Abstract

Guided-wave and free-space optical interconnects are compared based on insertion loss, link efficiency, connection density, time delay, and power dissipation for three types of connection networks. Three types of free-space interconnect systems are analyzed that are representative of a wide variety of free-space systems: space-variant basis-set and space-invarient systems. Results indicate that the connection density of a space-variant free space system has a connection density roughly equivalent to a two level guided-wave system with a pitch of ~10 μm (for a 1-μm wavelength) and a core refractive index of 2.0. It is also shown that the connection density of basis-set and space-invariant free-space systems can be several orders of magnitude higher than fundamental limits on the connection density of dual-level guided-wave interconnect systems when large-scale highly connected networks are employed.

© 1994 Optical Society of America

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References

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  1. E. E. E. Frietman, W. van Nifterick, L. Dekker, T. J. M. Jongeling, “Parallel optical interconnects: implementation of optoelectronics in multiprocessor architecture,” Appl. Opt. 29, 1161–1167(1990).
    [CrossRef] [PubMed]
  2. Y. Yamada, M. Yamada, H. Terui, M. Kobayashi, “Optical interconnections using a silica-based waveguide on a silicon substrate,” Opt. Eng. 28, 1281–1287 (1989).
  3. R. Selvaraj, H. T. Lin, J. F. McDonald, “Integrated optical waveguides in polyimide for wafer scale integration,” J. Lightwave Technol. 6, 1034–1037 (1988).
    [CrossRef]
  4. A. Guha, J. Briston, C. Sullivan, A. Husain, “Optical interconnects for massively parallel architectures,” Appl. Opt. 29, 1077–1093 (1990).
    [CrossRef] [PubMed]
  5. M. R. Feldman, C. C. Guest, “Interconnect density capabilities of computer generated holograms for optical interconnection of very large scale integrated circuits,” Appl. Opt. 28, 3134–3137(1989).
    [CrossRef] [PubMed]
  6. M. R. Feldman, C. C. Guest, “Computer generated holograms for optical interconnection of very large scale integrated circuits,” Appl. Opt. 26, 4377–4384 (1987).
    [CrossRef] [PubMed]
  7. M. R. Feldman, C. C. Guest, T. J. Drabik, S. C. Esener, “Comparison between electrical and free-space optical interconnects for fine grain processor arrays based on interconnect density capabilities,” Appl. Opt. 28, 3820–3829 (1989).
    [CrossRef] [PubMed]
  8. B. K. Jenkins, P. Chavel, R. Forchheimer, A. A. Sawchuck, T. C. Strand, “Architectural implications of a digital optical processor,” Appl. Opt. 23, 3465–3474 (1984).
    [CrossRef] [PubMed]
  9. C. W. Stirk, R. A. Athale, M. W. Haney, “Folded perfect shuffle optical processor,” Appl. Opt. 27, 202–203 (1988).
    [CrossRef] [PubMed]
  10. C. D. Thompson, “Area–time complexity for VLSI,” presented at the Eleventh Annual Association for Computing Machinery Symposium on the Theory of Computing, Atlanta, Ga., 30 April 1979.
  11. J. Turunen, J. Fagerholm, A. Vasara, M. Tahizadeh, “Detour-phase kinoform interconnects: the concept and fabrication considerations,” J. Opt. Soc. Am. A 7, 1202–1208 (1990).
    [CrossRef]
  12. F. Hickernell, “Optical waveguides on silicon,” Solid State Technol.83–87 (1988).
  13. J. D. Stack, M. R. Feldman, “Recursive mean-squared-error algorithm for iterative discrete on-axis encoded holograms,” Appl. Opt. 31, 4839–4846 (1992).
    [CrossRef] [PubMed]
  14. W. H. Welch, M. R. Feldman, “Iterative discrete on-axis encoding of diffractive optical elements,” in Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 72.
  15. J. Jahns, S. J. Walker, “Two-dimensional array of diffractive microlenses frabricated by thin film deposition,” Appl. Opt. 29, 931–936 (1990).
    [CrossRef] [PubMed]
  16. S. Somileno, B. Crosignani, P. D. Porto, Guiding Diffraction and Confinement of Optical Radiation (Academic, New York, 1986), p. 563.
  17. W. Stutius, W. Streiter, “Silicon nitride films on silicon for optical waveguides,” Appl. Opt. 16, 3218–3222 (1977).
    [CrossRef] [PubMed]
  18. M. R. Feldman, S. C. Esener, C. C. Guest, S. H. Lee, “Comparison between optical and electrical interconnects based on power and speed considerations,” Appl. Opt. 27, 1742–1751 (1988).
    [CrossRef] [PubMed]
  19. Y. Chung, R. Spickermann, D. B. Young, N. Dagli, “A low-loss beam splitter with an optimized waveguide structure,” IEEE Photon. Technol. Lett. 4, 1009–1011 (1992).
    [CrossRef]
  20. P. R. Haugen, S. Rychnovsky, A. Husain, L. D. Hutcheson, “Optical interconnects for high speed computing,” Opt. Eng. 25, 1076–1085 (1986).
  21. H. Kogelnik, “Limits of integrated optics,” Proc. IEEE 69, 232–238(1981).
    [CrossRef]
  22. D. Marcuse, Light Transmission Optics, 2nd ed. (Van Nostrand Reinhold, New York, 1982), p. 425.
  23. Ref. 22, p. 427.
  24. W. H. Welch, J. E. Morris, M. R. Feldman, “Iterative discrete on-axis encoding of radially symmetric computer-generated holograms,” J. Opt. Soc. Am. A 10, 1729–1738 (1993).
    [CrossRef]
  25. T. Baba, Y. Kokobun, “High efficiency light coupling from antiresonant reflecting optical waveguide to integrated photodetector using an antireflecting layer,” Appl. Opt. 29, 2781–2791 (1990).
    [CrossRef] [PubMed]
  26. T. E. V. Eck, A. J. Ticknor, R. Lytel, G. F. Lipscomb, “A complementary optical tap fabricated in an electro-optic polymer waveguide,” Appl. Phys. Lett. (to be published).
  27. G. Mak, D. Bruce, P. Jessop, “Waveguide–detector couplers for integrated optics and monolithic switching arrays,” Appl. Opt. 28, 4629–4636 (1989).
    [CrossRef] [PubMed]
  28. J. Schwider, W. Stork, N. Streibl, R. Völkel, “Possibilities and limitations of space-variant holographic elements for switching networks and general interconnects,” Appl. Opt. 31, 7403–7410 (1992).
    [CrossRef] [PubMed]

