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MOSFET Modeling for Low Noise, RF Circuit Design by she20208

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									 MOSFET Modeling for Low Noise,
      RF Circuit Design

M. Jamal Deen, Chih-Hung Chen and Yuhua Cheng*

     Electrical and Computer Engineering Department
   McMaster University, Hamilton, ON, Canada L8S 4K1
 *Conexant Systems Inc., Newport Beach, California, USA

                E-mail: jamal@mcmaster.ca


                                Microelectronics Research Laboratory
                                ECE Department, McMaster University
             RF Performance of MOSFETs
            50 V =1.0V                        W=10x6µm                     6                             : L=0.97µm
                DS                                                                   f = 2 GHz
                                                                                                         : L=0.64µm
                                                                                     W = 10x6 µm         : L=0.42µm
            40                                                             5
                                                   L=0.18µm                          VDS = 1.0 V         : L=0.27µm




                                                              NFmin (dB)
                                                                           4                             : L=0.18µm
            30
 fT (GHz)




                                                                           3
            20                                 L=0.27µm
                                                                           2
                                               L=0.42µm
            10
                                               L=0.64µm                    1
                                               L=0.97µm
            0                                                              0
                 0.5     1.0      1.5        2.0                               0.5     1.0         1.5    2.0
                          VGS (Volt)                                                    VGS (Volt)

• DUTs are fabricated in 0.18 µm CMOS technology and measured at VDS = 1.0 V.
• Maximum fT is around 50 GHz and the best NFmin is about 0.5 dB at 2 GHz.

Sec. 11.1, IEEE CICC2002, Orlando, Florida                                                               Page 2 of 40
 What’s inside your Cellular Phone?



                                             LNA    Band-pass
                                                      filter

                                                                             Low frequency
                                                                LO   Channel signal
                                Diplexer
                                                                     select  processing


                                               PA   Band-pass
                                                      filter




Sec. 11.1, IEEE CICC2002, Orlando, Florida                                        Page 3 of 40
                                             Outline
• RF Modeling of MOSFETs
     - Parasitic resistances and capacitances
     - Non-Quasi-Static (NQS) effects
• Noise Modeling of MOSFETs
     - What does the device noise look like?
     - Equivalent noise circuit model
     - Channel noise, Induced gate noise and their correlations
     - Noise modeling for RF IC applications
• Design Strategy of low noise amplifiers (LNA)
  - Selection of the device size, geometry and bias condition
  - Impact of the Accuracy of Noise Sources
• Conclusions
Sec. 11.1, IEEE CICC2002, Orlando, Florida                        Page 4 of 40
         RF Model Including Parasitics

                                                        G
                                                CGSO           CGDO
                                               RS                 RD
                       B                   S              RG           D
                                                                                          B


                  P+                 N+                RDS                  N+            P+
         trench             trench        N-                           N-        trench        trench
                                               DSB              DDB
                                                       RBDS


                                  RSB                  P-SUB                RDB



•    Y. Cheng, C. H. Chen, C. Enz, M. Matloubian and M. J. Deen, ICCDCS 2000, Cancun,
     Mexico, pp. D23 1-8 (15-17 March 2000).

Sec. 11.1, IEEE CICC2002, Orlando, Florida                                                              Page 5 of 40
                               Gate Resistance
                                                 RRg,poly
                                                  g,poly




                                             G



               Cox
                S                                 Rch       D
                                       Rch


• At high frequencies, the effective gate resistance consists of the poly-
  silicon resistance (Rg,poly) and distributed channel resistance (Rch)


Sec. 11.1, IEEE CICC2002, Orlando, Florida                            Page 6 of 40
         Source and Drain Resistances
                                                                    Rvia
                                                                     Rvia



                                                                      Rsalicide
                                                                   Rsalicide
                                             Rd
                                             Rldldd
                                                      Rc
                                                      Rc
            Rs,d = Rvia + Rsalicide + Rc + Rldd ~ Rc + Rldd
• The source and drain series resistances include the via resistance (Rvia),
  the salicide resistance (Rsalicide), the salicide-to-salicide contact resis-
  tance (Rc) and the sheet resistance in the LDD region (Rldd).

Sec. 11.1, IEEE CICC2002, Orlando, Florida                               Page 7 of 40
                          Substrate Network
                                                        G
                   B                         S                       D
                                                                                        B



      trench               trench                                              trench       trench
                                                 Dsb           Ddb

                                                       Rdsb


                                    Rsb                P-sub             Rdb




• At high frequencies, the signal at the drain will be coupled to the
  source and the body terminals through the substrate resistances (Rdb,
  Rsb and Rdsb) and junction capacitances at drain and source.

