Abstract

We study the limiting-amplification capability of a saturated Semiconductor Optical Amplifier (SOA) followed by an optical band-pass filter. We experimentally demonstrate that this simple optical circuit can be effectively exploited to realize a low-power optical limiter for amplitude-modulated pulse trains at multi-GHz repetition rate. We report very large amplitude-modulation-reduction factors for the case of 20 and 40 GHz pulse trains that are super-imposed with modulating frequencies ranging from 100kHz to several GHz.

© 2007 Optical Society of America

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  1. J. Leuthold, W. Freude, G. Boettger, J. Wang, A. Marculescu, P. Vorreau, and R. Bonk, "All-Optical Regeneration," International Conference on Transparent Optical Networks (IEEE, New York, 2006) 28 - 31.
  2. S. Nakamura, Y. Ueno, and K. Tajima, "168-Gb/s all-optical wavelength conversion with a symmetric-Mach-Zehnder-type switch," IEEE Photon. Technol. Lett. 13, 1091 - 1093 (2001).
    [CrossRef]
  3. M. Attygalle, A. Nirmalathas, and H. F. Liu, "Novel technique for reduction of amplitude modulation of pulse trains generated by subharmonic synchronous mode-locked," IEEE Photon. Technol. Lett. 14, 543 - 545 (2002).
    [CrossRef]
  4. K. Vlachos, G. Theophilopoulos, A. Hatziefremidis, and H. Avramopoulos, "30 Gb/s all-optical clock recovery circuit," IEEE Photon. Technol. Lett. 12, 705-707 (2000).
    [CrossRef]
  5. G. Contestabile, M. Presi, N. Calabretta, and E. Ciaramella, "All-optical clock recovery for NRZ-DPSK signals," IEEE Photon. Technol. Lett. 18, 2544 - 2546 (2006).
    [CrossRef]
  6. G. Contestabile, M. Presi, N. Calabretta, and E. Ciaramella, "All-optical clock recovery from 40 Gbit/s NRZ signal based on clock line enhancement and sharp periodic filtering," Electron. Lett. 40, pp. 1361 - 1362 (2004)
    [CrossRef]
  7. C. Kouloumentas, A. Tzanakaki, and I. Tomkos, "Clock recovery at 160 Gb/s and beyond using a fiber-based optical power limiter," IEEE Photon. Technol. Lett. 18, 2365 - 2367 (2006).
    [CrossRef]
  8. N. Pleros, C. Bintjas, G.T. Kanellos, K. Vlachos, H. Avramopoulos and, G. Guekos, "Recipe for intensity modulation reduction in SOA-based interferometric switches," J. Lightwave Technol. 22, 2834 - 2841 (2004)
    [CrossRef]
  9. M. Presi; N. Calabretta; G. Contestabile, and E. Ciaramella, "Wide dynamic range all-optical clock and data recovery from preamble-free NRZ-DPSK packets," IEEE Photon. Technol. Lett. 19, 372 - 374 (2007).
    [CrossRef]
  10. G. P. Agrawal and N. A. Olsson, "Self-phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers," IEEE J. Quantum Electron. 25, 2297 - 2306 (1989).
    [CrossRef]
  11. Y. Liu, E. Tangdiongga, Z. Li, S. Zhang, H. de Waardt, G. D. Khoe, and H. J. S. Dorren, "Error-free all-optical wavelength conversion at 160 gb/s using a semiconductor optical amplifier and an optical bandpass filter," J. Lightwave Technol. 24, 230 - 236 (2006).
    [CrossRef]
  12. Y. Ueno, S. Nakamura, and K. Tajima, "Nonlinear phase shift induced by semiconductor optical amplifiers with control pulses at repetition frequencies in the 40-160 GHz range for use in ultrahigh-speed all-optical signal processing," J. Opt. Soc. B 19, 2573 - 2589 (2002).
    [CrossRef]
  13. M.L. Nielsen, B.-E. Olsson, and D.J. Blumenthal, "Pulse extinction ratio improvement using SPM in an SOA for OTDM systems applications," IEEE Photon. Technol. Lett. 14, 245 - 247 (2002).
    [CrossRef]
  14. U. Keller, K. D. Li, M. J. W. Rodwell, and D. M. Bloom, "Noise characterization of femtosecond fiber Raman soliton lasers," IEEE J. Quantum Electron. 25, 280 - 288 (1989).
    [CrossRef]
  15. S. Dommers, V. V. Temnov, U. Woggon, J. Gomis, J. Martinez-Pastor, M. Laemmlin, and D. Bimberg "Gain dynamics after ultrashort pulse trains in quantum dot based semiconductor optical amplifiers" in Conference on Lasers and Electro-Optics 2007 Technical Digest (Optical Society of America, Washington, DC, 2007) CMM4

