3.3 State Equations
129
R 1
L 1
C 1
i C1
+
−
v C1
i L1
−
+
v L1
R 2
i R2
+
−
v R2
R 3
L 2
i L2
+
−
v L2
sin(2t)
(a)
R 1
i b1
v a1
i a1
+
−
v b1
R 2
i R2
+
−
v R2
R 3
i b2
−
+
v b2
sin(2t)
C
(b)
Fig. 3.16 (a) Third-order nonlinear network and (b) resistive network for finding the hybrid
representation
normal form
dv C 1
dt
= −
1
C 1
(v
2
C 1
+
v C 1
R 3
− ϕ
3
L 1
− i L 2 −
sin(2t)
R 3
)
dϕ L 1
dt
= −v C 1 − R 1 ϕ
3
L 1
di L 2
dt
= −
1
L 2
(−v C 1 + sin(2t)).
Remark 3.8 Let us consider the special case where the multi-port N in Fig. 3.15
contains only linear resistors and independent voltage or current sources. Then, h a
129
R 1
L 1
C 1
i C1
+
−
v C1
i L1
−
+
v L1
R 2
i R2
+
−
v R2
R 3
L 2
i L2
+
−
v L2
sin(2t)
(a)
R 1
i b1
v a1
i a1
+
−
v b1
R 2
i R2
+
−
v R2
R 3
i b2
−
+
v b2
sin(2t)
C
(b)
Fig. 3.16 (a) Third-order nonlinear network and (b) resistive network for finding the hybrid
representation
normal form
dv C 1
dt
= −
1
C 1
(v
2
C 1
+
v C 1
R 3
− ϕ
3
L 1
− i L 2 −
sin(2t)
R 3
)
dϕ L 1
dt
= −v C 1 − R 1 ϕ
3
L 1
di L 2
dt
= −
1
L 2
(−v C 1 + sin(2t)).
Remark 3.8 Let us consider the special case where the multi-port N in Fig. 3.15
contains only linear resistors and independent voltage or current sources. Then, h a