Sec. 11.1, IEEE CICC2002, Orlando, Florida                                                   Page 8 of 40
                     Parasitic Capacitances

                                                    G
                                                    O



         O                                                                            O   D
             S
                       CFO                   CFI CGSI CGDI CFI CGDOL          CFO
                                     CGSOL

                          CGSO      n-
                                                                       CGDO
             n+      xJ                                                         xJ

                             CJS                                               CJD



                                                         P-sub



Sec. 11.1, IEEE CICC2002, Orlando, Florida                                           Page 9 of 40
       Sub-Circuit Model For MOSFET
                                                   G
                                                               Core/Intrinsic
                                                    RG          MOSFET

                           CGSP                                     CDBP
                   S                         Si          Di                D
                          RS                                         RD
                                     CSB                      CDB


                                   RSB       Bi   RDSB          RDB

                                        Substrate Network



Sec. 11.1, IEEE CICC2002, Orlando, Florida                                      Page 10 of 40
     Results of Y- Parameter Fitting
                                  4x10-3
                                                                                                                                                        0.0

                                                          3x12µmx0.36µm
                                                                                      Vd=Vg=1.5V
                                                                                                                                                                                                          Re(Y12)
                                           -3                                                                                                                -4
                                  3x10                                                                                                             -2.0x10
       Re(Y11)&Im(Y11) (A/V)



                                                      Solid lines: Model




                                                                                                                      Re(Y12)&Im(Y12) (A/V)
                                                      Symbols: Measure data
                                                                                                           Im(Y11)
                                                                                                                                                             -4
                                                                                                                                                   -4.0x10
                                  2x10     -3                                                                                                                         3x12µmx0.36µ m


                                                                                                                                                   -6.0x10-4           Vd=Vg=1.5V


                                                                                                                                                                       Solid lines: Model
                                  1x10-3
                                                                                                       Re(Y11)                                               -4        Symbols: Measure data
                                                                                                                                                   -8.0x10                                                Im(Y12)




                                           0                                                                                                       -1.0x10-3
                                                 0              2             4           6        8             10                                               0           2          4       6        8             10

                                                                              Frequency (GHz)                                                                                           Frequency (GHz)

                                                                                                                                                   3.0x10-3
                                       8.0x10-3
                                                                                                                                                                      Solid lines: Model
                                                                                                                                                             -3
                                                                                                                                                   2.5x10             Symbols: Measure data
                                                                                                           Re(Y21)
               Re(Y21)&Im(Y21) (A/V)




                                                                                                                                                                      3x12µmx0.36 µm
                                       4.0x10-3                                                                                                                                                       Im(Y22)




                                                                                                                           Re(Y22)&Im(Y22) (A/V)
                                                                                                                                                             -3
                                                                                                                                                   2.0x10             Vd=Vg=1.5V

                                                0.0
                                                                                                            Im(Y21)                                1.5x10-3


                                                           Solid lines: Model
                                                                                                                                                             -3
                                       -4.0x10-3           Symbols: Measure data                                                                   1.0x10
                                                                                                                                                                                                              Re(Y22)
                                                            3x12µ mx0.36µ m
                                                                                                                                                             -4
                                                                                                                                                   5.0x10
                                       -8.0x10-3            Vd=Vg=1.5V

                                                                                                                                                        0.0
                                                      0             2             4           6        8         10                                               0           2          4       6        8             10
                                                                               Frequency (GHz)                                                                                          Frequency (GHz)
•    Y. Cheng, C. H. Chen, C. Enz, M. Matloubian and M. J. Deen, ICCDCS 2000, pp. D23 1-8 (15-17 March 2000).