1993 (1)

1992 (3)

1990 (5)

1989 (4)

1988 (4)

R. Selvaraj, H. T. Lin, J. F. McDonald, “Integrated optical waveguides in polyimide for wafer scale integration,” J. Lightwave Technol. 6, 1034–1037 (1988).
[CrossRef]

F. Hickernell, “Optical waveguides on silicon,” Solid State Technol.83–87 (1988).

C. W. Stirk, R. A. Athale, M. W. Haney, “Folded perfect shuffle optical processor,” Appl. Opt. 27, 202–203 (1988).
[CrossRef] [PubMed]

M. R. Feldman, S. C. Esener, C. C. Guest, S. H. Lee, “Comparison between optical and electrical interconnects based on power and speed considerations,” Appl. Opt. 27, 1742–1751 (1988).
[CrossRef] [PubMed]

1987 (1)

1986 (1)

P. R. Haugen, S. Rychnovsky, A. Husain, L. D. Hutcheson, “Optical interconnects for high speed computing,” Opt. Eng. 25, 1076–1085 (1986).

1984 (1)

1981 (1)

H. Kogelnik, “Limits of integrated optics,” Proc. IEEE 69, 232–238(1981).
[CrossRef]

1977 (1)

Athale, R. A.

Baba, T.

Briston, J.

Bruce, D.

Chavel, P.

Chung, Y.

Y. Chung, R. Spickermann, D. B. Young, N. Dagli, “A low-loss beam splitter with an optimized waveguide structure,” IEEE Photon. Technol. Lett. 4, 1009–1011 (1992).
[CrossRef]

Crosignani, B.

S. Somileno, B. Crosignani, P. D. Porto, Guiding Diffraction and Confinement of Optical Radiation (Academic, New York, 1986), p. 563.

Dagli, N.

Y. Chung, R. Spickermann, D. B. Young, N. Dagli, “A low-loss beam splitter with an optimized waveguide structure,” IEEE Photon. Technol. Lett. 4, 1009–1011 (1992).
[CrossRef]

Dekker, L.

