AN-3008 RC Snubber Networks for Thyristor Power Control and ...

AN-3008
APPLICATION NOTE
The inverse laplace transform for each of the conditions gives:
Underdamped (Typical Snubber Design)
4.0
4.1
α
αt ξ
e = E–
V OL
Cos( ωt)
– --- sin( ωt)
e – + --- sin ( ωt)
e – αt
ω
ω
de
----- = V
dt OL
2αCos( ωt)
( ω 2 – α 2 )
+ ----------------------- sin( ωt)
e – αt
α
+ ξ Cos( ωt)
– --- sin( ωt)
e – αt
ω
ω
4.2
1
t PK ---tan – 1 2αV OL + ξ
= – -----------------------------------------------
ω
ω 2 – α 2
V OL
------------------
⎝
⎛ ω ⎠
⎞ –
ξα ------
ω
When M
= 0, R S = 0I , = 0 ; ωt PK = π
4.3
α
2 2
V PK = E + ----- – α t
ω PK ω 0 VOL + 2αξV OL
+ ξ 2
0
When I = 0, R L = 0M , = 1:
4.4
V
---------- PK
= ( 1+
e – α t
E
PK )
Average dV V
------ = ---------- PK
dt t PK
4.5
1
t max = ---ATN
ω
2
ω( 2 αξ–
V OL
( ω – 3α 2 ))
--------------------------------------------------------------------------
V OL
( α 3 – 3αω 2 ) + ξ( α 2 – ω 2 )
4.6
⎛dV
------ ⎞ =
⎝ dt ⎠max
2 2
V OL
ω 0 + 2αξ V OL
+ ξ 2 αt max
e –
No Damping
5.0
5.1
I
e = E( 1 – Cos( ω 0 t))
+ ---------- sin( ω
Cω 0 t)
0
de
I
----- = Eω
dt 0 sin( ω 0 t)
+ ---cos( ω
C 0 t)
5.2
⎛dV
------ ⎞
⎝ dt ⎠0
I
= --- = 0 when I = 0
C
5.3
5.4
5.5
5.6
5.7
π – tan – 1 ⎛--------------
I ⎞
⎝CEω 0
⎠
t PK = ------------------------------------------
ω 0
V PK = E+
E 2 + ---------------
I2
2 2
ω 0 C
⎛dV
------ ⎞
V
= ---------- PK
⎝ dt ⎠AVG
t PK
I
t max ----- tan – 1 ⎛--------------
ω EC 0 ⎞ I
=
= ----- π -- when I = 0
ω 0
⎝ I ⎠ ω 0 2
⎛dV
------ ⎞ I
--- E 2 2 2
= ω
⎝ dt ⎠max
C 0 C + I 2 = ω 0 E when I = 0
22 REV. 4.01 6/24/02