Bridging Theory in Practice
Transferring Technical Knowledge
to Practical Applications
Advanced Power Dissipation
and AC Thermal Analysis
Advanced Power Dissipation
and AC Thermal Analysis
Intended Audience:
• Engineers interested in advanced thermal design under AC
(variable duty cycle and transient) conditions
• A basic knowledge of DC thermal analysis is required
Topics Covered:
•
•
•
•
•
Modeling thermal performance with electrical parameters
Explanation of thermal RC networks
Introduction of the Zth Diagram
AC thermal calculations
Complex waveform (superposition principle) thermal calculations
Expected Time:
• Approximately 60 minutes
Advanced Power Dissipation
and AC Thermal Analysis
•
•
•
•
•
Electrical Parameters vs. Thermal Parameters
Thermal Resistance and Capacitance Networks
Understanding the Zth Diagram
Example AC Thermal Calculations
Complex Waveforms and Superposition
Electrical vs. Thermal
DC Parameters
Electrical Parameters
+
Thermal Parameters
+
V
T
R
I
-
Rth
-
PD
V=IR
T = PD Rth
R = Electrical Resistance ()
Rth = Thermal Resistance (C/W)
V = Potential Difference (V)
T = Temperature Difference (C)
I = Current (A)
PD = Power Dissipated (W)
Electrical Resistance
vs. Thermal Resistance
Electrical Resistance
I
+
A
}d
V
-

R
I = Current
A = Area
d = Thickness
 = Electrical Conductivity
R = Electrical Resistance ()
R 
d
A
Thermal Resistance
+
PD
A
}d
T
-
th
Rth
PD = Power Dissipated
A = Area
d = Thickness
th = Thermal Conductivity
Rth = Thermal Resistance (C/W)
R th 
d
A  th
Electrical Circuits vs. Thermal
Circuits
Electrical Circuits
+
V
Thermal Circuits
+
T
R
I
-
Rth
-
PD
I = 10A
R = 1
PD = 10W
Rth = 1C/W
V = IR
T = PDRth
V = (10A)(1) = 10V
10V Potential Difference
T = (10W)(1C/W) = 10C
10C Temperature Difference
Electrical vs.
Thermal Parameters
Electrical Parameters
Thermal Parameters
+
V
-
+
T
-
Q
C 
C
Q