2007 (1)

M. Presi; N. Calabretta; G. Contestabile, and E. Ciaramella, "Wide dynamic range all-optical clock and data recovery from preamble-free NRZ-DPSK packets," IEEE Photon. Technol. Lett. 19, 372 - 374 (2007).
[CrossRef]

2006 (3)

C. Kouloumentas, A. Tzanakaki, and I. Tomkos, "Clock recovery at 160 Gb/s and beyond using a fiber-based optical power limiter," IEEE Photon. Technol. Lett. 18, 2365 - 2367 (2006).
[CrossRef]

G. Contestabile, M. Presi, N. Calabretta, and E. Ciaramella, "All-optical clock recovery for NRZ-DPSK signals," IEEE Photon. Technol. Lett. 18, 2544 - 2546 (2006).
[CrossRef]

Y. Liu, E. Tangdiongga, Z. Li, S. Zhang, H. de Waardt, G. D. Khoe, and H. J. S. Dorren, "Error-free all-optical wavelength conversion at 160 gb/s using a semiconductor optical amplifier and an optical bandpass filter," J. Lightwave Technol. 24, 230 - 236 (2006).
[CrossRef]

2004 (2)

G. Contestabile, M. Presi, N. Calabretta, and E. Ciaramella, "All-optical clock recovery from 40 Gbit/s NRZ signal based on clock line enhancement and sharp periodic filtering," Electron. Lett. 40, pp. 1361 - 1362 (2004)
[CrossRef]

N. Pleros, C. Bintjas, G.T. Kanellos, K. Vlachos, H. Avramopoulos and, G. Guekos, "Recipe for intensity modulation reduction in SOA-based interferometric switches," J. Lightwave Technol. 22, 2834 - 2841 (2004)
[CrossRef]

2002 (3)

M. Attygalle, A. Nirmalathas, and H. F. Liu, "Novel technique for reduction of amplitude modulation of pulse trains generated by subharmonic synchronous mode-locked," IEEE Photon. Technol. Lett. 14, 543 - 545 (2002).
[CrossRef]

Y. Ueno, S. Nakamura, and K. Tajima, "Nonlinear phase shift induced by semiconductor optical amplifiers with control pulses at repetition frequencies in the 40-160 GHz range for use in ultrahigh-speed all-optical signal processing," J. Opt. Soc. B 19, 2573 - 2589 (2002).
[CrossRef]

M.L. Nielsen, B.-E. Olsson, and D.J. Blumenthal, "Pulse extinction ratio improvement using SPM in an SOA for OTDM systems applications," IEEE Photon. Technol. Lett. 14, 245 - 247 (2002).
[CrossRef]

2001 (1)

S. Nakamura, Y. Ueno, and K. Tajima, "168-Gb/s all-optical wavelength conversion with a symmetric-Mach-Zehnder-type switch," IEEE Photon. Technol. Lett. 13, 1091 - 1093 (2001).
[CrossRef]

2000 (1)

K. Vlachos, G. Theophilopoulos, A. Hatziefremidis, and H. Avramopoulos, "30 Gb/s all-optical clock recovery circuit," IEEE Photon. Technol. Lett. 12, 705-707 (2000).
[CrossRef]

1989 (2)

G. P. Agrawal and N. A. Olsson, "Self-phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers," IEEE J. Quantum Electron. 25, 2297 - 2306 (1989).
[CrossRef]

U. Keller, K. D. Li, M. J. W. Rodwell, and D. M. Bloom, "Noise characterization of femtosecond fiber Raman soliton lasers," IEEE J. Quantum Electron. 25, 280 - 288 (1989).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal and N. A. Olsson, "Self-phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers," IEEE J. Quantum Electron. 25, 2297 - 2306 (1989).
[CrossRef]

Attygalle, M.

