Math Editor

Electrical Power Assignment

Prepared by: Ibrahim Mohamed El-bastawisi

• Derive the generalized constants for a medium Transmission line??

End Condenser method

VS​=VR​+IS​Z

IS​=IR​+IC​

IC​=VR​Y

VS​=VR​+IR​Z+VR​YZ

A(1+YZ)​​VR​+BZ​​IR​

IS​=CY​​VR​+D1​​IR​

⎣⎡​VS​IS​​⎦⎤​=⎣⎡​1+YZY​Z1​⎦⎤​⎣⎡​VR​IR​​⎦⎤​

AD−BC=1+YZ−ZY=1

Nominal T method

VS​=V1​+IS​2Z​

IS​=IR​+IC​

IC​=V1​Y

V1​=VR​+IR​Z/2

VS​=VR​+IR​Z/2+(IR​+(VR​+IR​Z/2)Y)Z/2

A(1+YZ/2)​​VR​+BZ/2+Z/2+Y(Z/2)2​​IR​

IS​=IR​+(VR​+IR​Z/2)Y

CY​​VR​+D1+YZ/2​​IR​

⎣⎡​VS​IS​​⎦⎤​=⎣⎡​1+YZ/2Y​Z+Y(Z/2)21+YZ/2​⎦⎤​⎣⎡​VR​IR​​⎦⎤​

A=D=1+YZ/2

AD−BC=(1+YZ/2)2−Y(Z+Y(Z/2)2)

1+YZ+(YZ/2)2−YZ−Y2(Z/2)2=1

Nominal Pi method

VS​=VR​+IL​Z

IL​=IR​+IC1​

IC1​=VR​Y/2

VS​=VR​+(IR​+VR​Y/2)Z

A(1+YZ/2)​​VR​+BZ​​IR​

IS​=IL​+IC2​

IC2​=VS​Y/2

IS​=IR​+VR​Y/2+((1+YZ/2)VR​+ZIR​)Y/2

CY/2+Y/2+Z(Y/2)2​​VR​+D1+YZ/2​​IR​

⎣⎡​VS​IS​​⎦⎤​=⎣⎡​1+YZ/2Y+Z(Y/2)2​Z1+YZ/2​⎦⎤​⎣⎡​VR​IR​​⎦⎤​

A=D=1+YZ/2

AD−BC=(1+YZ/2)2−Z(Y+Z(Y/2)2)

1+YZ+(YZ/2)2−ZY−Z2(Y/2)2=1