V
i( t )  C
It
V
dV
dt
C = Capacitance
(Farads = A-sec / V)
E
C th 
Cth
E
T

PD ( t )  C th
PD t
T
dT
dt
Cth = Thermal Capacitance
(Joules / C = Watts-sec / C)
Advanced Power Dissipation
and AC Thermal Analysis
•
•
•
•
•
Electrical Parameters vs. Thermal Parameters
Thermal Resistance and Capacitance Networks
Understanding the Zth Diagram
Example AC Thermal Calculations
Complex Waveforms and Superposition
Thermal Resistance
& Capacitance
p+ Well
Example
Silicon Wafer
Cross Section
Cth1 - Rth1
Silicon
Cth2 – Rth2
Die Attach
Cth3 – Rth3
Metal
Leadframe
Leadframe
Thermal RC Network - Internal
Tjunction
Rth1
Rth2
Rth3
PD
Chip
T
Tambient
Cth1
Cth2
Cth3
Temperature ~ Voltage
Power ~ Current
Thermal RC Network – Total
Rth1
Tjunction
Rth2
Rth3
Tcase Rinteface
Rheatsink
PD
Chip
T
Cth1
Cth2
Cth3
Cinterface
Cheatsink
Heatsink
Tambient
Temperature ~ Voltage
Power ~ Current
Junction
Temperature Calculations
Rth1
Tjunction
Rth2
Rth3
Tcase
PD
Chip
T
Cth1
Cth2
Cth3
Heatsink
Tambient
With temperature analogous to voltage, T
Is determined by the PD and the RC network
Junction
Temperature Calculations
Rth1
Tjunction
Rth2
Rth3
Tcase
PD
Chip
T
Cth1
Cth2
Cth3
Heatsink
Tambient
The maximum junction temperature
is specified in the absolute maximum
section of the data sheet (Tj,max)
Junction
Temperature Calculations
Tjc
Rth1
Tjunction
Rth2
Rth3
Tcase
PD
Chip
T
Cth1
Cth2
Cth3
Heatsink
Tambient
The device junction-to-case thermal resistance (Rthjc) is
specified in the datasheet and determines Tjc.
Rthjc is usually valid for DC only
Junction
Temperature Calculations
Rth1
Tjunction
Rth2
Rth3
Tca
Tcase
PD
Chip
T
Cth1
Cth2
Cth3
Heatsink
Tambient
The external case-to-ambient thermal resistance,
(Rthca) is determined by the heatsink. This determines
the temperature change from the case to the ambient.
DC Junction
Temperature Calculations
Tjunction
Rth1
Rth2
Rth3
Tcase
PD
Chip
T
Heatsink
Tambient
Under DC conditions, power and temperature
reach steady state conditions and the thermal
capacitors are removed from the circuit model
DC Junction
Temperature Calculation
• Power Dissipation
PD = Ids2Rdson = (5A)2(24m) = 0.6W
• Thermal Resistance
Rthja = 55 C/W
• Junction Temperature
Tjunction = Tambient + PDRthja
Tjunction = 85C + (0.6W)(55C/W)
Tjunction = 85C + 33C = 118C
DC Calculations
are relatively
simple
AC Junction Temperature Calculation
of Transfer Function
Rth1
Tjunction
Rth2
Rth3
Tcase
PD
Chip
T
Tambient
Cth1
Cth2
Cth3
Zth(j) = ?
Zth(t) = ?
Heatsink
AC Junction Temperature Calculation
of Transfer Function
Z th ( j  ) 
1
1
j  C th 1 
R th 1 
1
1
j  C th 2 
R th 2 
1
1
j  C th 3 
R th 3 
1
j  C th 4  ... 
1
R th , n
Simplified AC
Thermal RC Network
Tjunction
R’th1
R’th2
R’th3 T
case
C’th1
C’th2
C’th3
PD
Chip
T
Heatsink
Tambient
Thermal capacitance now in
parallel with thermal resistance
Simplified AC
Thermal RC Network
Tjunction
R’th1
R’th2
R’th3 T
case
C’th1
C’th2
C’th3
PD
Chip
T
Heatsink
Tambient
The new RC component values of the simplified network are obtained
by mathematical transformations. They do NOT refer to any
physical layer. Together, they describe the overall thermal
behavior
and performance of the device and heatsink.
Simplified AC
Thermal RC Network
Tjunction
R’th1
R’th2
R’th3 T
case
C’th1
C’th2
C’th3
PD
Chip
T
Frequency Z ( j  ) 
th , i
Domain
1
1 Heatsink
 j  C th ,i
R th ,i
Tambient
Time
Domain


t
Z th ,i ( t )  R th ,i 1  exp  
 R C
th , i th ,i






AC Temperature Calculation Simplified
Transfer Function
T(t) = PD(t) Zth(t)
Z th ( t ) 
P(t)
n
 R th , i
i 1


