LTC3812-5_15 Datasheet, PDF (24/34 Pages) Linear Technology – 60V Current Mode Synchronous Switching Regulator Controller

LTC3812-5
APPLICATIONS INFORMATION
Mathematical software such as MATHCAD or MATLAB can
also be used to generate plots using the following transfer
function of the modulator:

H(s) = _

V_SENSE(MAX) 
1.2
•
R_DS(ON)


•


1+ s •
1+ s
R_ESR
• R_L •
• C_OUT
C_OUT


• R_L
(2)
s = j2
f
With the gain/phase plot in hand, a loop crossover fre-
quency can be chosen. Usually the curves look something
like Figure 12. Choose the crossover frequency about 25%
of the switching frequency for maximum bandwidth. Al-
though it may be tempting to go beyond f_SW/4, remember
that significant phase shift occurs at half the switching
frequency that isn’t modeled in the above H(s) equation
and PSPICE code. Note the gain (GAIN, in dB) and phase
(PHASE, in degrees) at this point. The desired feedback
amplifier gain will be –GAIN to make the loop gain at 0dB
at this frequency. Now calculate the needed phase boost,
assuming 60° as a target phase margin:
BOOST = – (PHASE + 30°)
If the required BOOST is less than 60°, a Type 2 loop can
be used successfully, saving two external components.
BOOST values greater than 60° usually require Type 3
loops for satisfactory performance.
Finally, choose a convenient resistor value for R1 (10k
is usually a good value). Now calculate the remaining
values:
GAIN
0
0
(K is a constant used in the calculations)
f = chosen crossover frequency
G = 10^(GAIN/20) (this converts GAIN in dB to G in
absolute gain)
TYPE 2 Loop:
K
=
tan^
BOOST
2
+
45°^
C2 =
1
2 • f • G • K • R1
( ) ^{C1= C2 K2
1}
R2
=
2
K
•f
•
C1
R_B
=
V_REF (R1)
V_OUT
V_REF
TYPE 3 Loop:
K
=
tan²


BOOST
4
+
45°^
C2 =
1
2 • f • G • R1
C1= C2(K
1)
R2
=
2
•
K
f•
C1
R3 = ^R1
K
1
C3 =
1
2f K • R3
R_B
=
V_REF (R1)
V_OUT
V_REF
PHASE
–90
FREQUENCY (Hz)
–180
38125 F12
Figure 12. Transfer Function of Buck Modulator
24
SPICE or mathematical software can be used to generate
the gain/phase plots for the compensated power supply to
do a sanity check on the component values before trying
them out on the actual hardware. For software, use the
following transfer function:
T(s) = A(s)H(s)
38125fc