Abstract

Abstract: This paper presents a new technique for realizing continuous 0°-360° RF signal phase shift over a very wide bandwidth. It is based on using single-sideband modulation together with optical filtering to largely suppress one of the RF modulation sidebands over a wide input RF frequency range, and controlling the phase of the optical carrier to shift an RF signal phase. The technique does not require expensive electrical or optical components to realize an RF signal phase shift over 2–40 GHz frequency range with a flat amplitude and phase response performance. This overcomes the current technology limitation in which no reported phase shifter structure has demonstrated the capability of operating in such a wide bandwidth. Experimental results demonstrate only ± 1 dB amplitude variation and ± 5° phase deviation from the desired RF signal phase shift over 2–40 GHz bandwidth and the RF signal amplitude control function. The phase shifter wavelength insensitive performance is also demonstrated experimentally.

© 2017 Optical Society of America

Full Article  |  PDF Article
More Like This
Broadband photonic microwave phase shifter based on controlling two RF modulation sidebands via a Fourier-domain optical processor

J. Yang, E. H. W. Chan, X. Wang, X. Feng, and B. Guan
Opt. Express 23(9) 12100-12110 (2015)

A wideband 360° photonic-assisted microwave phase shifter using a polarization modulator and a polarization-maintaining fiber Bragg grating

Wangzhe Li, Weifeng Zhang, and Jianping Yao
Opt. Express 20(28) 29838-29843 (2012)

Microwave photonic phase-tunable mixer

Tianwei Jiang, Ruihuan Wu, Song Yu, Dongsheng Wang, and Wanyi Gu
Opt. Express 25(4) 4519-4527 (2017)

View More...

References

  • View by:
  • Article Order
  • Year
  • Author
  • Publication
  1. M. E. Manka, “Microwave photonics electronic warfare technologies for Australian defence,” IEEE International Topical Meeting on Microwave Photonics (MWP 2008), 1–2 (2008).
  2. R. A. Minasian, E. H. W. Chan, and X. Yi, “Microwave photonic signal processing,” Opt. Express 21(19), 22918–22936 (2013).
    [Crossref] [PubMed]
  3. W. Xue, S. Sales, J. Capmany, and J. Mørk, “Wideband 360 ° microwave photonic phase shifter based on slow light in semiconductor optical amplifiers,” Opt. Express 18(6), 6156–6163 (2010).
    [Crossref] [PubMed]
  4. S. Pan and Y. Zhang, “Tunable and wideband microwave photonic phase shifter based on a single-sideband polarization modulator and a polarizer,” Opt. Lett. 37(21), 4483–4485 (2012).
    [Crossref] [PubMed]
  5. W. Li, W. H. Sun, W. T. Wang, and N. H. Zhu, “Optically controlled microwave phase shifter based on nonlinear polarization rotation in a highly nonlinear fiber,” Opt. Lett. 39(11), 3290–3293 (2014).
    [Crossref] [PubMed]
  6. W. Li, W. T. Wang, and N. H. Zhu, “Broadband microwave photonic splitter with arbitrary amplitude ratio and phase shift,” IEEE Photonics J. 6(6), 5501507 (2014).
    [Crossref]
  7. W. Liu and J. Yao, “Ultra-wideband microwave photonic phase shifter with a 360° tunable phase shift based on an erbium-ytterbium co-doped linearly chirped FBG,” Opt. Lett. 39(4), 922–924 (2014).
    [Crossref] [PubMed]
  8. H. Emami, L. A. Bui, S. Mansoori, and A. Mitchell, “Quadrature hybrid coupler using photonic transversal approach,” Australian Conference on Optical Fibre Technology, 1–3 (2006).
    [Crossref]
  9. “Hybrid coupler basic,” MECA Electronics Inc., http://www.e-meca.com/rf-microwave-blog/hybrid-coupler-basics .
  10. K. Higuma, S. Oikawa, Y. Hashimoto, H. Nagata, and M. Izutsu, “X-cut lithium niobate optical single-sideband modulator,” Electron. Lett. 37(8), 515–516 (2001).
    [Crossref]
  11. ARCOptix polarisation rotator, http://www.arcoptix.com/polarization_rotator.htm .
  12. K. Noguchi, O. Mitomi, H. Miyazawa, and S. Seki, “A broadband Ti:LiNbO3 optical modulator with a ridge structure,” J. Lightwave Technol. 13(6), 1164–1168 (1995).
    [Crossref]
  13. T. Niu, X. Wang, E. H. W. Chan, X. Feng, and B. Guan, “Dual-polarisation dual-parallel MZM and optical phase controller based microwave photonic phase controller,” IEEE Photonics J. 8(4), 5501114 (2016).
    [Crossref]
  14. T. Niu, E. H. W. Chan, X. Wang, X. Feng, and B. Guan, “Broadband dual-polarization dual-parallel Mach Zehnder modulator based photonic microwave phase shifter,” Optoelectronics and Communications Conference, 1–3 (2016).
  15. E. H. W. Chan, W. Zhang, and R. A. Minasian, “Photonic RF phase shifter based on optical carrier and RF modulation sidebands amplitude and phase control,” J. Lightwave Technol. 30(23), 3672–3678 (2012).
    [Crossref]
  16. A. Loayssa and F. J. Lahoz, “Broad-band RF photonic phase shifter based on stimulated Brillouin scattering and single-sideband modulation,” IEEE Photonics Technol. Lett. 18(1), 208–210 (2006).
    [Crossref]
  17. X. Xue, X. Zheng, H. Zhang, and B. Zhou, “Tunable 360° photonic radio frequency phase shifter based on optical quadrature double-sideband modulation and differential detection,” Opt. Lett. 36(23), 4641–4643 (2011).
    [Crossref] [PubMed]
  18. C. Cox, E. Ackerman, R. Helkey, and G. E. Betts, “Techniques and performance of intensity-modulation direct-detection analog optical links,” IEEE Trans. Microw. Theory Tech. 45(8), 1375–1383 (1997).
    [Crossref]
  19. X. Wang, E. H. W. Chan, and R. A. Minasian, “All-optical photonic microwave phase shifter based on an optical filter with a nonlinear phase response,” J. Lightwave Technol. 31(20), 3323–3330 (2013).
    [Crossref]
  20. C. T. DeRose, R. D. Kekatpure, D. C. Trotter, A. Starbuck, J. R. Wendt, A. Yaacobi, M. R. Watts, U. Chettiar, N. Engheta, and P. S. Davids, “Electronically controlled optical beam-steering by an active phased array of metallic nanoantennas,” Opt. Express 21(4), 5198–5208 (2013).
    [Crossref] [PubMed]
  21. S. T. Winnall, A. C. Lindsay, and G. A. Knight, “A wide-band microwave photonic phase and frequency shifter,” IEEE Trans. Microw. Theory Tech. 45(6), 1003–1006 (1997).
    [Crossref]

