Electronic Circuit Analysis

232 Electronic Circuit Analysis
If the generator is to transfer maximum power to the laod, it is necessary only that the image
impedance Zli at terminals P,Q must be equal to R I . In other words, the load impedance R2 is
transformed by the T-network to a value at the P,Q terminals equal to R I .
When R2 is connected, the image impedance Zli must be
..... (41)
X may have either positive sign or negative sign, i.e., it may be either inductive or capacitive in
nature. Then, RI R2 + j RI (X 2 + X 3 )
By equating real terms,
= - (Xl X 2 + X 2 X3 + X3 Xl) + jR2 (Xl + X 3 )
RI R2 = - (Xl X2 + X2 X3 X3 + Xl) ..... (42)
In the above equation, RI R2 term on the LHS is positive. So the term on RHS must also be
positive. Since it is negative sign, one or more of the three terms on RHS must be positive. X can be
+ jWL or ;"b . In order that the product term Xl X 2 is positive, Xl can be +jXa and X 2 can be -jXa
:-jX b
) = +Xa X b· This requires that one reactive arm of the T-Network be opposite in sign to the sign
)f the other two arms. So the T-Network must consist of one capacitance and two inductances or
Vice-versa.
By equating imaginary terms,
RI (X 2 + X 3 ) = R2 (Xl + X 3 )
..... (43)
The above equation may be written as,
RI R2 = - [(Xl + X 3 ) (X 2 + X 3 ) - Xl] ..... (44)
..... (45)