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Phase _amp; Frequency Noise Metrology

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Phase _amp; Frequency Noise Metrology Powered By Docstoc
					Phase & Frequency
 Noise Metrology
               Enrico Rubiola




           Outline
  •   Introduction
  •   Measurement methods
  •   Microwave photonics
  •   Electronic and optical components
  •   AM noise and RIN




  home page http://rubiola.org
        Though frequency standards are                                                                    2


         moving to optics (and beyond),
eftf-fcs 2003                                                                                       12



        RF and microwaves are inevitable
                Example of Measured Spectrum



                    −164
                                Sα|ϕ ( f )
                                                                     P0 = 19 dBm
                                dB[rad 2 ]/Hz                        avg 10 spectra
                                                                     single channel
                                                                        ν0 = 9.2 GHz
                    −174
                                                                     Narda CNA 8596          Microwave
                                                                     s.no. 157               circulator
                    −184




                    −194
                                      instrument noise

                                                              Fourier frequency, Hz
                    −204
                           10                      102         103                     104


                Lower phase noiselikeis required
                 no post-processing is used to hide stray signals, vibrations or the mains
                                Phase noise & friends                                                                                                        3

    v(t) = Vp [1 + α(t)] cos [1 + ϕ(t)]                                             random walk freq.
                                                           Sϕ(f)                    b−4 f−4                                     signal sources only

             random phase fluctuation
   Sϕ (f ) = PSD of ϕ(t)                                                                  flicker freq.
                                                                                               b−3 f−3
                                                                                                                               both signal sources
                                                                                                                              and two-port devices
                power spectral density                                                               white freq.
                                                                                                         b−2 f−2
    it is measured as                                                                                                 flicker phase.
                                                                                                                    b−1 f−1
    Sϕ (f ) = E {Φ(f )Φ∗ (f )}             (expectation)                                                                              white phase   b0
                                                                                                                                                         f
    Sϕ (f ) ≈ Φ(f )Φ∗ (f ) m               (average)
                                                                                                          f2/ ν2
             1                                                                                       x         0

    L(f ) = Sϕ (f ) dBc
             2                                             Sy (f)
                                                                              h−2 f−2                                         h2 f2

                                                                      random                                                     white phase
                                                                      walk freq.        h−1 f−1
    random fractional-frequency fluctuation                                                                   h1 f
                                                                                                   h0
           ˙
          ϕ(t)                   f2                                            flicker freq.                       flicker phase
   y(t) =              ⇒     Sy = 2 Sϕ (f )                                                    white freq.
                                                                                                                                                         f
          2πν0                   ν0

                                                            2
              Allan variance                               σy (τ)
     (two-sample wavelet-like variance)
                    1
                                                                                                                                           freq.
                                       2
   σy (τ )
    2
             =E       y k+1 − y k             .                     flicker phase
                                                                     white phase
                                                                                                                                           drift
                    2                                                           white freq.
                                                                                                   flicker freq.            random walk freq.
                                                                                                                         (2π ) 2
approaches a half-octave bandpass filter (for white noise),                          h0 /2 τ        2ln(2)h −1
                                                                                                                           6
                                                                                                                                 h−2 τ
                                                                                                                                                         τ
    hence it converges for processes steeper than 1/f
                                                                                                      4
                          Mechanical stability
Sϕ (f )
          10–18 rad2/Hz @ 1 Hz
                                                Any phase fluctuation can be
           h−                                  converted into length fluctuation
               1 /f
                                                              1 c
                              f                           L=
                                                             2π ν0
                1 c                        b–1 = –180 dBrad2/Hz and ν0 = 10 GHz is equivalent to
            L=                                       SL = 1.46x10–23 m2/Hz at f = 1 Hz
               2π ν0
SL (f )   1.5x10–23 m2/Hz @ 1 Hz
          h−                                   Any flicker spectrum h–1/f can be
             1 /f
                                              converted into a flat Allan variance
                              f
                                                        σL = 2 ln(2) h−1
                                                         2


          σ 2 = 2 ln(2) h−1

                                            A residual flicker of –180 dBrad2/Hz at f = 1 Hz
σL (τ )                                         off the 10 GHz carrier is equivalent to

            4.5x10–12 m
                                             σ2 = 2x10–23 m2 thus            σ = 4.5x10–12 m
                                  τ        for reference, the Bohr radius of the electron is R = 0.529 Å

                 •    Don’t think “this is just engineering” !!!
                 •    Learn from non-optical microscopy (bulk matter, 5x10–14 m)
                 •    Careful DC section (capacitance and piezoelectricity)
                 •    The best advice is to be at least paranoiac
1 – Measurement methods
                                                                                                           6
              Correlation measurements
                                              x = c–a     Two separate instruments
                                                          measure the same DUT.
                                                          Only the DUT noise is common
           DUT             c(t)           FFT
                                                           a(t), b(t) –> instrument noise
                                                           c(t) –> DUT noise
                                             y = c–b
          b(t)
                                                                  phase noise measurements
basics of correlation                                       DUT noise,        a, b    instrument noise
                                                            normal use        c       DUT noise
Syx (f ) = E {Y (f )X ∗ (f )}                               background,       a, b    instrument noise
         = E {(C − A)(C − B)∗ }                             ideal case        c=0     no DUT
                                                            background,       a, b    instrument noise
         = E {CC ∗ − AC ∗ − CB ∗ + AB ∗ }                   with AM noise     c≠0     AM-to-DC noise
         = E {CC ∗ }
                            0  0      0                                       single-channel
Syx (f ) = Scc (f )


                                                          S!(f)
in practice, average on m realizations
 Syx (f ) = Y (f )X ∗ (f ) m                                                                   1/"m
          = CC ∗ − AC ∗ − CB ∗ + AB ∗ m
                                                                      correlation
                                                 0 as
        = CC ∗     m   + O(1/m)                  1/√m
                                                                                               frequency
   E. Rubiola, The magic of cross-spectrum measurements from DC to optics, http://rubiola.org
                                                                                                                                                                                                                   7

                          Cross-spectrum, increasing m
                                                                           |Re{Syx}| with C≠0,
  #!                                               #!                                               #!                                               #!
            m=1 g=0.32                                       m=2 g=0.32                                       m=4 g=0.32                                        m=8 g=0.32
            |Sxx|                                            |Sxx|                                            |Sxx|                                             |Sxx|
   #        |Re{Syx}|                               #                                                #                                                #
                                                             |Re{Syx}|                                        |Re{Syx}|                                         |Re{Syx}|
  !%#                                              !%#                                              !%#                                              !%#
            |Scc|                                            |Scc|                                            |Scc|                                             |Scc|

 !%!#                                             !%!#                                             !%!#                                             !%!#

                               frequency                                        frequency                                        frequency                                                     frequency
!%!!#                                            !%!!#                                            !%!!#                                            !%!!#
        !           "!   #!!    #"!        $!!           !           "!   #!!    #"!        $!!           !           "!   #!!    #"!        $!!           !             "!          #!!          #"!       $!!
  #!                                               #!                                               #!                                               #!
            m=16 g=0.32                                      m=32 g=0.32                                      m=64 g=0.32                                       m=128 g=0.32
            |Sxx|                                            |Sxx|                                            |Sxx|                                             |Sxx|
   #                                                #                                                #                                                #
            |Re{Syx}|                                        |Re{Syx}|                                        |Re{Syx}|
  !%#                                              !%#                                              !%#                                              !%#
                                                                                                                                                                |Re{Syx}|
            |Scc|                                            |Scc|                                            |Scc|                                             |Scc|

 !%!#                                             !%!#                                             !%!#                                             !%!#

