Transcript Slajd 1 - Akademia Morska w Gdyni

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The method of a fast
electrothermal transient analysis
of a buck converter
Krzysztof Górecki and Janusz Zarębski
Department of Marine Electronics
Gdynia Maritime University, POLAND
S
Outline
 Introduction
 The conception of the method
 The FAST algorithm
 The analytical dependences
 Verification of the method
 Conclusions
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Introduction
 Dc-dc converters belong to the class of „stiff
circuits”
 The time of analysis is unacceptable long
 In literature some methods of shortening
calculations time are proposed
 These methods needs to use the very
simplified models of semiconductor devices:
 piecewise-linear dc characteristics
 Inertialess
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Introduction (cont.)
 In semiconductor devices selfheating phenomenon is


strongly observed
Selfheating – results from changing the electrical
energy into the heat at non-ideal cooling conditions
Due to selfheating
 Internal temperatures of semiconductor devices increase
 Characteristics and parameters values of dc-dc converters
change
 Electrothermal analysis – analysis with selfheating

taken into account
The classical methods of electrothermal analysis
cannot be used for analysis of dc-dc converters (the
time of analysis is unacceptable long)
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In the paper
 A new method of a fast electrothermal analysis of dc
dc converters is proposed
The verification of correctness of this method was
performed for buck converter
T1
L
RG
Vin
D1
C
R0
Vctr
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The general conception of the
method
 In the network analogue of semiconductor device thermal



models and in dc-dc converters the parallely connected RC
elements exist
The impulse response of such RC networks has the form of the
sum of exponential functions and it can be calculated with the
use of the memoryless algorithm [1]
In the steady-state the time dependences of currents, voltages
and junction temperatures in dc-dc converters are periodical
If the step of calculations is equal to the period of the control
signal, than the values of currents, voltages and temperatures
are the sums of the geometrical progression
[1] Zarębski J., Górecki K.: Properties of Some Convolution Algorithms for the Thermal
Analysis of Semiconductor Devices. Applied Mathematical Modelling, Elsevier, Vol. 31,
No. 8, 2007, pp.1489 – 1496.
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The general conception of the
method (cont.)
 If the values of the considered quantities of the begin (Sb) and the
end (Se) of the period TS are known, the value of these quantities
Sn after n periods can be estimated with the use of the formula
1  n
S n  Sb    S X 
1 
n
where
S X  Se    Sb
 TS 




  exp 
 Because of the nonlinearity of semiconductor devices, the
calculations must be realized iteratively
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The FAST algorithm
START
The electrothermal transient analysis
for the final time equals to 2 T S
Determination of the changes of
values of the capacitors voltages SC
and junction temperatures of
semiconductor devices for one
period TS
Ekstrapolation of the values of the
converter output voltage VC and
semiconductor devices junction
temperatures Tj in the steady state with
the use of the convolution algorithm
NO
Calculations of the coil current I L in the
steady state using the extrapolated voltage
VC, the values of the network components
and parameters of the control signal
Transient analysis for the final time
equals to 2 TS with initial conditions
VC, I L, Tj
Determination of the values of
capacitors voltages VC1, coil current
IL1 semiconductor devices junction
temperatures Tj1 on the end of the
second period of analysis
UC – UC1< U, IL
– I L1< L and Tj –
Tj1<T?
YES
STOP
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The analytical dependences
T1
L
• The peak-to-peak value of the inductor current
RG
D1
C
R0 Vout
DVL
Vin
tp
L
Vctr
where L – the inductance of the inductor,
tp – the time of the diode conducting, DVL – the voltage on the inductor at the end of the
period of the control signal
DI L 
DVL  Vout  VD
•
Vout – the converter output voltage, VD – the voltage drop on the diode
The average value of the inductor current
I Lsr  Vout R0
•
•
R0 – the load resistance
In the continuous conducting mode (CCM) IL = ILsr-DIL/2
In the discontinuous conducting mode (DCM) IL = 0
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Results of investigations
b)
0
BUCK
Vin = -20 V
-2
Vout [V]
-4
70
-8
60
R0 = 5 W
-10
-12
R0 = 10 W
R0 = 5 W
50
40
30
-16
20
BUCK
-18
10
Vin = -20 V
-20
0
0
0,2
0,4
0,6
0,8
1
400
BUCK
Vin = -20 V
350
R0 = 5 W
300
250
200
150
R0 = 10 W
100
50
0
0
0,2
0,4
0
0,2
0,4
0,6
0,8
1
d
d
DTjT [K]
R0 = 10 W
80
-6
-14
c)
100
90
h [%]
a)
0,6
0,8
1
d
the FAST algorithm
clasical transient analysis
•Two nonphysical thermal time constants
are used tth1 = 1 ms and tth2 = 10 ms.
• The convergence of calculations with
FAST algorithm is observed after
analysis of 16 -32 x TS.
• The steady state in the classical
algorithm is observed after 6000 x TS.
• The FAST algorithm is over 200 times
faster than the classical algorithm.
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Conclusions
• The FAST algorithm is universal, that means, it can be
•
•
used for each model of semiconductor switch devices
implemented in SPICE, such as: diodes, BJTs, MOSFETs or
IGBTs.
The FAST algorithm can be especially profitable in the
analyses of switching circuits operating at switching
frequencies equal to some hundreds kHz and with
semiconductor devices situated on heat-sinks.
The analysis of such a circuit by the classical method
would demand the calculations during the time longer than
a lot of millions (or even billions) periods of the control
signal. On the other hand, the FAST algorithm allows
shortening the time of the analyses up to the time
indispensable for the analysis of several periods of the
control signal.
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Thank you for your attention
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