Abstract

In this paper the effect of mismatch and loss of the input lossy impedance matching network on the noise figure (NF) of microwave photonic links (MWPLs) operating under large radio frequency (RF) signal modulation is theoretically investigated. An intensity-modulation with direct-detection (IMDD) MWPL in which the external modulator is a Mach-Zehnder modulator (MZM) is studied here. The nonlinear input-output relationship of the MZM under large RF signal modulation can lead this link to operate in the nonlinear large-signal regime. The main goal of this paper is to investigate and find the input impedance mismatch conditions for minimizing large-signal NF of MWPLs. To the best of our knowledge, this is the first study on this subject. It is found that large-signal NF of an IMDD MWPL depends on the input impedance mismatch factor and input applied RF power. It is shown that for M0.39 the NF can be minimized that is approximately 0.95dB lower compared to the NF at the perfect match (M=1). Regarding a generic optoelectronic oscillator (OEO) containing a MWPL at saturation, the value of this analytical approach is to study the effect of such large-signal NF on the OEO phase noise performance.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007).
    [Crossref]
  2. S. Iezekiel, Microwave Photonics: Devices and Applications (Wiley, 2009).
  3. J. Yao, “Microwave photonics,” J. Lightwave Technol. 27(3), 314–335 (2009).
    [Crossref]
  4. X. S. Yao and L. Maleki, “Optoelectronic microwave oscillator,” J. Opt. Soc. Am. 13(8), 1725–1735 (1996).
    [Crossref]
  5. S. E. Hosseini, A. Banai, and F. X. Kartner, “Tunable low-jitter low-drift spurious-free transposed-frequency optoelectronic oscillator,” IEEE Trans. Microw. Theory Tech. 65(7), 2625–2635 (2017).
    [Crossref]
  6. S. E. Hosseini, A. Banai, and F. X. Kartner, “Low-drift optoelectronic oscillator based on a phase modulator in a sagnac loop,” IEEE Trans. Microw. Theory Tech. 65(7), 2617–2624 (2017).
    [Crossref]
  7. K. Saleh, R. Henriet, S. Diallo, G. Lin, R. Martinenghi, I. V. Balakireva, P. Salzenstein, A. Coillet, and Y. K. Chembo, “Phase noise performance comparison between optoelectronic oscillators based on optical delay lines and whispering gallery mode resonators,” Opt. Express 22(26), 32158–32173 (2014).
    [Crossref] [PubMed]
  8. S. E. Hosseini, S. Shojaeddin, and H. Abiri, “Theoretical investigation of an ultra-low phase noise microwave oscillator based on an IF crystal resonator-amplifier and a microwave photonic frequency transposer,” J. Opt. Soc. Am. B 35(6), 1422–1432 (2018).
    [Crossref]
  9. E. I. Ackerman, C. Cox, G. Betts, H. Roussell, F. O’Donnell, and K. Ray, “Input impedance conditions for minimizing the noise figure of an analog optical link,” IEEE Trans. Microw. Theory Tech. 46(12), 2025–2031 (1998).
    [Crossref]
  10. S. E. Hosseini and A. Banai, “Noise figure of microwave photonic links operating under large-signal modulation and its application to optoelectronic oscillators,” Appl. Opt. 53(28), 6414–6421 (2014).
    [Crossref] [PubMed]
  11. C. H. Cox, Analog Optical Links: Theory and Practice (Cambridge University Press, 2006).
  12. H. T. Friis, “Noise figures of radio receivers,” Proc. IRE, 419–422 (1944).
  13. “IRE standards on methods of measuring noise in linear two ports,” Proc. IRE48(1), 60–68 (1959).
  14. “IEEE Standard 100” The Authoritative Dictionary of IEEE Standards Terms 7th ed. (2000).
  15. E. Robert Collin, Foundations for Microwave Engineering (John Wiley & Sons, 2007).
  16. D. M. Pozar, Microwave Engineering (Wiley, 1997).
  17. E. Rubiola, Phase Noise and Frequency Stability in Oscillators, 1 ed. (Cambridge University Press, 2009).

2018 (1)

2017 (2)

S. E. Hosseini, A. Banai, and F. X. Kartner, “Tunable low-jitter low-drift spurious-free transposed-frequency optoelectronic oscillator,” IEEE Trans. Microw. Theory Tech. 65(7), 2625–2635 (2017).
[Crossref]

S. E. Hosseini, A. Banai, and F. X. Kartner, “Low-drift optoelectronic oscillator based on a phase modulator in a sagnac loop,” IEEE Trans. Microw. Theory Tech. 65(7), 2617–2624 (2017).
[Crossref]

2014 (2)

2009 (1)

2007 (1)

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

1998 (1)

E. I. Ackerman, C. Cox, G. Betts, H. Roussell, F. O’Donnell, and K. Ray, “Input impedance conditions for minimizing the noise figure of an analog optical link,” IEEE Trans. Microw. Theory Tech. 46(12), 2025–2031 (1998).
[Crossref]

1996 (1)

X. S. Yao and L. Maleki, “Optoelectronic microwave oscillator,” J. Opt. Soc. Am. 13(8), 1725–1735 (1996).
[Crossref]

Abiri, H.

