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CMOS BIAS GENERATORS

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					                                                    CMOS BIAS GENERATORS

Master – Constant gm with Temp – The early generation
                                             R = [1-2/3]{2/gm}
                                                                                                                VB1'
                                         = [2/3]{1/gm} =185 ohmsw
              gm = 8xWs/Ls kp Veff
                 = 8x6/0.4x 2.5x60uA/V^2 x1/5
                    =3.6mS
                                                                                                                                   1/8 Ws/Ls Veff
                                 Inter digitate 2

                 {8xWs}/Ls                              {(9/4)8xWs}/Ls


                     VB1                                                                                               kRxWL/LL




                  8xWL/LL                            8xWL/LL                                 144 uA/leg                                  Veff = 200mV
                                                                                                      8xWL/LL
                                144 uA/leg
                     VB3                                                                 8xWL/LL                                    LL = 1 um, LLP = 1 um,
                                                                                                                                   LS = 0.4 um, WS = 6 um,
                                                                                                                                   WLP = 15 um, WL = 6 um,
                                                                         VB4                                              200 fF
                  8xWL/LL                            8xWL/LL                                  VB4
                                                                               8xWL/LL
                                                                                                    8xWL/LL
                                 Inter digitate 4         Lerr < 5.5%
                                                          Werr < 0.24%



                             gm = 10ms, kpn = 150uA/V^2
                                    Ws/Ls >????

 1. Determine the value of ID for all legs of current in the bias generator.
 2. Determine the value of VB1, VB3, and VB4.
 3. Find a general equation describing the minimum supply voltage for the bipolar bias generator.
4. Show gm is independent of temperature if R can be composed of a temperature independent
   resistor.
5. R is composed of two poly resistors; Rpn(1 + kn T) and Rpp(1 - kp T) where kp = -1.94x10-4/C,
   kn -1.79 x10-4/C, Rshn =89.6 ohms/sq, and Rshn =402 ohms/sq. Determine the ratio of lengths
   Rn to Rp required to develop a temperature independent resistor. Assume both resistors are 20 w
   minimum.
SLAVE – The early generation
                                VDD
                                                                                                   8xWLp/LLp
                                                                                                                                     Veff = 200mV
                                Inter digitate 3                                           VB1 = VDD – VT – V


                  8xkRxWL/LL                            8xkRxWL/LL                16xkRxWL/LL                                    LL = 1 um, LLP = 1 um,
                                                                                                                                LS = 0.4 um, WS = 6 um,
                      VB1                                                              VB2 = VDD – VT – 3V+.58V               WLP = 15 um, WL = 6 um,
                                                        VB2                     VB2


                 2xkRxWS/LS                                                          48xkRxWS/LS

                                      24xkRxWS/LS

                                                                                       288 uA/leg
                                                             Inter digitate 3
                                                   144 uA/leg
                                                                                                VB4 = VSS + VT + V
                  144 uA/leg
                                                       VB4
                                                                                                      VB3 = VSS + VT + 2.83V

                                           8xWL/LL                                         2xWL/LL


                                                                                                               VB3
                                                                  Inter digitate 2
                      gm = 10ms, kpn = 160uA/V^2
                             Ws/Ls > ???
                                                                            VSS                 Lerr < 5.5%
                                                                                                Werr < 0.24%



 1. Determine the value of ID for all legs of current in the bias generator where the input current is
    from the master bias generator.
 2. Determine the value of VB1, VB3, and VB4.
Master ALL in one – Constant gm with Temp - wide swing generation
                                             R = [1-2/3]{2/gm}
                                         = [2/3]{1/gm} =185 ohms                                                                   VB1'
                                                                         w
            gm = 8xWs/Ls kp Veff
               = 8x6/0.4x 2.5x60uA/V^2 x1/5                                              {2xWL}/LL
                  =3.6mS
                                                                                                                                                         1/8 Ws/Ls Veff
                                Inter digitate 2                                                                              VB2

                                                               VB1     8xWL/LL
                8xWL/LL              VB1                                           VB2


                                                                                                                                            kRxWL/LL
                                                                 VB2   {8xWs}/Ls
                                     VB2           {8xWs}/Ls
                {8xWs}/Ls

                                                           VB4                                                      Veff = 200mV
                                                                             VB3


               {8xWs}/Ls           VB3                                              {8xWs}/Ls
                                                                                                                      144 uA/leg
                                             {8xWs}/Ls                        VB3
                               144 uA/leg                              2xWL/LL
                                                                                                                 {8xWs}/Ls
                                                                                                                                          {8xWs}/Ls


                                                                                                     VB4                                        200 fF
                8xWL/LL                              8xWL/LL                                                           VB4
                                                                                   VB4      8xWL/LL    8xWL/LL
                                                                                                                             8xWL/LL
                                Inter digitate 4          Lerr < 5.5%
                                                          Werr < 0.24%

                                                                                                                                      LL = 1 um, LLP = 1 um,
                            gm = 10ms, kpn = 150uA/V^2                                                                               LS = 0.4 um, WS = 6 um,
                                   Ws/Ls >????                                                                                       WLP = 15 um, WL = 6 um,




 1. Determine the value of ID for all legs of current in the bias generator.
 2. Determine the value of VB1, VB2, VB3, and VB4.
 3. Find a general equation describing the minimum supply voltage for the bipolar bias generator.
Master – Constant gm with Temp - wide swing generation
                                           R = [1-2/3]{2/gm}
                                       = [2/3]{1/gm} =185 ohms                                                                        VB1'
                                                                           w
            gm = 8xWs/Ls kp Veff
               = 8x6/0.4x 2.5x60uA/V^2 x1/5                                                {2xWL}/LL
                  =3.6mS
                                                                                                                                                           1/8 Ws/Ls Veff
                              Inter digitate 2                                                                                      VB2

