Interconnection of Networks

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
Figure:1 Parallel connection of two networks

We know the basic Y parameter equation as:

From the figure, it can be seen that

V1 =        V1a          =             V1b

V2 =        V2a          =             V2b

And currents in parallel

I1             =             I1a           +             I1b

I2             =             I2a           +             I2b

The Y parameters in series are the additive

I1   =  Y11a V1a +   Y12a V2a = (Y11a + Y11b)V1     +  (Y12a + Y12b)V2

I2   =  Y21a V1a +   Y22a V2a  = (Y21a + Y21b)V1     + (Y22a + Y22b)V2

Therefore the admittance parameters are:

Y11 = (Y11a + Y11b)               Y12 = (Y12a + Y12b)

Y21 =(Y21a + Y21b)                 Y22  =(Y22a + Y22b)

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

2. Series Connection

Series connection of 2-port networks

From the figure it can be seen that

I1 =         I1a           =             I1b

I2 =         I2a           =             I2b

And in terms of voltage

V1           =             V1a          +             V1b

V2           =             V2a          +             V2b

The Z parameters in series are the additive

V1    =   Z11a I1a   +    Z12a I2a   =   (Z11a + Z11b)I1      +    (Z12a + Z12b)I2

V2      =   Z21a I1a   +    Z22a I2a     =   (Z21a + Z21b)I1      +   (Z22a + Z22b)I2

Therefore the series impedance parameters are:

Z11 = (Z11a + Z11b)               Z12 = (Z12a + Z12b)

Z21 =(Z21a + Z21b)                Z22  =(Z22a + Z22b)

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

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