8.4 The Natural Response of a Series/Parallel RLC Circuit

8.6 State EquationR∴v = e - ( i + i )RR43 4R4 s L1 L2R+R3 4R+R3 4C.T. Pan67Step5⎡1⎤⎢0 0 0C ⎥10⎢⎥⎡ ⎤⎡vC1⎤ ⎢1 1 ⎥ ⎡vC1⎤⎢0⎥⎢ 0 0d v⎥ ⎢C2 C2 C⎥ ⎢2 v⎥⎢ ⎥⎢ ⎥ C2 1 R= ⎢⎥ ⎢ ⎥⎢ ⎥+ 4 esdt ⎢iL1⎥ ⎢⎢1 1 (R1 R 2)R iL1L⎥− − − + − ⎥ ⎢ ⎥ 1 R 3+R4⎢ ⎥ ⎢⎥ ⎢ ⎥⎢ ⎥⎣iL2⎦ ⎢L1 L1 L1 L1⎥ ⎣iL2⎦ ⎢ 1 ⎥⎢⎢ ⎥−1 −R− (R2+ R) ⎥ L0⎣ 2 ⎦⎢⎥⎣ L2 L2 L2⎦C.T. Pan8.6 State Equation⎡vC1⎤⎡ -R3R4 -R3R4 ⎤⎢v⎥C2 Rv4R4 = ⎢0 0 ⎥ ⎢ ⎥ + es⎣ R3 + R4 R3 + R4⎦ ⎢ iL1⎥ R3 + R4⎢ ⎥⎣iL2⎦RRwhere R @ R 3 45 + R 3 +R 468