t
1  exp  
 R th ,i C th ,i

Zth




Tj(t)
Advanced Power Dissipation
and AC Thermal Analysis
•
•
•
•
•
Electrical Parameters vs. Thermal Parameters
Thermal Resistance and Capacitance Networks
Understanding the Zth Diagram
Example AC Thermal Calculations
Complex Waveforms and Superposition
Development of the
Zth Diagram
• Create test set-up for integrated circuit package
types
• Power is generated in the integrated circuit for
defined lengths of time
• The resulting temperature rise is measured
• A thermal impedance (Zth) diagram is generated
P(t)
Zth
Tj(t)
Zth Diagram for the TO-263
Package
100
100.0
ZthJA [K/W]
Zthja (C / W)
10.0
10
1.01
Duty Cycle
D=
50%
0.5
20%
0.2
10%
0.1
5%
0.05
2%
0.02
1%
0.01
Single
0
0.10,1
Pulse
0.01
0,01
1E-5
1E-5
1E-4
1E-3
1E-3
1E-2
1E-1
1E-1
1E0
1E+1
1E1
1E2
tpulse (sec)
1E+3
1E3
Zth Diagram for the TO-263
Package
100
100.0
Single Pulse
PD
tpulse
ZthJA [K/W]
Zthja (C / W)
10.0
10
P(t)
1.01
Duty Cycle
D=
50%
0.5
20%
0.2
10%
0.1
5%
0.05
2%
0.02
1%
0.01
Single
0
0.10,1
Pulse
0.01
0,01
1E-5
1E-5
1E-4
1E-3
1E-3
1E-2
1E-1
1E-1
1E0
1E+1
1E1
1E2
tpulse (sec)
1E+3
1E3
Zth Diagram for the TO-263
Package
100
100.0
Periodic event:
PD
tpulse
T
ZthJA [K/W]
Zthja (C / W)
10.0
10
P(t)
1.01
Duty Cycle:
Duty Cycle
D=
0.5
50%
0.2
20%
0.1
10%
0.05
5%
0.02
2%
0.01
1%
Single
0
0.10,1
D 
t pulse
T
D  50 %
Pulse
0.01
0,01
1E-5
1E-5
1E-4
1E-3
1E-3
1E-2
1E-1
1E-1
1E0
1E+1
1E1
1E2
tpulse (sec)
1E+3
1E3
Zth Diagrams for Different
Packages
TO-263-5-1
tp = 1s
Zthja  2C/W
TO-252-3-1
tp = 1s
Zthja  4C/W
SOT-223
tp = 1s
Zthja  30C/W
SO-8
tp = 1s
Zthja  65C/W
Advanced Power Dissipation
and AC Thermal Analysis
•
•
•
•
•
Electrical Parameters vs. Thermal Parameters
Thermal Resistance and Capacitance Networks
Understanding the Zth Diagram
Example AC Thermal Calculations
Complex Waveforms and Superposition
Single Pulse in a
TO-263 Package
PD
400W
tpulse
tpulse = 200µs
Tiunction(t)
Tpeak
Tpeak = ?
25C
Single Pulse in a
TO-263 Package
100
100.0
tpulse = 2E-4 s
Zthja  0.083 C/W
ZthJA [K/W]
Zthja (C / W)
10.010
1.0 1
Duty Cycle
D=
50%
0.5
20%
0.2
10%
0.1
5%
0.05
2%
0.02
1%
0.01
Single
Single
0
0.10,1
Pulse
Pulse
0.01
0,01
1E-5
1E-5
1E-4
1E-3
1E-3
1E-2
1E-1
1E-1
1E0
1E+1
1E1
1E2
tpulse (sec)
1E+3
1E3
Single Pulse in a
TO-263 Package
• Power Dissipation
PD = 400W
• Thermal Resistance
Zthja = 0.083 C/W
• Junction Temperature
Tjunction,peak = Tambient + PDZthja
Tjunction,peak = 25C + (400W)(0.083C/W)
Tjunction,peak = 25C + 33C = 58C
Single Pulse – TO-263
Package Saber Simulation
55C
400W
350W
50C
Tjunction,peak = 55C
45C
300W
250W
200W
40C
150W
35C
100W
30C
50W
PD,max = 400W
25C
0
