Predicting Operating Temperature and Expected Lifetime of

Aluminum-Electrolytic Bus Capacitors with Thermal Modeling

Sam G. Parler, Jr. and Laird L. Macomber

Cornell Dubilier
140 Technology Place
Liberty, SC 29657

Abstract ! Large-can aluminum electrolytic capaci- An aluminum electrolytic capacitor is generally com-
tors are widely used as bus capacitors in variable-speed prised of a cylindrical winding of aluminum anode and
drives, UPS systems and inverter power systems. Accu- cathode foils separated by papers impregnated with a
rate thermal modeling of the capacitor’s internal tem- liquid electrolyte, usually based on ethylene glycol. See
perature is needed to predict life, and this is a challenge Fig. 1. The anode and cathode foils are made of alumi-
because of the anisotropic nature of the capacitor wind- num, and the foils are usually highly etched. There is a
ing and the complexity of the thermal coupling between thin coating of aluminum oxide on the surface of the
the winding and the capacitor case. This paper trans-
anode. The anode and cathode foils are contacted by
lates analytical models for heat flow in bus capacitors
aluminum tabs that are extended from the winding.
into an equivalent three-loop, seven-resistor, lumped-pa-
These tabs are attached to aluminum terminals in a poly-
rameter thermal circuit model. This paper presents the
results of a Finite-Element Analysis (FEA)-based par-
meric top. The wet winding is sealed into an aluminum
tial differential equation solution and the results of the can.
three-loop thermal circuit model. The latter model is the Analytical and FEA models have been developed and
basis for an operating temperature and expected life- recently published by one of the authors of the present
time Java applet which enables power-system designers paper, and the reader is referred to [2]. The present pa-
to accurately predict capacitor operating temperature per focuses on the embodiment of these models into a
and expected life from operating conditions. Operating lumped-parameter circuit model and a corresponding
conditions permitted as inputs include applied voltage, Java applet.
ambient air temperature, air speed, thermal resistance
of any heatsink attached, and capacitor characteristics
like capacitance, ESR and case size.

I. INTRODUCTION

The useful life of an aluminum electrolytic capacitor

is related to temperature exponentially, approximately
doubling for each 10 ºC the capacitor’s core tempera-
ture is reduced [1]. The temperature rise of the core is
directly proportional to the core-to-ambient thermal re-
sistance, and this paper models this thermal resistance
for various capacitor construction techniques. Results
are adapted for use in a new, lumped-parameter model
suitable for use in a spreadsheet or a Java applet.
This paper focuses on modeling computergrade, or
screw terminal, capacitors. However, the concepts can
be applied to other aluminum electrolytic capacitor con-
structions, such as snapmount, radial, and axial capaci-
Fig. 1. Typical screw terminal capacitor constructions:
tors. pitch (left) and pitchless (right).