M. Attygalle, A. Nirmalathas, and H. F. Liu, "Novel technique for reduction of amplitude modulation of pulse trains generated by subharmonic synchronous mode-locked," IEEE Photon. Technol. Lett. 14, 543 - 545 (2002).
[CrossRef]

Avramopoulos, H.

K. Vlachos, G. Theophilopoulos, A. Hatziefremidis, and H. Avramopoulos, "30 Gb/s all-optical clock recovery circuit," IEEE Photon. Technol. Lett. 12, 705-707 (2000).
[CrossRef]

Bintjas, C.

Bloom, D. M.

U. Keller, K. D. Li, M. J. W. Rodwell, and D. M. Bloom, "Noise characterization of femtosecond fiber Raman soliton lasers," IEEE J. Quantum Electron. 25, 280 - 288 (1989).
[CrossRef]

Blumenthal, D.J.

M.L. Nielsen, B.-E. Olsson, and D.J. Blumenthal, "Pulse extinction ratio improvement using SPM in an SOA for OTDM systems applications," IEEE Photon. Technol. Lett. 14, 245 - 247 (2002).
[CrossRef]

Calabretta, N.

M. Presi; N. Calabretta; G. Contestabile, and E. Ciaramella, "Wide dynamic range all-optical clock and data recovery from preamble-free NRZ-DPSK packets," IEEE Photon. Technol. Lett. 19, 372 - 374 (2007).
[CrossRef]

G. Contestabile, M. Presi, N. Calabretta, and E. Ciaramella, "All-optical clock recovery for NRZ-DPSK signals," IEEE Photon. Technol. Lett. 18, 2544 - 2546 (2006).
[CrossRef]

G. Contestabile, M. Presi, N. Calabretta, and E. Ciaramella, "All-optical clock recovery from 40 Gbit/s NRZ signal based on clock line enhancement and sharp periodic filtering," Electron. Lett. 40, pp. 1361 - 1362 (2004)
[CrossRef]

Ciaramella, E.

M. Presi; N. Calabretta; G. Contestabile, and E. Ciaramella, "Wide dynamic range all-optical clock and data recovery from preamble-free NRZ-DPSK packets," IEEE Photon. Technol. Lett. 19, 372 - 374 (2007).
[CrossRef]

G. Contestabile, M. Presi, N. Calabretta, and E. Ciaramella, "All-optical clock recovery for NRZ-DPSK signals," IEEE Photon. Technol. Lett. 18, 2544 - 2546 (2006).
[CrossRef]

G. Contestabile, M. Presi, N. Calabretta, and E. Ciaramella, "All-optical clock recovery from 40 Gbit/s NRZ signal based on clock line enhancement and sharp periodic filtering," Electron. Lett. 40, pp. 1361 - 1362 (2004)
[CrossRef]

Contestabile, G.

M. Presi; N. Calabretta; G. Contestabile, and E. Ciaramella, "Wide dynamic range all-optical clock and data recovery from preamble-free NRZ-DPSK packets," IEEE Photon. Technol. Lett. 19, 372 - 374 (2007).
[CrossRef]

G. Contestabile, M. Presi, N. Calabretta, and E. Ciaramella, "All-optical clock recovery for NRZ-DPSK signals," IEEE Photon. Technol. Lett. 18, 2544 - 2546 (2006).
[CrossRef]

G. Contestabile, M. Presi, N. Calabretta, and E. Ciaramella, "All-optical clock recovery from 40 Gbit/s NRZ signal based on clock line enhancement and sharp periodic filtering," Electron. Lett. 40, pp. 1361 - 1362 (2004)
[CrossRef]

de Waardt, H.

Dorren, H. J. S.

Hatziefremidis, A.

K. Vlachos, G. Theophilopoulos, A. Hatziefremidis, and H. Avramopoulos, "30 Gb/s all-optical clock recovery circuit," IEEE Photon. Technol. Lett. 12, 705-707 (2000).
[CrossRef]

Kanellos, G.T.

Keller, U.

U. Keller, K. D. Li, M. J. W. Rodwell, and D. M. Bloom, "Noise characterization of femtosecond fiber Raman soliton lasers," IEEE J. Quantum Electron. 25, 280 - 288 (1989).
[CrossRef]

Khoe, G. D.

