Abstract

We present a detailed look at using Mach-Zehnder modulator generated distortion for identifying the magnitude and relative sign of photodiode generated second order intermodulation distortion (IMD2). Previous discussions introduced the concept for characterizing a test device. Analysis is expanded to IMD2 as a function of voltage, photocurrent and frequency.

© 2014 Optical Society of America

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References

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  1. V. J. Urick, M. N. Hutchinson, J. M. Singley, J. D. McKinney, K. J. Williams, “Suppression of even-order photodiode distortions via predistortion linearization with a bias-shifted Mach-Zehnder modulator,” Opt. Express 21(12), 14368–14376 (2013).
    [CrossRef] [PubMed]
  2. S. Itakura, K. Sakai, T. Nagatsuka, E. Ishimura, M. Nakaji, H. Otsuka, K. Mori, Y. Hirano, “High-current backside-illuminated photodiode array module for optical analog links,” J. Lightwave Technol. 28(6), 965–971 (2010).
    [CrossRef]
  3. A. S. Hastings, V. J. Urick, C. Sunderman, J. F. Diehl, J. D. McKinney, D. A. Tulchinsky, P. S. Devgan, K. J. Williams, “Suppression of even-order photodiode nonlinearities in multioctave photonic links,” J. Lightwave Technol. 26(15), 2557–2562 (2008).
    [CrossRef]
  4. A. Joshi, “Highly linear dual photodiodes for Ku-Band applications,” in 2009IEEE Avionics Fiber Optics and Photonics Conference Digest, pp. 9–10.
  5. S. R. Harmon, M. N. Hutchinson, V. J. Urick, and K. J. Williams, “Determining the magnitude and relative phase of photodiode IMD2 using amplitude matched MZM-distortion cancellation technique,” in 2013IEEE International Meeting on Microwave Photonics Digest, pp. 17–20.
  6. V. J. Urick, F. Bucholtz, J. D. McKinney, P. S. Devgan, A. L. Campillo, J. L. Dexter, K. J. Williams, “Long-haul analog photonics,” J. Lightwave Technol. 29(8), 1182–1205 (2011).
    [CrossRef]
  7. Y. Fu, H. Pan, Z. Li, A. Beling, J. C. Campbell, “Characterizing and modeling nonlinear intermodulation distortions in modified uni-traveling carrier photodiodes,” J. Quantum Electron. 47(10), 1312–1319 (2011).
    [CrossRef]
  8. M. Vaidyanathan, M. Iwamoto, L. E. Larson, P. S. Gudem, P. M. Asbeck, “A Theory of high-frequency distortion in bipolar transistors,” IEEE Trans. Microw. Theory Tech. 51(2), 448–461 (2003).
    [CrossRef]
  9. C. P. Lee, W. Ma, N. L. Wang, “Averaging and cancellation effect of high-order nonlinearity of a power amplifier,” IEEE Trans. Circ. Syst. 54(12), 2733–2740 (2007).
  10. Y. Hu, C. R. Menyuk, V. J. Urick, and K. J. Williams, “Sources of nonlinearity in a PIN photodetector at high applied reverse bias,” in 2013IEEE International Meeting on Microwave Photonics Digest, pp. 282–285.
  11. N. B. de Carvalho, J. C. Pedro, “Large- and small-signal IMD behavior of microwave power amplifiers,” IEEE Trans. Microw. Theory Tech. 47(12), 2364–2374 (1999).
    [CrossRef]
  12. S. Narayanan, “Transistor distortion analysis using Volterra series representation,” Bell Syst. Tech. J. 46(5), 991–1024 (1967).
    [CrossRef]
  13. K. J. Williams, R. D. Esman, M. Dagenais, “Nonlinearities in p-i-n microwave photodetectors,” J. Lightwave Technol. 14(1), 84–96 (1996).
    [CrossRef]
  14. M. N. Draa, A. S. Hastings, K. J. Williams, “Comparison of photodiode nonlinearity measurement systems,” Opt. Express 19(13), 12635–12645 (2011).
    [CrossRef] [PubMed]

2013 (1)

2011 (3)

2010 (1)

2008 (1)

2007 (1)

C. P. Lee, W. Ma, N. L. Wang, “Averaging and cancellation effect of high-order nonlinearity of a power amplifier,” IEEE Trans. Circ. Syst. 54(12), 2733–2740 (2007).

