IALB-Institute of Electrical Drives, Power Electronics and Components i,R+L dt 2 l di, U differential equations l di, U r dt 2R r dt 2R C1 C1 2R 2R 2r 20//ex general solution lze 2R-41-e)+o Initial value(V): ILo=0 when t→∞ 2R newⅣV: 2R when t→∞ 2R UpI I When t→∞ U newⅣV: 2R Diagram 2. 3 shows the current and voltage characteristics t,: time in which S, is closed t2 time in which S2 is closed Generally the average voltage ur is as following: (1 l1+l2 where To= t1+ t2IALB – Institute of Electrical Drives, Power Electronics and Components - 8 - 0 0 1 1 2 2 2 2 L t L D D t L L D L L D L i e i R U R U i C e R U dt di R L i U dt di i R L +⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ − ⎠ ⎞ ⎜ ⎝ ⎛ − = + = + = + = − − τ τ differential equations general solution 0 0 1 1 2 2 2 2 L t L D D t L L D L L D L i e i R U R U i C e R U dt di R L i U dt di i R L +⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ − ⎠ ⎞ ⎜ ⎝ ⎛ − − = − = + = − + = − − − τ τ Initial value (IV): iL0 = 0 ⇒ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = − − τ t D L e R U i 1 2 new IV: R U i D L 2 0 = − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⇒ = − − τ t D L e R U i 2 1 when t → ∞ when t → ∞ when t → ∞ new IV: R U i D L 2 0 = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⇒ = − − − τ t D L e R U i 2 1 new IV: R U i D L 2 0 = Diagram 2.3 shows the current and voltage characteristics. t1: time in which S1 is closed t2: time in which S2 is closed Generally the average voltage u L is as following: 2 2 D L D U u U− < ≤ ( ) ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = − + − = 2 1 2 2 0 1 1 2 1 2 T U t t t U t t u D D L where T0 = t1 + t2