Kouloumentas, C.

C. Kouloumentas, A. Tzanakaki, and I. Tomkos, "Clock recovery at 160 Gb/s and beyond using a fiber-based optical power limiter," IEEE Photon. Technol. Lett. 18, 2365 - 2367 (2006).
[CrossRef]

Li, K. D.

U. Keller, K. D. Li, M. J. W. Rodwell, and D. M. Bloom, "Noise characterization of femtosecond fiber Raman soliton lasers," IEEE J. Quantum Electron. 25, 280 - 288 (1989).
[CrossRef]

Li, Z.

Liu, H. F.

M. Attygalle, A. Nirmalathas, and H. F. Liu, "Novel technique for reduction of amplitude modulation of pulse trains generated by subharmonic synchronous mode-locked," IEEE Photon. Technol. Lett. 14, 543 - 545 (2002).
[CrossRef]

Liu, Y.

Nakamura, S.

Y. Ueno, S. Nakamura, and K. Tajima, "Nonlinear phase shift induced by semiconductor optical amplifiers with control pulses at repetition frequencies in the 40-160 GHz range for use in ultrahigh-speed all-optical signal processing," J. Opt. Soc. B 19, 2573 - 2589 (2002).
[CrossRef]

S. Nakamura, Y. Ueno, and K. Tajima, "168-Gb/s all-optical wavelength conversion with a symmetric-Mach-Zehnder-type switch," IEEE Photon. Technol. Lett. 13, 1091 - 1093 (2001).
[CrossRef]

Nielsen, M.L.

M.L. Nielsen, B.-E. Olsson, and D.J. Blumenthal, "Pulse extinction ratio improvement using SPM in an SOA for OTDM systems applications," IEEE Photon. Technol. Lett. 14, 245 - 247 (2002).
[CrossRef]

Nirmalathas, A.

M. Attygalle, A. Nirmalathas, and H. F. Liu, "Novel technique for reduction of amplitude modulation of pulse trains generated by subharmonic synchronous mode-locked," IEEE Photon. Technol. Lett. 14, 543 - 545 (2002).
[CrossRef]

Olsson, B.-E.

M.L. Nielsen, B.-E. Olsson, and D.J. Blumenthal, "Pulse extinction ratio improvement using SPM in an SOA for OTDM systems applications," IEEE Photon. Technol. Lett. 14, 245 - 247 (2002).
[CrossRef]

Olsson, N. A.

G. P. Agrawal and N. A. Olsson, "Self-phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers," IEEE J. Quantum Electron. 25, 2297 - 2306 (1989).
[CrossRef]

Pleros, N.

Presi, M.

M. Presi; N. Calabretta; G. Contestabile, and E. Ciaramella, "Wide dynamic range all-optical clock and data recovery from preamble-free NRZ-DPSK packets," IEEE Photon. Technol. Lett. 19, 372 - 374 (2007).
[CrossRef]

G. Contestabile, M. Presi, N. Calabretta, and E. Ciaramella, "All-optical clock recovery for NRZ-DPSK signals," IEEE Photon. Technol. Lett. 18, 2544 - 2546 (2006).
[CrossRef]

G. Contestabile, M. Presi, N. Calabretta, and E. Ciaramella, "All-optical clock recovery from 40 Gbit/s NRZ signal based on clock line enhancement and sharp periodic filtering," Electron. Lett. 40, pp. 1361 - 1362 (2004)
[CrossRef]

Rodwell, M. J. W.

U. Keller, K. D. Li, M. J. W. Rodwell, and D. M. Bloom, "Noise characterization of femtosecond fiber Raman soliton lasers," IEEE J. Quantum Electron. 25, 280 - 288 (1989).
[CrossRef]

Tajima, K.

Y. Ueno, S. Nakamura, and K. Tajima, "Nonlinear phase shift induced by semiconductor optical amplifiers with control pulses at repetition frequencies in the 40-160 GHz range for use in ultrahigh-speed all-optical signal processing," J. Opt. Soc. B 19, 2573 - 2589 (2002).
[CrossRef]

S. Nakamura, Y. Ueno, and K. Tajima, "168-Gb/s all-optical wavelength conversion with a symmetric-Mach-Zehnder-type switch," IEEE Photon. Technol. Lett. 13, 1091 - 1093 (2001).
[CrossRef]

Tangdiongga, E.