2003 (1)

M. Vaidyanathan, M. Iwamoto, L. E. Larson, P. S. Gudem, P. M. Asbeck, “A Theory of high-frequency distortion in bipolar transistors,” IEEE Trans. Microw. Theory Tech. 51(2), 448–461 (2003).
[CrossRef]

1999 (1)

N. B. de Carvalho, J. C. Pedro, “Large- and small-signal IMD behavior of microwave power amplifiers,” IEEE Trans. Microw. Theory Tech. 47(12), 2364–2374 (1999).
[CrossRef]

1996 (1)

K. J. Williams, R. D. Esman, M. Dagenais, “Nonlinearities in p-i-n microwave photodetectors,” J. Lightwave Technol. 14(1), 84–96 (1996).
[CrossRef]

1967 (1)

S. Narayanan, “Transistor distortion analysis using Volterra series representation,” Bell Syst. Tech. J. 46(5), 991–1024 (1967).
[CrossRef]

Asbeck, P. M.

M. Vaidyanathan, M. Iwamoto, L. E. Larson, P. S. Gudem, P. M. Asbeck, “A Theory of high-frequency distortion in bipolar transistors,” IEEE Trans. Microw. Theory Tech. 51(2), 448–461 (2003).
[CrossRef]

Beling, A.

Y. Fu, H. Pan, Z. Li, A. Beling, J. C. Campbell, “Characterizing and modeling nonlinear intermodulation distortions in modified uni-traveling carrier photodiodes,” J. Quantum Electron. 47(10), 1312–1319 (2011).
[CrossRef]

Bucholtz, F.

Campbell, J. C.

Y. Fu, H. Pan, Z. Li, A. Beling, J. C. Campbell, “Characterizing and modeling nonlinear intermodulation distortions in modified uni-traveling carrier photodiodes,” J. Quantum Electron. 47(10), 1312–1319 (2011).
[CrossRef]

Campillo, A. L.

Dagenais, M.

K. J. Williams, R. D. Esman, M. Dagenais, “Nonlinearities in p-i-n microwave photodetectors,” J. Lightwave Technol. 14(1), 84–96 (1996).
[CrossRef]

de Carvalho, N. B.

N. B. de Carvalho, J. C. Pedro, “Large- and small-signal IMD behavior of microwave power amplifiers,” IEEE Trans. Microw. Theory Tech. 47(12), 2364–2374 (1999).
[CrossRef]

Devgan, P. S.

Dexter, J. L.

Diehl, J. F.

Draa, M. N.

Esman, R. D.

K. J. Williams, R. D. Esman, M. Dagenais, “Nonlinearities in p-i-n microwave photodetectors,” J. Lightwave Technol. 14(1), 84–96 (1996).
[CrossRef]

Fu, Y.

Y. Fu, H. Pan, Z. Li, A. Beling, J. C. Campbell, “Characterizing and modeling nonlinear intermodulation distortions in modified uni-traveling carrier photodiodes,” J. Quantum Electron. 47(10), 1312–1319 (2011).
[CrossRef]

Gudem, P. S.

M. Vaidyanathan, M. Iwamoto, L. E. Larson, P. S. Gudem, P. M. Asbeck, “A Theory of high-frequency distortion in bipolar transistors,” IEEE Trans. Microw. Theory Tech. 51(2), 448–461 (2003).
[CrossRef]

Hastings, A. S.

Hirano, Y.

Hutchinson, M. N.

Ishimura, E.

Itakura, S.

Iwamoto, M.

M. Vaidyanathan, M. Iwamoto, L. E. Larson, P. S. Gudem, P. M. Asbeck, “A Theory of high-frequency distortion in bipolar transistors,” IEEE Trans. Microw. Theory Tech. 51(2), 448–461 (2003).
[CrossRef]

Larson, L. E.