Drabik, T. J.

Eck, T. E. V.

T. E. V. Eck, A. J. Ticknor, R. Lytel, G. F. Lipscomb, “A complementary optical tap fabricated in an electro-optic polymer waveguide,” Appl. Phys. Lett. (to be published).

Esener, S. C.

Fagerholm, J.

Feldman, M. R.

Forchheimer, R.

Frietman, E. E. E.

Guest, C. C.

Guha, A.

Haney, M. W.

Haugen, P. R.

P. R. Haugen, S. Rychnovsky, A. Husain, L. D. Hutcheson, “Optical interconnects for high speed computing,” Opt. Eng. 25, 1076–1085 (1986).

Hickernell, F.

F. Hickernell, “Optical waveguides on silicon,” Solid State Technol.83–87 (1988).

Husain, A.

A. Guha, J. Briston, C. Sullivan, A. Husain, “Optical interconnects for massively parallel architectures,” Appl. Opt. 29, 1077–1093 (1990).
[CrossRef] [PubMed]

P. R. Haugen, S. Rychnovsky, A. Husain, L. D. Hutcheson, “Optical interconnects for high speed computing,” Opt. Eng. 25, 1076–1085 (1986).

Hutcheson, L. D.

P. R. Haugen, S. Rychnovsky, A. Husain, L. D. Hutcheson, “Optical interconnects for high speed computing,” Opt. Eng. 25, 1076–1085 (1986).

Jahns, J.

Jenkins, B. K.

Jessop, P.

Jongeling, T. J. M.

Kobayashi, M.

Y. Yamada, M. Yamada, H. Terui, M. Kobayashi, “Optical interconnections using a silica-based waveguide on a silicon substrate,” Opt. Eng. 28, 1281–1287 (1989).

Kogelnik, H.

H. Kogelnik, “Limits of integrated optics,” Proc. IEEE 69, 232–238(1981).
[CrossRef]

Kokobun, Y.

Lee, S. H.

Lin, H. T.

R. Selvaraj, H. T. Lin, J. F. McDonald, “Integrated optical waveguides in polyimide for wafer scale integration,” J. Lightwave Technol. 6, 1034–1037 (1988).
[CrossRef]

Lipscomb, G. F.

T. E. V. Eck, A. J. Ticknor, R. Lytel, G. F. Lipscomb, “A complementary optical tap fabricated in an electro-optic polymer waveguide,” Appl. Phys. Lett. (to be published).

Lytel, R.

T. E. V. Eck, A. J. Ticknor, R. Lytel, G. F. Lipscomb, “A complementary optical tap fabricated in an electro-optic polymer waveguide,” Appl. Phys. Lett. (to be published).

Mak, G.

Marcuse, D.

D. Marcuse, Light Transmission Optics, 2nd ed. (Van Nostrand Reinhold, New York, 1982), p. 425.

McDonald, J. F.

R. Selvaraj, H. T. Lin, J. F. McDonald, “Integrated optical waveguides in polyimide for wafer scale integration,” J. Lightwave Technol. 6, 1034–1037 (1988).
[CrossRef]

Morris, J. E.

Porto, P. D.

S. Somileno, B. Crosignani, P. D. Porto, Guiding Diffraction and Confinement of Optical Radiation (Academic, New York, 1986), p. 563.

Rychnovsky, S.

P. R. Haugen, S. Rychnovsky, A. Husain, L. D. Hutcheson, “Optical interconnects for high speed computing,” Opt. Eng. 25, 1076–1085 (1986).

Sawchuck, A. A.

Schwider, J.

Selvaraj, R.

R. Selvaraj, H. T. Lin, J. F. McDonald, “Integrated optical waveguides in polyimide for wafer scale integration,” J. Lightwave Technol. 6, 1034–1037 (1988).
[CrossRef]

Somileno, S.

S. Somileno, B. Crosignani, P. D. Porto, Guiding Diffraction and Confinement of Optical Radiation (Academic, New York, 1986), p. 563.

Spickermann, R.

Y. Chung, R. Spickermann, D. B. Young, N. Dagli, “A low-loss beam splitter with an optimized waveguide structure,” IEEE Photon. Technol. Lett. 4, 1009–1011 (1992).
[CrossRef]

Stack, J. D.

Stirk, C. W.

