Two Port Networks are in Tandem or Series

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