W. Fichtner, “Galvanic Coupling Enabling Wireless Implant Communications,” IEEE Trans. Instrum. Meas. 58(8), 2618–2625 (2009).
    [CrossRef]
  5. Y. Song, Q. Hao, K. Zhang, M. Wang, Y. Chu, and B. Kang, “The Simulation Method of the Galvanic Coupling Intra-body Communication with Different Signal Transmission Paths,” IEEE Trans. Instrum. Meas. 60(4), 1257–1266 (2011).
    [CrossRef]
  6. A. Sasaki, M. Shinagawa, and K. Ochiai, “Principles and Demonstration of Intrabody Communication with a Sensitive Electrooptic Sensor,” IEEE Trans. Instrum. Meas. 58(2), 457–466 (2009).
    [CrossRef]
  7. K. Hachisuka, A. Nakata, T. Takeda, K. Shiba, K. Sasaki, H. Hosaka, and K. Itao, “Development of wearable intra-body communication devices,” Sens. Actuators A Phys. 105(1), 109–115 (2003).
    [CrossRef]
  8. A. Sasaki and M. Shinagawa, “Principle and Application of a Sensitive Handy Electrooptic Probe for Sub-100-MHz Frequency Range Signal Measurements,” IEEE Trans. Instrum. Meas. 57(5), 1005–1013 (2008).
    [CrossRef]
  9. C. E. Rogers, J. L. Carini, J. A. Pechkis, and P. L. Gould, “Characterization and compensation of the residual chirp in a Mach-Zehnder-type electro-optical intensity modulator,” Opt. Express 18(2), 1166–1176 (2010).
    [CrossRef] [PubMed]
  10. J. M. Brosi, C. Koos, L. C. Andreani, M. Waldow, J. Leuthold, and W. Freude, “High-speed low-voltage electro-optic modulator with a polymer-infiltrated silicon photonic crystal waveguide,” Opt. Express 16(6), 4177–4191 (2008).
    [CrossRef] [PubMed]
  11. J. William, M. J. Green, M. J. Rooks, L. Sekaric, and Y. A. Vlasov, “Ultra-compact, low RF power, 10 Gb/s silicon Mach-Zehnder modulator,” Opt. Express 15, 17107–17113 (2007).
  12. R. W. Boyd, “Electrooptic Modulators,” in Nonlinear Optics (Academic, Rochester, New York, 2008).
  13. G. N. Lu and G. Sou, “A CMOS Op Amp using a regulated-cascade transimpedance building block for high-gain, low-voltage achievement,” in Proceedings of 1997 IEEE International Symposium on Circuits and Systems (Hong Kong,1997).165–168.
  14. H. J. Zhu, R. Y. Xu, and J. Yuan, “High Speed Intra-Body Communication for Personal Health Care,” in Proceedings of 31st Annual International Conference of the IEEE EMBS Minneapolis (Minnesota, 2009), 709–712.
  15. D. L. Zhang, Q. Z. Yang, P. R. Hua, H. L. Liu, Y. M. Cui, L. Sun, Y. H. Xu, and E. Y. B. Pun, “Sellmeier equation for doubly Er/Mg-doped congruent LiNbO3 crystals,” J. Opt. Soc. Am. B 26, 620–626 (2009).

2011

Y. Song, Q. Hao, K. Zhang, M. Wang, Y. Chu, and B. Kang, “The Simulation Method of the Galvanic Coupling Intra-body Communication with Different Signal Transmission Paths,” IEEE Trans. Instrum. Meas. 60(4), 1257–1266 (2011).
[CrossRef]

2010

M. S. Wegmueller, M. Oberle, N. Felber, N. Kuster, and W. Fichtner, “Signal Transmission by Galvanic Coupling Through the Human Body,” IEEE Trans. Instrum. Meas. 59(4), 963–969 (2010).
[CrossRef]