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Presented at PCIM / Powersystems World, November 1999
 II. THE 7R THERMAL CIRCUIT MODEL R1 = Thermal resistance, can bottom to heatsink/ambient
R2 = Thermal resistance, winding to can bottom
From recently developed thermal models [2] we find R3 = Axial thermal resistance of winding
that the hot spot is generally in the top center of the R4 = Radial thermal resistance of winding
winding. This hot spot is thermally isolated from the R5 = Thermal resistance, winding to can wall
polymer top due to the low thermal conductivity of the R6 = Thermal resistance, can wall to ambient
top. The aluminum tabs have a high thermal conductiv- R7 = Thermal resistance of can wall
ity, but due to their thin, narrow, and long dimensions, RA = R2 + R3
and the usual thermal isolation of the terminals, the tabs/ RB = R4 + R5
terminals are generally not conducive to heat transfer. V1 = Heatsink or ambient temperature (ºC)
Thermal conduction within the winding occurs readily V2 = Ambient temperature (ºC)
in the axial direction and somewhat less in the radial V3 = Temperature of can bottom (ºC)
direction, due to the fact that the thermal conductivity is V4 = Temperature of can side (ºC)
much larger in the axial direction than in the radial di- VC = Core temperature (ºC)
rection. This anisotropism occurs because the papers IS = Dissipated power (W)
are effectively in parallel in the axial direction but in I1 = Heat flow in loop 1 (W)
series in the radial direction, and the conductivity of the I2 = Heat flow in loop 2 (W)
foil is nearly 1,000 times than that of the papers, even I3 = Heat flow in loop 3 (W) (1)
when the papers are wet with electrolyte.
The radial heat flow from the winding to the can is All resistance units are (ºC/W). Using Kirchoff’s Volt-
inhibited by a poor thermal path of either pitch or wet age Law around Loop 1, we have
air. On the other hand, the axial thermal path from the
bottom of the winding to the can bottom can be quite VC = V1 ! I1R1 !(I1 ! I3)RA , (2)
good, especially when an extended cathode construc-
tion is used instead of the more common wet paper and/
(a)
or pitch. Therefore the principal heat flow is along the (R5) (R6)
aluminum can from the capacitor bottom to the capaci-
(R4)
tor sides, and power is radiated and convected away (R3)
from the capacitor bottom and sides to the environment. (R7)
A heatsink mounted to the bottom of the capacitor is
(R2)
an effective heat transfer mechanism since the lowest-
resistance thermal path is axial. Extended cathode con-
struction is a must when a heatsink is attached to the (R1)
capacitor bottom in order to realize the advantage of the
heatsink, because the primary thermal path is axial.
From the discussion thus far, it is apparent that there
is an axial heatflow path, a radial path, and a coupling (b)
path via the capacitor can. This naturally leads to mod-
eling the capacitor’s thermal characteristics as a three-
loop circuit. See Fig. 2a. Using an electrical circuit anal-
ogy, thermal power is analogous to electrical current,
temperature is analogous to voltage, and thermal resis-
tance is analogous to electrical resistance. See Fig. 2b.
Assuming that the two ambient temperatures and the
seven thermal resistances are known, the value of the
Fig. 2. (a,top) Thermal circuit equivalent for bus capacitor;
core temperature is determined as follows. We define (b,bottom) electrical circuit analogy.

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and around Loop 2 we have III. THE THERMAL RESISTANCE VALUES

VC = V2 + I2R6 !(I2 ! I3)RB . (3) There are seven thermal resistances in this model as
defined in (1). The value of the seven resistances may
Around the outer loop we obtain be calculated using the heat conduction equation and
radiation/convection heat transfer theory along with the
V1 = I3R7 + I1R1 + (V2 + I2R6) . (4) capacitor dimensions, effective thermal conductivities,
and thermal properties of the environment. The neces-
Equations (2), (3) and (4) may be combined to yield an sary equations are presented in [2].
expression relating I3 to VC in terms of known quanti- The thermal resistance, R1, from the can bottom to a
ties as heatsink or to the ambient, is either a conduction or a
convection value, depending on whether the contact is
I3 = BVC + C (5) to a metal plate or to air, respectively. For contact to a
metal plate, R1 is a contact resistance whose value is
where dictated by the clamping force, surface flatness, can
R1 R6 bottom surface area ACB [m2], and interfacial material
! properties. An approximate value for a conventional,
R1 + RA R6 + RB
B= R1RA R6RB (6) sleeved capacitor is
R7 + +
R1 + RA R6 + RB
R1COND ≈ 0.0059 / ACB [ºC/W]. (12)
and
R1V1 R6V2 Adding a SilPad reduces this value by about 20%, while
V1 ! V2 ! + a bare aluminum can bottom clamped to a flat metal
R1 + RA R6 + RB
C= R1RA R6RB (7) surface can reduce (12) by about 70%. The effective
R7 + + thermal resistance of a heatsink or chassis plate is de-
R1 + RA R6 + RB
rived in the next section.
Noting that IS = I2 ! I1 , we may use (2) and (3) to ob- For direct contact to moving air of velocity v [m/s],
tain the convective thermal resistance is

