MIC2875 Datasheet, PDF (15/24 Pages) Microchip Technology – 4.8A ISW, Synchronous Boost Regulator with Bi-Directional Load Disconnect

7.0 POWER DISSIPATION
As with all power devices, the ultimate current rating of
the output is limited by the thermal properties of the
device package and the PCB on which the device is
mounted. There is a simple, Ohm’s law-type
relationship between thermal resistance, power
dissipation, and temperature which are analogous to
an electrical circuit (see Figure 7-1):
FIGURE 7-1:
Circuit.
Series Electrical Resistance
From this simple circuit we can calculate V_X if we know
I_SOURCE, V_Z, and the resistor values, R_XY and R_YZ
using Equation 7-1:
EQUATION 7-1:
V _X = I_SOURCE  R_XY + R_YZ + V _Z
Thermal circuits can be considered using this same
rule and can be drawn similarly by replacing current
sources with power dissipation (in watts), resistance
with thermal resistance (in °C/W) and voltage sources
with temperature (in °C).
FIGURE 7-2:
Circuit.
Series Thermal Resistance
Now replacing the variables in the equation for V_X, we
can find the junction temperature (T_J) from the power
dissipation, ambient temperature and the known
thermal resistance of the PCB (θ_CA) and the package
(θ_JC).
MIC2875
EQUATION 7-2:
T _J = P_DISS  _JC + _CA + T _A
As can be seen in the diagram, total thermal resistance
θ_JA = θ_JC + θ_CA. This can also be written as in
Equation 7-3:
EQUATION 7-3:
T _J = P_DISS  _JA + T _A
Given that all of the power losses (minus the inductor
losses) are effectively in the converter are dissipated
within the MIC2875 package, P_DISS can be calculated
thusly:
EQUATION 7-4: LINEAR MODE
P_DISS =
P_OUT



-1--

–
1_
– I_OUT²  DCR
EQUATION 7-5: BOOST MODE
P_DISS =
P_OUT  _{}-1-- – 1_
–


1-^{I--O--–--U---}D^{-T- }
2

DCR
EQUATION 7-6: DUTY CYCLE (BOOST)
D + -^V----^O----^U----^T----–-----^V----^I--^N--
V _OUT
In the equations above, ƞ is the efficiency taken from
the efficiency curves and DCR represents the inductor
DCR. θ_JC and θ_JA are found in the temperature
specifications section of the data sheet.
Where the real board area differs from 1” square, θ_CA
(the PCB thermal resistance), values for various PCB
copper areas can be taken from Figure 7-3.
 2015 Microchip Technology Inc.
DS20005549A-page 15