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Two-Port Networks

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					Two-Port Networks

     Lecture 12
                        Introduction
                  I1              I2

             V1                        V2

              Port 1              Port 2
              (Input)             (Output)

• An access point is named as a port
• Regardless of what is inside the circuit if you know the
  relationship between V1, I1, I2 and V2 you can find out
  what happens to a parameter when one or more other
  parameters are changed
• Two-Port parameters
   –   Impedance
   –   Admittance
   –   Hybrid
   –   Transmission                                          2
   Admittance (y) Parameters
                          I1          I2
I1 = y11V1 + y12V2   V1                    V2
I2 = y21V1 + y22V2
                      Port 1          Port 2
                      (Input)         (Output)

When V2 = 0          When V1 = 0
         I1                 I1
  y 11              y 12 
         V1                 V2
          I2                     I2
 y 21               y 22      
          V1                     V2
                                                 3
       Admittance Parameters
•   y11 -   short-circuit input admittance
•   y12 -   short-circuit transfer admittance
•   y21 -   short-circuit transfer admittance
•   y22 -   short-circuit output admittance




                                                4
                 Example 01
      I1         2Ω          I2
                                       Find y parameters
 V1                               V2
            1Ω        3Ω                I1 = y11V1 + y12V2
                                        I2 = y21V1 + y22V2

     3                        1
y11  S                y21   S
     2                        2
                                5
       1
y12   S                  y22  S
       2                        6

                                                             5
                 Example 02
• Substitute port 1 with a 2A current source
  and port 2 with a 4Ω resistor. Find I2.
 I1 = y11V1 + y12V2
 I2 = y21V1 + y22V2
                      I1  2A   V2  I 2  4
      3    1                      2
 2  V1  V2               I2   A
      2    2                     11
        1    5
 I 2   V1  V2
        2    6
                                                6
    Impedance (z) Parameters
V1 = z11I1 + z12I2
V2 = z21I1 + z22I2

When I2 = 0          When I1 = 0
          V1                V1
   z 11             z 12 
          I1                I2
          V2                  V2
   z 21             z 22   
          I1                  I2
                                   7
     Impedance (z) Parameters
•   z11 - open-circuit input impedance
•   z12 - open-circuit transfer impedance
•   z21 - open-circuit transfer impedance
•   z22 - open-circuit output impedance




                                            8
                 Example 03
     I1   2Ω            j2Ω    I2

                                           Find z parameters
V1                                    V2
                 -j4Ω




        V1                           V1
 z 11      2  j4           z 12       j4
        I1                           I2

        V2                              V2
 z 21       j4              z 22         j2
        I1                              I2
                                                               9
                  Example 04
• Substitute Port 1 with a 120V voltage
  source with an internal resistance of 1Ω
  and port 2 with a 4Ω resistor. Find V2.
  V1 = z11I1 + z12I2   120  I1  ( 2  j4)I1  j4I 2
  V2 = z21I1 + z22I2   V2   j4I1  j2I 2
                       I 2  1.61137A
 V2 = -I2*4

                                                          10
      Hybrid (h) Parameters
V1 = h11I1 + h12V2
I2 = h21I1 + h22V2

When V2 = 0            When I1 = 0
        V1                  V1
 h 11               h 12 
        I1                  V2
        I2                  I2
 h 21               h 22 
        I1                  V2
                                     11
        Hybrid (h) Parameters
•   h11 - short-circuit input impedance
•   h12 - open-circuit reverse voltage gain
•   h21 - short-circuit forward current gain
•   h22 - open-circuit output admittance




                                               12
                        Example
             I1                    I2

                  12Ω        3Ω
       V1                               V2
                        6Ω

                                         V1 = h11I1 + h12V2
                                         I2 = h21I1 + h22V2
h11  14 Ω                        2
                         h 21  
                                  3
      2                        1
h12 
      3
                        h 22      S
                               9
                                                              13
    Transmission Parameters
V1 = AV2 - BI2
I1 = CV2 - DI2

When I2 = 0      When V2 = 0
     V1
  A              B
                      V1
     V2
                      I2
    I1
 C                   I1
    V2            D
                      I2       14
      Transmission Parameters
•   A - open-circuit voltage ratio
•   B - negative short- circuit transfer impedance
•   C - open-circuit transfer admittance
•   D - negative short-circuit current ratio




