Méthode de superposition

Présentation au sujet: "Méthode de superposition"— Transcription de la présentation:

1 Méthode de superposition
x1 = 9 V x2 = 4,5 V r1 = r2 = r3 = 2 kW i”1 I1 i’1 x1 x1 r1 x2 x2 i’2 I2 i”2 r2 i’3 I3 i”3 r3 loi des noeuds: i’1 = i’2 + i’3 i’’2 = i’’1 + i’’3

2 Courants provoqués par x1
x1 = 9 V x2 = 4,5 V r1 = r2 = r3 = 2 kW i’1 x1 x1 r1 x2 i’2 r2 i’3 r3

3 Courants provoqués par x1
x1 = 9 V x2 = 4,5 V r1 = r2 = r3 = 2 kW i’1 x1 r1 r2 // r3 = r2 r3 / (r2 + r3) = 1 kW r2 i’2 r123 = r23 + r1 = 1 kW + 2 kW = 3 kW i’3 i’1 = x1 / r123 = 9 V / 3 kW = 3 mA r123 r23 r3

4 Courants provoqués par x1
x1 = 9 V x2 = 4,5 V r1 = r2 = r3 = 2 kW i’1 x1 x1 r1 r2 i’2 r2 // r3 = r2 r3 / (r2 + r3) = 1 kW r123 = r23 + r1 = 1 kW + 2 kW = 3 kW i’3 i’1 = x1 / r123 = 9 V / 3 kW = 3 mA r3 loi des noeuds: i’1 = i’2 + i’3 comme r2 = r3 i’2 = i’3 = i’1 / 2 = 3 mA /2 = 1,5 mA Donc: i’1 = 3 mA i’2 = 1,5 mA i’3 = 1,5 mA

5 Courants provoqués par x2
x1 = 9 V x2 = 4,5 V r1 = r2 = r3 = 2 kW i”1 x1 r1 x2 x2 i”2 r2 i”3 r3

6 Courants provoqués par x2
x1 = 9 V x2 = 4,5 V r1 = r2 = r3 = 2 kW i”1 r1 r1 // r3 = r1 r3 / (r1 + r3) = 1 kW i”2 x2 r2 r123 = r13 + r2 = 1 kW + 2 kW = 3 kW i’’2 = x2 / r123 = 4,5 V / 3 kW = 1,5 mA i”3 r123 r13 r3

7 Courants provoqués par x2
x1 = 9 V x2 = 4,5 V r1 = r2 = r3 = 2 kW i”1 r1 r1 // r3 = r1 r3 / (r1 + r3) = 1 kW i”2 x2 r2 r123 = r13 + r2 = 1 kW + 2 kW = 3 kW i’’2 = x2 / r123 = 4,5 V / 3 kW = 1,5 mA i”3 r3 loi des noeuds: i’’2 = i’’1 + i’’3 comme r1 = r3 i’’1 = i’’3 = i’’2 / 2 = 1,5 mA /2 = 0,75 mA Donc: i’’1 = 0,75 mA i’’2 = 1,5 mA i’’3 = 0,75 mA

8 Courants provoqués par x1 et x2
i”1 I1 i’1 x1 = 9 V x2 = 4,5 V r1 = r2 = r3 = 2 kW x1 r1 I1 = i’1 + i”1 = 3 + 0,75 = 3,75 mA x2 i’2 I2 i”2 I2 = i’2 + i”2 = 1,5 + 1,5 = 3,0 mA r2 I3 = i’3 - i”3 = 1,5 - 0,75 = 0,75 mA I3 i’3 i”3 r3 i’1 = 3 mA i’2 = 1,5 mA i’3 = 1,5 mA i’’1 = 0,75 mA i’’2 = 1,5 mA i’’3 = 0,75 mA