M. Vaidyanathan, M. Iwamoto, L. E. Larson, P. S. Gudem, P. M. Asbeck, “A Theory of high-frequency distortion in bipolar transistors,” IEEE Trans. Microw. Theory Tech. 51(2), 448–461 (2003).
[CrossRef]

Lee, C. P.

C. P. Lee, W. Ma, N. L. Wang, “Averaging and cancellation effect of high-order nonlinearity of a power amplifier,” IEEE Trans. Circ. Syst. 54(12), 2733–2740 (2007).

Li, Z.

Y. Fu, H. Pan, Z. Li, A. Beling, J. C. Campbell, “Characterizing and modeling nonlinear intermodulation distortions in modified uni-traveling carrier photodiodes,” J. Quantum Electron. 47(10), 1312–1319 (2011).
[CrossRef]

Ma, W.

C. P. Lee, W. Ma, N. L. Wang, “Averaging and cancellation effect of high-order nonlinearity of a power amplifier,” IEEE Trans. Circ. Syst. 54(12), 2733–2740 (2007).

McKinney, J. D.

Mori, K.

Nagatsuka, T.

Nakaji, M.

Narayanan, S.

S. Narayanan, “Transistor distortion analysis using Volterra series representation,” Bell Syst. Tech. J. 46(5), 991–1024 (1967).
[CrossRef]

Otsuka, H.

Pan, H.

Y. Fu, H. Pan, Z. Li, A. Beling, J. C. Campbell, “Characterizing and modeling nonlinear intermodulation distortions in modified uni-traveling carrier photodiodes,” J. Quantum Electron. 47(10), 1312–1319 (2011).
[CrossRef]

Pedro, J. C.

N. B. de Carvalho, J. C. Pedro, “Large- and small-signal IMD behavior of microwave power amplifiers,” IEEE Trans. Microw. Theory Tech. 47(12), 2364–2374 (1999).
[CrossRef]

Sakai, K.

Singley, J. M.

Sunderman, C.

Tulchinsky, D. A.

Urick, V. J.

Vaidyanathan, M.

M. Vaidyanathan, M. Iwamoto, L. E. Larson, P. S. Gudem, P. M. Asbeck, “A Theory of high-frequency distortion in bipolar transistors,” IEEE Trans. Microw. Theory Tech. 51(2), 448–461 (2003).
[CrossRef]

Wang, N. L.

C. P. Lee, W. Ma, N. L. Wang, “Averaging and cancellation effect of high-order nonlinearity of a power amplifier,” IEEE Trans. Circ. Syst. 54(12), 2733–2740 (2007).

Williams, K. J.

Bell Syst. Tech. J. (1)

S. Narayanan, “Transistor distortion analysis using Volterra series representation,” Bell Syst. Tech. J. 46(5), 991–1024 (1967).
[CrossRef]

IEEE Trans. Circ. Syst. (1)

C. P. Lee, W. Ma, N. L. Wang, “Averaging and cancellation effect of high-order nonlinearity of a power amplifier,” IEEE Trans. Circ. Syst. 54(12), 2733–2740 (2007).

IEEE Trans. Microw. Theory Tech. (2)

N. B. de Carvalho, J. C. Pedro, “Large- and small-signal IMD behavior of microwave power amplifiers,” IEEE Trans. Microw. Theory Tech. 47(12), 2364–2374 (1999).
[CrossRef]

M. Vaidyanathan, M. Iwamoto, L. E. Larson, P. S. Gudem, P. M. Asbeck, “A Theory of high-frequency distortion in bipolar transistors,” IEEE Trans. Microw. Theory Tech. 51(2), 448–461 (2003).
[CrossRef]

J. Lightwave Technol. (4)

J. Quantum Electron. (1)

Y. Fu, H. Pan, Z. Li, A. Beling, J. C. Campbell, “Characterizing and modeling nonlinear intermodulation distortions in modified uni-traveling carrier photodiodes,” J. Quantum Electron. 47(10), 1312–1319 (2011).
[CrossRef]

Opt. Express (2)

Other (3)

Y. Hu, C. R. Menyuk, V. J. Urick, and K. J. Williams, “Sources of nonlinearity in a PIN photodetector at high applied reverse bias,” in 2013IEEE International Meeting on Microwave Photonics Digest, pp. 282–285.