Sec. 11.1, IEEE CICC2002, Orlando, Florida                                                                                                                                                                              Page 11 of 40
                                     fT vs. Bias Currents
                                           30
                                                    +: Vd=0.5V
                                                    o: Vd=1V
                                           25                                                    10fx12umx0.36um
                                                    *: Vd=1.5V


                                           20       Solid lines: Model
                     fT (GHz)

                                                    Symbols: Measured data
                                fT (GHz)




                                           15
                                                         2fx12umx0.36um

                                           10



                                            5

                                                                                                 10fx12umx0.56um
                                            0
                                               -6              -5         -4          -3    -2             -1        0
                                            10            10         10          10        10         10        10
                                                                               IDS (A)


Sec. 11.1, IEEE CICC2002, Orlando, Florida                                                                               Page 12 of 40
                                                   NQS Effects
                               0.010
                                                                         Real(Y21)
  Re_Y21 and Imag_Y21 (A/V))




                               0.005


                               0.000

                                                                                        Vgs=1V
                               -0.005                                   IMAG(Y21)       Vds=1V

                                              W=10x15µ m
                               -0.010         L=1.35µ m

                                              Symbols: Measured data
                               -0.015         Solid lines: Model with NQS
                                              Dotted lines: Model without NQS

                               -0.020
                                        0.0      2.0x10 9     4.0x109      6.0x109   8.0x10 9    1.0x1010

                                                                  Frequency (Hz)
Sec. 11.1, IEEE CICC2002, Orlando, Florida                                                          Page 13 of 40
                 I am going to present...
• RF Modeling of MOSFETs
     - Parasitic resistances and capacitances
     - Non-Quasi-Static (NQS) effects
• Noise Modeling of MOSFETs
     - What does the device noise look like?
     - Equivalent noise circuit model
     - Channel noise, Induced gate noise and their correlations
     - Noise modeling for RF IC applications
• Design Strategy of low noise amplifiers (LNA)
  - Selection of the device size, geometry and bias condition
  - Impact of the Accuracy of Noise Sources
• Conclusions
Sec. 11.1, IEEE CICC2002, Orlando, Florida                        Page 14 of 40
    What does the Noise Look Like?
                                             Io                      IDS
          +                             Drain                              Io
                     Gate                         Substrate (Body)
        VD
         _          +
                 VG                     Source
                  _
                                                                                                  time
                                     VG
                                      L
                                                        VD
                                                                     channel
                                                                                        FT
                   W         Gate                                    noise
                        induced gate noise
        Source       e-                            Drain                        1/f noise
           n+                                 n+                                             white noise
                  gDS(x)∆v(x)                  E lateral field
 p-substrate      channel noise
                                                                                             frequency

Sec. 11.1, IEEE CICC2002, Orlando, Florida                                                      Page 15 of 40
    Why the Device Noise Matters?
   Pout
   (dB)                                                       Burn out
                            ideal amplifier
    10                                           saturation
     0
   -10                                                 Power
   -20
                 dynamic                                                 battery life time
                 range
   -30
   -40
                                noise floor
   -50                                                  Distance         distance
   -60
   -70

          -80     -60     -40                0    20
                Pin1 Pin2
                                  -20
                                                              Pin (dB)


• The battery life time and the distance between the wireless components
   will be limited by the noise floor of the front-end amplifier.

Sec. 11.1, IEEE CICC2002, Orlando, Florida                                           Page 16 of 40
         AC Noise Model of MOSFETs

       G          G                      3        C                      4               R         D

        1                                         +                                                2
                                          C       GS
                                                  -
                                                                                    DB    2
                 G                                                                       iD
                                    i2        i        m GS        RDS
                       C                                                     d



                                                              SB         R
                                         i2            S
                                                                    2
                                                                   iSB              DB        i2
                                                      RSB                     2
                                                                             iDSB
                                                                         y = gm (1- ωτ

Sec. 11.1, IEEE CICC2002, Orlando, Florida
                      Noise Source Extraction
                                            RF & Noise Parameter Measurements

                                                               De-embedding of Pads
                                                               and Interconnections
         Intrinsic S-Parameters                                                                       Intrinsic Noise Parameters

         Parameter Extraction                                   Y-Parameter Calculation
            & Verification                                       at two-port (33’-44’)
                                           Intrinsic Part
           G     RG              3           CGD                    4                 RD      D    Noise Parameter Deembedding
            1                               +                                                 2          to ports 33’ and 44’
                                  CGS       vGS
                                             -
                  2                                                             CDB    2
                 iG                                                                   iD

                                                                                                    Extracting ig2, id2 and igid*
                             2
                            ig        Ri          ym vGS      RDS i 2
                      CGB                                          d


                                 3’                                 4’
                                                        CSB         RDSB
                                  2
                                 iS              RS
                                                 RSB
                                                               2
                                                              iSB               RDB         2
                                                                                           iDB     Noise Parameter Verification
            1’                                                            2                   2’
                                                                         iDSB
                                                  S/B
                                                                    ym = gm×(1-jωτ)
• C. H. Chen, M. J. Deen, Y. Cheng and M. Matloubian, IEEE Trans. on Electron Devices, Vol. 48(12), pp. 2884-2892, Dec. 2001.

