L6714 View Datasheet(PDF) - STMicroelectronics
Part Name
Description
MFG CO.
L6714
STMicroelectronics
'L6714' PDF : 70 Pages View PDF
System control loop compensation
L6714
Where:
● RSENSE is the MOSFET RdsON or the Inductor DCR depending on the sensing element
selected;
●
RDROOP
function;
=
-R----S---E----N----S---E--
Rg
⋅
RFB
is the equivalent output resistance determined by the droop
● ZP(s) is the impedance resulting by the parallel of the output capacitor (and its ESR)
and the applied load RO;
● ZF(s) is the compensation network impedance;
● ZL(s) is the parallel of the N inductor impedance;
● A(s) is the error amplifier gain;
●
PWM
=
4--
5
⋅
-----V-----I-N-------
∆VOSC
is the PWM transfer function where ∆VOSC is the oscillator ramp
amplitude and has a typical value of 4V.
Removing the dependence from the Error Amplifier gain, so assuming this gain high
enough, and with further simplifications, the control loop gain results:
GLOOP(s) = –45-- ⋅
∆-----V-V---O-I---N-S----C--- ⋅
-Z---F-----(--s----)
RFB
⋅
R-----O------+-----R-----D----R-----O-----O------P--
RO
+
R-----L--
N
⋅
----------------------------1-----+-----s----⋅------C----O-------⋅-----(---R----D-----R-----O-----O-----P-----/-/---R----O------+-----E-----S----R-----)----------------------------
s2 ⋅
CO ⋅
--L--
N
+
s
⋅
----------L-----------
N ⋅ RO
+
CO
⋅
ESR + CO ⋅
R-----L--
N
+1
The system Control Loop gain (See Figure 23) is designed in order to obtain a high DC gain
to minimize static error and to cross the 0dB axes with a constant -20dB/dec slope with the
desired crossover frequency ωT. Neglecting the effect of ZF(s), the transfer function has one
zero and two poles; both the poles are fixed once the output filter is designed (LC filter
resonance ωLC) and the zero (ωESR) is fixed by ESR and the Droop resistance.
Figure 23. Equivalent control loop block diagram (left) and bode diagram (right).
PWM
d VOUT L / N
VOUT
ESR
CO
RO
REMOTE BUFFER
64k
VID
VOUT
64k
FBG
DROOP FB
COMP
64k
FBR
dB
K
RF[dB]
GLOOP(s)
ZF(s)
ZFB(s)
RF CF VSEN
RFB
ωLC = ωF
ωESR
ZF(s)
ω
ωT
To obtain the desired shape an RF - CF series network is considered for the ZF(s)
implementation. A zero at ωF = 1/RFCF is then introduced together with an integrator. This
integrator minimizes the static error while placing the zero ωF in correspondence with the L-
C resonance assures a simple -20dB/dec shape of the gain.
In fact, considering the usual value for the output filter, the LC resonance results to be at
frequency lower than the above reported zero.
58/70
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