I3 = EVC + F . (8) R1CONV = R1COND + 1 / hACB (13)

where where h [W/m2K] is the combined convection/radiation

R6 + RB + R1 + RA
coefficient [2]
E = R (R + R ) ! R (R +R ) (9)
A 6 B B 1 A
h ≈ 5 + 17 ( v + 0.1 )0.66 (14)
and
V1 V2
The value of h increases slightly for small capacitors,
IS +
R1 + RA
+
R6 + RB
varying as the negative one-fourth power of the diam-
F= RB RA (10) eter [3].
! The thermal resistance R2 from the capacitor winding
R6 + RB R1 + RA
to the capacitor bottom depends on the surface contact
Now (5) and (8) together yield area AW , the contact pressure, and the interface con-
ductivity and thickness. For a tightly compressed screw
VC = (F-C)/(B-E) , (11) terminal capacitor with wet paper or pitch providing
the contact between the winding and the can bottom,
which is the core temperature we seek.

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R2 ≈ 0.0075 / AW . (15) be done iteratively or by using other techniques.
The thermal resistance R6 from the can wall to the
The coefficient indicated by (15) is reduced about 90% ambient environment is obtained from
when extended cathode construction is used along with
tight compression. This coefficient is also reduced some- R6 ≈ 1 / hACW (20)
what in small-diameter capacitors and snapmount ca-
pacitors due to their narrower interface dimensions. where ACW is the area of the can wall [m2] and h is given
The axial thermal resistance R3 of the capacitor wind- by (14).
ing is straightforward to calculate when the winding axial Finally, the thermal resistance of the can wall is readily
conductivity kZ (related to the relative foil and paper determined by heat conduction theory. This parameter
thicknesses) is known, along with the winding inner ra- should include the radial thermal resistance of the wind-
dius RI , winding outer radius RO , and winding length ing and can bottom as well as the axial thermal resis-
LW . Bearing in mind that the power is uniformly dis- tance of the can wall.
tributed, we have
R7 = R4 // RCAN BOTTOM + RSIDE (21)
R3 ≈ LW / [2π kZ ( RO2 ! RI2) ]. (16)
where “//” indicates the parallel operation (a//b = ab/
The radial thermal resistance R4 of the capacitor wind- (a+b)) and
ing is also straightforward to calculate when the radial
thermal conductivity kR is known. RCAN BOTTOM ≈
[2RI2 ln(RI/RO )/(RO2 ! RI2) + 1] / ( 4π kAL dB ). (22)
R4 ≈ [2RI2 ln(RI/RO )/(RO2 ! RI2) + 1] / ( 4π kR LW ).
(17) Here kAL is the thermal conductivity of aluminum and
dB is the thickness of the can bottom. Also
The radial thermal resistance R5 from the capacitor
winding to the can wall occurs via convection and ra- RSIDE = L / (4π kAL RC dC ) (23)
diation [2]. For an inner can diameter of DC , an outer
winding diameter of DW , we have where L is the can length, RC is the effective can radius
and dC is the can wall thickness.
R5 ≈ ln(DC / DW ) / ( 2π kRWC LW ) (18) There are inherent limitations to the accuracy of the
lumped parameter thermal model. First, some sources
where kRWC denotes the effective thermal conductivity of error arise from the assumption that the can is at a
in the region between the winding and the can wall. For constant temperature. We expect to make further refine-
pitch, kRWC ≈ 0.2 - 0.3 W/m·K. ments in estimating the effective average temperature
For a vapor gap [2], of the can. Second, the contact resistances R1 and R2
vary with the contact force. Some capacitor designs have
σ DW( TW4 ! TC4 )ln(DC / DW)
kRWC≈ 0.030 + 0.65 (19) higher compression than others, and the width of the
[1 1!εC DW
εW + εC [ ]]
D C
∆T paper or cathode margin at the bottom of the winding
varies from one design to another.
Verification of the vapor gap conductivity has been
where σ denotes the Stefan-Boltzmann constant, εW is difficult, and we are still in the process of measuring the
the emissivity of the winding’s outer surface, εC is the effect of can wall and winding emissivity variation ex-
emissivity of the can’s inner surface, TW [K] is the wind- periments. Equation (19) provides winding-to-can-wall
ing surface temperature, TC [K] is the can temperature, results that correlate with experimental data with εW =
and ∆T = TW ! TC . Since TW and TC are not known, 0.85 and εC = 0.40.
(19) requires that they be estimated. This estimation can

