BSTJ 60: 7. September 1981: Current-Carrying Capacity of Fine-Line Printed Conductors. (Rainal, A.J.)

5.8 MB·English

Current-Carrying Capacity of Fine-Line Printed
Conductors

By AJ. BAINAL,
(dasa eeceived Fatnry 20, 1901

This paper presents simple equations, olong with experimentally
determined pareanctrs, to calculate the transient temperature rise of
current-carrying, fne-line (~7 mils) contactors on various styles of
circuit packs. The siies of circuit packs include wre wrap, double

‘ded, metal, bonded, and various multilayer boards, All styler of
circuit packs in the BBLLPAC™ syotem feanity are inctuded. The
rmarimtun steady state temperature rise of a nicked o constricted
current-carrying conductor is alsa treated, The enlelated traatent
fan steady-state temperatury rises agree with experiment rests

|. INTRODUCTION

Printed witing vechnology prescndly provides the physical drigner
‘with finetine capper condone ty kalevunaect integrated cieuita
and other rommpnnonts athe civult-pack (C2) level. ‘Pheae fine line

Conductors now haves rina width o7 ma, and nominal thicknest
of L mil For auch yelacvely all conductor ses, (AWC), the
current-carrying enpacity of che conduceors becomes an important
rater af concern. Can such fineline nonducbors cary the required
cumeent to operate the various components on acm without causing en
xcesive temperature rine? What ne emaperalure zie during nor-
‘al curren flow? Te fult-occnrs and a earrent of 10-4 flow far 100
ts will The c be damaged? Questions of This navury are becoming
‘ery importa pine wivingvechlogy provides fier conductors
for the electrical incereonnectinne.

‘Also, aa large-scale intagrated (131) ctcuica are introdured, the
assembled crs are hosoming more expansive. "Therefor, there ie more
neue proleel Un: cP from powable damage we rene of an over

‘Some eanly work by W. Aung and A. J; Glued" has showa that a
75-8 cmrrent fling thrangh 2 fneTine prints} consular iaide
multayer lard {mn} can cauee the MLB to break into flames in
bouts Also, W."L, Smith’ reperted Uhl a cument fe through 3
finectine printed conductor (28-mil (hic) ahould be limited to about
5A if temperature rises ao to be limited to 120°C.

Clearly, 0 avoid posible disaster ar damage, che physical designer
of electronic equipment mul he able ly extimate the feansient tem
perature rise of no-line, eurront-carrving conductors on all etylee of
‘Sreut packs and backplune.

Daring the past few yuirs he Rell System haa introduced a modular
packaging system (BELLPAC* eyscem’) for packaging electronic
‘squint This system snakes use of a numberof CP styles Ural have
‘mmo lealures micable for eomputay-aided design Fine ine printed
fonductone are availabe form anany ofthe cps Tho BELLPAC
fyntem project bas provided ux with Tle opportunity to study the
frrent-oaying capucny of fiaeline conductors on @ varery of CP
syle

"Ths purpose of this paper ist present some useful rill oonenen
ing the current carrying capacity of fncline cenductars on various
acgles of cre, ‘The renlix include the trandenc temperature rise of
furreot-currying prinled conductor, and the marimum steady-state
temperature rise of a conductor nich my be nickel or erste

or the special case ofa double-sided cpoxy prinied wiring board
(dex or rig, some remote conesmning tho steady-state temperate
Toe of inne printed conductons have been reporll in Rai. 4 and
5: Although the methods reporced in cheso ewo referees dir, Une
resus igre well wich one another.

“A liscng af the GP style of nurs in Ui paper, along with a short
‘description of cach is presen in Table [Figur | shows che eorre-
‘sponding physical layups of the ev stylea. Thee physical layup
Ines sll of the cp styles presently in the BELLPAC weet. We
‘hl se thav the remalta inthis paper ean be applied to eslimale the
‘carrent-carying capacity of fine-ine conductors on any layer of way of
the cP siglo shown ia Fig.

