18-1 Nonlinear elements 1. Nonlinear resistor A nonlinear resistor is an element whose voltage and current are related by a nonlinear equation
18-1 Nonlinear elements 1. Nonlinear resistor A nonlinear resistor is an element whose voltage and current are related by a nonlinear equation. i + −
If the current can be expressed as an explicit(单值) function of the voltage i=f(D)--A voltage-controlled nonlinear resistor If the voltage can be expressed as an explicit function of the current u=h(i)----A current-controlled nonlinear resistor
i i If the current can be expressed as an explicit(单值) function of the voltage. i = f () ----A voltage-controlled nonlinear resistor. If the voltage can be expressed as an explicit function of the current = h(i ) ----A current-controlled nonlinear resistor
2. Nonlinear inductor A nonlinear inductor is one in which the flux is a nonlinear function of the current i(t. o =f(i) d_d、dir症 dt (一 L,=2--D ynamic inductance Example: The flux as a function of the current is somewhat like in shown in fig. P B l4→L B →l→l D A→B→C→D B D
2. Nonlinear inductor A nonlinear inductor is one in which the flux is a nonlinear function of the current i(t). = f (i) Dynamic induc tance di d L dt di L dt di di d dt d ( t ) d d = − − = = = Example: The flux as a function of the current is somewhat like in shown in Fig. i A B C D A i B i C i D i A B C D i i i i A B C D → → → → → → i(t) +(t)−
3. Nonlinear capacitor A nonlinear capacitor is one whose stored charge is a nonlinear function of the voltage across it. =f(o) If q=ko2 i(t) g db k U2)dU 十 dt do dt 2 dt d=-n 22-dynamic capacitance Example: If u=v(1+asin),q=kvu(a<<1). Findi(). dqdq du k k Va cos t 丿 a cos t dt du dt 2 2√(1+ a sint) kav cost(1-3asint 2 vv(cost-I a 2t)
3. Nonlinear capacitor A nonlinear capacitor is one whose stored charge is a nonlinear function of the voltage across it. q = f () dt d C dt k d dt d d dq dt dq i t If q k d = = = = = − ) 2 ( ) ( 2 1 2 1 + − i 2 1 2 − = k Cd Example:If Find =V(1+ sint), q = k ( 1). i(t). (1 sin ) cos 2 cos 1 2 ( ) V t k V t V t k dt d d dq dt dq i t + = = = = sin ) 2 1 cos (1 2 V t t k − sin2 ) 4 1 (cos 2 V t t k − − −dynamic capacitance
