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:

- Parallel connection
- Series Connection

- Parallel Connection of two-port networks

**We know the basic Y parameter equation as:**

From the figure, it can be seen that

V_{1} = V_{1a} = V_{1b}

V_{2} = V_{2a} = V_{2b}

And currents in parallel

I_{1} = I_{1a} + I_{1b}

I_{2} = I_{2a} + I_{2b}

The Y parameters in series are the additive

I_{1} = Y_{11a} V_{1a} + Y_{12a} V_{2a} = (Y_{11a} + Y_{11b})V_{1} + (Y_{12a} + Y_{12b})V_{2}

I_{2} = Y_{21a} V_{1a} + Y_{22a} V_{2a } = (Y_{21a} + Y_{21b})V_{1} + (Y_{22a} + Y_{22b})V_{2}

Therefore the admittance parameters are:

Y_{11 }= (Y_{11a} + Y_{11b}) Y_{12} = (Y_{12a} + Y_{12b})

Y_{21} =(Y_{21a} + Y_{21b}) Y_{22 }=(Y_{22a} + Y_{22b})

From the figure it can be seen that

I_{1} = I_{1a} = I_{1b}

I_{2} = I_{2a} = I_{2b}

And in terms of voltage

V_{1} = V_{1a} + V_{1b}

V_{2} = V_{2a} + V_{2b}

The Z parameters in series are the additive

V_{1} = Z_{11a} I_{1a} + Z_{12a} I_{2a} = (Z_{11a} + Z_{11b})I_{1} + (Z_{12a} + Z_{12b})I_{2}

V_{2} = Z_{21a} I_{1a} + Z_{22a} I_{2a }= (Z_{21a} + Z_{21b})I_{1} + (Z_{22a} + Z_{22b})I_{2}

Therefore the series impedance parameters are:

Z_{11 }= (Z_{11a} + Z_{11b}) Z_{12} = (Z_{12a} + Z_{12b})

Z_{21} =(Z_{21a} + Z_{21b}) Z_{22 }=(Z_{22a} + Z_{22b})