2016 (1)

T. Niu, X. Wang, E. H. W. Chan, X. Feng, and B. Guan, “Dual-polarisation dual-parallel MZM and optical phase controller based microwave photonic phase controller,” IEEE Photonics J. 8(4), 5501114 (2016).
[Crossref]

2014 (3)

2013 (3)

2012 (2)

2011 (1)

2010 (1)

2006 (1)

A. Loayssa and F. J. Lahoz, “Broad-band RF photonic phase shifter based on stimulated Brillouin scattering and single-sideband modulation,” IEEE Photonics Technol. Lett. 18(1), 208–210 (2006).
[Crossref]

2001 (1)

K. Higuma, S. Oikawa, Y. Hashimoto, H. Nagata, and M. Izutsu, “X-cut lithium niobate optical single-sideband modulator,” Electron. Lett. 37(8), 515–516 (2001).
[Crossref]

1997 (2)

C. Cox, E. Ackerman, R. Helkey, and G. E. Betts, “Techniques and performance of intensity-modulation direct-detection analog optical links,” IEEE Trans. Microw. Theory Tech. 45(8), 1375–1383 (1997).
[Crossref]

S. T. Winnall, A. C. Lindsay, and G. A. Knight, “A wide-band microwave photonic phase and frequency shifter,” IEEE Trans. Microw. Theory Tech. 45(6), 1003–1006 (1997).
[Crossref]

1995 (1)

K. Noguchi, O. Mitomi, H. Miyazawa, and S. Seki, “A broadband Ti:LiNbO3 optical modulator with a ridge structure,” J. Lightwave Technol. 13(6), 1164–1168 (1995).
[Crossref]

Ackerman, E.

C. Cox, E. Ackerman, R. Helkey, and G. E. Betts, “Techniques and performance of intensity-modulation direct-detection analog optical links,” IEEE Trans. Microw. Theory Tech. 45(8), 1375–1383 (1997).
[Crossref]

Betts, G. E.