                               frequency                                        frequency                                        frequency                                                     frequency
!%!!#                                            !%!!#                                            !%!!#                                            !%!!#
        !           "!   #!!    #"!        $!!           !           "!   #!!    #"!        $!!           !           "!   #!!    #"!        $!!           !             "!          #!!          #"!       $!!
  #!                                               #!                                               #!                                               #
            m=256 g=0.32                                     m=512 g=0.32                                     m=1024 g=0.32                                                 aver
                                                                                                                                                                                 age
                                                                                                                                                                                             |Re{Syx}|
            |Sxx|                                            |Sxx|                                            |Sxx|
   #                                                #                                                #

            |Re{Syx}|                                        |Re{Syx}|                                        |Re{Syx}|                             !%#
  !%#                                              !%#                                              !%#                                                                       devi
            |Scc|                                            |Scc|                                            |Scc|                                                                ation

 !%!#                                             !%!#                                             !%!#                                                       &'()*+,)-./0!+)1!##!#!$2!!3#4!05+6)789
                                                                                                                                                                                                        m
                                                                                                                                                              :%6;5'<(0=*0,/*$!!>
                                                                                                                                                   !%!#
                               frequency                                        frequency                                        frequency                #                 #!              #!!             #!!!
!%!!#                                            !%!!#                                            !%!!#
        !           "!   #!!    #"!        $!!           !           "!   #!!    #"!        $!!           !           "!   #!!    #"!        $!!

                                                                     Increasing m:
                                                 first, Syx decreases => single-channel noise rejection
                                                    then, Sxx shrinks => increased confidence level
               E. Rubiola, The magic of cross-spectrum measurements from DC to optics, http://rubiola.org
                                                                                                            8

  The thermal noise is rejected as any signal.
      The limit Sφ = P0/kT does not apply


                             A                      X=A+B
                   T2                   0º




                                        0º
                                                       Syx = k (T2 – T1) / 2
                             B           180        X=A–B
                   T1                        º
                                        0º



                           X and Y are uncorrelated
         The cross spectrum is proportional to the temperature difference


C. M. Allred, A precision noise spectral density comparator, J. Res. NBS 66C no.4 p.323-330, Oct-Dec 1962
   Application to AM/PM noise: E. Rubiola, V. Giordano, Rev. Sci. Instrum. 71(8) p.3085-3091, Aug 2000
                                                                                       9
                  Carrier recirculation


                                    gas cell



                     Invented by J. Hall for gas spectroscopy.
The gain is increased by the number of times the light beam circulates in the cavity




                                       DUT
    Also works with RF/microwave carrier, provided the DUT be “transparent”.
         For small no. of roundtrips, gives the appearance of “real-time”
                                                                                                             10

          Bridge (interferometric) method
V0 cos("0t)                                                             fluctuating error δZ => noise sidebands
                                                           pump
                                                                        ℜ{δZ} => AM noise x(t) cos(ω0t)
                                                  0º         –90º       ℑ{δZ} => PM noise –y(t) sin(ω0t)
                            (microwave)
                                                                        x(t)
        bridge    –        error amplifier
                                      !(t)




                                                                               FFT
                       !
                  +    hybrid                                           y(t)
                      junction
    Z            Z DUT

                                        x(t) cos("0t) – y(t) sin("0t)




                                                       Basic ideas
          • Carrier suppression => the error amplifier cannot flicker: it does know ω0
          • High gain, due to the (microwave) error amplifier
          • Low noise floor => the noise figure of the (microwave) error amplifier
          • High immunity to the low-frequency magnetic fields due to the microwave
            amplification before detecting
          • Rejection of the master oscillator’s noise
          • Detection is a scalar product => signal-processing techniques
              Derives from H. Sann, MTT 16(9) 1968, and F. Labaar, Microwaves 21(3) 1982
                 Later, E. Ivanov, MTT 46(10) oct 1998, and Rubiola, RSI 70(1) jan 1999
                                                                                                                                                                     11

                                       Actual block diagram
                            E. Rubiola, V. Giordano, Rev. Sci. Instrum. 73(6) pp.2445-2457, June 2002

                                                                                                                channel b (optional)
                                                                                                               I v1             readout      w1
                                                                       rf virtual gnd                RF I−Q                  G          B
                                                                       null Re & Im                     detect Q v2        matrix     matrix w2
                                                                                               g ~ 40dB     LO
                              inner interferometer                                                    pump
                                                                 x( t )                                                                                     FFT
                            CP1                      CP2                       R0       CP4
                                                                                                                             channel a                     analyz.
                                       DUT
                                                                                                                  I     v1               readout    w1
                                                           Δ’        CP3                            RF
      R 0 =50 Ω




                                             γ                                                           I−Q                       G           B
                                                                                                        detect Q v2               matrix      matrix w2
                                                           10−20dB                             g ~ 40dB     LO
                                                                               R0
                                                           coupl.
                                       arbitrary phase                                                pump                          G: Gram Schmidt ortho
                       atten                                                                                                        normalization
                                                                                                                                    B: frame rotation
      power splitter




                                       manual carr. suppr.
                                                                                               automatic carrier
                       atten                     ’    γ’                                      suppression control                   I−Q detector/modulator
                                        var. att. & phase                       atten                     diagonaliz.                                  I
                                                                                                                                      RF
                                                                               RF     I u1               z1                                            Q
                                       arbitrary phase          pump      LO     I−Q               dual         D
                       atten                                                    modul Q u2        integr z 2   matrix                    LO −90°      0°


                       Im                                        Concepts
                                  Up                            • Coarse and fine carrier suppression reduces the flicker noise
                             v(t)/!2
                                                                • Scalar product gives v1(t) and v2(t) in Cartesian frame. Linear algebra
         v(t)
                                                                  fixes the arbitrary phase, gain asymmetry and quadrature defect
     null fluct                    Re
                            v(t)/!2                             • Closed-loop control of the carrier suppression works as a RF VGND
                                  Dn
                                                                • Correlation is possible, using two amplifiers and two detectors
           1                                                    • Correlating the signals detected on two orthogonal axes (±45º)
Sud (f ) =   Sα (f ) − Sϕ (f )                                    eliminates the amplifier noise. Works with a single amplifier!
           2
                                                                                                                                                                                              12

                                                            Example of results
                   Noise of a by-step attenuator                                                    Background noise of the fixed-value bridge
!!K"C$                                                                                           !!L"AK
               S!9 f :          $
                           ;<'/;..=78                                    P" H.!#CI.;<0           5!!%LA%7       S"1 f +         #
                                                                                                                           ,-(2,33./0                                    P" @3!%A!3,-6
                                                    plot 459
>!!MKCM?
               S"9 f :        ;<=78                                      /E-.#F!.*G(%@'/                        S!1 f +    ,-./0                                         2<;3=#38>)&?(2
                                                                         @A&.'3.%B/,,C                                                                                   ?B'3(43&C2::A
                           N'3
                         >..........;<0=78?                              /'0.!/6.!D                               N(4
                                                                                                                53333333333,-6./07                                       2(63!2E3!F
!!J"C$                                         *+,-)(./'0                /,-)(.2,%/)C            !!M"AK                                                                  2:;*)3D:&2*A
>!!FKCM?                                                                                         5!!KLA%7                                             89:;*)32(6



!!I"C$                                                                                           !!J"AK             &'(()*
>!!KKCM?                  %&''()                                                                 5!!LLA%7

                                                                                    $                                                                                          #
                                                                                                                                                       kBT" .P" @3!!JJA!3,-5(2,337./0
                                                            kBT" =P" H.!!IJCI.;<>'/;..?=78

!!L"C$                                                                                           !!="AK
>!!JKCM?                                                                                         5!!MLA%7