Stork, W.

Strand, T. C.

Streibl, N.

Streiter, W.

Stutius, W.

Sullivan, C.

Tahizadeh, M.

Terui, H.

Y. Yamada, M. Yamada, H. Terui, M. Kobayashi, “Optical interconnections using a silica-based waveguide on a silicon substrate,” Opt. Eng. 28, 1281–1287 (1989).

Thompson, C. D.

C. D. Thompson, “Area–time complexity for VLSI,” presented at the Eleventh Annual Association for Computing Machinery Symposium on the Theory of Computing, Atlanta, Ga., 30 April 1979.

Ticknor, A. J.

T. E. V. Eck, A. J. Ticknor, R. Lytel, G. F. Lipscomb, “A complementary optical tap fabricated in an electro-optic polymer waveguide,” Appl. Phys. Lett. (to be published).

Turunen, J.

van Nifterick, W.

Vasara, A.

Völkel, R.

Walker, S. J.

Welch, W. H.

W. H. Welch, J. E. Morris, M. R. Feldman, “Iterative discrete on-axis encoding of radially symmetric computer-generated holograms,” J. Opt. Soc. Am. A 10, 1729–1738 (1993).
[CrossRef]

W. H. Welch, M. R. Feldman, “Iterative discrete on-axis encoding of diffractive optical elements,” in Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 72.

Yamada, M.

Y. Yamada, M. Yamada, H. Terui, M. Kobayashi, “Optical interconnections using a silica-based waveguide on a silicon substrate,” Opt. Eng. 28, 1281–1287 (1989).

Yamada, Y.

Y. Yamada, M. Yamada, H. Terui, M. Kobayashi, “Optical interconnections using a silica-based waveguide on a silicon substrate,” Opt. Eng. 28, 1281–1287 (1989).

Young, D. B.

Y. Chung, R. Spickermann, D. B. Young, N. Dagli, “A low-loss beam splitter with an optimized waveguide structure,” IEEE Photon. Technol. Lett. 4, 1009–1011 (1992).
[CrossRef]

Appl. Opt. (14)

W. Stutius, W. Streiter, “Silicon nitride films on silicon for optical waveguides,” Appl. Opt. 16, 3218–3222 (1977).
[CrossRef] [PubMed]

B. K. Jenkins, P. Chavel, R. Forchheimer, A. A. Sawchuck, T. C. Strand, “Architectural implications of a digital optical processor,” Appl. Opt. 23, 3465–3474 (1984).
[CrossRef] [PubMed]

M. R. Feldman, C. C. Guest, “Computer generated holograms for optical interconnection of very large scale integrated circuits,” Appl. Opt. 26, 4377–4384 (1987).
[CrossRef] [PubMed]

M. R. Feldman, S. C. Esener, C. C. Guest, S. H. Lee, “Comparison between optical and electrical interconnects based on power and speed considerations,” Appl. Opt. 27, 1742–1751 (1988).
[CrossRef] [PubMed]

M. R. Feldman, C. C. Guest, “Interconnect density capabilities of computer generated holograms for optical interconnection of very large scale integrated circuits,” Appl. Opt. 28, 3134–3137(1989).
[CrossRef] [PubMed]

M. R. Feldman, C. C. Guest, T. J. Drabik, S. C. Esener, “Comparison between electrical and free-space optical interconnects for fine grain processor arrays based on interconnect density capabilities,” Appl. Opt. 28, 3820–3829 (1989).
[CrossRef] [PubMed]

G. Mak, D. Bruce, P. Jessop, “Waveguide–detector couplers for integrated optics and monolithic switching arrays,” Appl. Opt. 28, 4629–4636 (1989).
[CrossRef] [PubMed]

A. Guha, J. Briston, C. Sullivan, A. Husain, “Optical interconnects for massively parallel architectures,” Appl. Opt. 29, 1077–1093 (1990).
[CrossRef] [PubMed]

E. E. E. Frietman, W. van Nifterick, L. Dekker, T. J. M. Jongeling, “Parallel optical interconnects: implementation of optoelectronics in multiprocessor architecture,” Appl. Opt. 29, 1161–1167(1990).
[CrossRef] [PubMed]

T. Baba, Y. Kokobun, “High efficiency light coupling from antiresonant reflecting optical waveguide to integrated photodetector using an antireflecting layer,” Appl. Opt. 29, 2781–2791 (1990).
[CrossRef] [PubMed]