C. Cox, E. Ackerman, R. Helkey, and G. E. Betts, “Techniques and performance of intensity-modulation direct-detection analog optical links,” IEEE Trans. Microw. Theory Tech. 45(8), 1375–1383 (1997).
[Crossref]

Bui, L. A.

H. Emami, L. A. Bui, S. Mansoori, and A. Mitchell, “Quadrature hybrid coupler using photonic transversal approach,” Australian Conference on Optical Fibre Technology, 1–3 (2006).
[Crossref]

Capmany, J.

Chan, E. H. W.

T. Niu, X. Wang, E. H. W. Chan, X. Feng, and B. Guan, “Dual-polarisation dual-parallel MZM and optical phase controller based microwave photonic phase controller,” IEEE Photonics J. 8(4), 5501114 (2016).
[Crossref]

R. A. Minasian, E. H. W. Chan, and X. Yi, “Microwave photonic signal processing,” Opt. Express 21(19), 22918–22936 (2013).
[Crossref] [PubMed]

X. Wang, E. H. W. Chan, and R. A. Minasian, “All-optical photonic microwave phase shifter based on an optical filter with a nonlinear phase response,” J. Lightwave Technol. 31(20), 3323–3330 (2013).
[Crossref]

E. H. W. Chan, W. Zhang, and R. A. Minasian, “Photonic RF phase shifter based on optical carrier and RF modulation sidebands amplitude and phase control,” J. Lightwave Technol. 30(23), 3672–3678 (2012).
[Crossref]

T. Niu, E. H. W. Chan, X. Wang, X. Feng, and B. Guan, “Broadband dual-polarization dual-parallel Mach Zehnder modulator based photonic microwave phase shifter,” Optoelectronics and Communications Conference, 1–3 (2016).

Chettiar, U.

Cox, C.

C. Cox, E. Ackerman, R. Helkey, and G. E. Betts, “Techniques and performance of intensity-modulation direct-detection analog optical links,” IEEE Trans. Microw. Theory Tech. 45(8), 1375–1383 (1997).
[Crossref]

Davids, P. S.

DeRose, C. T.

Emami, H.

H. Emami, L. A. Bui, S. Mansoori, and A. Mitchell, “Quadrature hybrid coupler using photonic transversal approach,” Australian Conference on Optical Fibre Technology, 1–3 (2006).
[Crossref]

Engheta, N.

Feng, X.

T. Niu, X. Wang, E. H. W. Chan, X. Feng, and B. Guan, “Dual-polarisation dual-parallel MZM and optical phase controller based microwave photonic phase controller,” IEEE Photonics J. 8(4), 5501114 (2016).
[Crossref]

T. Niu, E. H. W. Chan, X. Wang, X. Feng, and B. Guan, “Broadband dual-polarization dual-parallel Mach Zehnder modulator based photonic microwave phase shifter,” Optoelectronics and Communications Conference, 1–3 (2016).

Guan, B.

T. Niu, X. Wang, E. H. W. Chan, X. Feng, and B. Guan, “Dual-polarisation dual-parallel MZM and optical phase controller based microwave photonic phase controller,” IEEE Photonics J. 8(4), 5501114 (2016).
[Crossref]

T. Niu, E. H. W. Chan, X. Wang, X. Feng, and B. Guan, “Broadband dual-polarization dual-parallel Mach Zehnder modulator based photonic microwave phase shifter,” Optoelectronics and Communications Conference, 1–3 (2016).

Hashimoto, Y.

K. Higuma, S. Oikawa, Y. Hashimoto, H. Nagata, and M. Izutsu, “X-cut lithium niobate optical single-sideband modulator,” Electron. Lett. 37(8), 515–516 (2001).
[Crossref]

Helkey, R.

C. Cox, E. Ackerman, R. Helkey, and G. E. Betts, “Techniques and performance of intensity-modulation direct-detection analog optical links,” IEEE Trans. Microw. Theory Tech. 45(8), 1375–1383 (1997).
[Crossref]

Higuma, K.

K. Higuma, S. Oikawa, Y. Hashimoto, H. Nagata, and M. Izutsu, “X-cut lithium niobate optical single-sideband modulator,” Electron. Lett. 37(8), 515–516 (2001).
[Crossref]

Izutsu, M.

