, . , (.2.4. ), z u1(t)=Umcosωt Uo. , ν=ωt (. 2.4, , ). . . ∆i = S ∆u, ( ), .
. 2.4. :
; , .
(.2.4, ), :
i(t)=Io+ Incosnωt. (2.5)
Io In .
.
u(t)=Uo+Umcosωt (2.6)
, :
i(u)=ao+a1(u-Uo)+a2(u-Uo)2+a3(u-Uo)3+ (2.7)
(2.6) (2.7),
i(u)=ao+a1Umcosωt+a2Um2cos2ωt+ a3Um3cos3ωt+
:
cos2x= (1+cos2x); cos3x= (3cosx+cos3x); cos4x= (3+4cos2x+cos4x); ..
, :
i(t)=(ao+ a2Um2+ a4Um4+)+(a1Um+ a3Um3+ a5Um5+)cosωt+( a2Um2+
a4Um4+)cos2ωt+( a3Um3+ a5Um5+)cos3ωt+ (2.8)
(2.8)
i(t)=Io+I1cosωt+ I2cos2ωt+ I3cos2ωt+ (2.9)
:
Io=ao+ a2Um2+ a4Um4+;
I1= a1Um+ a3Um3+ a5Um5+;
I2= a2Um2+ a4Um4+;
I3= a3Um3+ a5Um5+. (2.10)
, . , .
- . (2.6) , - (2.4). , , (. 2.5).
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. 2.5. - .
θ ( ), Im , . , , 2θ. . 2.5. , ωt=0 =Uo+Umcosθ,
osθ=(- Uo)/ Um (2.11)
(2.4) (2.6) , :
i(ωt)=SUm(cosωt-cosθ), -θ<ωt<θ (2.12)
i(ωt) (2.12) , 2π, 2θ, ν= ωt. :
Io= (cosωt-cosθ)dωt= (sinθ-θcosθ). (2.13)
I1= (cosωt-cosθ)cosωtdωt= (θ-sinθcosθ). (2.14)
In n=2,3, . :
In= . (2.15)
:
Io=SUmγo; I1=SUmγ1; ; In=SUmγn; (2.16)
γo, γ1, , γn , , , :
γn= (sinθ-θcosθ),
γn= (sinθ-θcosθ),
γn= , n=2.3, (2.17)
2.3. - , =0,6 , S=0,25 /. ( ) u(t)=0,2+0,8cosωt . , .
. (2.11), , cosθ=0,6- 0,2)/0,8=0,5. , , θ=60. , , γ=0,11; γ1=0,2. (2.16), : Io=2 , I1=4 .
, , , . .
10.