                                              1&2'+('.3'(42(,%56.78                                                                                           G'D(9)(34()HD):&IE3/0
!$""C$                                                                                           !#""AK
>!!IKCM?                                                                                         5!!JLA%7
           !                            !"                        !"$                   !"#                 !                !"                !"#         !"$           !"%            !"K

     Noise of a pair of HH-109 hybrid junctions                                               Background noise of the fixed-value bridge (larger m)
!!>DE$                                                                                           !!J">#
1!!$MEC3       S", f &         #
                          '(-.'//)*+                                      P" L/!DED/'(2          :!!#I>%;           S! , f -           $
                                                                                                                                  ./)0.11234            5678+*10)9       P" =1!%>!1./9
               S!, f &                                                    .F@/!G/?H8;B-.                                                                                 0?81&$@15A*'B)0
                          '()*+                                                                                     S" , f -      ./234
                                                                          BI5/-0/;J.::E
                 N-0
               1//////////'(2)*+3                                         .-2/!.=/!K
!!CDE$                                                                    .:@A8/6:;.AE           !!H">#               N )<
                                                                                                                    :1111111111111./9234;
1!!%MEC3                                                                                         :!!II>%;                                                                BC(1)<1'D077>
                           ?7:@A8/.-2                                                                                                                           $        0)91!0F1!G
                                                                                                                                        kBT" 2P" =1!!HH>!1./:)0.11;234   078+*1E7'0+>

!!DDE$                                                                                           !!K">#
1!!>MEC3                                                                                         :!!JI>%;
                                                                                                                               '())*+


!!GDE$                                                                                           !$"">#
1!!CMEC3                                                                                         :!!HI>%;

               7:?B-628:B/:57?8
                                                               456-78-/0-8968:;<=/*+                                                                         L(E)6*)1<)*ME*7'NF134
!!MDE$                                                                                           !$!">#
1!!DMEC3                                                                                         :!!KI>%;
           !                !"                !"#           !"$           !"%          !">                  !"$                         !"&                      !"%                    !"#



                                                            Averaged spectra must be smooth
                                               Average on m spectra: confidence of a point improves by 1/m1/2
                                                  interchange ensemble with frequency: smoothness 1/m1/2
                                 13

The complete machine (100 MHz)
                               14

A 10 GHz experiment
     (dc circuits not shown)
                                                                                                                       15

Comparison of the background noise
   Sϕ (f) dBrad2/Hz                                                                      real−time
   −140                                                                                  correl. & avg.
                                                                                         mixer, interferometer
   −150                   sat
                              ura
                                    ted                                                  nested interferometer
                            int           mix
                     dou        e rfe         e
   −160                   ble          rom r
                                int         ete
                         cor        erf         r                                       saturated mixer
                                        ero
                              rel           me
                                  . sa
   −170                                t. m ter
                res                         ix.
                    idu
                        al f
               res           lick                                                  interferometer
                   idu            er,
   −180        res al f                by−
                   idu lick                 ste
              res      al f      er,            p in                                  correl. saturated mixer
                  idu lick fix                       ter
                      al f       er, ed i                fer
   −190                    lick       fix nte
                                er, ed i rfer
                                                             om
                                                                ete
                                     fix      nte      om           r                           double interf.
                                         ed       rfe
                                            int       rom eter
                                                erf
   −200                                            ero eter                          measured floor, m=32k
                                                       me
                                                            ter
                                                               , ±4
                                                                    5°d
   −210                                                                 ete
                                                                           ctio    expected, m=4x106
                                                                               n
               Fourier frequency, Hz
   −220
          1                         10                   10 2                 10 3             104               105
                                                                 16
              AM-PM calibration

• In most cases the phase detector is a double-balanced
  mixer saturated at both inputs
• In a double-balanced mixer, the offset is affected by power,
• AM noise is detected as it was PM noise, which is
  conceptually incorrect
• kφ/kα can be as low as 5

• In the bridge, the effect of AM noise is divided by the
  microwave gain
                                                                                                                                                                                                    17
                                      Primary AM-PM calibration                                  E. Rubiola – unpublished

A                                                                                       RF input                                                  RF output




                                                                      − y sin( ω 0t)
                            nal
                    ted sig




                                                      n
              odula                                                                     V0 cos(ω 0t)                                 V0 cos(ω 0t) + x cos(ω 0t) − ysin( ω 0t)



                                                 atio
            m                                                                                                     carrier


                                           dul
                carrier


                                         mo
              V0 cos(ω 0t)

                                      x cos(ω 0t)
                                                                                                              LO                                                                    I−Q modulator
B                   V0                                                                                      I−Q RF               modulation sidebands
               α=                                                                                          modul                                                                    LO pump
                 x                                                                                                               x cos(ω 0t) − y sin( ω 0t)
     amplitude−modulated signal                                                                          I       Q
                                        in−phase                                                                                                                                    90°       RF
                 carrier                modulation
                                                                                                         x    y       modul. input                                                            output
              V0 cos(ω 0t)              x cos(ω 0t)


C                    V0
                ϕ=
                      y                                                                AM and PM can be defined as                                                               I         Q

                                                                                       αrms =
                                         − ysin( ω 0t)




                      signal
                                                         modulation




                                                                                                                            P0 = power of the carrier
                                                                                                          Px /P0
                                                         quadrature




             ulated
         −mod
    phase                         ϕ                                                                                         Px = power of the in-phase
                 carrier
              V0 cos(ω 0t)                                                                                                       sidebands
                                                                                       ϕrms =             Py /P0            Py = power of the quadrature
                                                                                                                                 sidebands


                                                                                                       Basic ideas
                •    Generate reference AM and PM by adding sidebands to a carrier
                •    Power detectors provide absolute reference of PM as a null of AM
                •    Accurate (0.02 dB) power-ratio measurement with commercial power-meters
                •    Correct IQ modulators and detectors with linear algebra (2x2 matrices)
                •    Transfer the accuracy of a LF (kHz range) lock-in amplifier to RF/microwave
                •    Worst-case accuracy 0.3 dB => improvement in progress
                                                                                                                                                                                             18

     Bridge (interferometric) instrument
                                                                           power                                    AM out
                                                                           meter

                      inner interferometer                                     RF                                                       channel b
                                                                           virtual gnd
              CP1                                 CP2                                                              ampli & detector                  readout
                                                                                                                                        I   v 1b                w 1b
                 °           DUT                   −9                                    Δ"         CP4
             −90                                     0   °       Δ’           CP3                                          RF    I−Q                  R
            −9                                               °
                                                                                                        0°          g           detect Q v 2b        matrix     w 2b
                                                       0




                                                                                                        180 0°
               0°                   γ               −9




                                                                                                           °
                                                                           −20 dB
                                                                                                                                   LO
                                                                                                        0°

                                                                                                  by−pass
                                                                                                                                                                dual channel
                                                                                                                                                               FFT analyzer
                    fine carrier control
                                                                                                                                        channel a
                   −90°         I       0°                                                                         ampli & det.                      readout
                                                                                                                                   LO I     v 1a                w 1a
                                         0° 80°
                     0°0°




                                          1




                                Q                                                                                          RF    I−Q                  R
                                                                      0°                                            g           detect Q v 2a        matrix     w 2a
                   −90°                 0°                             180 0°
                                                                          °




                                                                                                                                                                               from AM out
                                                                      0°
                                                                                                                                                        to AM/PM
                                                                      automatic carrier control                                                         modul input

                                                    RF                 I            u1                       z1
                                        LO           I−Q   Σ                                                       D                                              osc lock−in in
                                                    modul Q u2                                z (t)dt        z2   matrix
                                                                             Σ                                                                                       amplifier