C. E. Rogers, J. L. Carini, J. A. Pechkis, and P. L. Gould, “Characterization and compensation of the residual chirp in a Mach-Zehnder-type electro-optical intensity modulator,” Opt. Express 18(2), 1166–1176 (2010).
[CrossRef] [PubMed]

2009

M. S. Wegmueller, S. Huclova, J. Froehlich, M. Oberle, N. Felber, N. Kuster, and W. Fichtner, “Galvanic Coupling Enabling Wireless Implant Communications,” IEEE Trans. Instrum. Meas. 58(8), 2618–2625 (2009).
[CrossRef]

A. Sasaki, M. Shinagawa, and K. Ochiai, “Principles and Demonstration of Intrabody Communication with a Sensitive Electrooptic Sensor,” IEEE Trans. Instrum. Meas. 58(2), 457–466 (2009).
[CrossRef]

D. L. Zhang, Q. Z. Yang, P. R. Hua, H. L. Liu, Y. M. Cui, L. Sun, Y. H. Xu, and E. Y. B. Pun, “Sellmeier equation for doubly Er/Mg-doped congruent LiNbO3 crystals,” J. Opt. Soc. Am. B 26, 620–626 (2009).

2008

A. Sasaki and M. Shinagawa, “Principle and Application of a Sensitive Handy Electrooptic Probe for Sub-100-MHz Frequency Range Signal Measurements,” IEEE Trans. Instrum. Meas. 57(5), 1005–1013 (2008).
[CrossRef]

J. M. Brosi, C. Koos, L. C. Andreani, M. Waldow, J. Leuthold, and W. Freude, “High-speed low-voltage electro-optic modulator with a polymer-infiltrated silicon photonic crystal waveguide,” Opt. Express 16(6), 4177–4191 (2008).
[CrossRef] [PubMed]

2007

J. William, M. J. Green, M. J. Rooks, L. Sekaric, and Y. A. Vlasov, “Ultra-compact, low RF power, 10 Gb/s silicon Mach-Zehnder modulator,” Opt. Express 15, 17107–17113 (2007).

2004

M. Shinagawa, M. Fukumoto, K. Ochiai, and H. Kyuragi, “A Near-Field-Sensing Transceiver for Intrabody Communication Based on the Electrooptic Effect,” IEEE Trans. Instrum. Meas. 53(6), 1533–1538 (2004).
[CrossRef]

2003

K. Hachisuka, A. Nakata, T. Takeda, K. Shiba, K. Sasaki, H. Hosaka, and K. Itao, “Development of wearable intra-body communication devices,” Sens. Actuators A Phys. 105(1), 109–115 (2003).
[CrossRef]

Andreani, L. C.

Brosi, J. M.

Carini, J. L.

Chu, Y.

Y. Song, Q. Hao, K. Zhang, M. Wang, Y. Chu, and B. Kang, “The Simulation Method of the Galvanic Coupling Intra-body Communication with Different Signal Transmission Paths,” IEEE Trans. Instrum. Meas. 60(4), 1257–1266 (2011).
[CrossRef]

Cui, Y. M.

Felber, N.

M. S. Wegmueller, M. Oberle, N. Felber, N. Kuster, and W. Fichtner, “Signal Transmission by Galvanic Coupling Through the Human Body,” IEEE Trans. Instrum. Meas. 59(4), 963–969 (2010).
[CrossRef]

M. S. Wegmueller, S. Huclova, J. Froehlich, M. Oberle, N. Felber, N. Kuster, and W. Fichtner, “Galvanic Coupling Enabling Wireless Implant Communications,” IEEE Trans. Instrum. Meas. 58(8), 2618–2625 (2009).
[CrossRef]

Fichtner, W.

