11
Thermal Resistance Measurement
The diagram of ACFL-5211T for measurement is shown in Figure 17. This is a multi-chip package with four heat sources,
the eect of heating of one die due to the adjacent dice are considered by applying the theory of linear superposition.
Here, one die is heated rst and the temperatures of all the dice are recorded after thermal equilibrium is reached. Then,
the 2nd die is heated and all the dice temperatures are recorded and so on until the 4th die is heated. With the known
ambient temperature, the die junction temperature and power dissipation, the thermal resistance can be calculated.
The thermal resistance calculation can be cast in matrix form. This yields a 4 by 4 matrix for our case of two heat sources.
Figure 17. Diagram of ACFL-5211T for measurement
R
11
: Thermal Resistance of Die1 due to heating of Die1 (˚C/W)
R
12
: Thermal Resistance of Die1 due to heating of Die2 (˚C/W)
R
13
: Thermal Resistance of Die1 due to heating of Die3 (˚C/W)
R
14
: Thermal Resistance of Die1 due to heating of Die4 (˚C/W)
R
21
: Thermal Resistance of Die2 due to heating of Die1 (˚C/W)
R
22
: Thermal Resistance of Die2 due to heating of Die2 (˚C/W)
R
23
: Thermal Resistance of Die2 due to heating of Die3 (˚C/W)
R
24
: Thermal Resistance of Die2 due to heating of Die4 (˚C/W)
R
31
: Thermal Resistance of Die3 due to heating of Die1 (˚C/W)
R
32
: Thermal Resistance of Die3 due to heating of Die2 (˚C/W)
R
33
: Thermal Resistance of Die3 due to heating of Die3 (˚C/W)
R
34
: Thermal Resistance of Die3 due to heating of Die4 (˚C/W)
R
41
: Thermal Resistance of Die4 due to heating of Die1 (˚C/W)
R
42
: Thermal Resistance of Die4 due to heating of Die2 (˚C/W)
R
43
: Thermal Resistance of Die4 due to heating of Die3 (˚C/W)
R
44
: Thermal Resistance of Die4 due to heating of Die4 (˚C/W)
P
1
: Power dissipation of Die1 (W)
P
2
: Power dissipation of Die2 (W)
P
3
: Power dissipation of Die3 (W)
P
4
: Power dissipation of Die4 (W)
T
1
: Junction temperature of Die1 due to heat from all dice (°C)
T
2
: Junction temperature of Die2 due to heat from all dice (°C)
T
3
: Junction temperature of Die3 due to heat from all dice (°C)
T
4
: Junction temperature of Die4 due to heat from all dice (°C)
Ta: Ambient temperature.
∆T
1
: Temperature dierence between Die1 junction and ambient (°C)
∆T
2
: Temperature deference between Die2 junction and ambient (°C)
∆T
3
: Temperature dierence between Die3 junction and ambient (°C)
∆T
4
: Temperature deference between Die4 junction and ambient (°C)
T
1
= (R
11
x P
1
+ R
12
x P
2
+ R
13
x P
3
+ R
14
x P
4
) + Ta -- (1)
T
2
= (R
21
x P
1
+ R
22
x P
2
+ R
23
x P
3
+ R
24
x P
4
) + Ta -- (2)
T
3
= (R
31
x P
1
+ R
32
x P
2
+ R
33
x P
3
+ R
34
x P
4
) + Ta -- (3)
T
4
= (R
41
x P
1
+ R
42
x P
2
+ R
43
x P
3
+ R
44
x P
4
) + Ta -- (4)
Measurement data on a low K (conductivity) board:
R
11
= 181 °C/W
R
21
= 103 °C/W
R
31
= 82 °C/W
R
41
= 110 °C/W
R
12
= 91 °C/W
R
22
= 232 °C/W
R
32
= 97 °C/W
R
42
= 86 °C/W
R
13
= 85 °C/W
R
23
= 109 °C/W
R
33
= 180 °C/W
R
43
= 101 °C/W
R
14
= 112 °C/W
R
24
= 91 °C/W
R
34
= 91 °C/W
R
44
= 277 °C/W
Measurement data on a high K (conductivity) board:
R
11
= 117 °C/W
R
21
= 37 °C/W
R
31
= 35 °C/W
R
41
= 47 °C/W
R
12
= 42 °C/W
R
22
= 161 °C/W
R
32
= 53°C/W
R
42
= 30 °C/W
R
13
= 32 °C/W
R
23
= 39 °C/W
R
33
= 114 °C/W
R
43
= 29 °C/W
R
14
= 60 °C/W
R
24
= 33 °C/W
R
34
= 34 °C/W
R
44
= 189 °C/W
1
2
3
4
5
6
12
11
10
9
8
7
Die 1:
IC1
Die 4:
LED2
Die 2:
LED1
Die 3:
IC2
R11 R12 R13 R14
•
P1
=
∆T1
R21 R22 R23 R24 P2 ∆T2
R31 R32 R33 R34 P3 ∆T3
R41 R42 R43 R44 P4 ∆T4
