AN557 Datasheet, PDF (8/52 Pages) STMicroelectronics – EASY APPLICATION DESIGN WITH THE L4970A

AN557 APPLICATION NOTE
Figure 5. Equivalent Circuit Showing Recirculation when Q1 is Turned Off.
From the behaviour shown in Fig. 4 it may be calculated that the charge current of the output capacitor,
within a period, is ∆I_L/4, which is supplied for a time T/2. It follows therefore that :
∆V_C
=
∆_----I_{--L- T---}
4C 2
=
∆_----I_--L---T_--
8C
=
-^∆----^I-^L--
8fc
(19)
but, remembering expression (4) :
∆I_L+
=
-⁽--^V----ⁱ---–----^V----^o----⁾--^T----^O----^N--
L
and
T_ON
=
V_-----o-
V_i
T
therefore equation (19) becomes :
Finally, calculating C it follows that :
∆V_C
=
(_---V_{----i---–----}V_----o----)_--V_----o-
8 V_if²LC
where :
L is in Henrys
C is in Farads
f is in Hz
C = ----⁽---^V----ⁱ---–----^V----^o----⁾--^V----^o----- (20)
8 V_i ∆V_C f² L
Finally, the following expression should be true :
ESR_max
=
-^∆---^V----^C----^m-----^a---^x-
∆I_L
(21)
It may happen that to satisfy relation (21) a capacitance value much greater than the value calculated
through (20) must be used.
TRANSIENT RESPONSE
Sudden variations of the load current give rise to overvoltages and undervoltages on the output voltage.
Since i_c = C (dv_c/dt) (22), where dv_c = ∆V_o, the instantaneous variation of the load current ∆I_o is supplied
during the transient by the output capacitor. During the transient, also current through the coil tends to
change its value. Moreover, the following is true :
v_L
=
L
-^d---ⁱ--^L-
dt
(23)
where di_L = ∆I_o
v_L = V_i – V_o for a load increase
v_L = Vo
for a load decrease
8/52