M. S. Wegmueller, M. Oberle, N. Felber, N. Kuster, and W. Fichtner, “Signal Transmission by Galvanic Coupling Through the Human Body,” IEEE Trans. Instrum. Meas. 59(4), 963–969 (2010).
[CrossRef]

M. S. Wegmueller, S. Huclova, J. Froehlich, M. Oberle, N. Felber, N. Kuster, and W. Fichtner, “Galvanic Coupling Enabling Wireless Implant Communications,” IEEE Trans. Instrum. Meas. 58(8), 2618–2625 (2009).
[CrossRef]

Freude, W.

Froehlich, J.

M. S. Wegmueller, S. Huclova, J. Froehlich, M. Oberle, N. Felber, N. Kuster, and W. Fichtner, “Galvanic Coupling Enabling Wireless Implant Communications,” IEEE Trans. Instrum. Meas. 58(8), 2618–2625 (2009).
[CrossRef]

Fukumoto, M.

M. Shinagawa, M. Fukumoto, K. Ochiai, and H. Kyuragi, “A Near-Field-Sensing Transceiver for Intrabody Communication Based on the Electrooptic Effect,” IEEE Trans. Instrum. Meas. 53(6), 1533–1538 (2004).
[CrossRef]

Gould, P. L.

Green, M. J.

J. William, M. J. Green, M. J. Rooks, L. Sekaric, and Y. A. Vlasov, “Ultra-compact, low RF power, 10 Gb/s silicon Mach-Zehnder modulator,” Opt. Express 15, 17107–17113 (2007).

Hachisuka, K.

K. Hachisuka, A. Nakata, T. Takeda, K. Shiba, K. Sasaki, H. Hosaka, and K. Itao, “Development of wearable intra-body communication devices,” Sens. Actuators A Phys. 105(1), 109–115 (2003).
[CrossRef]

Hao, Q.

Y. Song, Q. Hao, K. Zhang, M. Wang, Y. Chu, and B. Kang, “The Simulation Method of the Galvanic Coupling Intra-body Communication with Different Signal Transmission Paths,” IEEE Trans. Instrum. Meas. 60(4), 1257–1266 (2011).
[CrossRef]

Hosaka, H.

K. Hachisuka, A. Nakata, T. Takeda, K. Shiba, K. Sasaki, H. Hosaka, and K. Itao, “Development of wearable intra-body communication devices,” Sens. Actuators A Phys. 105(1), 109–115 (2003).
[CrossRef]

Hua, P. R.

Huclova, S.

M. S. Wegmueller, S. Huclova, J. Froehlich, M. Oberle, N. Felber, N. Kuster, and W. Fichtner, “Galvanic Coupling Enabling Wireless Implant Communications,” IEEE Trans. Instrum. Meas. 58(8), 2618–2625 (2009).
[CrossRef]

Itao, K.

K. Hachisuka, A. Nakata, T. Takeda, K. Shiba, K. Sasaki, H. Hosaka, and K. Itao, “Development of wearable intra-body communication devices,” Sens. Actuators A Phys. 105(1), 109–115 (2003).
[CrossRef]

Kang, B.

Y. Song, Q. Hao, K. Zhang, M. Wang, Y. Chu, and B. Kang, “The Simulation Method of the Galvanic Coupling Intra-body Communication with Different Signal Transmission Paths,” IEEE Trans. Instrum. Meas. 60(4), 1257–1266 (2011).
[CrossRef]

Koos, C.

Kuster, N.

M. S. Wegmueller, M. Oberle, N. Felber, N. Kuster, and W. Fichtner, “Signal Transmission by Galvanic Coupling Through the Human Body,” IEEE Trans. Instrum. Meas. 59(4), 963–969 (2010).
[CrossRef]

M. S. Wegmueller, S. Huclova, J. Froehlich, M. Oberle, N. Felber, N. Kuster, and W. Fichtner, “Galvanic Coupling Enabling Wireless Implant Communications,” IEEE Trans. Instrum. Meas. 58(8), 2618–2625 (2009).
[CrossRef]

Kyuragi, H.