K. Higuma, S. Oikawa, Y. Hashimoto, H. Nagata, and M. Izutsu, “X-cut lithium niobate optical single-sideband modulator,” Electron. Lett. 37(8), 515–516 (2001).
[Crossref]

Kekatpure, R. D.

Knight, G. A.

S. T. Winnall, A. C. Lindsay, and G. A. Knight, “A wide-band microwave photonic phase and frequency shifter,” IEEE Trans. Microw. Theory Tech. 45(6), 1003–1006 (1997).
[Crossref]

Lahoz, F. J.

A. Loayssa and F. J. Lahoz, “Broad-band RF photonic phase shifter based on stimulated Brillouin scattering and single-sideband modulation,” IEEE Photonics Technol. Lett. 18(1), 208–210 (2006).
[Crossref]

Li, W.

W. Li, W. H. Sun, W. T. Wang, and N. H. Zhu, “Optically controlled microwave phase shifter based on nonlinear polarization rotation in a highly nonlinear fiber,” Opt. Lett. 39(11), 3290–3293 (2014).
[Crossref] [PubMed]

W. Li, W. T. Wang, and N. H. Zhu, “Broadband microwave photonic splitter with arbitrary amplitude ratio and phase shift,” IEEE Photonics J. 6(6), 5501507 (2014).
[Crossref]

Lindsay, A. C.

S. T. Winnall, A. C. Lindsay, and G. A. Knight, “A wide-band microwave photonic phase and frequency shifter,” IEEE Trans. Microw. Theory Tech. 45(6), 1003–1006 (1997).
[Crossref]

Liu, W.

Loayssa, A.

A. Loayssa and F. J. Lahoz, “Broad-band RF photonic phase shifter based on stimulated Brillouin scattering and single-sideband modulation,” IEEE Photonics Technol. Lett. 18(1), 208–210 (2006).
[Crossref]

Mansoori, S.

H. Emami, L. A. Bui, S. Mansoori, and A. Mitchell, “Quadrature hybrid coupler using photonic transversal approach,” Australian Conference on Optical Fibre Technology, 1–3 (2006).
[Crossref]

Minasian, R. A.

Mitchell, A.

H. Emami, L. A. Bui, S. Mansoori, and A. Mitchell, “Quadrature hybrid coupler using photonic transversal approach,” Australian Conference on Optical Fibre Technology, 1–3 (2006).
[Crossref]

Mitomi, O.

K. Noguchi, O. Mitomi, H. Miyazawa, and S. Seki, “A broadband Ti:LiNbO3 optical modulator with a ridge structure,” J. Lightwave Technol. 13(6), 1164–1168 (1995).
[Crossref]

Miyazawa, H.

K. Noguchi, O. Mitomi, H. Miyazawa, and S. Seki, “A broadband Ti:LiNbO3 optical modulator with a ridge structure,” J. Lightwave Technol. 13(6), 1164–1168 (1995).
[Crossref]

Mørk, J.

Nagata, H.

K. Higuma, S. Oikawa, Y. Hashimoto, H. Nagata, and M. Izutsu, “X-cut lithium niobate optical single-sideband modulator,” Electron. Lett. 37(8), 515–516 (2001).
[Crossref]

Niu, T.

T. Niu, X. Wang, E. H. W. Chan, X. Feng, and B. Guan, “Dual-polarisation dual-parallel MZM and optical phase controller based microwave photonic phase controller,” IEEE Photonics J. 8(4), 5501114 (2016).
[Crossref]

T. Niu, E. H. W. Chan, X. Wang, X. Feng, and B. Guan, “Broadband dual-polarization dual-parallel Mach Zehnder modulator based photonic microwave phase shifter,” Optoelectronics and Communications Conference, 1–3 (2016).

Noguchi, K.

K. Noguchi, O. Mitomi, H. Miyazawa, and S. Seki, “A broadband Ti:LiNbO3 optical modulator with a ridge structure,” J. Lightwave Technol. 13(6), 1164–1168 (1995).
[Crossref]

Oikawa, S.

K. Higuma, S. Oikawa, Y. Hashimoto, H. Nagata, and M. Izutsu, “X-cut lithium niobate optical single-sideband modulator,” Electron. Lett. 37(8), 515–516 (2001).
[Crossref]

Pan, S.

Sales, S.

Seki, S.