1 asic equaTioNS

For a genera eurrentearrying conductor, the consorvarion of heat
‘energy reine that the average temperstire ran satiny the following
‘ferential equation

PR(L+ ATM = CAT + Fa i)

4976 THE BELL SYSTEM TECHNICAL JOURNAL. SEPTENGER 1801
Table I—Deserition ofthe circu pack stv

Trea See Desi
tener board (Foe aun, pa lever, gen aver, power)

‘Sr eta ever pre oti comiocas

Bautleea (eat ‘Brahe ee etl rr

Binns". Ported ony mac nd
Sia oe ‘Lace a2 inl ee ad a tie
sis ef Fee ETS
ear 4 Ie Ga ha

eri ages, 2 ayn 4 sign layer, Pod Gon

where

4 = current flow through the rnduclor (amperes)
‘y= Feisuanco of the conductor at ambient temperature (ohms)

‘01 ambient tomperarure coefiient (per degree C}

= [B+ 24445)" (a good approximation in the cate nfenppes}

17, = ambient tomperacare °C)

{= time duration ofthe current low (aecands)

(O= Uneral eapacity ofthe material heated (J/°C)
-Ry~ thennal estan. of the eanvluelur on Une GP style of interest

‘BE ~ average temperature ge (°C) along Une length ofthe conductor.

‘The lefL-hand vide of. 17 represents the eure lisp aml the
Ivo terms on Use righ wide reprevet the lore ane rained
nents, respecively. More general forms of © (1) ate aiscussed i
Re

Taboraiory measurement show that lhe Unermal pacity, C,
‘ime dependent. The physical eason fer this dependence i that more
and more of the marerial is heated as time goes on. Initially only the
Conductor und u stull porion of the substrate and covercoat are
Tent

However if the time avi is partitioned inty appropriate time ina
vals it urns out Unat the thereal capacity, ©, is wpprusimately
Fonstant aver each ofthe time interals. The solution 19 eq 1} in the
ase ochre aul ine interenleis gven By

BRU expC PR Re}] OstE%
cain ‘ ;
L Sacre: | .
pees ee
—
a vs aE,
oe wrace

= |

i ince a
{ F ie trAae
*: if

1a EH p

yop men oot

i geen

_—s

a cee
7 g DiELECTMC + fe ema
ne

See peel

ie {aya thon st sk ls

41978 THEBELL SYSTEM TECHIWCAL JOURNAL, SEPTEMBER 1981
-a. [1- mse ora Pats)

,
1 o
aF-H, beafen 1 = PRRoe)
OO Ot
* Ga” Fa
where
rere . ae
ga Rte — ead ste average temperae rie
.= thermal eae dung these nerf
Go thermalcaecty ding he tne cereal,
GS thermal capac during eee ere
In genera, one can praton the Ge ai into continuous tne

invervals and obtain a set of m equations Por our purposes, = 3
proved to he sufficient,

"The current-carrying copacity of « conductor is inited by the
permissible tomperitire rise of the eanduecor above the ambient
temperature, Therelore, once the pertinens parameters aro known, tbe
tove equations can be iad to enletnte the cusent-carrying capacity
tof a particular conductor

Tn Section TM, we dereribe the experimental method uscd o measure
all ofthe pertinent parameter

2.2 Some special cases

‘Tho functional form of ST, shows that aronavray or critical euren,
i exits for which BT — =. That i, a8 J > LSP» > ©, and the
feurene-carrying conductor never Teaches sloulyslale (umporate
"The value of lf given by

t
Tee,
The phenomenon of runsway snd the value of runaway cient ix
consistent with our experience inthe laboratory. We foutel thal an we
approached the critical value, 2, the temperature of the conductor
ses rapidly beyond the colerable limita of the substrate and perma-
nent damage routs,

2.2.2 Small — initia! temperature rise

From eq 2), we find that as ¢—+ 0, we have

fem

6

FPNE-LINE PRINTED CONDUCTORS 1979
rhe

G
[Notice that this sell i ieeepeawent of Une thermal rsilance Rr
‘That i the initial heating process a adiabatic.

C

2.2.3 Large t ~ steady state temperature oe
‘Brom 09, (4), with T< J, we nee that as ¢—+ 2 we have

. Rite a
Ape Oh TP Ra o

Equation (7) shows thatthe stely-late uampralre ree depend
‘om ce product ofthe cloctrial resistance (a property ofthe conductor)
tind the thermal resistance (a property of the environment of the
fanduetor|. Fora given curent J, and ambient 7, ono ean only soduco
BT. by reducing the produce Rin

[EXPERIMENTAL DETERMINATION OF THE PARAMETERS.

Tn onder to carry out this study, appropriate west boards were
designed fo each or style shown in Fg. Except forthe double-sided
metal board, all test boards were fabricatod at che Western Hletric
printed cveut manufacturing plant et Richmond, Vieginia. The dow-
be-sded metal board was cuactufucred athe Weatarn Rleere plant

in Kearny, New Jersey.