Sec. 11.1, IEEE CICC2002, Orlando, Florida                                                                                     Page 18 of 40
                      Noise Sources vs. Frequency
                          VDS = 1.0V VGS = 1.2V                                         -22
                                                                                     1x10     W = 10×6µm                  L=0.97µm
                                                                                                                          L=0.64µm
           1x10
                  -21
                                                      L=0.18µm                                     2
                                                                                                  ig ∝ f
                                                                                                           2
                                                                                                                          L=0.42µm
 id2 (Amp2/Hz)




                                                          L=0.27µm                                                        L=0.27µm




                                                                     ig2 (Amp2/Hz)
                                                                                        -23
                                                                                     1x10
                                                          L=0.42µm                                                        L=0.18µm

                                                      L=0.64µm                          -24
                                                                                     1x10
                                                      L=0.97µm                                                     VDS = 1.0V
                          W=10×6µm                                                                                 VGS = 1.2V
                  -22                                                                   -25
                 10                                                                  1x10
                      0     1    2   3    4       5   6     7                                 1                                 10
                                 Frequency (GHz)                                                       Frequency (GHz)

• The noise sources are directly extracted from intrinsic noise parameters.
• i d is frequency independent and i g is proportional to f 2.
    2                                2

Sec. 11.1, IEEE CICC2002, Orlando, Florida                                                                               Page 19 of 40
                        Noise Sources vs. Frequency
                                                                                                                                            W = 10×6µm
                     -23
                 8x10        VDS = 1.0V                    W = 10×6µm                                   0.6 VDS = 1.0V




                                                                        Cross-correlation Coefficient
                             VGS = 1.2V                                                                        VGS = 1.2V
                     -23                                    L=0.97µm                                                                            L=0.97µm
    igid (Amp /Hz)




                 6x10
                                                                                                        0.4
                                           *                L=0.64µm                                                                            L=0.64µm
                                        igid ∝ f
 2




                 4x10
                     -23
                                                                                                                                                L=0.42µm
 *




                                                            L=0.42µm                                    0.2
                     -23                                                                                                                        L=0.27µm
                 2x10
                                                             L=0.27µm
                                                                                                                                                L=0.18µm
                                                            L=0.18µm
                        0                                                                               0.0
                         0     1    2       3      4   5   6 7                                             0      1       2   3    4   5    6     7
                                    Frequency (GHz)                                                                       Frequency (GHz)

•              Cross-correlation C is defined as                c = igid∗ ⁄                                    ig i d .
                                                                                                                2 2

•               i g i d∗ is proportional to f, and C is frequency independent.

Sec. 11.1, IEEE CICC2002, Orlando, Florida                                                                                                  Page 20 of 40
       Noise Parameters vs. Frequency
                6 L=0.97µm                                                 2.3
                                       2      2                                              VDS = 1.0V, VGS = 1.2V
                        W=10x6µm      id and ig
                5                                                          2.2                           IDS = 4.4mA

                4 All noise sources                                                                  All noise sources




                                                           rn (Rn / 50Ω)
                                                                           2.1
   NFmin (dB)




                3                                                                                             2
                                                                                         2       2           id only
                                                                           2.0       id and ig
                2
                                                  2
                                             id only                       1.9
                1

                0                                                          1.8
                    0     1   2    3     4    5        6                         0   1       2    3     4    5          6
                              Frequency (GHz)                                                Frequency (GHz)

• The extracted noise sources are fed into the a.c. noise model for noise source
  verification.
• The induced gate noise has a great influence on the NFmin of long channel
  devices but does not affect the equivalent noise resistance.

Sec. 11.1, IEEE CICC2002, Orlando, Florida                                                                        Page 21 of 40
                          Channel Noise vs. VDS Bias
                      -22
                 3.0x10
                                L = 0.97µm                                                 -21    L = 0.18µm
                                                                                      1.5x10
                                W = 10x6µm                                                        W = 10x6µm




                                                                      id2 (Amp2/Hz)
 id2 (Amp2/Hz)




