MIC2128 Datasheet, PDF (21/32 Pages) Microchip Technology – 75V, Synchronous Buck Controller Featuring Adaptive On-Time Control with External Soft Start

EQUATION 5-8:
t_R
=
-Q----^S---^W----^--^H----^S--^---^-----^---R----^D---^H----^--^P---^U----^L---^L---^_--^U---^P----^---⁺-----R---^H----^S---^--^G----^A---^T---^E---^--^
V_DD – V_TH
EQUATION 5-9:
t_F
=
Q-----_{S---W------H----S-----}_-----_{---R----D---H------P---U----L---L---_--D---O----W----N------}+_{-----R----H----S----G----A---T---E------}
V_TH
Where:
R_DH(PULL-UP)
= High-side gate driver pull-up
resistance
R_{DH(PULL-DOWN)} = High-side gate driver pull-down
resistance
R_HS(GATE)
V_TH
= High-side MOSFET gate resistance
= Gate threshold voltage of the
high-side MOSFET
Q_SW(HS)
= Switching gate charge of the
high-side MOSFET which can be
approximated by Equation 5-10.
EQUATION 5-10:
Where:
Q_GS(HS)
Q_GD(HS)
Q_{SWHS} = ^Q-----G----^S₂--^--^H----^S---^ + Q_{GDHS}
= High-side MOSFET gate to source
charge
= High-side MOSFET gate to drain charge
5.4.2
LOW-SIDE MOSFET POWER
LOSSES
The total power loss in the low-side MOSFET (P_LSFET)
is the sum of the power losses because of conduction
(P_{CONDUCTION(LS)}) and body diode conduction during
the dead time (P_DT) as calculated in Equation 5-11.
EQUATION 5-11:
P_LSFET = P_{CONDUCTIONLS} + P_DT
P_{CONDUCTIONLS} = I_{RMSLS}²  R_{DSON_LS}
P_DT = 2  V_F  I_LOAD  t_DT  f_SW
Where:
R_{DS(ON_LS)}
V_F
t_DT
f_SW
I_RMS(LS)
= On-resistance of the low-side MOSFET
= Low-side MOSFET body diode forward
voltage drop
= Dead time which is approximately 20 ns
= Switching Frequency
= RMS current of the low-side MOSFET
which can be calculated using
Equation 5-12
MIC2128
EQUATION 5-12:
I_{RMSLS} = I_LOAD  1 – D
I_LOAD is the load current and D is the operating duty
cycle.
5.5 Inductor Selection
Inductance value, saturation and RMS currents are
required to select the output inductor. The input and
output voltages and the inductance value determine
the peak-to-peak inductor ripple current.
The lower the inductance value, the higher the
peak-to-peak ripple current through the inductor, which
increases the core losses in the inductor. Higher
inductor ripple current also requires more output
capacitance to smooth out the ripple current. The
greater the inductance value, the lower the
peak-to-peak ripple current, which results in a larger
and more expensive inductor.
A good compromise between size, loss and cost is to
set the inductor ripple current to be equal to 30% of the
maximum output current.
The inductance value is calculated by Equation 5-13:
EQUATION 5-13:
Where:
V_IN
f_SW
I_FL
V_OUT
L = ^V-V---O-_I--_N-^U----^T_----^-f--_S--^_W--V----_^I--^N---₀--^–-_.-₃--V---_-^O---I-^U--_F-^T--_L-^-
= Input voltage
= Switching frequency
= Full load current
= Output voltage
For a selected Inductor, the peak-to-peak inductor
ripple current ripple can be calculated using
Equation 5-14.
EQUATION 5-14:
I_{L_PP} = ^V----O----^U---V-^T---_I-^-_N----^--V---f-^I-_S-^N--_W---^–--_--V---L-^O----^U----^T---^
The peak inductor current is equal to the load current
plus one half of the peak-to-peak inductor current ripple
which is shown in Equation 5-15.
EQUATION 5-15:
I_{L_PK}
=
I_LOAD
+
_-----I_{--L--_---P---P-}
2
 2016 Microchip Technology Inc.
DS20005620A-page 21