M. Shinagawa, M. Fukumoto, K. Ochiai, and H. Kyuragi, “A Near-Field-Sensing Transceiver for Intrabody Communication Based on the Electrooptic Effect,” IEEE Trans. Instrum. Meas. 53(6), 1533–1538 (2004).
[CrossRef]

Leuthold, J.

Liu, H. L.

Nakata, A.

K. Hachisuka, A. Nakata, T. Takeda, K. Shiba, K. Sasaki, H. Hosaka, and K. Itao, “Development of wearable intra-body communication devices,” Sens. Actuators A Phys. 105(1), 109–115 (2003).
[CrossRef]

Oberle, M.

M. S. Wegmueller, M. Oberle, N. Felber, N. Kuster, and W. Fichtner, “Signal Transmission by Galvanic Coupling Through the Human Body,” IEEE Trans. Instrum. Meas. 59(4), 963–969 (2010).
[CrossRef]

M. S. Wegmueller, S. Huclova, J. Froehlich, M. Oberle, N. Felber, N. Kuster, and W. Fichtner, “Galvanic Coupling Enabling Wireless Implant Communications,” IEEE Trans. Instrum. Meas. 58(8), 2618–2625 (2009).
[CrossRef]

Ochiai, K.

A. Sasaki, M. Shinagawa, and K. Ochiai, “Principles and Demonstration of Intrabody Communication with a Sensitive Electrooptic Sensor,” IEEE Trans. Instrum. Meas. 58(2), 457–466 (2009).
[CrossRef]

M. Shinagawa, M. Fukumoto, K. Ochiai, and H. Kyuragi, “A Near-Field-Sensing Transceiver for Intrabody Communication Based on the Electrooptic Effect,” IEEE Trans. Instrum. Meas. 53(6), 1533–1538 (2004).
[CrossRef]

Pechkis, J. A.

Pun, E. Y. B.

Rogers, C. E.

Rooks, M. J.

J. William, M. J. Green, M. J. Rooks, L. Sekaric, and Y. A. Vlasov, “Ultra-compact, low RF power, 10 Gb/s silicon Mach-Zehnder modulator,” Opt. Express 15, 17107–17113 (2007).

Sasaki, A.

A. Sasaki, M. Shinagawa, and K. Ochiai, “Principles and Demonstration of Intrabody Communication with a Sensitive Electrooptic Sensor,” IEEE Trans. Instrum. Meas. 58(2), 457–466 (2009).
[CrossRef]

A. Sasaki and M. Shinagawa, “Principle and Application of a Sensitive Handy Electrooptic Probe for Sub-100-MHz Frequency Range Signal Measurements,” IEEE Trans. Instrum. Meas. 57(5), 1005–1013 (2008).
[CrossRef]

Sasaki, K.

K. Hachisuka, A. Nakata, T. Takeda, K. Shiba, K. Sasaki, H. Hosaka, and K. Itao, “Development of wearable intra-body communication devices,” Sens. Actuators A Phys. 105(1), 109–115 (2003).
[CrossRef]

Sekaric, L.

J. William, M. J. Green, M. J. Rooks, L. Sekaric, and Y. A. Vlasov, “Ultra-compact, low RF power, 10 Gb/s silicon Mach-Zehnder modulator,” Opt. Express 15, 17107–17113 (2007).

Shiba, K.

K. Hachisuka, A. Nakata, T. Takeda, K. Shiba, K. Sasaki, H. Hosaka, and K. Itao, “Development of wearable intra-body communication devices,” Sens. Actuators A Phys. 105(1), 109–115 (2003).
[CrossRef]

Shinagawa, M.