                      -22                                                                  -21
                 2.0x10                                                               1.0x10
                                                       : VDS = 1.0V                                                   : VDS = 1.0V
                                                       : VDS = 1.2V                                                   : VDS = 1.2V
                                                       : VDS = 1.5V
                                                                                           -22
                                                                                      5.0x10                          : VDS = 1.5V
                      -22
                 1.0x10                                : VDS = 1.8V                                                   : VDS = 1.8V
                                                       : VDS = 2.0V                                                   : VDS = 2.0V
                                                                                          0.0
                          0.5       1.0       1.5        2.0                                     0.5   1.0     1.5       2.0
                                          VGS (Volt)                                                     VGS (Volt)

• Channel-length modulation (CLM) effect => higher local output conductance
  gDS(xo) => i d increased at higher VDS for L = 0.18 µm devices.
               2

Sec. 11.1, IEEE CICC2002, Orlando, Florida                                                                             Page 22 of 40
                   Noise Parameters vs. Models
              6                                                                2.5
                                    2
                                id = 8kTgdo/3                                                              VDS=1.0V L=0.97µm
                                                                                      Measured Data
                                2
                                                                                                           VGS=1.2V W=10x6µm
                   Extracted id
              4                                                                2.0




                                                               rn (Rn / 50Ω)
                                                                                                   2
                                                                                      Extracted id
 NFmin (dB)




                                            Measured Data
                                             2                                         2
              2                             id = 8kTgm/3                       1.5    id = 8kTgdo/3
                            L=0.97µm            VDS=1.0V                               2
                                                                                      id = 8kTgm/3
                            W=10x6µm VGS=1.2V
              0                                                                1.0
               0      1     2           3   4      5       6                      0        1   2       3      4    5     6
                            Frequency (GHz)                                                    Frequency (GHz)

• The channel noise equations i d = 8kTgm/3 and i d = 8kTgdo/3 suggested for the
                                2                 2

  long channel devices predict lower equivalent noise resistance Rn.

Sec. 11.1, IEEE CICC2002, Orlando, Florida                                                                          Page 23 of 40
     Coefficients vs. Channel Lengths
       1.5                                                                                 8
                                                                                                     δ




                                                                         δ and ε at 2GHz
                                                                                           6                           W=10x6µm
       1.0
                                                                                                                       VDS=1.0V
                                                              0.67                         4
                                                                                                                       VGS=1.2V
γ




                   W=10x6µm
       0.5
                   VDS=1.0V                                                                2     ε
                   VGS=1.2V
                                                                                                                           0.12
                                                                                                                                   0.11
       0.0                                                                                 0
                                 0.5                         1.0                           0.0                   0.5              1.0
                           Channel Length (µm)                                                       Channel Length (µm)


                                                                                          i g i d∗
                                2                      2
                              id                     i g ⋅ g do
•   γ, δ and ε are γ = ----------------- , δ = -------------------------- and ε = -------------------------- .
                                       -
                                                             2 2
                                                                        -
                       4kTg do                 4kTω C GS                          j4kTωC GS

Sec. 11.1, IEEE CICC2002, Orlando, Florida                                                                                 Page 24 of 40
 Cross Section of MOSFET Channel
                                              VDS
                                    VDSsat


                                       I                     II
      S                                                           D
                                      Lelec                  ∆L
                                                     Ecrit
                                              Leff   vsat
                                              x

Sec. 11.1, IEEE CICC2002, Orlando, Florida                        Page 25 of 40
        Channel Noise in Linear Region
• Noise current from the gradual channel region:
     4kT o                                   4kT o I ds
 d = ----------- µ eff ( – Q inv ) + δ hot --------------------- DS
i2
          2
               -
                                               2          2
                                                               -V
      L eff                                L eff E crit

                                                                                                         
                                       A b VDS                               2 2
                                                                          A b VDS                         
Q inv    = –W eff L eff C ox ⋅  V GT – --------------- + ----------------------------------------------- 
                                                      -                                                 -
                                              2                      V – A b VDS 
                                                         12 ⋅ GT ---------------                   -
                                                                                             2 

-> δhot is used to model the hot electron effect.
-> VDS becomes VDSsat in the saturation mode.
-> Using Lelec instead of Leff in the saturation mode.
Sec. 11.1, IEEE CICC2002, Orlando, Florida                                                                    Page 26 of 40
Channel Noise in Saturation Region
• Noise current from velocity saturation is zero [1]:

-> Thermal noise theory (4kTR) cannot be applied in the veloc-
   ity saturation region.

-> Physical noise mechanism in the velocity saturation region is
   unknown - though a drifting dipole layer model [2] and a dif-
   fusion noise model [3] were proposed for the thermal noise
   modeling of FETs.