                                                                                                                           AM
                                                                                                                  matrix   PM     modulation input




                              Light blue: work in progress
     The dual-bridge contains almost all the blocks needed to calibrate the measurement
E. Rubiola, V. Giordano, Rev. Sci. Instrum 73 6 p.2445–57, jun 2002. Also arXiv:physics/0503015
2 – Microwave photonics
                                                                                                                                                      20
                              Opto-electronic discriminator
                              Rubiola, Salik, Huang, Yu, Maleki, JOSA-B 22(5) p.987–997 (2005)

                         Pλ     τd = 1.. 100 µ s                                                           Laplace transforms
                                                             phase
                               (0.2−20 km)                  detector
    laser
                  EOM
  1.55 µm                           _
                                  τd∼ 0            R0 20−40                 vo (t)                        Φ(s) = Hϕ (s)Φi (s)
                                 (calib.)              dB                    out




                                                                                     analyz.
                     100




                                                                                      FFT
  microwave          mW                                  10
                                                         mW                                               |Hϕ (f )|2 = 4 sin2 (πf τ )
  input                            _
                                  τ∼ 0                                   52 dB
           power ampli         Qeq = πν0 τ               90° adjust

The short arm can be a microwave cable or a photonic channel                                          Sy (f ) = |Hy (f )|2 Sϕ i (s)
                                                                                                                   4ν02
                         Laplace transforms                                                            |Hy (f )|2 = 2 sin2 (πf τ )
                                                                                                                    f
                  e−s τ                            mixer                                       990   J. Opt. Soc. Am. B / Vol. 22, No. 5 / May 2005

  Φi (s)                              −                          Vo(s) = k ϕ Φo (s)
                                          Φo(s)                                                                                                        tur
                                  Σ                 kϕ                                                                                                 the
                                      +                                                                                                                log
                                                                                                                                                       str
                                          Φo (s) = (1−e−sτ ) Φ i(s)                                                                                    rel
                                                                                                                                                       lim
                                                                                                                                                       mo
      •     delay –> frequency-to-phase conversion                                                           10 GHz, 10 μs
                                                                                                             10 GHz, 10 μs                             sec
      •     works at any frequency
      •     long delay (microseconds) is necessary for high sensitivity                                                                                4.
                                                                                                                                                       Th
      •     the delay line must be an optical fiber                                                                                                     sh
            fiber: attenuation 0.2 dB/km, thermal coeff. 6.8 10-6/K
            cable: attenuation 0.8 dB/m, thermal coeff. ~ 10-3/K                                                                                       In
                                                                                                                                                     21
     Measurement of a sapphire oscillator
        Volyanskiy & al., JOSAB (in press). Also arXiv:0807.3494v1 [physics.optics] July 2008.
                                   Modulateur
 Diode Laser
                                  Mach-Zehnder                                  Ampli
JDS Uniphase                                                      Photodiode
    laser
    =1,5 µm                             EOM
                                  JDS Uniphase
                                                                   DSC40S
                                                                                 AML
                                                                           SiGe ampli
                                                                               8-12GHz

                  Contrôleur                                                                        Analyseur FFT
                                                         2 2 Km
                                                       Fibrekm                        5 dBm
                                                                                                     (HP 3561A)
                de polarisation                                                  RF

                                        Att      3dB                                           DC       FFT
     sapphire oscillator                                                         LO
                                                                                         Ampli DC
                                                                                      10 dBm

                                              Coupleur               Déphaseur
                                                                      phase
                                               10 dB


                                      Ampli RF


     ISO            ISO

       Oscillateur Saphir




                                                                                                       • The instrument noise scales as 1/τ, yet the
                                                                                                          blue and black plots overlap
                                                                                                          magenta, red, green => instrument noise
                                                                                                          blue, black => noise of the sapphire
                                                                                                          oscillator under test
                                                                                                       • We can measure the 1/f3 phase noise
                                                                                                          (frequency flicker) of a 10 GHz sapphire
                                                                                                          oscillator (the lowest-noise microwave
                                                                                                          oscillator)
                                                                                                       • Low AM noise of the oscillator under test is
                                                                                                          necessary
                                                                                                                                                                                                                22
    Dual-channel (correlation) measurement
          Volyanskiy & al., JOSAB (in press) and arXiv:0807.3494v1 [physics.optics] July 2008.
Derives from: E. Salik, N. Yu, L. Maleki, E. Rubiola, Proc. Ultrasonics-FCS Joint Conf., Montreal, Aug 2004 p.303-306

                                                                                                                                                                      J.Cussey 20/02/07 Mesure200avg.txt
                                                                             !#"
                                                                                                                                                                               J.Cussey 20/02/07 Mesure200avg.txt
                                                                                           –20
                                                                                             !#"
                                                                                            !#"
                                                                                                                                                                              J.Cussey 20/02/07 Mesure200avg.txt
                                                                                                                                                                               J.Cussey 20/02/07 Mesure200avg.txt
                                                                                                                                       ;<9/0=.*17.1>*-?@17.1A=9B.19C.011-/1*.@9*717.1!"DB12E?>*.1#FG5
                                                                                                 !#"                                                                          J.Cussey 20/02/07 Mesure200avg.txt
                                                                                                !#"
                                                                             !%"
                                                                                                                                       residual phase noise (cross-spectrum),
                                                                                                                                       6A.01H.*IE<.J1K!"F3419C.01-/1*.@9*717.1#"DB12E?>*.1%FG51
                                                                                                                                                ;<9/0=.*17.1>*-?@17.1A=9B.19C.011-/1*.@9*717.1!"DB12E?>*.1#FG5
                                                                                                                                               ;<9/0=.*17.1>*-?@17.1A=9B.19C.011-/1*.@9*717.1!"DB12E?>*.1#FG5
                                                                                                                                                ;<9/0=.*17.1>*-?@17.1A=9B.19C.011-/1*.@9*717.1!"DB12E?>*.1#FG5
                                                                                                                                                6A.01H.*IE<.J1K!"F3419C.01-/1*.@9*717.1#"DB12E?>*.1%FG51
                                                                                           –40
                                                                                             !%"
                                                                                            !%"
                                                                                                                                       short delay ("!0), m=200 averaged spectra,
                                                                                                                                               ;<9/0=.*17.1>*-?@17.1A=9B.19C.011-/1*.@9*717.1!"DB12E?>*.1#FG5
                                                                                                                                               6A.01H.*IE<.J1K!"F3419C.01-/1*.@9*717.1#"DB12E?>*.1%FG51
                                                                                                                                                6A.01H.*IE<.J1K!"F3419C.01-/1*.@9*717.1#"DB12E?>*.1%FG51
                                                                                                                                               6A.01H.*IE<.J1K!"F3419C.01-/1*.@9*717.1#"DB12E?>*.1%FG51
                                                                                                 !%"
                                                                                                !%"                                    unapplying the delay eq. with "=10 "s (2 km)
                                                                             !("
                                                                                           –60
                                                                                             !("                               !
                                                                                            !("  !("
                                                                                                !("                                y   =1
                                                                             !'"
                                                                                                                                            0 –12
                                                                                           –80                                                      ba
                                                                                             !'"
                                                                                            !'"                                                          sel




                                                           6!12781*97#:345
                                                                                                 !'"
                                                                                                !'"                                                            ine




                                                                                      6!12781*97#:345
                                                                    !!""




