Tech pill #48 Generalized primary equivalent inductance of multi-output forward converter Arturo Galgani
[email protected]
Forward converter are widely used to generate multiple outputs thanks to its good cross-regulation due to coupled output inductor. In case of peak current control, an estimation of equivalent primary inductance is needed to properly design the control loop. This report gives a generalized expression of equivalent inductance seen on primary side for forward converter working in Continuous Conduction Mode (CCM), suitable for this purpose.
Let L1 be the coupled output inductor (with p outputs) and Lext an extra non-coupled inductor. N1 is the transformer turns ratio between regulated output and primary winding (Ns1/Np). K is the coupling factor of L1 windings, and β the transformer turns ratio between non-coupled output and primary winding (Next/Np).
Ns1 Np
L1 Vreg
p outputs
Lext
nL1
nLn Next
Nsn
For proper voltage balance, the following relationship holds : nLn/NL1=Nsn/Ns1 In this case equivalent inductance seen on primary side results:
Leq
Lext⋅ [ ( p − 1) ⋅ k + 1] ⋅ 1 Lext 2 2 [ ( p − 1) ⋅ k + 1] ⋅ β + p ⋅ N1 L1
Special case of equivalent inductance value:
Case of K=1
Leq
L1⋅ Lext 2
for any p
Lext⋅ N1 + L1⋅ N3
2
This expression can be further generalised in case of n uncoupled outputs :
1
Leq N1
2
L1 Case of non-coupled inductor absence (Lext ∞)
Leq
+ ...
Nn
2
Ln
[ k⋅ ( p − 1) + 1] ⋅ L1 2
N1 ⋅ p If K=1
Leq
L1 N1
for any p, as for “standard” multi-output coupled case
2
http://cbasso.pagesperso-orange.fr/Downloads/Book/corrections%202nd%20print.pdf
Feel free to copy and distribute to anyone, anytime, anywhere.
