MAX15003 Datasheet, PDF (23/32 Pages) Maxim Integrated Products – Triple-Output Buck Controller with Tracking/Sequencing

Triple-Output Buck Controller with
Tracking/Sequencing
Type II: Compensation When f_CO > f_{ZERO, ESR}
V_OUT
R₁
-
g_M
R₂
V_REF +
R_F
C_F
COMP
C_CF
Figure 6a. Type II Compensation Network
GAIN
(dB)
1ST ASYMPTOTE
G_MODV_REFV_OUT-1(ωC_F)^-1
2ND ASYMPTOTE
G_MODV_REFV_OUT-1R_F
3RD ASYMPTOTE
G_MODV_REFV_OUT-1(ωC_CF)^-1
1ST POLE 1ST ZERO
(AT ORIGIN) (R_FC_F)^-1
2ND POLE ^ω(rad/s)
(R_FC_CF)^-1
Figure 6b. Type II Compensation Network Response
When the f_ZERO,ESR is lower than f_CO and close to f_LC,
a Type II compensation network provides the neces-
sary closed-loop response. The Type II compensation
network provides a mid-band compensating zero and
high-frequency pole (see Figures 6a and 6b).
R_FC_F provides the mid-band zero f_MID,ZERO, and
R_FC_CF provides the high-frequency pole. Use the fol-
lowing procedure to calculate the compensation net-
work components.
1) Calculate the f_ZERO,ESR and LC double pole, f_LC:
f_ZERO,ESR
=
1
2π ×ESR× COUT
f_LC
=
2π×
1
L × COUT
2) Calculate the unity-gain crossover frequency as:
f_CO
≤
fSW
10
3) Determine R_F from the following:
R_F
=
VRAMP(2π×fCO ×L)VOUT
VFB ×VIN ×gm ×ESR
Note: R_F is derived by setting the total loop gain at
crossover frequency to unity, e.g., G_EA(f_CO) x G_M(f_CO)
= 1V/V. The transconductance error amplifier gain is
G_EA(f_CO) = g_M x R_F while the modulator gain is:
( ) ^G_MOD ^f_CO
=
VIN
VRAMP
×
ESR
2π×fCO ×L
×
VFB
VOUT
The total loop gain can be expressed logarithmically as
follows:
20log10_[gmRF _] +
20log10
⎡
⎢
⎣⎢
(2π
×
ESR×VIN ×VFB
fCO ×L)×VOUT ×VRAMP
⎤
⎥
⎦⎥
=
0dB
where V_RAMP is the peak-to-peak ramp amplitude
equal to 2V.
4) Place a zero at or below the LC double pole, f_LC:
C_F
=
1
2π×RF ×fLC
5) Place a high-frequency pole at or below f_P = 0.5 x
f_SW:
C_CF
=
1
π×RF ×fSW
6) Choose an appropriately sized R1 (connected from
OUT_ to FB_, start with a 10kΩ). Once R1 is select-
ed, calculate R2 using the following equation:
R₂
=
R1 ×
VFB
VOUT −VFB
where V_FB = 0.6V.
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