LTC3883 Datasheet, PDF (60/112 Pages) Linear Technology – Single Phase Step-Down DC/DC Controller with Digital Power System Management

LTC3883/LTC3883-1
Applications Information
Accurate DCR Temperature Compensation
Using the DC resistance of the inductor as a current shunt
element has several advantages—no additional power
loss, lower circuit complexity and cost. However, the
strong temperature dependence of the inductor resistance
and the difficulty in measuring the exact inductor core
temperature introduce errors in the current measurement.
For copper, a change of inductor temperature of only 1°C
corresponds to approximately 0.39% current gain change.
Figure 30 shows a DC/DC converter sample layout (right)
and its corresponding thermal image (left). The converter
is providing 1.8V, 1.5A to the output load.
Heat dissipation in the inductor under high load condi-
tions creates transient and steady state thermal gradients
between the inductor and the temperature sensor, and the
sensed temperature does not accurately represent the
inductor core temperature. This temperature gradient is
clearly visible in the thermal image of Figure 30. In addition,
transient heating/cooling effects have to be accounted for
in order to reduce the transient errors introduced when
load current changes are faster than heat transfer time
constants of the inductor. Both of these problems are
addressed by introducing two additional parameters: the
thermal resistance θ_IS from the inductor core to the on-
board temperature sensor, and the inductor thermal time
constant τ. The thermal resistance θ_IS [°C/W], is used to
calculate the steady-state difference between the sensed
temperature T_S and the internal inductor temperature T_I
for a given power dissipated in the inductor P_I:
T_I – T_S = θ_IS P_I = θ_IS V_DCR I_OUT
The additional temperature rise is used for a more accurate
estimate of the inductor DC resistance R_I:
R_I = R0 (1 + a [T_S – T_REF + θ_IS V_DCR I_OUT])
In the equations above, V_DCR is the inductor DC voltage
drop, I_OUT is the RMS value of the output current, R0 is
the inductor DC resistance at the reference temperature
T_REF and α is the temperature coefficient of the resistance.
Since most inductors are made of copper, we can expect
a temperature coefficient close to α_CU = 3900ppm/°C.
For a given α, the remaining parameters θ_IS and R0 can
be calibrated at a single temperature using only two load
currents:
( ) ^RO
=
α
(
T2
–
(R2 – R1)(P2 + P1) – (R2 + R1)(P2 – P1)
T1)(P2+P1)–(P2–P1) 2+ α_[T1+ T2–
2T_REF
]
(( )) ^θIS
=
1
αRO
•
α(R1+R2)(T2– T1)
α(T2– T1)(P2+P1)
–
–
(R2 – R1)
(P2 – P1)
2+ α_[T1+ T2 – 2T_{REF ]}
2+ α_[T1+ T2 – 2T_{REF ]}
The inductor resistance, R_K = V_DCR(K)/I_OUT(K), power dis-
sipation P_K = V_DCR(K) I_OUT(K) and the sensed temperature
T_K, (K = 1, 2) are recorded for each load current. To increase
DC/DC
CONVERTER
INDUCTOR
TEMPERATURE
SENSOR
3883 F30
Figure 30. Thermal Image and Layout Photo
3883f
60