HW5%20solutions_EG - MAE 3780 MECHATRONICS FALL 2009...

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MAE 3780 MECHATRONICS FALL 2009 1 HOMEWORK 5 SOULUTIONS 1. Calculate V out (t) in the circuit shown below in Figure 1 using the offset diode model . You are given that V S (t) = 5sin( ω t) and V 6 . 0 = γ V . Assuming that neither diode is conducting: (V D1 <0.6 V D2 <0.6) Vout(t)=0 due to open circuit V V V V V V V V V V V V V V V V V V V V V V R V R V V i S S s s A D S s s A D S A S A A A S A A S 2 . 3 2 . 1 2 . 3 6 . 0 1 2 1 2 1 2 1 2 2 . 1 6 . 0 2 1 1 2 1 1 1 1 2 1 2 2 2 2 2 1 < < < < = + = = > < = = = + = + = = = =
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MAE 3780 MECHATRONICS FALL 2009 2 Assuming that only D 1 is conducting: (i D1 >0 V D2 <0.6) Vout(t)=0 due to open circuit Assuming both diodes are conducting: (i D1 >0 i D2 >0) R i V R i V V R i V V V V V V A A 2 . 2 2 2 . 0 2 6 . 0 4 . 0 6 . 0 1 4 4 4 = = = = = Î Contradiction (i 4 must be > 0 for D 2 to conduct) Assume only D 2 is conducting: : (i D2 >0 V D1 <0.6) 07 . 1 3 1 2 6 . 0 533 . 1 3 1 2 6 . 0 533 . 1 3 1 2 6 . 2 2 2 6 . 0 3 2 1 = = + = + = + = + + = + = Vs V V V V V V V V V V V V R V V R V V V R V V i i i out out S out A C A A A A S A A A S V V V R R i R i R V R V R i V V R i i i V V V V V V V s S S A A S A D A 2 . 1 0 1 2 . 1 6 . 1 4 . 0 1 ) 2 ( 1 ) ( 1 6 . 1 2 4 . 0 6 . 0 1 2 2 2 3 2 1 2 < > = = + = + = + = = =
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MAE 3780 MECHATRONICS FALL 2009 3 2. Determine i(t) for the circuit shown below. Assume that the system is a steady state when the switch opens at t=0 and use the ideal diode model. Given: steady state at t = 0, ideal diode model Find: i(t) First, assume that the diode is not conducting for t 0, i.e. when the switch is closed. Apply KVL around the circuit: () R V i iR V V V V V S R S R L S = = = = 0 0 Current will continue to flow in the same direction when the switch is opened. This is because the current through an inductor must be continuous (therefore i(t) cannot suddenly jump). Now, instead of flowing into ground like before, the current will flow in a clockwise loop
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This note was uploaded on 10/02/2010 for the course MAE 3780 taught by Professor Wickenhieser during the Fall '08 term at Cornell University (Engineering School).

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HW5%20solutions_EG - MAE 3780 MECHATRONICS FALL 2009...

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