AN437

Revision history

17/18

●

Overdamped oscillating circuit:

ξ > 1

Equation 18

With damped natural resonance

Equation 19

Thanks to these three equations and their derivatives, the variation between the peak

voltage and the slope of the voltage rise can be defined according to the damping factor and

the resistive load.

The damping factor determines the shape of the voltage wave (refer to Figure 14).

Figure 14.

When

ξ is lower than 0.5, the voltage shape is not exponential and the maximum

instantaneous slope of voltage rise occurs at a time later than t = 0.

When

ξ is equal and higher than 1, some overshoots occur even if the oscillating circuit is

damped and overdamped.

Revision history

t

p

p

0

p

T

0

e

)

t

sinh(

)·

1

)

M

1

·(

2

(

)

t

cosh(

·

E

E

)

t

(

V

·

·

-

.

·

·

.

-

-

·

-

ω

ξ

ω

ω

ω

ξ

ω

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+

=

1

2

0

p

−

.ξ

ω

ω =

0

100

200

300

400

500

600

700

0

0.25

0.5

0.75

1

1.25

1.5

î = 0

î = 0.25

î = 0.5

î = 0.75

î = 1

î = 1.5

E = final value

decreases

ξ

Time: t (µs)

Triac voltage VT (t) (V)

Table 1.

Document revision history

Date

Revision

Changes

1995

1

Initial release.

22-Oct-2007

2

Reformatted to current standards. Complete rewrite for text and

graphics. Part numbers updated for current products.