__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

You
may also like to read these articles : |

**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

## No comments:

## Post a Comment