-> For a given voltage fluctuation, it generates zero noise fluc-
   tuation because of the local gDS(xo) = 0.
1.   C. H. Chen and M. J. Deen, IEEE Trans. on Electron Devices, In Press.
2.   E. Statz, H. A. Haus and R. A. Pucel, IEEE Trans. on Electron Devices, vol. ED-21, pp. 549 - 562, Sep. 1974.
3.   Jean-Pierre Nougier, IEEE Trans. on Electron Devices, vol. 41, no. 11, pp. 2034 - 2049, November 1994.


Sec. 11.1, IEEE CICC2002, Orlando, Florida                                                             Page 27 of 40
                               Channel Noise vs. VGS and VDS
                                    -21                                                                                   -21
                               1.6x10                                                                                1.0x10                                      L = 0.18 µm
  Channel Noise id (Amp /Hz)



                                                                        L = 0.18 µm




                                                                                       Channel Noise id2 (Amp2/Hz)
                                    -21    W = 10x6 µm
                               1.4x10
 2




                                                                                                                          -22                              Lelec
                                    -21    VDS = 1.5V                 Lelec                                          8.0x10
                               1.2x10
                                    -21                                       Leff
                               1.0x10                                                                                           VGS = 1.0V                Leff
 2




                                                                                                                          -22
                                                                                                                     6.0x10
                                    -22
                               8.0x10
                                                                                                                                W = 10x6 µm
                                    -22                                L = 0.42 µm                                        -22
                                                                                                                     4.0x10                                      L = 0.42 µm
                               6.0x10
                                    -22
                               4.0x10
                                                                       L = 0.97 µm                                        -22
                                                                                                                     2.0x10
                                    -22
                               2.0x10
                                                                                                                                                                 L = 0.97 µm
                                   0.0                                                                                   0.0
                                     0.5           1.0          1.5              2.0                                            1.0   1.2     1.4    1.6           1.8
                                                    VGS Bias (Volt)                                                                     VDS Bias (Volt)


• Hot electron is not important (δhot = 0) in the channel noise modeling.
• No noise current from velocity saturation (region II) is found.
• Using Lelec to catch the increasing trend in the channel noise vs. VDS charac-
  teristics.
Sec. 11.1, IEEE CICC2002, Orlando, Florida                                                                                                                   Page 28 of 40
                                   γ vs. VGS Bias
    2.0                   2                                   2.0
                         id = γ 4kTgdso
                                                                                                      2
                                                                                 L = 0.18µm        id = γ 4kTgdso
                         W = 10x6µm                                              W = 10x6µm          VDS = 1.5V
    1.5                  VDS = 1.5V                           1.5
                                                                                  Lelec + measured gdo

                                             L = 0.18µm                                                      measured γ
γ




                                                          γ
    1.0                                                       1.0
                                             L = 0.42µm               Leff + simulated gdo

                                             L = 10.0µm
    0.5                                                       0.5
      0.5          1.0           1.5           2.0              0.5             1.0            1.5            2.0
                   VGS Bias (Volt)                                               VGS Bias (Volt)


•    Simulated γ for long channel devices L = 10 µm is 0.68 at VGS = 1.8 V which is
     close to the theoretical value 2/3.
•    The γ value increases from 0.68 to 1.2 or 1.8 (depending on the VGS bias) when
     the channel length is decreased because of CLM effect.

Sec. 11.1, IEEE CICC2002, Orlando, Florida                                                                  Page 29 of 40
    Gate Noise and Correlation Noise
• Induced gate noise from position xo in region I:
                                 CGS                     ∆id(xo)
               jωWL elec C ox g ( V o )∆v ( x o )
∆i g ( x o ) = ------------------------------- ⋅ ------------------------------- [ V as – V ( x o ) ]
                                             -
                            I ds                           L elec

                             1                                                 1 2
                             -- ( V GS – V TH )VDS – -- V DS
                              -                                                 -
                             2                                                 6
where V as                                                                                -
                    = V DS – --------------------------------------------------------------
                                         VGS – V TH – 1 V DS         -
                                                                    --
                                                                    2
-> Induced gate noise ∆ig(xo) is fully correlated with the
   channel thermal noise ∆id(xo).
-> VDS becomes VDSsat in the saturation mode.
Sec. 11.1, IEEE CICC2002, Orlando, Florida                                                              Page 30 of 40
                        Gate and Correlation Noise vs. f
                                     -21                                                                                           -23
                                  1x10     VDS = 1.5 V W = 6x10 µm                                                            5.0x10
 Induced Gate Noise ig2 (A2/Hz)




