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L6919C
–
is the ACM PWM transfer function where
VOSC is the oscillator ramp amplitude
and has a typical value of 2V
Removing the dependence from the Error Amplifier gain, so assuming this gain high enough, the control loop
gain results:
With further simplifications, it results:
Considering now that in the application of interest it can be assumed that Ro>>RL; ESR<<Ro and
RDROOP<<Ro, it results:
The ACM control loop gain is designed to obtain a high DC gain to minimize static error and 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 and the
zero is fixed by ESR and the Droop resistance. To obtain the desired shape an RF-CF series network is consid-
ered for the ZF(s) implementation. A zero at ωF=1/RFCF is then introduced together with an integrator. This in-
tegrator minimizes the static error while placing the zero in correspondence with the L-C resonance a simple -
20dB/dec shape of the gain is assured (See Figure 14). In fact, considering the usual value for the output filter,
the LC resonance results to be at frequency lower than the above reported zero.Compensation network can be
simply designed placing
ωZ = ωLC and imposing the cross-over frequency ωT as desired obtaining:
Figure 14. ACM Control Loop Gain Block Diagram (left) and Bode Diagram (right)
PWM
4
5
---
V
IN
V
OSC
-------------------
=
G
LOOP s
()
4
5
---
V
IN
V
OS C
-------------------
Z
F s
()
Z
P s
() Z
L s
()
+
------------------------------------
Rs
Rg
--------
Z
P s
()
R
FB
---------------
+
–
=
G
LOO P s
()
4
5
---
V
IN
V
OSC
-------------------
Z
F s
()
R
FB
---------------
Ro
R
DROOP
+
Ro
R
L
2
-------
+
--------------------------------------
1s Co
R
DROOP//Ro
ESR
+
()
+
s
2
Co
L
2
---
s
L
2R o
---------------
Co ESR
Co
R
L
2
-------
+
+
1
+
+
----------------------------------------------------------------------------------------------------------------------------------
–
=
G
LOO P s
()
4
5
---
V
IN
V
OSC
-------------------
Z
F s
()
R
FB
---------------
1s Co
R
DROOP
ESR
+
()
+
s
2
Co
L
2
---
s
L
2Ro
---------------
Co ESR
Co
R
L
2
-------
+
+
1
+
+
----------------------------------------------------------------------------------------------------------------------------------
–
=
R
F
R
FB
V
OSC
V
IN
----------------------------------
5
4
---
ω
T
L
2R
DROOP
ESR
+
()
--------------------------------------------------------
=
C
F
Co
L
2
---
R
F
--------------------
=
Rout
Cout
ESR
L/2
RFB
RF
CF
REF
PWM
IFB
VCOMP
VOUT
d
VIN
ZF
dB
ω
T
ω
Z
ω
LC
GLOOP
ZF(s)
K
4
5
---
V
IN
V
osc
---------------
1
R
FB
----------
dB
=