ps04 - ECEN 2250 Circuits/Electronics 1 Fall 2007 P Mathys...

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ECEN 2250 Circuits/Electronics 1 Fall 2007 9-19-07 P. Mathys Problem Set 4 (Solutions are due Fri. 9-28-07) 1) The ﬁgure below shows a resistive Y (“Wye”) network and a resistive Δ (“Delta”) network. R X R Y R Z - v 1 + - v 2 + i 1 →← i 2 Y -network R A R B R C - v 1 + - v 2 + i 1 i 2 Δ-network Both networks are 2-ports that can be characterized by equations of the form v 1 = R 11 i 1 + R 12 i 2 , v 2 = R 21 i 1 + R 22 i 2 . For the Y -network R 11 = R X + R Z , R 12 = R 21 = R Z , R 22 = R Y + R Z . For the Δ-network R 11 = R A ( R B + R C ) R A + R B + R C , R 12 = R 21 = R A R B R A + R B + R C , R 22 = R B ( R A + R C ) R A + R B + R C . Two 2-ports are said to be equivalent if both are characterized by the same set of resistance parameters R 11 , R 12 , R 21 , R 22 . Use the results given above to derive the Δ-

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ps04 - ECEN 2250 Circuits/Electronics 1 Fall 2007 P Mathys...

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