                                                                                            Correlation Noise igid* (A2/Hz)
                                                                                                                                             VDS = 1.5 V W = 6x10 µm
                                     -22
                                   10      VGS = 1.2 V calculated data       L = 0.97 µm                                           -23
                                                                                                                              4.0x10         VGS = 1.2 V calculated data
                                                                                                                                                                               L = 0.97 µm
                                     -23                                      L = 0.64 µm
                                  1x10                                        L = 0.42 µm                                          -23
                                                                                                                                             extracted data
                                                                                                                              3.0x10
                                     -24                                                                                                                                       L = 0.64 µm
                                  1x10                                        L = 0.18 µm                                          -23
                                                                                                                              2.0x10
                                     -25                                                                                                                                       L = 0.42 µm
                                   10
                                                                                                                                   -23
                                                                                                                              1.0x10
                                   10
                                     -26                            extracted data                                                                                             L = 0.18 µm

                                                     9                                                                                                   9         9            9
                                                   10                                                                                  0.0        2.0x10      4.0x10       6.0x10
                                                    Frequency (Hz)                                                                                     Frequency (Hz)

• Induced gate noise ig and its correlation with the channel noise ig id∗ are
                      2

  obtained by integrating ∆i g ( x )∆i g ( x )∗ and ∆i g ( x )∆i d ( x )∗ over region I only.

• No induced gate noise generated from the velocity saturation region because
  ∆id(xo) = 0 in region II.
Sec. 11.1, IEEE CICC2002, Orlando, Florida                                                                                                                                    Page 31 of 40
                 I am going to present...
• RF Modeling of MOSFETs
     - Parasitic resistances and capacitances
     - Non-Quasi-Static (NQS) effects
• Noise Modeling of MOSFETs
     - What does the device noise look like?
     - Equivalent noise circuit model
     - Channel noise, Induced gate noise and their correlations
     - Noise modeling for RF IC applications
• Design Strategy of low noise amplifiers (LNA)
  - Selection of the device size, geometry and bias condition
  - Impact of the Accuracy of Noise Sources
• Conclusions
Sec. 11.1, IEEE CICC2002, Orlando, Florida                        Page 32 of 40
 Choosing Device Sizes - Channel L
                                                                     6
                                             L=0.27µm
          0.02                                                       5         L=0.97µm
                                             L=0.42µm

                                             L=0.64µm
                                                                     4              L     NFmin




                                                        NFmin (dB)
 gm (S)




                                                                     3
          0.01
                                             L=0.97µm
                                                                     2                           L=0.64µm
                              L       gm_max
                                                                                                     L=0.42µm
                                                                     1
                                                                                                      L=0.27µm
          0.00                                                       0
                 0.5    1.0        1.5       2.0                         0.5        1.0     1.5        2.0
                         VGS (Volt)                                                 VGS (Volt)

• Channel length of devices reduced => (1) gm increased (2) the peak value of gm
  happens at lower VGS value.
• The faster increase in gm makes (1) the NFmin reduced and (2) the lowest NFmin
  shifted to the lower VGS region.

Sec. 11.1, IEEE CICC2002, Orlando, Florida                                                           Page 33 of 40
                  Choosing DC Bias Conditions
          0.012                                VDS=2.0V
                                                                               NMOSFETs
                  NMOSFETs                         VDS=1.5V                4
                                                                               L=0.97µm
                  L=0.97µm
                                    gm                                         W=10x6µm
          0.009   W=10x6µm                     VDS=1.0V                                          VDS




                                                              NFmin (dB)
 gm (S)




                                                                           3                               VDS=1.0V
                                   VDS                                                          NFmin
                                                                                                           VDS=1.5V
          0.006
                                                                           2                               VDS=2.0V


                   0.5       1.0     1.5     2.0                                0.5       1.0      1.5   2.0
                             VGS (Volt)                                                   VGS (Volt)

• Higher VDS bias will increase gm at the higher VGS region.
• Higher gm will decrease NFmin at higher VGS region.
• Decreased NFmin at higher VGS region makes the lowest NFmin less sensitive to
  VGS bias.

