# Tandem ( Series ) Connection of Two Port Network

- Two networks are connected in series such that output of one network is connected to input of another network, such type of connection is called as Tandem connection of two port network.
- It is considered that network 1 is connected to network 2 in tandem.

Let

A1,
B1, C1 and D1 – Constant of network 1

A2,
B2, C2 and D2 – Constant of network 2

__Network
1__

V_{S} = A1V’ + B1I’……. ( 1 )

I_{S }= C1 V’ + D1 I’……..( 2 )

Where

- V
_{S}= Sending end voltage - I
_{S }= Sending end current - V’ = Receiving end voltage of network 1
- I’ = Receiving end voltage of network 1

__Network
2__

V’= A2V_{R} + B2I_{R}……. ( 3
)

I’_{
}= C2V_{R} + D2 I_{R}……..( 4 )

Where

- V’ = Sending end voltage
- I’ = Sending end current
- V
_{R}= Receiving end voltage of network 2 - I
_{R}= Receiving end voltage of network 2

Substitute
equation ( 3 ) and ( 4 ) into equation ( 1 ) and ( 2 )

V_{S}
= A1 ( A2V_{R} + B2I_{R} ) + B1 ( C2V_{R} + D2 I_{R}
)……. ( 5 )

V_{S}
= A1A2 V_{R }+ A1 B2I_{R }+ B1 C2V_{R} + B1D2 I_{R}

V_{S}
= ( A1A2 + B1 C2 )V_{R} + ( A1 B2 + B1D2 )I_{R }….. ( 6
)

Compare
equation ( 6 ) with Vs = AV_{R} + BI_{R}

A = A1A2 + B1 C2

B = A1 B2 + B1D2

I_{S
}= C1 ( A2V_{R} + B2I_{R} ) + D1 ( C2V_{R} + D2 I_{R}
)

I_{S
}= C1 A2V_{R} + C1B2I_{R} + D1 C2V_{R} + D1D2 I_{R}

I_{S
}= ( C1 A2 + D1 C2 ) V_{R} + ( C1B2 + D1D2 ) I_{R}…….( 7 )

Compare
equation ( 7 ) with Is = CV_{R} + DI_{R}

C = C1 A2 + D1 C2 and

D = C1B2 + D1D2

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**Summary, constant
of two port networks when they are connected in series or tandem.**

A = A1A2
+ B1 C2

B = A1 B2
+ B1D2

C = C1 A2
+ D1 C2 and

D = C1B2
+ D1D2

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