A. Joshi, “Highly linear dual photodiodes for Ku-Band applications,” in 2009IEEE Avionics Fiber Optics and Photonics Conference Digest, pp. 9–10.

S. R. Harmon, M. N. Hutchinson, V. J. Urick, and K. J. Williams, “Determining the magnitude and relative phase of photodiode IMD2 using amplitude matched MZM-distortion cancellation technique,” in 2013IEEE International Meeting on Microwave Photonics Digest, pp. 17–20.

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Figures (5)

Fig. 1
Fig. 1

Intensity-modulation direct-detection link employing an external MZM.

Fig. 2
Fig. 2

Second order intermodulation distortion coefficient ( a 2 ) as a function of voltage for input RF tones, f 1 =2.789GHz and f 2 =3.124GHz at 6 mA photocurrent.

Fig. 3
Fig. 3

Second order intermodulation distortion coefficient ( a 2 ) as a function of photocurrent for input RF tones, f 1 =2.789GHz and f 2 =3.124GHz at 5 V bias voltage.

Fig. 4
Fig. 4

Second order intermodulation distortion coefficient ( a 2 ) as a function of photocurrent for input RF tones, f 1 =2.789GHz and f 2 =3.124GHz at 0.5 V. The measurement for a 2+ observed two nulls between 5.5 mA and 6 mA, one on either side of quadrature. The data for a 2+ with negative relative phase is graphed with blue squares and for a 2+ with positive relative phase is graphed with blue diamonds.

Fig. 5
Fig. 5

Second order intermodulation distortion coefficient ( a 2 ) as a function of frequency for input RF tones at 6mA photocurrent and 2V (red) and 5V (blue) bias voltage.

Equations (13)

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[ E 1 ( t ) E 2 ( t ) ]= 1 2 [ 1 i i 1 ][ e iϕ( t )/2 0 0 e iϕ( t )/2 ][ 1 i i 1 ][ E in ( t ) 0 ],
ϕ(t)= ϕ dc + ϕ 1 sin( Ω 1 t )+ ϕ 2 sin( Ω 2 t ),
I fund,MZM =ϕ I dc,q sin( ϕ dc )[ sin( Ω 1 t )+sin( Ω 2 t ) ] I even,MZM =2cos( ϕ dc ) I dc,q
×{ 1 4 ϕ 2 cos[ ( Ω 2 Ω 1 )t ] 1 4 ϕ 2 cos[ ( Ω 2 + Ω 1 )t ] },
I Ω 2 Ω 1 ,MZM =± ϕ 2 I dc,q cos( ϕ dc ) 2 cos[ ( Ω 2 Ω 1 )t ].
I PD = a 0 + a 1 ( I in I dc )+ a 2 ( I in I dc ) 2 +,
a = m 1 m! d m I pd d I in m .
I PD =( a 0 + a 2 I 2 )+ a 1 Isin( Ω 1 t )+ a 1 Isin( Ω 2 t ) a 2 I 2 2 cos( 2 Ω 1 t )
a 2 I 2 2 cos( 2 Ω 2 t )+ a 2 I 2 cos[ ( Ω 1 Ω 2 )t ] a 2 I 2 cos[ ( Ω 1 + Ω 2 )t ]+,
I imd2,PD =± a 2 ϕ 2 I dc,q 2 sin 2 ( ϕ dc )cos[ ( Ω 2 Ω 1 )t ].
OIP 2 PD = P fund,PD 2 P imd2,PD 2 = a 1 4 R 2 a 2 2 .
I imd2,peak =± ϕ 2 I dc,q [ cos( ϕ dc ) 2 + a 2 I dc,q sin 2 ( ϕ dc ) ],
a 2 = cos( ϕ dc ) 2 I dc,q sin 2 ( ϕ dc ) .

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