A. Sasaki, M. Shinagawa, and K. Ochiai, “Principles and Demonstration of Intrabody Communication with a Sensitive Electrooptic Sensor,” IEEE Trans. Instrum. Meas. 58(2), 457–466 (2009).
[CrossRef]

A. Sasaki and M. Shinagawa, “Principle and Application of a Sensitive Handy Electrooptic Probe for Sub-100-MHz Frequency Range Signal Measurements,” IEEE Trans. Instrum. Meas. 57(5), 1005–1013 (2008).
[CrossRef]

M. Shinagawa, M. Fukumoto, K. Ochiai, and H. Kyuragi, “A Near-Field-Sensing Transceiver for Intrabody Communication Based on the Electrooptic Effect,” IEEE Trans. Instrum. Meas. 53(6), 1533–1538 (2004).
[CrossRef]

Song, Y.

Y. Song, Q. Hao, K. Zhang, M. Wang, Y. Chu, and B. Kang, “The Simulation Method of the Galvanic Coupling Intra-body Communication with Different Signal Transmission Paths,” IEEE Trans. Instrum. Meas. 60(4), 1257–1266 (2011).
[CrossRef]

Sun, L.

Takeda, T.

K. Hachisuka, A. Nakata, T. Takeda, K. Shiba, K. Sasaki, H. Hosaka, and K. Itao, “Development of wearable intra-body communication devices,” Sens. Actuators A Phys. 105(1), 109–115 (2003).
[CrossRef]

Vlasov, Y. A.

J. William, M. J. Green, M. J. Rooks, L. Sekaric, and Y. A. Vlasov, “Ultra-compact, low RF power, 10 Gb/s silicon Mach-Zehnder modulator,” Opt. Express 15, 17107–17113 (2007).

Waldow, M.

Wang, M.

Y. Song, Q. Hao, K. Zhang, M. Wang, Y. Chu, and B. Kang, “The Simulation Method of the Galvanic Coupling Intra-body Communication with Different Signal Transmission Paths,” IEEE Trans. Instrum. Meas. 60(4), 1257–1266 (2011).
[CrossRef]

Wegmueller, M. S.

M. S. Wegmueller, M. Oberle, N. Felber, N. Kuster, and W. Fichtner, “Signal Transmission by Galvanic Coupling Through the Human Body,” IEEE Trans. Instrum. Meas. 59(4), 963–969 (2010).
[CrossRef]

M. S. Wegmueller, S. Huclova, J. Froehlich, M. Oberle, N. Felber, N. Kuster, and W. Fichtner, “Galvanic Coupling Enabling Wireless Implant Communications,” IEEE Trans. Instrum. Meas. 58(8), 2618–2625 (2009).
[CrossRef]

William, J.

J. William, M. J. Green, M. J. Rooks, L. Sekaric, and Y. A. Vlasov, “Ultra-compact, low RF power, 10 Gb/s silicon Mach-Zehnder modulator,” Opt. Express 15, 17107–17113 (2007).

Xu, Y. H.

Yang, Q. Z.

Zhang, D. L.

Zhang, K.

Y. Song, Q. Hao, K. Zhang, M. Wang, Y. Chu, and B. Kang, “The Simulation Method of the Galvanic Coupling Intra-body Communication with Different Signal Transmission Paths,” IEEE Trans. Instrum. Meas. 60(4), 1257–1266 (2011).
[CrossRef]

IEEE Trans. Instrum. Meas.

M. S. Wegmueller, M. Oberle, N. Felber, N. Kuster, and W. Fichtner, “Signal Transmission by Galvanic Coupling Through the Human Body,” IEEE Trans. Instrum. Meas. 59(4), 963–969 (2010).
[CrossRef]

M. Shinagawa, M. Fukumoto, K. Ochiai, and H. Kyuragi, “A Near-Field-Sensing Transceiver for Intrabody Communication Based on the Electrooptic Effect,” IEEE Trans. Instrum. Meas. 53(6), 1533–1538 (2004).
[CrossRef]

M. S. Wegmueller, S. Huclova, J. Froehlich, M. Oberle, N. Felber, N. Kuster, and W. Fichtner, “Galvanic Coupling Enabling Wireless Implant Communications,” IEEE Trans. Instrum. Meas. 58(8), 2618–2625 (2009).
[CrossRef]