                                                                                     6!12781*97#:345
                                                                                    6!12781*97#:345
                                                                                   6!12781*97#:345
                                                                                    –100
                                                                                      !!""
                                                                                     !!""   !!""
                                                                                           !!""
                                                                    !!#"                                                                                                                     FFT e
                                                                                                                                                                                                 ag
                                                                                                                                                                                            aver ect




                                                                                                          S!(f), dBrad2/Hz
                                                                                    –120
                                                                                      !!#"
                                                                                     !!#"   !!#"                                                                                              eff
                                                                                           !!#"
                                                                                                                              FFT e
                                                                    !!%"                                                           ag
                                                                                    –140                                     aver ect
                                                                                      !!%"
                                                                                     !!%"                                      ef f
                                                                                            !!%"
                                                                                           !!%"
                                                                    !!("
                                                                                    –160                                                                    FFT e
                                                                                      !!("
                                                                                                                                                                ag
                                                                                                                                                           aver ect
                                                                                     !!("   !!("
                                                                                           !!("
                                                                    !!'"                                                                                     eff
                                                                                 –180
                                                                                    !!'"
                                                                                   !!'"
                                                                                 !  !!'"
                                                                               !" !!'"                                        !"
                                                                                                                                #
                                                                                                               J.Cussey, feb 2007
                                                                                                                                                          !"
                                                                                                                                                                 $               Fourier frequency, Hz
                                                                                                                                                                                 !"
                                                                                                                                                                                   %
                                                                                                                                                                                                !"
                                                                                                                                                                                                  &

                                                                                                                                                     )*+,-./0.12345 $
                                                                                                        101                              102                      103                    104                   105
                                                                                                           !                                 #                                              %                       &
                                                                                                         !"
                                                                                                          !
                                                                                                        !"! !                             !"
                                                                                                                                           #
                                                                                                                                         !"# #                     !"
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                                                                                                                                                                  !"$ $                   !"
                                                                                                                                                                                           %
                                                                                                                                                                                         !"% %                  !"
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                                                                                                                                                                                                               !"& &
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                                                                                                        !"                                !"
                                                                                                                                         !"                        !"
                                                                                                                                                             )*+,-./0.12345
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                                                                                                                                                                                         !"                     !"
                                                                                                                                                                                                               !"
                                                                                                                                                            )*+,-./0.12345
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                                                                                                                                                            )*+,-./0.12345




          Improvements
          • Understanding flicker (photodetectors and amplifiers)
          • SiGe technology provides lower 1/f phase noise
          • CATV laser diodes exhibit lower AM/FM noise
          • Low Vπ EOMs show higher stability because of the lower RF power
          • Optical fiber sub-mK temperature controlled
                                                                                                                                                                           23
               Delay-line oscillator – operation
                                                                                     H(s)                                                        jω
                                                            model output Vo (s)

                                                                                                                           ....                   ....
                                                   noise
                      Vi (s)
                               +                    free                    V’(s)
                                                                             o                                            l=+3                    +6π/τ d
initial conditions,                Σ           A
noise, or locking              +                                          true                                            l=+2                    +4π/τ d
signal                                                                  oscillator
                                                                         output                                           l=+1                    +2π/τ d
                                               delay
                                            β (s) = e−sτd                                                                 l=0                     0
                                                                                                                                                                           σ
                                                                                                                          l=−1                    −2π/τ d
            in practice, delay + selector
              delay
           βd(s) = e−sτd
                              selector
                                βf (s)
                                                 Barkhausen condition                                                     l=−2                    −4π/τ d

                                                 for oscillation: Aß = 1                                                  l=−3                    −6π/τ d

                                                                                                                           ....                   ....
General feedback theory                                                                                                              1 ln(A)
        V o (s)      1                                                                                                               τd
H (s) =          =
         V i (s)   1 A (s)                                                                              20
                                                                                                        19
                                                                                                        18
                                                                                                                 delay−line loop, no selection filter
                                                                                                                 file le−calc−hdly−flt                          A=1
                                                                                                                 src allplots−leeson
                                                                                                        17
                                                                                                        16
Delay-line oscillator




                                                                                       |H(jf)|^2
                                                                                                        15                                                      A=0.75
                                                                                                        14

             1
                                                                                                        13
                                                                                                        12
H (s) =                                                                                                 11                                                      A=0.71




                                                                                       transfer function
        1 A esτd
                                                                                                        10
                                                                                                         9
                                                                                                         8
                                                                                                         7                                                      A=0.65
                                                                                                         6
Location of the roots                                                                                    5
                                                                                                         4
                                                                                                                                                                A=0.50
     1           2                                                                                       3
                                                                                                         2
sl =   ln(A) + j    l                       integer l          (        ,      )                         1
                                                                                                                                                                  A=0.30
                                                                                                         0
                                                                                                             0                           1                  2              3
           d                           d                                                                                                       f * tau

E. Rubiola, Phase Noise and Frequency Stability in Oscillators, Cambridge 2008, ISBN 978-0521-88677-2
                                                                                                                                                      24
           Delay-line oscillator – phase noise
                                                     noise                         ω m = (2π/τd ) m             jω
   Ψ (s)                                              free     Φ (s)                                                                        ....
                          +
                               Σ                 1
                                                                                    Δω = −
                                                                                             2Q µ                    (2π/τd ) µ             µ=+2
phase noise                +                                 phase noise                      τd m
   input                                                       output                                                                       µ=+1
                                              delay                                                                                         µ=0
                                            B(s) = e−sτ d                     ωm                                                                      σ
                                                                              2Q                                                            µ=−1
                                                                                               µ
         in practice, delay + selector                                              Δω = − 2Q                        (2π/τd ) µ             µ=−2
                                                                                            τd m
        delay                 selector
      B(s) = e−sτ d      B(s) = 1 / (1+s τ f )                                                                                              ....

                                                                                                              2Q2 µ 2
                                                                                                          σ=−
                                                                                                               τd m

  General feedback theory
         Φ(s)        1                                                     1e+08
  H(s) =       =                                                                 phase noise |H(jf)|^2                      file le−calc−dly−hphase

         Ψ(s)    1 − B(s)
                                                                                                                            src allplots−leeson
                                                                           1e+07 delay−line oscillator with selector
                                                                           1e+06 parameters:
                                                                                    tau = 2E−5 s
  Delay-line oscillator                                                    1e+05    m = 2E5
                                                                                    nu_m = 10 GHz
                                                                                    Q = 2000
              1 + sτf
                                                                           10000

  H(s) =                                                                    1000
          1 + sτf − e−sτd                                                    100
                                                                              10
  Location of the roots                                                        1

         2Q2 µ 2        2π 2Q µ                                              0.1
  sµ = −             +j µ−                                                  0.01
                                                                                                                          frequency, Hz
          τd m          τd τd m                                                1000                   10000            1e+05                      1e+06

   E. Rubiola, Phase Noise and Frequency Stability in Oscillators, Cambridge 2008, ISBN 978-0521-88677-2
                                                                                          25
                          Delay-line oscillator




         ν0          Qeq = πν0 τ            Qeq=3×105 ← L=4km
    fL =
         2Q
                           1                               h−1 = b−3 /ν0
                                                                       2
                                                                              6.3×10–24
                    fL =                    fL=8kHz
                         4π 2 τ 2
                                    10–11                  σy = 2 ln(2) h−1
                                                            2
                                                                              8.8×10–24
                      2
Leeson              fL
formula   Sϕ (f )       S (f ) for f
                      2 ψ
                                             fL
                    f
                                                      σy      2.9×10−12 Allan deviation
          b–3 = 6.3×10–4 (–32 dB)
                                                                                                                          26
Delay-line oscillator - measured noise
                                              Phase noise of the opto-electronic oscillator (4 km)
                              0



        S!(f), dBrad2/Hz
                            –20
                                                our OEO
                            –40            b–3=10–3 (–30dB)