Theophilopoulos, G.

K. Vlachos, G. Theophilopoulos, A. Hatziefremidis, and H. Avramopoulos, "30 Gb/s all-optical clock recovery circuit," IEEE Photon. Technol. Lett. 12, 705-707 (2000).
[CrossRef]

Tomkos, I.

C. Kouloumentas, A. Tzanakaki, and I. Tomkos, "Clock recovery at 160 Gb/s and beyond using a fiber-based optical power limiter," IEEE Photon. Technol. Lett. 18, 2365 - 2367 (2006).
[CrossRef]

Tzanakaki, A.

C. Kouloumentas, A. Tzanakaki, and I. Tomkos, "Clock recovery at 160 Gb/s and beyond using a fiber-based optical power limiter," IEEE Photon. Technol. Lett. 18, 2365 - 2367 (2006).
[CrossRef]

Ueno, Y.

Y. Ueno, S. Nakamura, and K. Tajima, "Nonlinear phase shift induced by semiconductor optical amplifiers with control pulses at repetition frequencies in the 40-160 GHz range for use in ultrahigh-speed all-optical signal processing," J. Opt. Soc. B 19, 2573 - 2589 (2002).
[CrossRef]

S. Nakamura, Y. Ueno, and K. Tajima, "168-Gb/s all-optical wavelength conversion with a symmetric-Mach-Zehnder-type switch," IEEE Photon. Technol. Lett. 13, 1091 - 1093 (2001).
[CrossRef]

Vlachos, K.

N. Pleros, C. Bintjas, G.T. Kanellos, K. Vlachos, H. Avramopoulos and, G. Guekos, "Recipe for intensity modulation reduction in SOA-based interferometric switches," J. Lightwave Technol. 22, 2834 - 2841 (2004)
[CrossRef]

K. Vlachos, G. Theophilopoulos, A. Hatziefremidis, and H. Avramopoulos, "30 Gb/s all-optical clock recovery circuit," IEEE Photon. Technol. Lett. 12, 705-707 (2000).
[CrossRef]

Zhang, S.

Electron. Lett. (1)

G. Contestabile, M. Presi, N. Calabretta, and E. Ciaramella, "All-optical clock recovery from 40 Gbit/s NRZ signal based on clock line enhancement and sharp periodic filtering," Electron. Lett. 40, pp. 1361 - 1362 (2004)
[CrossRef]

IEEE J. Quantum Electron. (2)

G. P. Agrawal and N. A. Olsson, "Self-phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers," IEEE J. Quantum Electron. 25, 2297 - 2306 (1989).
[CrossRef]

U. Keller, K. D. Li, M. J. W. Rodwell, and D. M. Bloom, "Noise characterization of femtosecond fiber Raman soliton lasers," IEEE J. Quantum Electron. 25, 280 - 288 (1989).
[CrossRef]

IEEE Photon. Technol. Lett. (7)

M.L. Nielsen, B.-E. Olsson, and D.J. Blumenthal, "Pulse extinction ratio improvement using SPM in an SOA for OTDM systems applications," IEEE Photon. Technol. Lett. 14, 245 - 247 (2002).
[CrossRef]

C. Kouloumentas, A. Tzanakaki, and I. Tomkos, "Clock recovery at 160 Gb/s and beyond using a fiber-based optical power limiter," IEEE Photon. Technol. Lett. 18, 2365 - 2367 (2006).
[CrossRef]

M. Presi; N. Calabretta; G. Contestabile, and E. Ciaramella, "Wide dynamic range all-optical clock and data recovery from preamble-free NRZ-DPSK packets," IEEE Photon. Technol. Lett. 19, 372 - 374 (2007).
[CrossRef]

S. Nakamura, Y. Ueno, and K. Tajima, "168-Gb/s all-optical wavelength conversion with a symmetric-Mach-Zehnder-type switch," IEEE Photon. Technol. Lett. 13, 1091 - 1093 (2001).
[CrossRef]