Y. Song, Q. Hao, K. Zhang, M. Wang, Y. Chu, and B. Kang, “The Simulation Method of the Galvanic Coupling Intra-body Communication with Different Signal Transmission Paths,” IEEE Trans. Instrum. Meas. 60(4), 1257–1266 (2011).
[CrossRef]

A. Sasaki, M. Shinagawa, and K. Ochiai, “Principles and Demonstration of Intrabody Communication with a Sensitive Electrooptic Sensor,” IEEE Trans. Instrum. Meas. 58(2), 457–466 (2009).
[CrossRef]

A. Sasaki and M. Shinagawa, “Principle and Application of a Sensitive Handy Electrooptic Probe for Sub-100-MHz Frequency Range Signal Measurements,” IEEE Trans. Instrum. Meas. 57(5), 1005–1013 (2008).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Express

Sens. Actuators A Phys.

K. Hachisuka, A. Nakata, T. Takeda, K. Shiba, K. Sasaki, H. Hosaka, and K. Itao, “Development of wearable intra-body communication devices,” Sens. Actuators A Phys. 105(1), 109–115 (2003).
[CrossRef]

Other

R. W. Boyd, “Electrooptic Modulators,” in Nonlinear Optics (Academic, Rochester, New York, 2008).

G. N. Lu and G. Sou, “A CMOS Op Amp using a regulated-cascade transimpedance building block for high-gain, low-voltage achievement,” in Proceedings of 1997 IEEE International Symposium on Circuits and Systems (Hong Kong,1997).165–168.

H. J. Zhu, R. Y. Xu, and J. Yuan, “High Speed Intra-Body Communication for Personal Health Care,” in Proceedings of 31st Annual International Conference of the IEEE EMBS Minneapolis (Minnesota, 2009), 709–712.

T. G. Zimmerman, Personal Area Networks (PAN): Near-Field Intra-Body Communication, in Media Art and Science. Master Thesis: Massachusetts Institute of Technology (1995).

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Figures (11)

Fig. 1
Fig. 1

The biomedical monitoring based on IBC technology.

Fig. 2
Fig. 2

Approaches for detecting the signal transmitted within the human body: (a) Electrical detection method. (b) Electro-optical modulation method.

Fig. 3
Fig. 3

Model of the electrostatic coupling IBC based on Mach-Zehnder electro-optical modulator.

Fig. 4
Fig. 4

The circuit model of the electrostatic coupling IBC based on a Mach-Zehnder electro-optical modulator.

Fig. 5
Fig. 5

The electro-optical modulator used in IBC. (a) Bulk electro-optical modulator.(b) Mach-Zehnder electro-optical modulator.

Fig. 6
Fig. 6

Measured frequency response of the experimental setup together with curve fitting.

Fig. 7
Fig. 7

In-vivo measurements of the electrostatic coupling IBC based on the Mach-Zehnder electro-optical modulation

Fig. 8
Fig. 8

Comparison between in-vivo measurements and simulation results based on the proposed model given by Eq. (13).

Fig. 9
Fig. 9

Measurements of the electrostatic coupling IBC with various signal transmission paths, including the frequency responses of the IBC based on the electrical sensor and that based on Mach-Zehnder electro-optical modulation.

Fig. 10
Fig. 10

Simulations of attenuation corresponding to different ambient temperatures (283.15 K-305.15 K) of the bulk electro-optical sensor used in IBC.

Fig. 11
Fig. 11

Measurements and simulation of attenuation corresponding to various ambient temperatures (283.15 K-305.15 K) of the Mach-Zehnder electro-optical sensor used in IBC.

