RLC series circuit step response explanation

AN437

16/18

Final voltage value:

Equation 5

Snubber circuit divider ratio:

Equation 6

For each damping factor, the initial conditions to solve the differential equation are the same:

At t = 0

Equation 12

At t =

Equation 13

Note:

The recovery current due to the storage charge is not considered in the initial conditions.

●

Underdamped oscillating circuit: 0

≤ ξ ≤ 1

Equation 14

With damped natural resonance

Equation 15

●

Damped oscillating circuit:

ξ = 1

Equation 16

With damped natural resonance

Equation 17

)

sin(

V

2

E

RMS

ϕ

·

·

=

with

2

2

)

L

(

R

L

)

sin(

ω

ω

ϕ

·

+

·

=

R

R

R

M

S

S

+

=

L

R

·

E

dt

dV

S

0

T

=

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

¥

E

)

(

V

T

=

∞

t

p

p

0

p

T

0

e

)

t

sin(

)·

1

)

M

1

·(

2

(

)

t

cos(

·

E

E

)

t

(

V

·

·

-

·

·

·

.

-

-

·

-

ω

ξ

ω

ω

ω

ξ

ω

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+

=

2

0

p

1

ξ

ω

ω−

.

=

()

t

0

T

0

e

t

)·

1

)

M

1

·(

2

(

1

·

E

E

)

t

(

V

·

-

·

·

-

-

-

ω

ω

+

=

0

p

ω

ω =