J. D. Stack, M. R. Feldman, “Recursive mean-squared-error algorithm for iterative discrete on-axis encoded holograms,” Appl. Opt. 31, 4839–4846 (1992).
[CrossRef] [PubMed]

J. Schwider, W. Stork, N. Streibl, R. Völkel, “Possibilities and limitations of space-variant holographic elements for switching networks and general interconnects,” Appl. Opt. 31, 7403–7410 (1992).
[CrossRef] [PubMed]

J. Jahns, S. J. Walker, “Two-dimensional array of diffractive microlenses frabricated by thin film deposition,” Appl. Opt. 29, 931–936 (1990).
[CrossRef] [PubMed]

C. W. Stirk, R. A. Athale, M. W. Haney, “Folded perfect shuffle optical processor,” Appl. Opt. 27, 202–203 (1988).
[CrossRef] [PubMed]

IEEE Photon. Technol. Lett. (1)

Y. Chung, R. Spickermann, D. B. Young, N. Dagli, “A low-loss beam splitter with an optimized waveguide structure,” IEEE Photon. Technol. Lett. 4, 1009–1011 (1992).
[CrossRef]

J. Lightwave Technol. (1)

R. Selvaraj, H. T. Lin, J. F. McDonald, “Integrated optical waveguides in polyimide for wafer scale integration,” J. Lightwave Technol. 6, 1034–1037 (1988).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Eng. (2)

Y. Yamada, M. Yamada, H. Terui, M. Kobayashi, “Optical interconnections using a silica-based waveguide on a silicon substrate,” Opt. Eng. 28, 1281–1287 (1989).

P. R. Haugen, S. Rychnovsky, A. Husain, L. D. Hutcheson, “Optical interconnects for high speed computing,” Opt. Eng. 25, 1076–1085 (1986).

Proc. IEEE (1)

H. Kogelnik, “Limits of integrated optics,” Proc. IEEE 69, 232–238(1981).
[CrossRef]

Solid State Technol. (1)

F. Hickernell, “Optical waveguides on silicon,” Solid State Technol.83–87 (1988).

Other (6)

W. H. Welch, M. R. Feldman, “Iterative discrete on-axis encoding of diffractive optical elements,” in Annual Meeting, Vol. 15 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 72.

S. Somileno, B. Crosignani, P. D. Porto, Guiding Diffraction and Confinement of Optical Radiation (Academic, New York, 1986), p. 563.

C. D. Thompson, “Area–time complexity for VLSI,” presented at the Eleventh Annual Association for Computing Machinery Symposium on the Theory of Computing, Atlanta, Ga., 30 April 1979.

D. Marcuse, Light Transmission Optics, 2nd ed. (Van Nostrand Reinhold, New York, 1982), p. 425.

Ref. 22, p. 427.

T. E. V. Eck, A. J. Ticknor, R. Lytel, G. F. Lipscomb, “A complementary optical tap fabricated in an electro-optic polymer waveguide,” Appl. Phys. Lett. (to be published).

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Figures (11)

Fig. 1
Fig. 1

Double-pass hologram system configuration as assumed in derivations: n, index of refraction; L, distance between the laser and the detector; R, distance between the CGH and the mirror.

Fig. 2
Fig. 2

Folded-basis-set system: ϕ.

Fig. 3
Fig. 3

Basis-set hologram configuration.

Fig. 4
Fig. 4

Two-level waveguide configuration as assumed in Table 2.

Fig. 5
Fig. 5

Dependence of optical link efficiency on source-to-detector distance. Coupling efficiency is neglected.

Fig. 6
Fig. 6

Dependence of optical link efficiency for the longest link on the number of linear fan-out destinations. Connection length is 5 cm.

Fig. 7
Fig. 7

Connection-density limitations for waveguide optical interconnects. The fundamental limit on the number of connections in a 10-cm module diameter for guide index 2.0, cladding index 1.45, and 10% cross-talk loss is shown in Fig. 5. The number of connections that can be made in a hypercube if the tolerable loss is 10% and the number of connections that can be connected if the lowest tolerable SNR is 5 are shown.

Fig. 8
Fig. 8

Dependence of SNR on the number of processors connected in a hypercube and in fully connected networks. The signal-to-noise ratio corresponds to that of the longest connection in an array of a given number of processors.