                                                                                           Wenzel 501-04623
                            –60                                                             OCXO 100 MHz
                                                                     Agilent E8257c, 10
                                                                                            mult. to 10 GHz
                                                                     GHz, low-noise opt.
                            –80


                           –100


                           –120


                           –140
                                  E. Rubiola, apr 2008
                                  OEO: Kirill Volyanskiy, may 2007
                           –160
                               101                             102           103                104           105
                                                                         frequency, Hz

•   1.310 nm DFB CATV laser
•   Photodetector DSC 402 (R = 371 V/W)‫‏‬
•   RF filter ν0 = 10 GHz, Q = 125                                                               expected phase noise
•   RF amplifier AML812PNB1901 (gain +22dB)‫‏‬                                                     b–3 ≈ 6.3×10–4 (–32 dB)
                                                                                                            27
               Optical-fiber 10 GHz oscillator
                                                     !"#
                            3<,&6%A&=%</.
               3425.,&'+6   ></=6<,,+6                                           (&6%&),+.
                                                                                 <5=%>&,.><45,+6



                                                                       *+,&-.                      *+,&-.
                                             $%&'          78.96%:%/;.   ,%/+.                     ,%/+.
                                             ()%&'         5<6=         B.12                       0.12


                            78.&25,%@%+6 78.8%,=+6


                                                      CC      3?<=<9+=+>=<6


                                              D==                             3?<=<9+=+>=<6



   • use positive feedback with a short cable (3-5 ns) in the feedback path to implement
     the mode selector
!"#$#%&$&'$#()*+,-*./, filter
   • the positive feedback also increase the amplifier gain
     (AML SiGe parallel amplifiers exhibits lowest flicker, but low have gain 22 dB)
                   0
   • use the 2-km (10 µs) path to eliminate the 50-kHz noise peak due to the 4-km (20 µs)
   • the microwave power is changed by adjusting the laser power
               -2 0
   • high noise figure, due to the two power splitters/combiners
                -4 0                        Kiryll Volyanskiy, jan 2008
                                       e                                                 a
                                   Le r´sultat de mesure du bruit de phase d’oscillateur ` trois boucles
                                                                                                   28
Regenerative optical-fiber 10 GHz oscillator
                                     e    e
                                   pr´sent´ sur la figure 4.


                                                              0
 Prf is given, thus V0 =(2RP)1/2                                     b–4 = –7 dBrad2/Hz
                                                                                                                                   file 923-kirill-oeo
                                                                                                                                   E.R & K.Voliansky, jan 2008

 Vπ is estimated (4.5 V at 10                               !20

 GHz)                                                       !40
                                                                                     b–3 = –26 dBrad2/Hz


 Use
                                                            !60




                                         S! (dB rad2/Hz)
                πV0
     m = 2J1                                                !80
                 Vπ                                                                                                          the power is measured
                                                                                                                             at the amplifier output
                                                                                                                                           9dBm
 Get                                                       !100
                                                                                                                         11dBm
                                                                                                                                             8dBm
 P, dBm   Vp, V   πV0/Vπ      m                            !120     b–2 = –50.5 dBrad2/Hz (8 dBm)

   11     1.122   0.860    0.783                                                b–2 = –53 dBrad2/Hz (9 dBm)
                                                           !140
    9     0.891   0.683    0.644                                    (S!)min = –142 dBrad2/Hz (11 dBm)         b–2 = –57 dBrad2/Hz (11 dBm)

                                                           !160
    8     0.794   0.6.09   0.581                              10
                                                                1
                                                                                      10
                                                                                          2
                                                                                                             10
                                                                                                                  3
                                                                                                                                      10
                                                                                                                                         4
                                                                                                                                                             10
                                                                                                                                                                 5

                                                                                                        Frequency (Hz)



 The oscillator phase noise                                                                   a
                                   Fig. 4 – Courbes de mesure de bruit de phase d’oscillateur ` trois bou
                                        Feeding 8dBm – puissance qui est mesur´model
                                   (11dBm, 9dBm, the available data in theee ` la sortie de l’amplifi
                                                                                   a
 minima are 6 dB lower than        teur)                                  2
 b0=N/P0 (white noise)                              8    F k T hν            1        hν 1    B 0                 l                              l
                                      (Sϕ )min =                                                                              2   +2
                                   Nous observons que 2 pic `R0
                                                    m le                 qη     Pl e       η Pl
                                                                                            e
                                                               a 50kHz est supprim´ consid´rablement.
 m = 0.725 (Prf=11 dBm)                we get                        e e            e
                                   On conclut que nous avons am´lior´ la stabilit´ de phase d’un oscilla
 (Sφ)min = –142 dB                     e                                                    e
                                   opto´lectronique par l’utilisation des deux boucles suppl´mentaires.
                                       P0 = 6.4 μW (-22 dBm)
 F = 10 dB (incl. couplers)
 η = 0.6                               Pl ≈ 0.71 mW                                                           3
 νl = 194 THz                          There is room for engineering
3 – Electronic and optical
       components
 E. Rubiola – FCS 2004 2004
      E. Rubiola – FCS                                                                                                4    430

    Flicker electronic &microwave components
       Flicker noise in and optical amplifiers
Flicker in noise in RFRF and microwave amplifiers
                      no carrier
                          no carrier                                                        noise
                                                                                                noise
         S(f)   S(f)                                     S(f) S(f)
                 near-dc flicker
                       near-dc flicker                                                      up-conversion
                                                                                                up-conversion
  near-
                    no flicker
    dc                        f  f                                                          f   f
  noise              ω0 = ?                                                         ω0
       random modulation near-dc noise
  random modulation fromfrom near-dc noise
        stopband                                                    output bandwidth
                              output bandwidth , stopband, !t " , , !t "
                                                               n, n
                                             n , !t " n !t "                  noise-free
                                                                         noise-free
                       vi !t "#V i cos!$
                vi !t "#V i cos!$0 t " 0 t "                                                 v
                                                                                      v o !t " o !t "
                                           AM AM             PM PM         a1   a1
                               carrier       near-dc noise
                    v v !t
                         o
                                    jω0 t
                                         i
                                         i      %
                                             % substitute
  modulated signal: v i (t) o#VVe cos!$ (t) 0 t "&m(t) !t " cos!$is t "'m , !t "sin"sin !$ 0 a"
                                           cos!$ + , n , " ,
      modulated signal: !t " = " i # V + n t "&mjn, !t ncos!$ t "'m , , n ,in ,n’ and n”
                                                      0
                                                      carrier
                                                             the parametric nature ,of 1/f
                                                              noise 0 hidden   n , !t !$ t " t
                                                                                 0                              0   ( (a
                                                                                                                     1     1
                                                carrier                    AM
                                                                       AM noisenoise                PM
                                                                                                PM noisenoise
                                                (careful, this hides the down-conversion)

        the (t) =
          vo simplest i # + a vi (t)2+ . . .
  the simplest a1 vv (t) v o #2a1 x&a 2 x 2withwithx # V # V i cos!$0 t n &"n!t " *n !t**+1+1
                                         2
                          o
                              a1 x&a 2 x                   x cos!$ t " & " !t             "n!t "*
        nonlinearity
  nonlinearitynon-linear (parametric) amplifier              i          0
                                                                    carrier near-dc
                                                              carrier            near-dc
        yields:              expand and select the ω0
  yields:
                                               % %                                                    ( (
                                       terms
            v o# " a# a1 V i cos!$0 t "&a2 cos2cos2 !$0 t "&2 V i"n !t " cos!$0 t "&n"2 !t "
                                                  2
     v o !t "  !t     V cos!$0 t "&a 2 V i2     V i !$ t "&2 V n !t cos!$ t "&n 2 !t
                     1 i                              0         i              0
                                                                                  The noise sidebands are
                          2 (t) +
   vo (t) = Vi a1 + 2a2 n a n!t "jn (t) ejω0 t
                    2 a 2 n!t "
                              2                                   to 2 2 2
                                                     proportional 2 atheainput carrier
       AM noise: #
  AM noise: )!t " )!t " #                modulation index: m
                                      modulation index: m # # a
                         a1 a1
                    get AM and PM noise                            a1 1
       PM noise originates in the same way, but for a phase shift in the product
    PM noise originates in the same way, but for a 90°90° phase shift in the product
             a2                      a2
    α(t) = 2          n (t)          ϕ(t) = 2              n (t)              The AM and the PM noise are
                 a1                                   a1                    independent of Vi , thus of power
      There is also a linear parametric model, which yields the same results
                                                                                                       Avantek UTC573, 10 MHz