K. Noguchi, O. Mitomi, H. Miyazawa, and S. Seki, “A broadband Ti:LiNbO3 optical modulator with a ridge structure,” J. Lightwave Technol. 13(6), 1164–1168 (1995).
[Crossref]

Starbuck, A.

Sun, W. H.

Trotter, D. C.

Wang, W. T.

W. Li, W. H. Sun, W. T. Wang, and N. H. Zhu, “Optically controlled microwave phase shifter based on nonlinear polarization rotation in a highly nonlinear fiber,” Opt. Lett. 39(11), 3290–3293 (2014).
[Crossref] [PubMed]

W. Li, W. T. Wang, and N. H. Zhu, “Broadband microwave photonic splitter with arbitrary amplitude ratio and phase shift,” IEEE Photonics J. 6(6), 5501507 (2014).
[Crossref]

Wang, X.

T. Niu, X. Wang, E. H. W. Chan, X. Feng, and B. Guan, “Dual-polarisation dual-parallel MZM and optical phase controller based microwave photonic phase controller,” IEEE Photonics J. 8(4), 5501114 (2016).
[Crossref]

X. Wang, E. H. W. Chan, and R. A. Minasian, “All-optical photonic microwave phase shifter based on an optical filter with a nonlinear phase response,” J. Lightwave Technol. 31(20), 3323–3330 (2013).
[Crossref]

T. Niu, E. H. W. Chan, X. Wang, X. Feng, and B. Guan, “Broadband dual-polarization dual-parallel Mach Zehnder modulator based photonic microwave phase shifter,” Optoelectronics and Communications Conference, 1–3 (2016).

Watts, M. R.

Wendt, J. R.

Winnall, S. T.

S. T. Winnall, A. C. Lindsay, and G. A. Knight, “A wide-band microwave photonic phase and frequency shifter,” IEEE Trans. Microw. Theory Tech. 45(6), 1003–1006 (1997).
[Crossref]

Xue, W.

Xue, X.

Yaacobi, A.

Yao, J.

Yi, X.

Zhang, H.

Zhang, W.

Zhang, Y.

Zheng, X.

Zhou, B.

Zhu, N. H.

W. Li, W. T. Wang, and N. H. Zhu, “Broadband microwave photonic splitter with arbitrary amplitude ratio and phase shift,” IEEE Photonics J. 6(6), 5501507 (2014).
[Crossref]

W. Li, W. H. Sun, W. T. Wang, and N. H. Zhu, “Optically controlled microwave phase shifter based on nonlinear polarization rotation in a highly nonlinear fiber,” Opt. Lett. 39(11), 3290–3293 (2014).
[Crossref] [PubMed]

Electron. Lett. (1)

K. Higuma, S. Oikawa, Y. Hashimoto, H. Nagata, and M. Izutsu, “X-cut lithium niobate optical single-sideband modulator,” Electron. Lett. 37(8), 515–516 (2001).
[Crossref]

IEEE Photonics J. (2)

T. Niu, X. Wang, E. H. W. Chan, X. Feng, and B. Guan, “Dual-polarisation dual-parallel MZM and optical phase controller based microwave photonic phase controller,” IEEE Photonics J. 8(4), 5501114 (2016).
[Crossref]

W. Li, W. T. Wang, and N. H. Zhu, “Broadband microwave photonic splitter with arbitrary amplitude ratio and phase shift,” IEEE Photonics J. 6(6), 5501507 (2014).
[Crossref]

IEEE Photonics Technol. Lett. (1)

A. Loayssa and F. J. Lahoz, “Broad-band RF photonic phase shifter based on stimulated Brillouin scattering and single-sideband modulation,” IEEE Photonics Technol. Lett. 18(1), 208–210 (2006).
[Crossref]

IEEE Trans. Microw. Theory Tech. (2)

C. Cox, E. Ackerman, R. Helkey, and G. E. Betts, “Techniques and performance of intensity-modulation direct-detection analog optical links,” IEEE Trans. Microw. Theory Tech. 45(8), 1375–1383 (1997).
[Crossref]

S. T. Winnall, A. C. Lindsay, and G. A. Knight, “A wide-band microwave photonic phase and frequency shifter,” IEEE Trans. Microw. Theory Tech. 45(6), 1003–1006 (1997).
[Crossref]

J. Lightwave Technol. (3)

Opt. Express (3)

Opt. Lett. (4)

Other (5)

T. Niu, E. H. W. Chan, X. Wang, X. Feng, and B. Guan, “Broadband dual-polarization dual-parallel Mach Zehnder modulator based photonic microwave phase shifter,” Optoelectronics and Communications Conference, 1–3 (2016).

