ISL6377 Datasheet, PDF (30/36 Pages) Intersil Corporation – Multiphase PWM Regulator for AMD Fusion™ Desktop CPUs Using SVI 2.0

ISL6377
I_droop of 56.25µA. At full load current, I_omax, the I_sum current is
36µA and the resulting I_droop is 45µA. The ratio of I_sum at OCP
relative to full load current is 1.25. Therefore, the OCP current
trip level is 25% higher than the full load current.
For inductor DCR sensing, Equation 31 gives the DC relationship
of V_cn(s) and I_o(s):
⎛
⎞
V_Cn
=
⎜
⎜
⎜
⎝
-----------^R-----ⁿ---^t--^c---ⁿ----^e---^t-----------
R_nt
cn
e
t
+
-^R----^s---^u---^m---
N
×
D_-----CN_-----R_{---⎟⎟⎟}
⎠
× I_o
(EQ. 31)
Substitution of Equation 31 into Equation 2 gives Equation 32:
I_droop
=
5_--
4
×
--¹---
R_i
×
-----------^R-----ⁿ---^t--^c---ⁿ----^e---^t-----------
R_ntc
n
et
+
-^R----^s---^u---^m---
N
×
D_-----C_-----R_---
N
×
I_o
(EQ. 32)
Therefore:
R_i
=
5_--
4
×
---------------^R-----ⁿ---^t--^c---ⁿ----^e---^t---^×-----^D----^C-----^R------^×-----^I--^o----------------
N × _⎝⎛R_ntcnet + -^R----^s-_N--^u---^m---_⎠⎞ × I_droop
(EQ. 33)
Substitution of Equation 23 and application of the OCP condition
in Equation 33 gives Equation 34:
R_i
=
5_--
4
×
----------------^(-----RR---------^n-n------^tt----^cc------^ss--------++----------^RR--------ⁿⁿ--------^tt---^cc-------)--+----^×-----^R-----R----^p----^p-------^×-----^D-----^C----^R------^×-----^I--^o---^m-----^a---^x----------------
N
×
⎛
⎜
⎝
(_---R_{----n----t--c---s----+-----}R_{----n----t-c----})_---×_-----R_----p--
R_ntcs + R_ntc + R_p
+
-^R----^s-_N--^u---^m---_{⎠⎟⎞}
×
I_droopmax
(EQ. 34)
where I_omax is the full load current and I_droopmax is the
corresponding droop current. For example, given N = 4,
R_sum = 3.65kΩ, R_p = 11kΩ, R_ntcs = 2.61kΩ, R_ntc = 10kΩ,
DCR = 0.88mΩ, I_omax = 100A and I_droopmax = 45μA.
Equation 34 gives R_i = 529Ω.
For resistor sensing, Equation 35 gives the DC relationship of
V_cn(s) and I_o(s).
V_Cn
=
-^R----^s---^e---ⁿ--
N
×
I_o
(EQ. 35)
Substitution of Equation 35 into Equation 2 gives Equation 36:
I_droop
=
5_--
4
×
--¹---
R_i
×
R_{-----s---e---n--}
N
×
I_o
(EQ. 36)
Therefore:
R_i
=
5_--
4
×
N^--R----×^s---e--I^--nd---_r^-×--_o^---_o^I--o-_p^-
(EQ. 37)
Substitution of Equation 37 and application of the OCP condition
in Equation 33 gives Equation 38:
R_i
=
5_--
4
×
--^R----^s---^e----ⁿ----^×-----^I--^o---^m-----^a---^x---
N × I_droopmax
(EQ. 38)
where I_omax is the full load current and I_droopmax is the
corresponding droop current. For example, given N = 4,
R_sen = 1mΩ, I_omax = 100A and I_droopmax = 45µA, Equation 38
gives R_i = 694Ω.
Load Line Slope
See Figure 13 for load-line implementation.
For inductor DCR sensing, substitution of Equation 32 into
Equation 3 gives the load-line slope expression:
LL
=
V_{-----d---r--o----o---p-}
I_o
=
5_{-- × -}^R_----d_---r_---o_---o_---p_{- × -----------}^R_-----n_---t_--c_---n_----e_---t_{----------- ×} D_-----C_-----R_---
4
R_i
R_ntc
n
et
+
-^R----^s---^u---^m---
N
N
(EQ. 39)
For resistor sensing, substitution of Equation 36 into Equation 3
gives the load line slope expression:
LL
=
V_{-----d---r--o----o---p-}
I_o
=
5_--
4
×
-^R----^s---^e---ⁿ-----^×-----^R----^d----^r--^o---^o---^p--
N × R_i
(EQ. 40)
Substitution of Equation 33 and rewriting Equation 39, or
substitution of Equation 37 and rewriting Equation 40, gives the
same result as in Equation 41:
R_droop
=
-------^I--^o------- × LL
I_droop
(EQ. 41)
One can use the full-load condition to calculate R_droop. For
example, given I_omax = 100A, I_droopmax = 45µA and
LL = 2.1mΩ, Equation 41 gives R_droop = 4.67kΩ.
It is recommended to start with the R_droop value calculated by
Equation 41 and fine-tune it on the actual board to get accurate
load-line slope. One should record the output voltage readings at
no load and at full load for load-line slope calculation. Reading
the output voltage at lighter load instead of full load will increase
the measurement error.
Compensator
Figure 21 shows the desired load transient response waveforms.
Figure 27 shows the equivalent circuit of a voltage regulator (VR)
with the droop function. A VR is equivalent to a voltage source
(= VID) and output impedance Z_out(s). If Z_out(s) is equal to the
load-line slope LL, i.e., a constant output impedance, then in the
entire frequency range, V_o will have a square response when I_o
has a square change.
Z_out(s) = LL
i_o
VID
VR
LOAD V_o
FIGURE 27. VOLTAGE REGULATOR EQUIVALENT CIRCUIT
Intersil provides a Microsoft Excel-based spreadsheet to help
design the compensator and the current sensing network so that
VR achieves constant output impedance as a stable system.
A VR with active droop function is a dual-loop system consisting of
a voltage loop and a droop loop, which is a current loop. However,
neither loop alone is sufficient to describe the entire system. The
spreadsheet shows two loop gain transfer functions, T1(s) and
30
FN8336.0
August 6, 2012