Ackerman, E. I.

E. I. Ackerman, C. Cox, G. Betts, H. Roussell, F. O’Donnell, and K. Ray, “Input impedance conditions for minimizing the noise figure of an analog optical link,” IEEE Trans. Microw. Theory Tech. 46(12), 2025–2031 (1998).
[Crossref]

Balakireva, I. V.

Banai, A.

S. E. Hosseini, A. Banai, and F. X. Kartner, “Low-drift optoelectronic oscillator based on a phase modulator in a sagnac loop,” IEEE Trans. Microw. Theory Tech. 65(7), 2617–2624 (2017).
[Crossref]

S. E. Hosseini, A. Banai, and F. X. Kartner, “Tunable low-jitter low-drift spurious-free transposed-frequency optoelectronic oscillator,” IEEE Trans. Microw. Theory Tech. 65(7), 2625–2635 (2017).
[Crossref]

S. E. Hosseini and A. Banai, “Noise figure of microwave photonic links operating under large-signal modulation and its application to optoelectronic oscillators,” Appl. Opt. 53(28), 6414–6421 (2014).
[Crossref] [PubMed]

Betts, G.

E. I. Ackerman, C. Cox, G. Betts, H. Roussell, F. O’Donnell, and K. Ray, “Input impedance conditions for minimizing the noise figure of an analog optical link,” IEEE Trans. Microw. Theory Tech. 46(12), 2025–2031 (1998).
[Crossref]

Capmany, J.

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

Chembo, Y. K.

Coillet, A.

Cox, C.

E. I. Ackerman, C. Cox, G. Betts, H. Roussell, F. O’Donnell, and K. Ray, “Input impedance conditions for minimizing the noise figure of an analog optical link,” IEEE Trans. Microw. Theory Tech. 46(12), 2025–2031 (1998).
[Crossref]

Diallo, S.

Friis, H. T.

H. T. Friis, “Noise figures of radio receivers,” Proc. IRE, 419–422 (1944).

Henriet, R.

Hosseini, S. E.

S. E. Hosseini, S. Shojaeddin, and H. Abiri, “Theoretical investigation of an ultra-low phase noise microwave oscillator based on an IF crystal resonator-amplifier and a microwave photonic frequency transposer,” J. Opt. Soc. Am. B 35(6), 1422–1432 (2018).
[Crossref]

S. E. Hosseini, A. Banai, and F. X. Kartner, “Low-drift optoelectronic oscillator based on a phase modulator in a sagnac loop,” IEEE Trans. Microw. Theory Tech. 65(7), 2617–2624 (2017).
[Crossref]

S. E. Hosseini, A. Banai, and F. X. Kartner, “Tunable low-jitter low-drift spurious-free transposed-frequency optoelectronic oscillator,” IEEE Trans. Microw. Theory Tech. 65(7), 2625–2635 (2017).
[Crossref]

S. E. Hosseini and A. Banai, “Noise figure of microwave photonic links operating under large-signal modulation and its application to optoelectronic oscillators,” Appl. Opt. 53(28), 6414–6421 (2014).
[Crossref] [PubMed]

Kartner, F. X.

S. E. Hosseini, A. Banai, and F. X. Kartner, “Tunable low-jitter low-drift spurious-free transposed-frequency optoelectronic oscillator,” IEEE Trans. Microw. Theory Tech. 65(7), 2625–2635 (2017).
[Crossref]

S. E. Hosseini, A. Banai, and F. X. Kartner, “Low-drift optoelectronic oscillator based on a phase modulator in a sagnac loop,” IEEE Trans. Microw. Theory Tech. 65(7), 2617–2624 (2017).
[Crossref]

Lin, G.

Maleki, L.

X. S. Yao and L. Maleki, “Optoelectronic microwave oscillator,” J. Opt. Soc. Am. 13(8), 1725–1735 (1996).
[Crossref]

Martinenghi, R.

Novak, D.

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

O’Donnell, F.

E. I. Ackerman, C. Cox, G. Betts, H. Roussell, F. O’Donnell, and K. Ray, “Input impedance conditions for minimizing the noise figure of an analog optical link,” IEEE Trans. Microw. Theory Tech. 46(12), 2025–2031 (1998).
[Crossref]

Ray, K.

E. I. Ackerman, C. Cox, G. Betts, H. Roussell, F. O’Donnell, and K. Ray, “Input impedance conditions for minimizing the noise figure of an analog optical link,” IEEE Trans. Microw. Theory Tech. 46(12), 2025–2031 (1998).
[Crossref]

Roussell, H.

E. I. Ackerman, C. Cox, G. Betts, H. Roussell, F. O’Donnell, and K. Ray, “Input impedance conditions for minimizing the noise figure of an analog optical link,” IEEE Trans. Microw. Theory Tech. 46(12), 2025–2031 (1998).
[Crossref]

Saleh, K.

Salzenstein, P.

Shojaeddin, S.

Yao, J.

Yao, X. S.