Fig. 9
Fig. 9

Processor area, area required by waveguides, and hologram area for connecting processors in (a) a mesh interconnect network, (b) a hypercube configuration, and (c) a fully connected system.

Fig. 10
Fig. 10

Effects of planar constraints on signal delay in (a) a hypercube and (b) a fully connected network.

Fig. 11
Fig. 11

Switching energy for (a) a connection in a mesh configuration, (b) the longest connection for up to 100,000 processors connected in a hypercube configuration, and (c) the same as (b) for a fully connected network.

Tables (2)

Tables Icon

Table 1 Parameters for Three Connection Networks that Cover a Wide Range of Connectivity

Tables Icon

Table 2 Implementation-Dependent Connection Configuration Parameters for Two-Level Waveguide and Double-Pass Hologram Implementations

Equations (39)

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L MAX = L MAX N 1 / 2 / A 1 / 2 ,
η = P D / P L .
η SV = η h 2 / F ,
η bs = η h 3 / F .
η gw = κ wd κ sw Γ ( d ) ,
Γ ( d ) = log 1 ( γ d d / 10 ) ;
P L = 1 { F Γ s F 1 / [ ( Γ s ) k + 1 ] } × ( sum is for k = 0 to k = F 2 ) ,
Γ s = log 1 ( γ s / 10 ) .
η gw = κ wd κ sw [ Γ ( d ) Γ s ] F 1 / { [ Γ ( d ) Γ s ] k + 1 } ,
η gw = κ wd κ sw Γ ( d ) / F ,
W = λ / ( n w 2 n c 2 ) 1 / 2 .
PR = L 2 C 2 ,
C = ( n g 2 k 0 2 β 2 ) ( β 2 n c 2 k 0 2 ) β ( 1 + γ d ) k 0 2 ( n g 2 n c 2 ) exp [ γ ( W S ) ] ,
k 0 = 2 π / λ 0 , γ = ( k 0 2 n c 2 β 2 ) 1 / 2 , β 2 = n g 2 k 0 2 [ 1 2 ( Δ n ) 1 / 2 n g k 0 W ] ,
Δ n = ( n g 2 n c 2 ) n g 2 .
# c / A 1 / 2 = 1 / ( S + W ) = [ S + λ / ( n w 2 n c 2 ) 1 / 2 ] 1 .
B A 1 / 2 / ( S + W ) .
A h = N A s + N F A d = 2 N F A d
A d 4 ( 1 . 2 ) 2 λ 2 f 2 / A cos 4 Φ ,
A d = ( 1 . 2 ) 2 λ 2 / ( cos 4 Φ tan 2 Φ ) .
A 4 ( 1 . 2 ) 2 λ 2 N F .
B / A 1 / 2 = A 1 / 2 / [ 4 ( 1 . 2 ) 2 λ 2 ] .
η gw = κ log 1 ( γ d d / 10 ) log 1 ( γ x x / 10 ) .
signal = log 1 ( γ x x ) log 1 ( γ d d ) ,
noise = x log 1 ( noise x ) ,
SNR = log 1 ( γ x x ) log 1 ( γ d d ) x log 1 ( noise x ) .
A d = 16 ( 1 . 2 ) 2 λ 2 h 2 / ( D 2 cos 4 Φ ) ,
D 2 = F A d .
A d = 2 ( 1 . 2 ) λ L MAX / ( F 1 / 2 cos 2 Φ tan Φ ) ,
A = 16 ( 1 . 2 ) 2 λ 2 L MAX 2 N F / ( cos 4 Φ tan 2 Φ ) .
A 92 N F λ 2 L MAX 2 .
A 92 N F M λ 2 ,
d = 2 [ R 2 + ( d / 2 ) 2 ] 1 / 2 .
τ fs = 2 1 / 2 L / c .
τ gw = α L n / c .
N 1 / 2 W w g W pe n 2 1 / 2
E = 2 T P th + 2 ( C gate + C pd ) V cc h ν ηη s η d q ,
E gw = 2 P th T + 2 ( C gate + C pd ) h ν q V cc κ wd κ sw η s η d τ ( d ) .
E fs = 2 P th T + 2 ( C gate + C pd ) h ν q V cc η s η d η h .

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