M. E. Manka, “Microwave photonics electronic warfare technologies for Australian defence,” IEEE International Topical Meeting on Microwave Photonics (MWP 2008), 1–2 (2008).

ARCOptix polarisation rotator, http://www.arcoptix.com/polarization_rotator.htm .

H. Emami, L. A. Bui, S. Mansoori, and A. Mitchell, “Quadrature hybrid coupler using photonic transversal approach,” Australian Conference on Optical Fibre Technology, 1–3 (2006).
[Crossref]

“Hybrid coupler basic,” MECA Electronics Inc., http://www.e-meca.com/rf-microwave-blog/hybrid-coupler-basics .

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)
Fig. 1
Fig. 1 (a) Topology of the new ultra-wide bandwidth photonic microwave phase shifter and (b) the carrier (red line) at the bottom DPMZM output, and the carrier and sideband (black line) at the top DPMZM output. The frequency response of the optical filter used in the phase shifter structure (dashed line).

Download Full Size | PPT Slide | PDF

Fig. 2
Fig. 2 Measured (a) amplitude and (b) phase response at the 0° (blue dotted line) and 90° (red solid line) output port of a 2–26.5 GHz bandwidth 90° hybrid coupler.

Download Full Size | PPT Slide | PDF

Fig. 3
Fig. 3 Experimental setup of the new ultra-wide bandwidth photonic microwave phase shifter.

Download Full Size | PPT Slide | PDF

Fig. 4
Fig. 4 Measured optical spectrum (a) before and (b) after the optical filter with 15 GHz (red dotted line) and 30 GHz (blue solid line) RF signal frequency into the modulator. The spectrum of the optical filter used in the experiment (dashed line).

Download Full Size | PPT Slide | PDF

Fig. 5
Fig. 5 Measured (a) amplitude and (b) phase response of the ultra-wide bandwidth photonic microwave phase shifter for different phase shifts. Vb2 was fixed at −2.8 V to maximize the optical carrier amplitude and Vb3 was varied from −14.1 V to + 14.2 V to alter the optical carrier phase to realize −180° to 180° RF signal phase shift.

Download Full Size | PPT Slide | PDF

Fig. 6
Fig. 6 Measured (a) amplitude and (b) phase response of the ultra-wide bandwidth photonic microwave phase shifter for different phase shifts when the laser wavelength was 0.08 nm away from the desired value. Vb2 was fixed at −2.8 V to maximize the optical carrier amplitude and Vb3 was varied from −14.1 V to + 14.2 V to alter the optical carrier phase to realize −180° to 180° RF signal phase shift.

Download Full Size | PPT Slide | PDF

Fig. 7
Fig. 7 Measured (a) amplitude and (b) phase response of a conventional photonic microwave phase shifter implemented using only the optical filtering technique to realize SSB modulation. Measured (c) amplitude and (d) phase response of the same phase shifter when the laser wavelength was 0.08 nm away from the desired value.

Download Full Size | PPT Slide | PDF

Fig. 8
Fig. 8 Measured (a) amplitude and (b) phase response of the ultra-wide bandwidth photonic microwave phase shifter demonstrating the amplitude control function at 90° phase shift. Vb3 was fixed at 7.1 V to obtain 90° phase shift and Vb2 was varied from −2.8 V to 3.4 V to obtain 15 dB changes in the output RF signal amplitude.

Download Full Size | PPT Slide | PDF

Equations (5)

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

E o u t ( t ) = E i n 2 t f f L P o l L O F [ cos ( π V b 2 V π ) cos ( ω c t + π V b 3 V π ) + β R F sin ( ω c − ω R F ) t ]
I R F = − ℜ P i n 4 t f f L P o l L O F β R F cos ( π V b 2 V π ) sin ( ω R F t + π V b 3 V π )
P R F , o u t = ℜ 2 P i n 2 32 t f f 2 L P o l 2 L O F 2 β R F 2 cos 2 ( π V b 2 V π ) R o
θ R F , o u t = π V b 3 V π
G = P R F , o u t P R F , i n = ℜ 2 P i n 2 32 t f f 2 L P o l 2 L O F 2 ( π V π ) 2 cos 2 ( π V b 2 V π ) L R i n R o

Metrics