                                               !130       2Amps ! Pin=!5dBm
                                                                                                                    23 Jan 07
                                                                                                                                                                                                     31

                            Amplifier flicker noise – experiments
Phase noise, dBrad 2 /Hz S ! (f), dB.rad /Hz
                                                                                                       2Amps ! Pin=!22dBm
                                               !140
                                                                                                                 2Amps ! Pin=!19dBm


                                        2      !150

                                               !160
                                               −120
                                               −125       1Amp ! Pin=!5dBm                                           SiGe LPNT32
                                                                                                                     bias 2V, 20 mA
                                                                                                                                               Phase noise vs. power
                                               !170
                                               −130                                                       3 dB            NMS floor
                                                                                                                     R. Boudot 2006
                                                                                                                                               • The 1/f phase noise b–1 is about independent of
                                               −135
                                               !180
                                               −140 1                 10            100              Pin=−15dBm 10000
                                                                                                     1000                   100000               power
                                                                                                             Pin=−10dBm
                                               −145                                            f, Hz
                                                !50
                                               −150
                                                                                                                   Pin=−5dBm                   • The white noise b0 scales up/down as 1/P0, i.e., the
                                                             JS2
                                                                                                                                                 inverse of the carrier power
                                                                                                          Pin= !9dBm
                                               −155       29 Jan 2007
                                                 F IG                                                     Pin= !6dBm
                                                !70 . 18 – Phase noise of 1-stage and 2 stages cascaded amplifiers at 10MHz.
                                               −160                                                       Pin= !4dBm
                                                                                                                                               • Describing the 1/f noise in terms of fc is misleading
       S!(f), dB.rad 2/Hz




                                               −165                                                      Pin= !2 dBm
                                                !90      b!1= !106 dB.rad2 /Hz                            Pin= !1dBm
                                               −170
                                               −175
                                               !110 1
                                                                                            Pin=0dBm
                                                                                                                                                 because fc depends on the input power
                                                                 10              100            1000          10000         100000
                                                                                               f, Hz
                                               !120
                                               !130
                                                                                                       Avantek UTC573, 10 MHz
                                                                                                                   23 Jan 07
                                                                                                                                               Phase noise of cascaded amplifiers
                                                                                                                                               • The expected flicker of a cascade increases by:
                                               !130
                                               !150
                                                          2Amps ! Pin= !5dBm
              /Hz




                                                                                                                                                 3 dB, with 2 amplifiers
                                                                                                               3Amps ! Pin= !24dBm
                                               !140
                                               !170
S!(f), dB.rad 2




                                                      1              10             100                 1000         10000          100000

                                               !150
                                                                                               f, Hz
                                                                                                                                                 5 dB, with 3 amplifiers
                                               !160         F IG . 10 – Phase noise of 1 amplifier JS2 vs Pin at 10 GHz.
                                                          1Amp ! Pin=!5dBm                                                                     Regenerative amplifiers
                                               !170                                                        5!6 dB       NMS floor              • Phase noise increase as the squared gain because
                                               !180
                                                      1               10            100                 1000         10000            100000
                                                                                                                                                 the noise source at each roundtrip is correlated
                                                                                           f, Hz
                                                !50
                                                  JS2, 10 GHz
                                          !70     15 Feb 2007
                                      F IG . 19 – Phase noise of 1-stage, 2-stages and 3-stages cascaded amplifiers at 10MHz.                   Phase noise of paralleled amplifiers
                                                                                                                                               • Connecting two amplifiers in parallel, the phase-
                  /Hz




                                                !90
                                                                                                                                                 noise flicker is expected to decrease by 3 dB
    S!(f), dB.rad 2




                                                                                                          Single amplifier
                                               !110                                                         Pin= −6 dBm
                                                                                          12
                                               !130

                                               !150                                    2 parallel amplifiers
                                                                                               Pin= −5 dBm
                                               !170
                                                      1              10             100                 1000         10000          100000
                                                                                           f, Hz
                                                                                                                                                            32
                                 Photodetector 1/f noise                                                                                                2
                             Rubiola, Salik, Yu, Maleki, MTT 54(2) p.816-820, Feb 2006
                                        infrared
  1.32 µ m
                                                      iso    P!             Pµ r(t) hybrid %
    YAG (13dBm) EOM                                                                  !90°                             =6dB
    laser                                                   (!3dBm)      (!26dBm)                                   RF            v(t)




                                                                                              0° 0°
                                                               photodiodes                            g=37dB                                   FFT
                                        50% coupler             under test                                                IF                  analyz.
                                                      iso                         s(t)                &             LO
                     22dBm                                                                                                          g’=52dB
  monitor                                                                                !90°
  output                                  power                         phase & aten.                        phase $
                                          meter
                                                                      (carrier suppression)               (detection of " or #)

   100                          power
   MHz 9.9GHz                   ampli
               PLL
              synth.                                                        microwave                                                    near!dc
                                              Table 1: Flicker noise of the photodiodes.
Fig. 1.   Scheme of the measurement system.
                               photodiode               Sα (1 Hz)                          Sϕ (1 Hz)
                                                  estimate uncertainty               estimate    uncertainty
analyzer measures the output spectrum, Sϕ (f ) or Sα (f ). The where q is the electron charge, is the detector responsivity,
                            or kd =
gain, defined as kd = v/α HSD30 v/ϕ, is −122.7                                                modulation, and P λ the average
                                                            −7.1 m the index of intensity −8.6
                                                                          −127.6
                                                            +3.4                            +3.6
                                                                 optical power. This is proved by dividing the spectrum density
                       gPµ R0
              kd =             − dissipative ,
                           DSC30-1K   loss −119.8           (3) Si = 2qı −120.8 λ of the the output 2
                                                            −3.1
                                                            +2.4
                                                                           = 2q P           −1.8
                                                                                            +1.7 2
                                                                                                       current i by the average
                                                                 square microwave current i2 = P λ 1 m2 . The background
                                                                                             ac          2
                                                                                             noise
where g is the amplifier gain, Pµ the microwave power, R0 −1.5 amplitude and phase white−1.7 take the same value because
                           QDMH3           −114.3            =            −120.2
                                                            +1.4                            +1.6
50 Ω the characteristic resistance, and the mixer ssb loss. they result from additive random processes, and because the
Under the conditions of our setup (see below) the gain is 43 instrument gain/Hz is the same. The residual flicker noise is
                           unit            dB/Hz             dB         dBrad2 kd            dB
dBV[/rad], including the dc preamplifier. The notation [/rad] to be determined experimentally.
means that /rad appears when appropriate.                          The differential delay of the two branches of the bridge is
  Calibration the ∑ amplifier is not detected [Rubiola, Salik, Yu, Maleki, Electron. Lett. 39(19) p.1389-1390 (2003) ]
 The noise ofinvolves the assessment of kd and the adjustment kept small enough (nanoseconds) so that a discriminator effect
                                                                                                                                              33
                                 Photodetector 1/f noise
                           Rubiola, Salik, Yu, Maleki, MTT 54(2) p.816-820, Feb 2006


•    the photodetectors we measured are similar in
     AM and PM 1/f noise
•    the 1/f noise is about -120 dB[rad2]/Hz
•    other effects are easily mistaken for the
     photodetector 1/f noise
•    environment and packaging deserve attention
     in order to take the full benefit from the low
     noise of the junction

                                                                                   Figure 2: Example of measured spectra Sα (f ) and Sϕ (f ).