                                                15
        I1
                  Example
                                  I2

             1Ω            1Ω
   V1             1F                      V2




                                       V1 = AV2 - BI2
A = 1+jω               C = jω          I1 = CV2 - DI2



B = 2+jω               D = 1+jω
                                                        16
     Series Connection
                    V1
          I1
                    z1

          I2
                    z2
                    V2
     V1                  V2
I1             I2
     z1                  z2
               V              I1 = I 2
                              V = V1 + V2   17
          Series Connection

     I1         IA1               IA2         I2
                       Linear,
          VA1          Passive          VA2
                      Network A

V1                                             V2

                IB1               IB2
                       Linear,
          VB1          Passive          VB2
                      Network B




                                                    18
         I1         IA1                  IA2          I2
                           Linear,
              VA1          Passive             VA2
                          Network A

    V1                                                 V2

                    IB1                  IB2
                           Linear,
              VB1          Passive             VB2
                          Network B




Network A
                    [ ] [
                    VA1
                    VA2
                            =
                                      ZA11
                                      ZA21
                                               ZA12
                                               ZA22   ][ ]  IA1
                                                            IA2



Network B           [ ] [
                    VB1
                    VB2
                            =
                                      ZB11
                                      ZB21
                                               ZB12
                                               ZB22   ][ ]  IB1
                                                            IB2
                                                                  19
 Network A + Network B


[ ] [
VA1+VB1
VA2+VB2
          =
               ZA11+ZB11
               ZA21+ZB21           ][ ]
                           ZA12+ZB12
                           ZA22+ZB22
                                       I1
                                       I2



I1= IA1= IB1
I2= IA2= IB2



                                            20
     Parallel Connection

       V1                          V1
I1                            I1
       z1                          z1
                          I        V2
I2
       z2
                              I2   z2
       V2                          V
            I = I1+ I2
            V = V1 = V2
                                        21
          Parallel Connection

              IA1                     IA2
                        Linear,
                    Passive Network
             VA1                      VA2
                           A

     I1                                     I2


V1                                          V2

              IB1                     IB2
                        Linear,
                    Passive Network
             VB1                      VB2
                           B




                                                 22
             IA1                              IA2
                             Linear,
                         Passive Network
            VA1                               VA2
                                A

     I1                                                     I2


V1                                                          V2

             IB1                              IB2
                             Linear,
                         Passive Network
            VB1                               VB2
                                B




Network A
            [ ] [  IA1
                   IA2
                              =
                                           YA11
                                           YA21
                                                    YA12
                                                    YA22   ][ ]  VA1
                                                                 VA2



Network B   [ ] [  IB1
                   IB2
                              =
                                           YB11
                                           YB21
                                                    YB12
                                                    YB22   ][ ]  VB1
                                                                 VB2

                                                                       23
 Network A + Network B


[ ] [
 IA1+IB1
 IA2+IB2
           =
               YA11+YB11
               YA21+YB21
                           YA12+YB12
                           YA22+YB22   ][ ]
                                        V1
                                        V2



V1= VA1= VB1
V2= VA2= VB2



                                              24
             Cascade Connection
  IP1                   IP2                   IQ1                 IQ2

             Linear,                                  Linear,
             Passive                                  Passive
 VP1        Network P           VP2   VQ1            Network Q          VQ2




 NETWORK P                                      NETWORK Q



[ ] [ ][ ] [ ] [ ][ ]
VP1
IP1
        =
              AP BP
              CP DP
                              VP2
                              -IP2
                                               VQ1
                                               IQ1
                                                     =
                                                          AQ
                                                          CQ
                                                                 BQ
                                                                 DQ
                                                                          VQ2
                                                                          -IQ2

                                 VP2 = VQ1
                                 -IP2 = IQ1
                                                                                 25
     Substituting Network Q

     [ ] [ ] [ ][ ]
     V1
     I1
          =
              AP BP
              CP DP
                        AQ
                        CQ
                             BQ
                             DQ
                                   V2
                                   -I2




[ ][
V1
I1
      =
          APAQ+BPCQ
          CPAQ+DPCQ
                      APBQ+BPDQ
                      CPBQ+DPDQ   ][ ]
                                     V2
                                         -I2




                                               26

				
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