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Presented at PCIM / Powersystems World, November 1999
 IV. THERMAL RESISTANCE OF A and In(ar) and Kn(ar) are modified Bessel functions of
CHASSIS PLATE order n.
For the inner region r ≤ RC let
This discussion shows the effect of attaching the ca-
pacitor to a chassis plate for cooling. Generally the plate X2 = T ! [ TA + P / (πkPdPRC2)] r ≤ RC . (31)
area is larger than that of the capacitor can, and there is
some air movement and surface radiation. But the plate This leads to
cannot usually be treated as an isothermal or even a
constant-flux surface due to its appreciable conductance X2 = C3 I0(ar) + C4 K0(ar) (32)
losses.
Consider a circular plate of radius RP, thickness dP, There are four constants, so that four boundary condi-
and thermal conductivity kP, with a center-mounted ca- tions are required. First, by symmetry we know that the
pacitor of radius RC dissipating power P into the plate, heat flux at r=0 is zero so that
immersed in an environment (one side) of temperature
dX2
TA with combined radiation and convection coefficient (33)
dr = C3aI1(0) ! C4aK1(0) = 0
h. The temperature distribution T(r) may be found us- r=0
ing the heat equation in cylindrical coordinates, yielding C4 = 0. We know that there is zero heat flux at
g the outer edge where r = RP so that
1 d
r dT
C
r dr [ ]
dr
+
k
= 0. (24)
C1aI1(aRP) ! C2aK1(aRP) = 0 . (34)
where g is the volumetric power density and r is the
radial coordinate. We have two regions, Hence

g
k
= {!hP / ((πkT !d TR )) /!(kh d( T) ! T ) / (k d ) rr ≤> RR
P P
A

C
2
P P

A P P C
C (25) C2 = C1 × I1(aRP) / K1(aRP) . (35)

We enforce temperature continuity at r = RC and obtain

Let us consider solutions in these two regions. First, for
the outer region r > RC let (C1!C3) I0(aRC) + C2 K0(aRC) = P / (πRC2h) . (36)

X1 = T ! TA r > RC . (26) As the last boundary condition we apply Fourier’s Law

to the inward flux at r = RC, assuming T(RC) ≈ T(0) so
We have
d
dr [ r dXdr ] !
1
hX1r
kPdP
=0
(27)
P
which expands to Bessel’s equation
d2X1 dX1 h
r + ! rX = 0 (28)
dr2 dr kPdP 1
kP
whose solution is [4]

X1 = C1 I0(ar) + C2 K0(ar) (29)

where

a = √ h / (kPdP)
Fig. 3. Calculating the thermal resistance of
(30) a capacitor mounted to a chassis.

