Transcript Nieizotermiczne charakterystyki impulsowych układów zasilających

Application of the Electrothermal
Average Inductor Model for
Analyses of Boost Converters
Krzysztof Górecki, Janusz Zarębski,
Kalina Detka
Gdynia Maritime University
Department of Marine Electronics
Outline
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Introduction
The average electrothermal model
of the diode-transistor switch
The average electrothermal model
of the inductor
Results of calculations and measurements
Conclusions
Introduction (1)
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The boost converter is frequently used in switched-mode power
supplies.
The important parts of this converter are semiconductor devices
and an inductor with the ferromagnetic core.
In literature the properties of this circuit are analyzed, but the
consideration focused only on semiconductor devices ignoring
properties of magnetic elements.
In previous authors papers it is shown, that the nonlinearity
dependence L(i) significantly influences the course of
characteristics of the considered converter.
In the cited papers, in order to calculate the characteristics of dcdc converters the classical transient analysis method is used.
The analysis is time consuming, and there are often problems to
obtain convergence of computations.
During dc-dc converters operation the internal components
temperature rises due to a self-heating phenomenon.
Introduction (2)
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To take into account this phenomenon in the computer analysis,
special electrothermal models are required.
The average electrothermal model of the diode – transistor
switch for SPICE is proposed, but in this model non-linearity of
the inductor characteristics and self-heating in this element are
omitted.
In this paper the average electrothermal model of the inductor
dedicated to the electrothermal analysis of dc-dc converters is
proposed.
This model takes into account magnetic and thermal
phenomena in the inductor and power losses in the core and in
the winding.
The model is used to calculate non-isothermal characteristics of
the boost converter.
The average electrothermal model
of the diode-transistor switch
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I2av
I1av
+
Main
circuit
1
Er
U1av
3
CCM/DCM
+
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Va
V1
U2av
Et
Ga
Ra
Eu
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Gd
-
4
2
5
-
d
Aided block
Eron
Erd
Eud
Thermal
model
Ett
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Etd
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Control voltage sources Et and Er
represent the unipolar transistor,
connected to terminals 1, 2 and 5
The diode (between the terminals 3 and
4) is represented by the controlled
current source Gd.
The auxiliary circuit is used to determine
the mode of dc – dc converter (CCM or
DCM) including the considered switch.
The aided block model the temperature
changes of transistor resistance RON,
series diode resistance RD and voltage UD
on the forward biased p-n junction.
The internal diode and transistor
temperature are calculated in the thermal
model.
The average electrothermal model
of the inductor
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The average electrothermal model of the inductor refers to an
average value of voltage and current in the circuit, instead of the
transient values .
Main circuit uRS
uRN
i
VL RS0
A
ERS
B
ERN
L
Auxiliary circuits
B
Bsat
EB
EBsat
C
H
Ec
EH
ELs
TR
Bm
DiL
EDB
EDIL
Thermal model
PU
PR
EPU
EPR
TU
ETR
ETU
• The values of all the above
mentioned quantities can be
determined by the electrothermal
model of the inductor
• Terminals A and B are the terminals
of the inductor.
• Terminal L - the voltage
corresponding to the inductor
inductance,
• Terminal TU - the temperature of the
inductor winding,
• Terminal TR - the temperature of the
inductor core.
The average electrothermal model
of the inductor (2)
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In the main circuit:
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In the auxiliary block the controlled voltage sources are used to
calculate the value of:
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the voltage source VL with zero output voltage monitors the current of
the inductor,
the resistor RS0 represents the winding resistance of the inductor for
the direct current at the reference temperature T0
the controlled voltage source ERS describes the influence of
temperature and losses of the inductor series resistance.
the controlled voltage source ERN models the skin effect phenomenon
the magnetic force H,
flux density B,
Bsat saturation flux density
the auxiliary value C.
The thermal model allows calculating an excess of the core TR and
winding TU temperature above the ambient temperature Ta.
Results of calculations and
measurements
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The average electrothermal model of the inductor is used to
calculate the characteristics of the boost converter,
L
D1
RG
T1
C
R0 Uwy
Uwe
Uster
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the inductor L containing 27 turns of enamel copper wire of the
diameter of 0.8 mm wound on a toroidal ferrite core
RTF25x15x10 made of F867 material.
The considered circuit is excited by the DC voltage equal to
12 V, the frequency of the control signal is f = 50 kHz.
Results of calculations and
measurements (2)
1,2
50
curve c
d = 0.5
45
1
40
curve b
curve b
30
0,8
curve c
curve d
25
h
Uwy [V]
35
0,6
20
15
10
curve a
RTF
0
1
10
100
R0 [W]
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d = 0.5
f = 50 kHz
0,2
5
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curve a
0,4
curve d
1000
10000
RTF
0
1
10
100
1000
10000
R0 [W]
curves a - results of analyses obtained using average electrothermal models of
the diode-transistor switch and the inductor,
curves b – the results obtained using the average electrothermal model of the
diode-transistor switch and the linear inductor model without losses,
curves c - the results of analyses using isothermal models of considered
devices,
curves d - the results of the transient analysis obtained using the
electrothermal models of the transistor, the diode and the inductor.
Results of calculations and
measurements (3)
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It is easy to notice that in the considered range of load resistance the
boost converter operates in both CCM and DCM modes.
Taking into account non-linearity of L(i) caused the shifts of the
boundary between CCM and DCM mode towards bigger values of load
resistance R0.
In the range of small values of R0 it can be seen that using the
classical model without losses allows obtaining the constant output
voltage Uwy and watt-hour efficiency.
From both the considered models the increasing dependences Uwy(R0)
and (R0) are obtained,
Taking into account non-linearity of the inductor model reduces the
converter output voltage and watt-hour efficiency.
It is worth noticing, that taking into account the inductor nonlinearities and losses in the inductor causes the reduction of 50% in
the output voltage, and the watt-hour efficiency - as much as 60%.
Results of calculations and
measurements (4)
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140
d = 0.5
f = 50 kHz
TU, TR [oC]
120
100
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TU
80
60
TR
40
20
RTF
0
1
10
100
R0 [W]
1000
10000
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The considered dependences are
decreasing functions.
For the high resistance R0, the
core temperature is higher than
the winding temperature and for
the small resistance R0 the
winding temperature achieves
the higher value.
The computations time for the
presented characteristics using
average electrothermal models
was about a ten miliseconds,
whereas the determination of
these characteristics by the
transient electrothermal model
takes several hours.
Conclusions
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The paper presents the average electrothermal model of the
inductor dedicated to determine non-isothermal characteristics of
dc-dc converters using SPICE.
The proposed model takes into account the dependence of
inductance and series resistance on:
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the inductor current,
frequency,
temperature
inductor construction parameters
parameters of the core.
The results of computations show that taking into account in the
presented model the physical phenomenon clearly affect
characteristics of the considered circuit
In particular, the shift of the boundary between CCM and DCM
mode towards higher values of R0 resistance is observed.
Conclusions (2)
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The output voltage and watt-hour efficiency of the
boost converter in the range of small values of R0
decrease.
The modified model also allows the computation of the
core and winding temperature.
Simultaneously, the time needed to compute the nonisothermal characteristics of the considered converter is
much shorter than using the classical transient analysis
and the electrothermal model of the inductor.