X. S. Yao and L. Maleki, “Optoelectronic microwave oscillator,” J. Opt. Soc. Am. 13(8), 1725–1735 (1996).
[Crossref]

Appl. Opt. (1)

IEEE Trans. Microw. Theory Tech. (3)

S. E. Hosseini, A. Banai, and F. X. Kartner, “Tunable low-jitter low-drift spurious-free transposed-frequency optoelectronic oscillator,” IEEE Trans. Microw. Theory Tech. 65(7), 2625–2635 (2017).
[Crossref]

S. E. Hosseini, A. Banai, and F. X. Kartner, “Low-drift optoelectronic oscillator based on a phase modulator in a sagnac loop,” IEEE Trans. Microw. Theory Tech. 65(7), 2617–2624 (2017).
[Crossref]

E. I. Ackerman, C. Cox, G. Betts, H. Roussell, F. O’Donnell, and K. Ray, “Input impedance conditions for minimizing the noise figure of an analog optical link,” IEEE Trans. Microw. Theory Tech. 46(12), 2025–2031 (1998).
[Crossref]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. (1)

X. S. Yao and L. Maleki, “Optoelectronic microwave oscillator,” J. Opt. Soc. Am. 13(8), 1725–1735 (1996).
[Crossref]

J. Opt. Soc. Am. B (1)

Nat. Photonics (1)

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

Opt. Express (1)

Other (8)

S. Iezekiel, Microwave Photonics: Devices and Applications (Wiley, 2009).

C. H. Cox, Analog Optical Links: Theory and Practice (Cambridge University Press, 2006).

H. T. Friis, “Noise figures of radio receivers,” Proc. IRE, 419–422 (1944).

“IRE standards on methods of measuring noise in linear two ports,” Proc. IRE48(1), 60–68 (1959).

“IEEE Standard 100” The Authoritative Dictionary of IEEE Standards Terms 7th ed. (2000).

E. Robert Collin, Foundations for Microwave Engineering (John Wiley & Sons, 2007).

D. M. Pozar, Microwave Engineering (Wiley, 1997).

E. Rubiola, Phase Noise and Frequency Stability in Oscillators, 1 ed. (Cambridge University Press, 2009).

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Figures (7)

Fig. 1
Fig. 1 General schematic of externally intensity-modulated with direct-detection microwave photonic link, PD: Photodetector., CW: Continuous wave, MZM: Mach–Zehnder modulator, BPF: Bandpass filter.
Fig. 2
Fig. 2 Signal power gain ( G cm ) and noise power gain ( G nm ) versus input RF power.
Fig. 3
Fig. 3 Equivalent circuit model for an IMDD MWPL with input lossy matching network [‎9].
Fig. 4
Fig. 4 Noise figure versus impedance mismatch factor (M) for two values of RF input power ( P in ).
Fig. 5
Fig. 5 Noise figure versus RF input power ( P in ) for several values of impedance mismatch factor (M).
Fig. 6
Fig. 6 Input impedance matching circuit for realizing appropriate input impedance mismatch factor.
Fig. 7
Fig. 7 General schematic of an OEO, CW: continuous wave, MZM: Mach Zehnder modulator, PD: photodetector, BPF: bandpass filter, PS: phase shifter, Amp: amplifier . In this figure τ in and τ e determine the internal losses and the coupling losses respectively. The optical medium can be a long optical fiber or a whispering gallery mode (WGM) resonator.

Equations (13)

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v in ( t )= V B +x( t )
y(t)= V ph [ 1+cos( π V B V π + πx( t ) V π ) ]=g(x)
x( t )= V m cos( ω RF t )+n( t )
G cm ( P in )= 2 h 01 2 / R L P in
G nm ( P in )= B S y,N ( f )df σ 2 / R L
NF=10log[ ( S N ) in / ( S N ) out | T 0 =290°K ]=10log[ S in S out N out k T 0 ]=10log[ 1 G cm G nm k T 0 + N add k T 0 ]
M=4 R link R s / | Z link + Z s | 2
g m =( R link R 1 )/( R link + R 1 )
G c ( P in )=M g m G cm ( P in )
G n =M g m G nm
N add =kT G n 4 g m M R M 2 | R M + Z M | 2 +kT G n 1 g m 1+ g m R link R S +kT G n 1 g m 1+ g m 1 M g m [(1+ g m ) R S +(1 g m ) R link ] 2 + (1+ g m ) 2 X link 2 ( R link + R S ) 2 + X link 2 +kT+( i rin 2 + i sn 2 ) | Z D | 2 4 R D
NF=10log [ G nm G cm + G nm G cm 4 g m M R M 2 | R M + Z M | 2 + G nm G cm 1 g m 1+ g m R link R S + G nm G cm 1 g m 1+ g m 1 M g m [(1+ g m ) R S +(1 g m ) R link ] 2 ( R link + R S ) 2 + X link 2 + G nm G cm 1 g m 1+ g m 1 M g m (1+ g m ) 2 X link 2 ( R link + R S ) 2 + X link 2 + ( i rin 2 + i sn 2 ) | Z D | 2 4 R D +kT M g m G cm kT ]
L(f)=( 1+ ( f L f ) 2 )( F amp k B T 0 +G F MWPL k B T 0 P RF + κ f )

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