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Presented at PCIM / Powersystems World, November 1999
that V. TRANSIENT RESPONSE
dX1 hRC2X1(RC)! P
dr = C aI (aR ) ! C aK (aR ) ≈ (37) So far we have discussed steady-state temperatures,
1 1 C 2 1 C 2RCkPdP
r=RC but in many cases the capacitor core temperature re-
We may solve equations (35), (36), and (37) simulta- sponse to a transient current surge or ambient tempera-
neously to obtain ture change needs to be evaluated. The thermal time
constant τ of a capacitor is the time required for the
P
C1 = core to reach 63% (1-e-1) of a step change in the ambi-
2πRCkPdP
ent temperature. Once the effective thermal resistance
aK1(aRC) RChI0(aRC) πR 2hK (aR )I (aR )
K1(aRP) + 2kt + C 0 C 1 P
! aI1(aRC) from the core to the ambient is known, the thermal time
K (aR ) 1 P
constant of the capacitor may be calculated by lumped-
(38) parameter analysis if the Biot number Bi is much less
than unity [5]:
C2 = C1I1(aRP)/K1(aRP) (39)
Bi ≡ hL / k « 1 . (42)
C3 = C1 + [C2K0(aRC) ! P/(πRC2h)]/I0(aRC) (40)
Since per (14) the convection coefficient h < 100 W/
Fig. 4 shows a typical temperature distribution plot. The m2K for air velocities less than 10 m/s, the winding length
effective thermal resistance from the capacitor bottom L < 0.2 m, and the axial winding conductivity kW ≈ 100
to the air may be found as W/m·K [2], Bi < 0.2 and condition (42) is met for low
and moderate air velocities and no heatsink. If Bi > 0.2
θCA = (T(0) - TA)/P . (41) and a precise transient response is needed, FEA tran-
sient modeling techniques should be used. If Bi < 0.2,
In the example of Fig. 4, the chassis plate provides a
thermal resistance of less than 1 ºC/W to the ambient τ ≈ mCPθWA [s] (43)
air, which would greatly reduce the core temperature
and extend the life of the capacitor. where m is the capacitor mass [kg], θWA is the thermal
Air velocity = 800 lfm resistance from the winding to the ambient, and CP is
Plate thickness = 0.0625 in the specific heat [J/(kg·K)] of the winding, which we
Plate conductivity = 250 W/mK have measured to be approximately
Cap diameter = 3 in
Power = 20 W CP ≈ 1400 [J/(kg·K)] . (44)
Ambient temperature = 45 ºC
Plate diameter = 10 in
Temperature vs Radial Position The rate at which the core of a capacitor will heat
when subjected to a power P, assuming an adiabatic
64
process, where negligible heat energy transfer occurs
62
over the period of interest, is therefore
Temperature (ºC)

60

58 dTC/dt = P / (mCP) . [ºC/s] (45)

56

54 Integrating (45), assuming the power P is applied at

52 time t=0 and that the initial temperature is T0 [ºC], we
0 1 2 3 4 5 6 obtain the core temperature response
Radial Position (in)

Fig. 4. Graph of the radial temperature distributon TC(t) = T0 + P t / (mCP). (46)

of a circular aluminum chassis plate with a center mounted
capacitor.

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This equation is useful for examining the effect of a VI. THERMAL MODEL RESULTS
high-current transient event. For example, if a capaci-
tor is rated 10 amps rms but 40 amps rms is to be ap- Example output of an FEA-based partial differential
plied for one minute, (46) may be used to determine equation solver is shown in Fig. 6. The accuracy of this
whether the capacitor will overheat. For extremely high model has been discussed and is usually within 10%
current transients, other limitations such as tab fusing [2]. Fig. 7 shows a comparison of results of the lumped-
need to be addressed as well. Also, the capacitor mass parameter “7R” thermal model presented in the present
m should be that of the winding only, excluding the pitch paper to some test data and to the FEA model.
and other mass, when (45) with this lighter mass gives a
thermal rise rate of greater than about 0.03 ºC/s.
A capacitor’s transient core temperature response to VII. THE LIFE MODEL
a step increase or decrease in ambient temperature ∆T
is determined, subject to (42), by appealing to a DC The present life model that we use is based on test
electrical circuit model analogy. The model is of a ca- data and on life models used throughout the electrolytic
pacitor transient voltage response to a DC voltage source capacitor industry. The model is based on the Arrhenius
being switched at t=0 to a series RC circuit. See Fig. 5. equation and on the activation energy of anodic alumi-
By inspection, num oxide and the rate of decomposition of the electro-
lyte-spacer system. The life equation is used to model
TC(t) = T0 + ∆T [ 1 ! exp(-t /τ ) ] (47) the approximate time interval at which the 85 ºC effec-
tive series resistance (ESR) of a typical capacitor will
where T0 is the initial capacitor and ambient tempera- exceed twice its initial value.
ture. Equation (47) is useful for examining the effects The life model that we use at present is
on the core temperature of brief exposure to a high am-
bient temperature such as in a wave-solder or solder- L = LB × MV × 2 ^ [(TR!TC)/10] (48)
reflow machine. However, care must be taken to insure
that the capacitor sleeve is not overheated, as splitting where LB is the base life in hours at the DC life test
may occur. temperature at rated voltage VR and rated temperature