                                                                        modulator (EOM) is rejected. The amplitude noise of the source is re
                                                                        to the same degree of the carrier attenuation in ∆, as results from the g
                                                                        properties of the balanced bridge. This rejection applies to amplitude noi
                                                                        to the laser relative intensity noise (RIN).
                                                                            The power of the microwave source is set for the maximum modulation
                                                                        m, which is the Bessel function J1 (·) that results from the sinusoidal respo
                                                                        the EOM. This choice also provides increased rejection of the amplitude n
                                                                        the microwave source. The sinusoidal response of the EOM results in har
                                                                        distortion, mainly of odd order; however, these harmonics are out of the s
                                                                        bandwidth. The photodetectors are operated with some 0.5 mW input
    W:
waving a hand
 0.2 m/s,    S:
 single spectrum, with optical A:
 average spectrum, with optical           F:
 after bending a fiber, 1/f
                                                                         Figure is low enough for the detectors toexperimental a linear regime. This
                                                                                 3: Examples of environment effects operate in mistakes around
                                                                        which Examples of environment effects andand can increase unpredictably
                                                                    Figure 3:                                    noise experimental mistakes around
    3 m far from the system       connectors and no isolators        connectors and no isolators
    B:
 background noise          B:
 background noise                   the corner. high carrier the instrument Background noise which is stable
                                                                    the possible a the noise show suppression (50–60 dB) in ∆, (spectrum B) B) f
                                                                        corner. All All the plots show the instrumentbackgroundnoise (spectrum
                                                                     B:
 background plots                        B:
 Background noise
                                  P:
 photodiode noise                   the the noise spectrum of Photodiode an (spectrum also Plot 1 spectrum
                                                                         and noise spectrum of the the Photodiode hour), andP). Plot 1 spectrum
                                                                    andduration of the measurement (half pairpair (spectrum P).provides a high re
                                                                                                                 P:
 photodiode noise
    P:
 photodiode noise                                             P:
 photodiode noise
                                                                        of experimentalist andWaves a noise of(≈ (≈ m/s), 3 m3far far away from
                                                                         W: the experimentalist of hand gently the 0.2 m/s), m The coherence
                                                                    W: the the laser RIN Waves a the hand gently 0.2∆ amplifier. away from thethe len
                                                                                                          34
                               Microwave optical link
Sϕ (f )
               10–12 rad2/Hz @ 1 Hz
                                                           • Let’s be optimistic: a 10 GHz link is
               b−
                  1 /f                                       limited by the 1/f phase noise of a single
                                                             component, –120 dBrad2/Hz @ f=1 Hz
                                       f
                                                           • Well known rules give σy(τ) = 4x10–17/τ
                   f2
Sy (f )   Sy (f ) = 2 Sϕ (f )
                   ν0
                                                           • Realistically, –100 dBrad2/Hz @ f=1 Hz
                                                             yields σy(τ) = 4x10–16/τ
                 h 1f
                10–32 @ 1 Hz           f
                                                          h1 1
                 σy (τ )
                  2
                              = [1.038 + 3 ln(2πfH τ )]
                                                        (2π)2 τ 2
σy (τ )
          4x
               10 –1
                     7
                         /!
                                           τ
4 – AM noise and RIN
                                                                                                                                                                                                             36

                                    Amplitude noise & laser RIN
                                                                                            • In PM noise measurements, one can validate the instrument by
AM noise of RF/microwave sources
                                        Pa            va                                      feeding the same signal into the phase detector




                                                                     FFT analyzer
                                                                     dual channel
                                                                                            • In AM noise this is not possible without a lower-noise reference
                                        Pb           vb
 source
under test
                                                                                            • Provided the crosstalk was measured otherwise, correlation
                         monitor                                                              enables to validate the instrument
                   power                                                                                                                       Wenzel 501−04623E 100 MHz OCXO
                   meter
                                                                                                                        −123.1                                                        P0 = −10.2 dBm
                                                                                                                                                                                      avg 2100 spectra

 Laser RIN
                         optical                                dc                                                      −133.1




                                                                                                             dB/Hz
                                        Pa                 va
    source

                                                                         FFT analyzer
                                                                                                                        −143.1
                                                                         dual channel




                                                                                                            Sα ( f )
    under
     test                                                 R
               coupler       coupler
                                        Pb                vb
                                                                                                                        −153.1

                      monitor                             R
                  power                                                                                                                    Fourier frequency, Hz
                  meter                                                                                                 −163.1
                                                                                                                              10                  102              103           104                105


 AM noise of photonic RF/microwave sources                                                                                      !("
                                                                                                                                                             =>)'$&1789

                   optical                   microwave                          dc                                                                                        Kirill Volyanskiy
                                                                                                                                !'"
     source                        Pa                                 va
                                                                                        FFT analyzer
                                                                                        dual channel




     under
      test                                                                                                                     !!""
                                             R0                       R                                         678912:;<345
              coupler    coupler
                                   Pb                                 vb                                                                                                  60mA
                                                                                                                               !!!"                                              40mA
                     monitor                 R0                       R
                 power                                                                                                                  80mA                                                20mA
                 meter                                                                                                         !!#"
                                             monitor                                                                                                                                        30mA
                                                    power
                                                    meter                                                                      !!$"


   E. Rubiola, the measurement of AM noise, dec 2005                                                                           !!%" !                #               $
                                                                                                                                                                          100mA
                                                                                                                                                                                   %                     &
                                                                                                                                  !"               !"           !"               !"                !"
        arXiv:physics/0512082v1 [physics.ins-det]                                                                                                          )*+,-+./012345
                                                                             37
           AM noise of some sources
source                                        h−1 (flicker)       (σα )floor
Anritsu MG3690A synthesizer (10 GHz)     2.5×10−11   −106.0 dB   5.9×10−6
Marconi synthesizer (5 GHz)              1.1×10−12   −119.6 dB   1.2×10−6
Macom PLX 32-18 0.1 → 9.9 GHz multipl.   1.0×10−12   −120.0 dB   1.2×10−6
Omega DRV9R192-105F 9.2 GHz DRO          8.1×10−11   −100.9 dB   1.1×10−5
Narda DBP-0812N733 amplifier (9.9 GHz)    2.9×10−11   −105.4 dB   6.3×10−6
HP 8662A no. 1 synthesizer (100 MHz)     6.8×10−13   −121.7 dB   9.7×10−7
HP 8662A no. 2 synthesizer (100 MHz)     1.3×10−12   −118.8 dB   1.4×10−6
Fluke 6160B synthesizer                  1.5×10−12   −118.3 dB   1.5×10−6
Racal Dana 9087B synthesizer (100 MHz)   8.4×10−12   −110.8 dB   3.4×10−6
Wenzel 500-02789D 100 MHz OCXO           4.7×10−12   −113.3 dB   2.6×10−6
Wenzel 501-04623E no. 1 100 MHz OCXO     2.0×10−13   −127.1 dB   5.2×10−7
Wenzel 501-04623E no. 2 100 MHz OCXO     1.5×10−13   −128.2 dB   4.6×10−7


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