Abstract
+ C cosωinjt + D sin ωinjt. (41)
Using initial conditions of iM(0) = 0a n d (di M/dt)(0) = 0,
results in
A =− C (42)
B = αA − Dωinj
ωM
≈− D (for ωinj ≈ ωM). (43)
Substituting (42) and (43) in (41) results in
iM(t) =− [C cosωM t + D sin ωM t]e−αt
+ C cos ωinjt + D sin ωinjt (44)
which can be written in the form
iM(t)= R[sin(ωM t+φ+ωt)− e−αt sin(ωM t+φ)] (45)
where
ωinj = ωM + ω (46)
φ = tan− 1
C
D
= tan− 1
L Mω[2ωM + ω]
RM(ωM + ω)
≈ tan− 1
2L Mω
RM
(47)
R =
C2 + D2 = 4VINJ/π R