t=0

θW A

T 0 + ∆T
+
TC -
mCP
T C (0) = T 0 [ºC]

t=0

V 0 + ∆V
+
VC -
C
V C (0) = V 0 [V]
Fig. 6. Typical graphical output from FEA-based
equation solver thermal simulation. This capacitor has
Fig. 5. (a,top) Transient thermal circuit equivalent for bus extended cathode construction and is mounted to an annular
capacitor; (b,bottom) electrical circuit analogy. heatsink with a thermal resistance of 1 ºC/W.

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Presented at PCIM / Powersystems World, November 1999
TR, TC is the actual core temperature, and MV is the DC volt, ethylene glycol-based electrolyte-spacer system are
voltage multiplier, A = 40 and B = 0.6.
A typical value for DFOX is 0.015. Equation (51) can
MV = 4.3 ! 3.3 × VA / VR . (49) be refined by adding a slight positive temperature coef-
ficient multiple to the DFOX parameter.
All voltages are in volts and temperatures in ºC. It can be seen that the ESR has the largest magnitude
at low temperature, low frequency, and that the ESR
VIII. THE ESR MODEL has the smallest magnitude at high temperature, high
frequency. For a given capacitance and temperature,
The effective series resistance (ESR or RS) at 25 - there is a frequency fFLAT above which the additional
100ºC is relatively straightforward to model. RS con- ESR drop will be less than 10%:
tains a frequency-dependent dielectric loss ROX due to
the dissipation factor of the aluminum oxide dissipation fFLAT ≈ 5 DFOX / ( π RSP C) (53)
factor, DFOX, and a temperature-dependent loss RSP due
mostly to the electrolyte-impregnated paper and the liq- It is apparent that if the actual 25 ºC, 120 Hz ESR
uid electrolyte in the etched pits or tunnels of the foil. and the DFOX are known, that the ESR at all frequencies
and temperatures above 25 ºC can be found.
RS = ROX + RSP (50) A few cautionary statements should be made concern-
ing the use of this simple ESR model. When the ripple
where voltage

ROX (f) = DFOX / 2 π f C (51) VRMS ≈ IRMS / ( 2 π f C ) (54)

exceeds about 10% of the rated DC voltage, which can

and
occur at low frequency, high ripple current, special ca-
pacitor design is required, and the heating and stability
RSP (T) = RSP(25 ºC) × 2^[-((T-25)/A)^B] (52)
of a standard capacitor are often not well predicted by
25 ºC ≤ T ≤ 100 ºC
this simple ESR model.
Although RS accounts for capacitor heating by mod-
where the constants A and B are unique to the electro-
eling the capacitor losses as a series resistance, it should
lyte-spacer system. Typical parametric values for a 400-
be noted that the dielectric loss accounted for by ROX
actually occurs inside the dielectric and does not cause
Core Temperature
a voltage drop at the capacitor terminals when a pulse
80.0 current is applied.
Temperature (ºC)

