AN437

RLC series circuit step response explanation

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Appendix A

RLC series circuit step response explanation

The electrical circuit analyzed in this Appendix is shown in Figure 13

Figure 13.

Application circuit and its equivalent diagram at turn-off commutation

Note:

In this Appendix the equations 1 to 6 are reproduced here with the same numbering to

facilitate use of this application note.

For a second order linear differential equation with a step function input, the voltage

Equation 1

Equation 2

With damping factor:

Equation 3

Undamped natural resonance:

Equation 4

V

T

I

G

G

I

T

V

Mains

Load

LR

I

T

V

T

≈ E

Load

LR

R

S

C

S

R

S

C

S

Application circuit

Equivalent diagram at turn-off commutation

V

Cs

E

)

t

(

V

dt

)

t

(

dV

2

dt

)

t

(

V

d

1

Cs

Cs

0

2

Cs

2

2

0

=

+

+·

.

·

ω

ξ

ω

)

t

(

V

dt

)

t

(

dV

C

R

)

t

(

V

Cs

Cs

S

S

T

+

·

·

=

)

H

(

)

F

(

S

)

(

S

L

C

2

)

R

R

(

·

Ω

+

=

ξ

)

F

(

S

)

H

(

)

s

/

rad

(

0

C

L

1

·

=

ω