                                                              VB1      8xWL/LL
                8xWL/LL            VB1           {(9/4)8xWL}/LL                      VB2


                                                                                                                                              kRxWL/LL

                8xWL/LL                                          VB2      8xWL/LL
                                   VB2           8xWL/LL

                                                           VB4                                                         Veff = 200mV
                                                                               VB3


                                 VB3                                                 {8xWs}/Ls
                8xWL/LL                            8xWL/LL                                                               144 uA/leg
                                                                                 VB3
                             144 uA/leg                                2xWL/LL
                                                                                                                   8xWL/LL


                                                                                                       VB4                                        200 fF
                8xWL/LL                             8xWL/LL                                                                  VB4
                                                                                    VB4       8xWL/LL    8xWL/LL
                                                                                                                                   8xWL/LL
                              Inter digitate 4             Lerr < 5.5%
                                                           Werr < 0.24%

                                                                                                                                           LL = 1 um, LLP = 1 um,
                          gm = 10ms, kpn = 150uA/V^2                                                                                      LS = 0.4 um, WS = 6 um,
                                 Ws/Ls >????                                                                                              WLP = 15 um, WL = 6 um,

 1. Comment on the difference between the two wide swing master bias generators above. Be specific
    on the advantages of each. Use the geometries to guide your discussion.
SLAVE - wide swing generation

 2. Using the ideas presented above with wide swing mirrors develop a slave bias generator to
    develop VB1, VB2, VB3, and VB4. Assume the slave generator current per leg is ½ that of the
    master.



                               Insert Visio drawing here.
ALL in ONE

                                                                                                      VB1
                                                            w

                                        R = [4/3]{1/gm}          WLp/LLp
         gm =8xWs/Ls kp Veff                                                         8xWLp/LLp
                                                                                                                        1/8 Ws/Ls Veff
                            Inter digitate 2

                                                {(9/4)8xWs}/Ls
                                                                     VB2
                                                                                       VB1'
                VB1                                                                                         kRxWL/LL




             16xWL/LL                           2xWL/LL
                                                                                                                              Veff = 200mV



                VB3                                                                                                      L = 2um, LLP = 1um,
                                                                                                                        LS = 0.4um, WS = 6um,
                                                                                                                        WLP = 18um, WL = 6um,
                                                                     VB4                                       200 fF
             8xWL/LL                            8xWL/LL                               VB4
                                                                           8xWL/LL
                                                                                            8xWL/LL                             75 uA/leg
                            Inter digitate 4          Lerr < 5.5%
                                                      Werr < 0.24%


                        gm = 10ms, kpn = 170uA/V^2
                           Ws/Ls > 16fx4.25/0.4
BIPOLAR bias generator
                25 uA/leg
                                                                                                               kRxWL/LL



                                                                         kRxWL/LL
 kRxWL/LL                         kRxWL/LL
                                                                                                  VB1

                                             10 pf
 M1                                M2


      VB1                                            VB1                               VB2 =VCM         kRxWL/LL




                                                                          0.5Ws/Ls
 Q3                                 Q4




 Q1                                 Q2

              A:1 where A = 8
                                                           VB4                                          1 pF
            I =UT/RBLn(A ratio)
                                                                               10 pf
            gm =1/RBLn(A ratio)                                          VB4
                                                                 WL/LL                        WL/LL


                                                     WL/LL = 2WS/2LS

  1. Show by derivation that the bias current generated by the bipolar bias generator above is
     proportional to temperature.
  2. Find a general equation describing the minimum supply voltage for the bipolar bias generator.
  3. Find the geometry of M1 and M2 in terms of the bias resistor and bipolar ratio, veff and KPp.
BIPOLAR (Con’t)
                            25 uA/leg




                                                               Ic = Is e^(VBE/nUt)
      kRxWL/LL                                kRxWL/LL
                                                         VBE3 + VBE2 = IRB + VBE4 + VBE3

             VB1                                              Assuming IB << IC

                                                         RB = Ut/I LN[(A1 A4)/(A2 A3)]

                                                         I = Ut/R LN[(A1 A4)/(A2 A3)]
        Q3                                        Q1
                                                                    I PTAT
                   A3                             A1
                                                                   gm = I/ Ut

        Q4                                        Q2     gm = k/RB LN[(A1 A4)/(A2 A3)]
                   A4
                                                 A2
                        I =UT/RBLn(A ratio)                 Constant for All Temp
      RB
                        gm =1/RBLn(A ratio)
                                                                   gm = K/R
 1. Using the above ideas from bipolar generators develop an equivalent MOS subthreshold
   generator. Assume each leg is to have an ID of 100nA.

BIPOLAR (Con’t)
                                      kR WL/LL



                 VB1




                                       Rc
                       Vin-                            Vin+
                                        Re                                                     Vo-
                                                                              Vo+                    Vcm = VB2


                                    Rs = 500 ohm
                                    8.64 mA/leg



                                                                              1.08 mA/leg
                          4 WL/LL            4 WL/LL                ½ WL/LL         ½ WL/LL

                   VB4
                                                                                         VB4

                                                          w



                                                                     Vcmfb
             gm = k/R LN[(A1 A4)/(A2 A3)]
                                                               ADiff = RC/(1 + gmRS)
                Constant for All Temp
                                                              ADiff = RC/(1 + K RS/RB)
                         gm = K/R
1. Derive the transconductance for the amplifier above showing all work.
2. Derive the differential gain in terms of the bias resistor, RB above showing all your work.

				
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