FAN5059MX Datasheet, PDF (16/18 Pages) Fairchild Semiconductor – High Performance Programmable Synchronous DC-DC Controller for Multi-Voltage Platforms

FAN5059
PRODUCT SPECIFICATION
Appendix
Worst-Case Formulae for the Calculation of
Cin, Cout , R5, R7 and Roffset (Circuits similar to
Figure 1 only)
The following formulae design the FAN5059 for worst-case
operation, including initial tolerance and temperature dependence
of all of the IC parameters (initial setpoint, reference tolerance
and tempco, internal droop impedance, current sensor gain),
the initial tolerance and temperature dependence of the MOSFET,
and the ESR of the capacitors. The following information
must be provided:
V_S+, the value of the positive static voltage limit;
|V_S-|, the absolute value of the negative static voltage limit;
V_T+, the value of the positive transient voltage limit;
|V_T-|, the absolute value of the negative transient voltage limit;
I_O, the maximum output current;
V_nom, the nominal output voltage;
V_in, the input voltage (typically 5V);
I_rms, the ripple current rating of the input capacitors, per cap
(2A for the Sanyo parts shown in this datasheet);
R_D, the resistance of the current sensor (usually the MOSFET);
∆R_D, the tolerance of the current sensor (usually about 67%
for MOSFET sensing, including temperature); and
ESR, the ESR of the output capacitors, per cap (44mΩ for
the Sanyo parts shown in this datasheet).
IO *
C_in =
2
V_nom
V_nom
–
V_in
V_in
I_rms
R_offset = ^{VS+ – .024 * Vnom}
1.01 * V_nom
* 1KΩ
R7 = ^{IO* RD * (1 + ∆RD)}
45 * 10^-6
The value of R7 must be ≤ 8.3KΩ. If a greater value is calcu-
lated, R_D must be reduced.
Number of capacitors needed for C_out = the greater of:
ESR * I_O
X=
V_T- + V_S+ – .024 * V_nom
or
Y=
V_T+ – V_S+ +
ESR * I_O
14400 * I_O * R_D
18 * R5 * 1.1
Example: Suppose that the static limits are +89mV/-79mV,
transient limits are ±134mV, current I is 14.2A, and the
nominal voltage is 2.000V, using MOSFET current sensing.
We have V_S+ = 0.089, |V_S-| = 0.079, V_T+ = |V_T-| = 0.134, I_O
= 14.2, V_nom = 2.000, and ∆R_D = 1.67. We calculate:
Since Y > X, we choose Y, and round up to find we need 7
capacitors for C_OUT.
A detailed explanation of this calculation may be found in
Applications Bulletin AB-24.
14.2 *
C_in =
2
2.000 2.000
–
5
5
= 3.47 ⇒ 4 caps
2
R_offset = ^{0.089 – .024 * 2.000 *1000} = ^20.3Ω
1.01 * 2.000
R7 = ^{14.2 * 0.010 * (1 + 0.67)} = ^5.25KΩ
45 * 10^-6
R5 = ^{14400 * 14.2 * 0.020 * (1 + 0.67) * 1.1} = ^3.48KΩ
18 * (0.089 + 0.079 – .024 * 2.000)
0.044 * 14.2
X=
= 3.57
0.134 + 0.089 – .024 * 2.00
14400 * I_O* R_D * (1 + ∆R_D) *1.1
R5 =
18 * (V_S+ + V_S- – .024 * V_nom)
0.044 * 14.2
Y=
14400 * 14.2 * 0.020
0.134 – 0.089 +
18 * 3640 * 1.1
= 6.14
16
REV. 1.0.4 8/14/03