Sec. 11.1, IEEE CICC2002, Orlando, Florida                                                               Page 34 of 40
           Device Geometry and Layout
                                                                                  6
                      W                                                                     NMOSFETs     L = 0.8µm
         Gate
                                         L                                        5         f = 4GHz     VDS = 3.0V
         Signal traveling direction




                                                                     NFmin (dB)
                                 Distributed effects                              4
                                                                                          W = 1x60µm
           1            W                                                                                      1.5 dB
   RG    = -- × R gsh × ----
            -              -
           3             L                                                        3
                                                                                          W=6x10µm
                                                                                  2
                                                                                      0     2      4     6      8       10
         1            W⁄2 1                 1               W
   R G = -- × R gsh × ----------- × -- = -------- × R gsh × ----
          -                     - -             -              -                          Drain Current IDS (mA)
         3                L         2    3⋅4                 L
                                                 two resistors connected in parallel
                                             each signal travels half of the distance W

                            n transistors         1          W⁄n 1              R gsh ⋅ W
                            (width = W/n) R G = -- × R gsh × ----------- × -- =
             W                                    -                    - -      ----------------------------
                -
             ----
  ....




                                                  3              L         n                   2
             n              connected in parallel                                     3n L


Sec. 11.1, IEEE CICC2002, Orlando, Florida                                                                     Page 35 of 40
            Two-Port Network of LNAs
                                                          GT
                                                                 GP
                                         GA
                     Source Impedance                                 Load Impedance
                 PAVS                         PIN                     PAVN             PL

           Zo
                         Input                                           Output
                        Matching                    Transistor           Matching           Zo
       VS∠0°
                        Network                                          Network
                         (GS)                         (GO)                (GL)

                               ZS (or ΓS)                         ZL (or ΓL)
     ZNIN (or ΓNIN)                ZIN (or ΓIN)         ZOUT (or ΓOUT)       ZNOUT (or ΓNOUT)

• Design considerations: Stability, Power Gain, Noise Figure (NF) and Linearity
  (IP3)
Sec. 11.1, IEEE CICC2002, Orlando, Florida                                                  Page 36 of 40
       Schematic Diagram of an LNA
                               0.7 V             1.5 V         0.7 V    1.5 V
                                                                                     AC Load
            DC Bias &                Rb              Ld            Rb           Ld
            AC Open
                                                                                      Vout

                            Vin
                                                   M1                     M2 Cout
                                g            L
    Ld=7 nH
                                                             Cc
    Lg=8.3 nH
                 Noise Matching
    Ls=2 nH                                          Ls
    Rb=10 KΩ                                             DC Blockage &
    Cc=40 pF                                             Power Matching
    L=0.3 µm, W=120 µm, Ids = 3mA

• M1: minimize noise; M2: maximize gain.

Sec. 11.1, IEEE CICC2002, Orlando, Florida                                                   Page 37 of 40
         Impact of the Noise Sources

                                         7
                  Noise Figure NF (dB)

                                                                                    using Lelec
                                         6                                                  2
                                                                                    with id only
                                                                using Lelec
                                                                              using Leff
                                         5             ∆NF = 0.3 dB



                                                   1.62 GHz   1.72 GHz
                                         4
                                             1.0       1.5      2.0       2.5         3.0
                                                         Frequency (GHz)
• Impact of the noise sources: (1) optimal frequency (2) NF predicted

Sec. 11.1, IEEE CICC2002, Orlando, Florida                                                         Page 38 of 40
                                   Gain of the LNA

                  11.1 dB                                          100

             10                                                     50

                                                                     0




                                                         S21 ( )
|S21| (dB)




                                                         o
                                                                                o
                                                                    -50 -55.8
              5
                                                                   -100

                                                                   -150
                                        2.12 GHz                                                2.12 GHz
              0
                  1.0       1.5   2.0      2.5     3.0                    1.0       1.5   2.0      2.5        3.0
                            Frequency (GHz)                                         Frequency (GHz)



• The peak |S21| and the lowest NF don’t happen at the same frequency.


Sec. 11.1, IEEE CICC2002, Orlando, Florida                                                               Page 39 of 40
                                       Conclusions
• Substrate network => output matching network
• Parasitic capacitances => power & noise matching
• NQS effects => longer channel devices
• Channel noise modeling: CLM effect
• Induced gate noise modeling: CGS modeling
• LNA Design:
- Channel length selection => noise budget
- VGS bias => before peak gm
- VDS bias => sensitivity of VGS bias
- Geometry => multi-finger with dual inputs

Sec. 11.1, IEEE CICC2002, Orlando, Florida           Page 40 of 40

								
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