Datasheet
1P
=Z
1+D
OD
Cr x
3
=
0U
T
=
SNSCSH
RR500VD
xxx
c
620VD
x
c
( )
LIM
LED
RID1
xx+
( )
LIMHSP
RRD1 xx+
x
=
¨
¨
©
§
+
s
1
Z
1P
¸
¸
¹
·
0U
T
U
T
¨
¨
©
§
-
s
1
Z
1Z
¸
¸
¹
·
t
i
L
(t)
I
C
0
T
S
Ideal
i
L
(t)
Actual
i
L
(t)
2T
S
=
M
A
=
e5.7
12
1
L
2x
V
O
RRR
SNSSLPT
xx
LM3424
www.ti.com
SNVS603B –AUGUST 2009–REVISED OCTOBER 2009
The LM3424 mitigates current mode instability by implementing an aritifical ramp (commonly called slope
compensation) which is summed with the sensed MosFET current at the IS pin as shown in Figure 25. This
combined signal is compared to the COMP pin to generate the PWM signal. An increase in the ramp that is
added to the sense voltage will increase the maximum achievable duty cycle. It should be noted that as the
artificial ramp is increased more and more, the control method approaches standard voltage mode control and
the benefits of current mode control are reduced.
To program the slope compensation, an external resistor, R
SLP
, is connected from SLOPE to GND. This sets the
slope of the artificial ramp that is added to the MosFET current sense voltage. A smaller R
SLP
value will increase
the slope of the added ramp. A simple calculation is suggested to ensure any duty cycle is attainable while
preventing the addition of excessive ramp. This method requires the artifical ramp slope (M
A
) to be equal to half
the inductor slope during t
OFF
:
(14)
Figure 26. "Period Doubling" due to Current Mode Instability
CONTROL LOOP COMPENSATION
The LM3424 control loop is modeled like any current mode controller. Using a first order approximation, the
uncompensated loop can be modeled as a single pole created by the output capacitor and, in the boost and
buck-boost topologies, a right half plane zero created by the inductor, where both have a dependence on the
LED string dynamic resistance. There is also a high frequency pole in the model, however it is near the switching
frequency and plays no part in the compensation design process therefore it will be neglected. Since ceramic
capacitance is recommended for use with LED drivers due to long lifetimes and high ripple current rating, the
ESR of the output capacitor can also be neglected in the loop analysis. Finally, there is a DC gain of the
uncompensated loop which is dependent on internal controller gains and the external sensing network.
A buck-boost regulator will be used as an example case. See the Design Guide section for compensation of all
topologies.
The uncompensated loop gain for a buck-boost regulator is given by the following equation:
(15)
Where the uncompensated DC loop gain of the system is described as:
(16)
And the output pole (ω
P1
) is approximated:
(17)
Copyright © 2009, Texas Instruments Incorporated Submit Documentation Feedback 19
Product Folder Links: LM3424