Equations (13)

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

{ V e = V in Z g2 Z e ' ( R 0 + Z s1 + Z g1 + Z g2 )( Z s2 + Z e ' + Z g3 + Z g2 ) Z g2 2 , Z gi = 1 j2πf C gi (i=1,2,3) , Z e ' = Z e1 Z e2 Z e1 + Z e1 = 1 j2πf( C e1 + C e2 ) , Z si = R i + 1 j2πf C si (i=1,2) ,
G H =20 log 10 ( V e V in )=20 log 10 [ Z g2 Z e ' ( R 0 + Z s1 + Z g1 + Z g2 )( Z s2 + Z e ' + Z g3 + Z g2 ) Z g2 2 ].
P out = P in sin 2 ( Δφ 2 )= P in sin 2 [ πl λ ( n o n e )+ πl 2λd ( n e 3 γ 33 n o 3 γ 13 ) V e ],
V out = S R k 10 k 10 P in sin 2 [ πl λ ( n o n e )+ πl 2λd ( n e 3 γ 33 n o 3 γ 13 ) V e ],
E out = A 2 exp(jωt)[exp(j φ a )+exp(j φ b )] = Aexp{j[ωt+ 2πl λ 0 ( n e n o )]}cos[ ΓπL G λ 0 ( n e 3 γ 33 n o 3 γ 13 ) V e + φ 0 ],
P out = P in cos 2 [ ΓπL G λ 0 ( n e 3 γ 33 n o 3 γ 13 ) V e + φ 0 ].
V out = 10 10/k S R k P out .
G EO1 =20 log 10 ( d V out d V e )=20 log 10 d d V e { 10 k/10 S R k P in cos 2 [ ΓπL G λ 0 ( n e 3 γ 33 n o 3 γ 13 ) V e + φ 0 ]} =20 log 10 { 10 k/10 S R k P in ΓπL G λ 0 ( n e 3 γ 33 n o 3 γ 13 )sin[ 2ΓπL G λ 0 ( n e 3 γ 33 n o 3 γ 13 ) V e + φ 0 ]}.
G EO2 ={ 25.22 e 2.505 5 f 15.12 e 2.878 6 f (10kHzf500KHz), 1.639 15 f 2 1.356 7 f3.415 (500KHz<f40MHz).
G balun =1836 f 0.4761 +0.4708.
{ n o 2 =4.913+ 0.1173+1.64× 10 8 T 2 λ 2 (0.212+2.7× 10 8 T 2 ) 2 2.78× 10 2 λ 2 , n e 2 =4.5567+2.605× 10 7 T 2 + 0.097+2.7× 10 8 T 2 λ 2 (0.212+5.4× 10 8 T 2 ) 2 2.24× 10 2 λ 2 .
G Total = G H + G Balun + G EO1 + G EO2 K,
{ G Total = G H + G Balun + G EO1 + G EO2 K, G H =20 log 10 ( Z g2 Z e ' ( R 0 + Z s1 + Z g1 + Z g2 )( Z s2 + Z e ' + Z g3 + Z g2 ) Z g2 2 ), Z gi = 1 j2πf C gi (i=1,2,3), Z e ' = 1 j2πf( C e1 + C e2 ) , Z si = R i + 1 j2πf C si (i=1,2) , G EO1 =20 log 10 { 10 k 10 S R k P in ΓπL G λ 0 ( n e 3 γ 33 n o 3 γ 13 )sin[ 2ΓπL G λ 0 ( n e 3 γ 33 n o 3 γ 13 ) V e + φ 0 ]}, n o 2 =4.913+ 0.1173+1.64× 10 8 T 2 λ 2 (0.212+2.7× 10 8 T 2 ) 2 2.78× 10 2 λ 2 , n e 2 =4.5567+2.605× 10 7 T 2 + 0.097+2.7× 10 8 T 2 λ 2 (0.212+5.4× 10 8 T 2 ) 2 2.24× 10 2 λ 2 , G EO2 = 25.22 e 2.505 5 f 15.12 e 2.878 6 f (10kHzf500kHz ), G EO2 = 1.639 15 f 2 1.356 7 f3.415 (500kHz<f40MHz ), G balun =1836 f 0.4761 +0.4708.

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