70.0
For very low ESR capacitor designs (R S < 10
Model Core

60.0

50.0
milliohms) at f > fFLAT , a term accounting for the foil
40.0 and tab metal resistance should be added to (52) for
30.0 enhanced accuracy. This term is relatively frequency
30 40 50 60 70 80
Actual Core Temperature (ºC)
and temperature invariant, and has an inverse relation-
7R Model 7R Model Line of Perfect Fit FEA fit FEA fit
ship with the number of tabs.
At very high frequencies (above 50 kHz), the RSP di-
minishes an additional 10-50% due to a transmission-
Fig. 7. Comparison of results from the 7R lumped- line effect of the microscopic, electrolyte-filled, etched
parameter thermal model and FEA-equation solver model
versus test data. The test data includes capacitors in still air,
tunnels in the surface of the foil. The capacitance also
isothermal heat sink, and moving air from 80 to 1000 LFM. decreases along with the RSP , and together the roll-off
Core rise above ambient was generally 10 - 30 ºC. Capacitor occurs such that the tunnel impedance approaches a
sizes range from 1.375” diameter to 3.0” diameter.
phase angle of -45º.

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Presented at PCIM / Powersystems World, November 1999
 IX. THE JAVA APPLET temperature, and the core temperature is a function of
the power.
The thermal, life, and impedance models presented in Analytical solutions to this problem generally include
this paper have been combined and coded into a java functions (such as the Lambert W function) that are not
applet to predict life. See Fig. 8. The inputs fields are included in the math libraries of most spreadsheet and
selected or filled in as needed by the user. There is also Java development packages. In the iterative solution of
a database search feature to locate a catalog capacitor the java applet, the “seed” (initial guess) core tempera-
if desired. ture is set to the zero-power core temperature (usually
The seven resistances of the 7R thermal model are the same as the ambient temperature), and the calcula-
determined from the capacitor type (extended cathode tion loop usually settles to within 0.01 ºC of the previ-
or extended paper construction), winding size, and case ous calculation within 10 iterations.
size, as well as from the ambient parameters. The calculated core temperature is the expected ini-
The 25 ºC, 120 Hz ESR that the user has entered or tial core temperature of the capacitor under the operat-
that the database search feature has provided, along with ing conditions specified by the user.
the capacitor type, voltage rating, and capacitance, forms Since the ESR increases over the life of the capacitor,
the basis for calculating Rsp(25 ºC) and for establish- and the hot ESR is allowed to double, we base the life
ing the ESR model for all frequencies and temperatures. calculation on an “average” ESR that is 50% greater
The prediction of the initial core temperature is found than the initial ESR. If the core temperature associated
by calculating the power dissipation from the ESR model with this average ESR is greater than the maximum al-
and the core temperature from the 7R thermal model. lowable core temperature, the user is alerted and life
This is done iteratively because the dissipated power is calculations are not presented.
a function of the ESR, the ESR is a function of the core
X. CONCLUSIONS

In this paper we have developed a lumped parameter

seven-resistor thermal circuit model whose resistances
are based on the capacitor construction and relevant heat
transfer theory. We have presented an ESR model and a
life model. We have discussed the workings of a java
applet that combines these three tools to predict core
temperature and life.

REFERENCES

[1] Greason, W. D., Critchley, John, “Shelf-life evaluation of

aluminum electrolytic capacitors.” IEEE Transactions on Compo-
nents, Hybrids, and Manufacturing Technology, vol. 9, no. 3, Sep-
tember 1986, pp. 293-299.
[2] Parler, Sam G., Jr.., “Thermal modeling of aluminum elec-
trolytic capacitors.” 34th Annual Meeting of the IEEE IAS, Octo-
ber 1999.
[3] Gasperi, M. L., Gollhardt, N., “Heat transfer model for ca-
pacitor banks.” 33rd Annual Meeting of the IEEE IAS, October
1998.
[4] Beyer, William H., editor, CRC Standard Mathematical
Tables, 25th Edition. CRC Press, Inc., Boca Raton, 1979, pp. 418-
Fig. 8. Java Applet Life Calculator based on the 7R 419.
lumped-parameter thermal model, ESR model, and life [5] Incropera, F. P., DeWitt, D. P., Introduction to Heat Trans-
model presented in this paper. fer. John J. Wiley and Sons, New York, 1985, pp. 177-180.

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Presented at PCIM / Powersystems World, November 1999