LTC3813 Datasheet, PDF (28/32 Pages) Linear Technology – 100V Current Mode Synchronous Step-Up Controller

LTC3813
APPLICATIONS INFORMATION
Checking Transient Response
The regulator loop response can be checked by looking
at the load transient response. Switching regulators take
several cycles to respond to a step in load current. When
load step occurs, V_OUT immediately shifts by an amount
equal to ΔI_LOAD (ESR), where ESR is the effective series
resistance of C_OUT. ΔI_LOAD also begins to charge or dis-
charge C_OUT generating a feedback error signal used by the
regulator to return V_OUT to its steady-state value. During
this recovery time, V_OUT can be monitored for overshoot
or ringing that would indicate a stability problem.
Design Example
As a design example, take a supply with the following speci-
fications: V_IN = 12V± 20%, V_OUT = 24V ±5%, I_OUT(MAX) =
5A, f = 250kHz. Since V_IN can vary around the 12V nominal
value, connect a resistive divider from V_IN to V_OFF to keep
the frequency independent of V_IN changes:
R1
R2
=
12V
1.55V


1=
6.74
Choose R1 = 133k and R2 = 20k. Now calculate timing
resistor R_OFF:
R_OFF
=
1+ 133k / 20k
250kHz • 76pF
=
402.6k
The duty cycle is:
D
=
1

12V
24V
=
0.5
and the maximum input current is:
I_IN(MAX)
=
5A
1
0.5
=
10A
Choose the inductor for about 40% ripple current at the
maximum V_IN:
L
=
12V
250kHz • 0.4
•
10A


1

12V
24V


=
6μH
The peak inductor current is:
I_L(PEAK)
=
5A
1
0.5
+
1
2
(4A)
=
12A
Choose the CDEP147 5.9μH inductor with I_SAT = 16.4A
at 100°C.
Next, choose the bottom MOSFET switch. Since the drain
of the MOSFET will see the full output voltage plus any
ringing, choose a 40V MOSFET to provide a margin of
safety. The Si7848DP has:
BV_DSS = 40V
R_DS(ON) = 9mΩ(max)/7.5mΩ(nom),
δ = 0.006/°C,
C_MILLER = (14nC – 6nC)/20V = 400pF,
V_GS(MILLER) = 3.5V,
θ_JA= 20°C/W.
This yields a nominal sense voltage of:
V_SNS(NOM)
=
1.7
•
0.0075
1
0.5
•
5A
=
128mV
To guarantee proper current limit at worst-case conditions,
increase nominal V_SNS by 50% to 190mV. To check if the
current limit is acceptable at V_SNS = 190mV, assume a
junction temperature of about 30°C above a 70°C ambient
(ρ_100°C = 1.4):
I_IN(MAX)

190mV
1.4 • 0.009


1
2
• 4A
= 13A
I_OUT(MAX) = I_IN(MAX) • (1-D_MAX) = 6.5A
and double-check the assumed T_J in the MOSFET:
P_TOP
=


1
1
0.5


(6.5A)²
(1.4)(0.009)
=
1.06W
T_J = 70°C + 1.06W • 20°C/W = 91°C
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