100 200 300 400 500 600 700
0W
Time (s)
50% Duty Cycle in a
TO-263 Package
PD
tpulse = 200µs
1.44W
tperiod = 400µs
Tiunction(t)
Tpeak
Tpeak = ?
25C
50% Duty Cycle in a
TO-263 Package
100
100.0
tpulse = 2E-4 s
Zthja  23 C/W
ZthJA [K/W]
Zthja (C / W)
10.010
1.0 1
Duty Cycle
D=
50%
0.5
20%
0.2
10%
0.1
5%
0.05
2%
0.02
1%
0.01
Single
0
0.10,1
Pulse
0.01
0,01
1E-5
1E-5
1E-4
1E-3
1E-3
1E-2
1E-1
1E-1
1E0
1E+1
1E1
1E2
tpulse (sec)
1E+3
1E3
50% Duty Cycle in a
TO-263 Package
• Power Dissipation
PD = 1.44W
• Thermal Resistance
Zthja = 23 C/W
• Junction Temperature
Tjunction = Tambient + PDZthja
Tjunction = 25C + (1.44W)(23C/W)
Tjunction = 25C + 33C = 58C
Advanced Power Dissipation
and AC Thermal Analysis
•
•
•
•
•
Electrical Parameters vs. Thermal Parameters
Thermal Resistance and Capacitance Networks
Understanding the Zth Diagram
Example AC Thermal Calculations
Complex Waveforms and Superposition
Complex Pulse-Superposition
MOSFET Turn On
1. VIN goes HI
1. VIN
2. IDS increases
4. PLOSS
3. VDS decreases
2. IDS
4. PLOSS spikes
3. VDS
IDS
Complex Pulse-Superposition
MOSFET Turn On
Pulse 1:
tSTART 20µS
tSTOP 50µS
1. VIN
4. PLOSS
2. IDS
3. VDS
IDS
Pulse 2:
tSTART 25µS
tSTOP 50µS
Pulse 3(neg):
tSTART 40µS
tSTOP 50µS
Pulse 4(neg):
tSTART 45µS
tSTOP 50µS
Complex Pulse-Superposition
MOSFET Turn On
t=5µs
At t = 5µs:
Power
tPULSE,1 = 5µsec
tPULSE,2 = tPULSE,3 = tPULSE,4 = 0
Time
TJ1(5µs)
= ZTH(5µs)*PPULSE,1
Complex Pulse-Superposition
MOSFET Turn On
t=20µs
At t = 20µs:
Power
tPULSE,1 = 20µsec
tPULSE,2 = 15µsec
tPULSE,3 = tPULSE,4 = 0
Time
TJ2(20µs) = ZTH(20µs)*PPULSE,1
+ ZTH(15µs)*PPULSE,2
Complex Pulse-Superpositon
MOSFET Turn On
t=25µs
At t = 25µs:
Power
tPULSE,1 = 25µsec
tPULSE,2 = 20µsec
tPULSE,3 = 5µsec
tPULSE,4 = 0
Time
TJ3(25µs) = ZTH(25µs)*PPULSE,1
+ ZTH(20µs)*PPULSE,2
- ZTH(5µs)*PPULSE,3
Complex Pulse-Superpositon
MOSFET Turn On
t=30µs
At t = 30µs:
Power
tPULSE,1 = 30µsec
tPULSE,2 = 25µsec
tPULSE,3 = 10µsec
tPULSE,4 = 5µsec
Time
TJ4(30µs) = ZTH(30µs)*PPULSE,1
+ ZTH(25µs)*PPULSE,2
- ZTH(10µs)*PPULSE,3
- ZTH(5µs)*PPULSE,4
Complex Pulse-Superpositon
MOSFET Turn On
TJ1
Pulse 1:
tSTART 20µS
tSTOP 50µS
TJ2
TJ3
4. PLOSS
TJ4
IDS
Pulse 2:
tSTART 25µS
tSTOP 50µS
Pulse 3(neg):
tSTART 40µS
tSTOP 50µS
Pulse 4(neg):
tSTART 45µS
tSTOP 50µS
Advanced Power Dissipation
and AC Thermal Analysis
•
•
•
•
•
Electrical Parameters vs. Thermal Parameters
Thermal Resistance and Capacitance Networks
Understanding the Zth Diagram
Example AC Thermal Calculations
Complex Waveforms and Superposition
Advanced Power Dissipation
and AC Thermal Analysis
Thank you!
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