Interconnection of Networks:

With the concept that impedance in series are additive and admittance in parallel are additive, we can easily solve the series and parallel combination of networks in terms of Z and Y parameters respectively. Networks can be connected in:

1. Parallel connection
2. Series Connection

1. Parallel Connection of two-port networks

We know the basic Y parameter equation as:

From the figure, it can be seen that

V₁ =        V_1a          =             V_1b

V₂ =        V_2a          =             V_2b

And currents in parallel

I₁             =             I_1a           +             I_1b

I₂             =             I_2a           +             I_2b

The Y parameters in series are the additive

I₁   =  Y_11a V_1a +   Y_12a V_2a = (Y_11a + Y_11b)V₁     +  (Y_12a + Y_12b)V₂

I₂   =  Y_21a V_1a +   Y_22a V_2a  = (Y_21a + Y_21b)V₁     + (Y_22a + Y_22b)V₂

Therefore the admittance parameters are:

Y₁₁ = (Y_11a + Y_11b)               Y₁₂ = (Y_12a + Y_12b)

Y₂₁ =(Y_21a + Y_21b)                 Y₂₂  =(Y_22a + Y_22b)

Ex-1: Two identical two-port networks as shown below are connected in cascade. Determine the admittance parameters.

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2. Series Connection

From the figure it can be seen that

I₁ =         I_1a           =             I_1b

I₂ =         I_2a           =             I_2b

And in terms of voltage

V₁           =             V_1a          +             V_1b

V₂           =             V_2a          +             V_2b

The Z parameters in series are the additive

V₁    =   Z_11a I_1a   +    Z_12a I_2a   =   (Z_11a + Z_11b)I₁      +    (Z_12a + Z_12b)I₂

V₂      =   Z_21a I_1a   +    Z_22a I_2a     =   (Z_21a + Z_21b)I₁      +   (Z_22a + Z_22b)I₂

Therefore the series impedance parameters are:

Z₁₁ = (Z_11a + Z_11b)               Z₁₂ = (Z_12a + Z_12b)

Z₂₁ =(Z_21a + Z_21b)                Z₂₂  =(Z_22a + Z_22b)

Ex-2: Two identical networks as shown are connected in series, obtain the Z parameter.