M. Attygalle, A. Nirmalathas, and H. F. Liu, "Novel technique for reduction of amplitude modulation of pulse trains generated by subharmonic synchronous mode-locked," IEEE Photon. Technol. Lett. 14, 543 - 545 (2002).
[CrossRef]

K. Vlachos, G. Theophilopoulos, A. Hatziefremidis, and H. Avramopoulos, "30 Gb/s all-optical clock recovery circuit," IEEE Photon. Technol. Lett. 12, 705-707 (2000).
[CrossRef]

G. Contestabile, M. Presi, N. Calabretta, and E. Ciaramella, "All-optical clock recovery for NRZ-DPSK signals," IEEE Photon. Technol. Lett. 18, 2544 - 2546 (2006).
[CrossRef]

J. Lightwave Technol. (2)

J. Opt. Soc. B (1)

Y. Ueno, S. Nakamura, and K. Tajima, "Nonlinear phase shift induced by semiconductor optical amplifiers with control pulses at repetition frequencies in the 40-160 GHz range for use in ultrahigh-speed all-optical signal processing," J. Opt. Soc. B 19, 2573 - 2589 (2002).
[CrossRef]

Other (2)

S. Dommers, V. V. Temnov, U. Woggon, J. Gomis, J. Martinez-Pastor, M. Laemmlin, and D. Bimberg "Gain dynamics after ultrashort pulse trains in quantum dot based semiconductor optical amplifiers" in Conference on Lasers and Electro-Optics 2007 Technical Digest (Optical Society of America, Washington, DC, 2007) CMM4

J. Leuthold, W. Freude, G. Boettger, J. Wang, A. Marculescu, P. Vorreau, and R. Bonk, "All-Optical Regeneration," International Conference on Transparent Optical Networks (IEEE, New York, 2006) 28 - 31.

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Figures (14)

Fig. 1.
Fig. 1.

Scheme of the limiting amplification in a saturated SOA.

Fig. 2.
Fig. 2.

Typical evolution of the optical spectrum and of the oscilloscope trace (in persistence mode) of an over-modulated 20 GHz pulse train inside the limiting circuit.

Fig. 3.
Fig. 3.

Behavior of the SOA gain recovery as a function of pulse repetition rate.

Fig. 4.
Fig. 4.

Experimental set-up. TL: Tunable Laser, IM: Intensity Modulator, EDFA: Erbium Doped Fiber Amplifier, OI: Optical Isolator, SOA: Semiconductor Optical Amplifier, BPF: Band Pass Filter.

Fig. 5.
Fig. 5.

(a). Typical static transfer function of the limiting circuit at varying the output band-pass filter position. b) Detail of the transfer function.

Fig. 6.
Fig. 6.

AMR vs. SOA average input power for 20 GHz pulse trains overmodulated at 5 GHz at 50 and 80% modulation depths.

Fig. 7.
Fig. 7.

(a). AMR vs. modulation frequency for 20 GHz pulse trains with 50 and 80% modulation depths. b) Input/output evolution of 80%-modulated pulse train (at 200 MHz modulation frequency).

Fig. 8.
Fig. 8.

(a). AMR vs. modulation frequency for 20 GHz pulse trains with 80% modulation depth with and without output filter. b) Detail in linear scale.

Fig. 9.
Fig. 9.

(a). AMR vs. modulation frequency for 40 GHz pulse trains with 50 and 80% modulation depths. b) Input/output evolution of 80%-modulated pulse train (at 100 kHz modulation frequency).

Fig. 10.
Fig. 10.

Comparison of the AMR response in the GHz range with and without output filter.

Fig. 11.
Fig. 11.

AMR vs. modulation depth for 20 and 40 GHz pulse trains at 5 GHz overmodulation frequency.

Fig. 12.
Fig. 12.

Input/output evolution of 40 GHz pulse trains modulated with a) 86% modulation depth at 5 GHz; b) 58% modulation depth at 25 GHz.

Fig. 13.
Fig. 13.

AMR vs. filter detuning for 40 GHz pulse trains 80%-modulated at 100 MHz. In the insets, examples of corresponding oscilloscope traces.

Fig. 14.
Fig. 14.

Comparison of the Single Side Band Noise Spectrum of 20 GHz pulse train without overmodulation at the input and output of the limiting circuit.

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