{In all caze, the phen! dimensions of the princad conduecors had
‘the nominal values of loth L = 12 In, wddh = 7 ral, and copper
thickness ty — 8 to ml

"Tho experimental mafhod used to detemine the pertinent param
‘lure based on measuring, indvecls, che average temperature rise,
[AT along the conductor ans fonction of time whon a stop function of
‘ument ia spplied. ‘The measurement basil on the wellknown
resistance thermometer formula™™

RoR + aT) Cc

where
V = voltage across the consucor,
= muito of the slep function of cument,
R= meanured resistance of the conductor

‘The procedure used to ameanure OT is a follows The amblont
Lenpemtive 7) 8 recorded and 1, is measured by means of an ac
Kelvin bridge. Thit measurement involves a amall carent (100 mA. or
lose) which causes neglxible traperatare rice ‘Then a step function
(of T anperos is directed throagh the conductor of interest, and the

4980 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1051
_csultingvollage dup, V, aera the conductor in ecomled af
of time, Equation (6 ia then used to deduce the coresponding AF
2 finetion a Hime

‘To help esse tho data gathering, u Kaye Instruments dissin
franamiteer we uted lo formal Use i for print su and magnet
tape storage on a Text Ineirumeats model 783 dal ere, Subse
‘wendy, the data was tranemitted (via an acoustical coupler! over the
felephone line te che eamputation vonlur for storage, AC this point,
serial compuver programs were used to edit the stored dala and (0
produce the eampotar pots

‘The procedure wail lo decerine dhe constants apeating i. eq8
(2), (3), awed (4) a follows ‘The average cemperatore vse i fst
computed frum e4, (6 by using the steady stata voltage value come
poniing (0 9 cnevent flow of 7 amperes fora suiciently long time
fasually about 10 min). "This i repeated for a number of different
values of current, Thea, the bet value (minimum mean-aquare-eror
tense! ofthe profiel RR is determine from che measured data and
fou () which wat be reverie a

Eu
Trait,

IF the left-hand side of oa, (ie plottd as «fonction of 1, the slope,

‘atts, of te bee filing fine isthe quart of iteret Sine the value

Uf Bre known, Ry ean be deter,
According to eqs. 2), (3), and (2), a plot ofthe measured values of

RRs o

y=-inl1- 22
cm
‘versus tee yields points which tnd wo fia series of approximately
broken ins of postive lope, Prom thi pl, vals off an can he
selected aa che Ureuk pnts of these Broker fines Ti the region 0 ¢
2 fy, the best value of Cj (minimum meunsuar-eror sense) is
‘eerie by equating the spe of the sing ine ta the lope
the negative of the exponent fn eq. @) To x xiilar manner, Cit
Avermined by using dhe teasured data and the slope of the negative
of the exponent in eq, (3). Finals, C ia determined by usiog the
‘eatured dca andthe slope ofthe ncative af the exponent ine. 8.
[At this point, ail ofthe pmmmcters need ino 2, and (8) are
finwwn, wed These equations can be used ta earulate the average
Aemperalure slung the vadaclr asa fancion of wpe current ie,
conduct rsieanes, nd ambien epee.
‘In this manner, the pertinent parauelers were determined for fe
ting conductors om ll Sal liye al cds slung Thi,

FINE-LINE PRINIED CONDUCTORS. 1301
eating parameter ae presented ip "Table IL "The vanes of = 056
‘and fe = 38 8 were found co apply ¢o all ofthe cP ssles, Te reulte
‘aru sealed conductor Yength of 12 in. and width of 7 mi by using
tho sealing ws Gi~ Ly Ro-~ 1/0, and A= 1) W.

“The valuot of Hf listed in Fig. 2 and Table UL ore steady-state
parameters wd wil he diacnsted in more detail in Section V.

1. EXPERIMENTAL VERIFICATION

Figure 2 prosents the expcrimental values of Yt) for the eve of
‘touble-sided epexy printed wiring board (ews) with covercost. The
parameters, fr Cy, Ce Cig and Rr wore detcrmined by the methoda
Aescribed in Seccon TM. The ful C: were devermiced by wversKiog
tho romlts over three diferent values of eurent.

Far the fouled epoxy cP, Fig. 3 eomparen the experimencal
valucs of the irons emporatnee rie, A), withthe coneqpondi
(heoreteal values. The theoretical values were determined by using

Ti Bepa ag Yh Spee ke Se temic eae

13982 THE BELL SYSTEM TECHHICAL JOURNAL, SEPTEMBER 1961
‘able —Mencured parameter for various crcut-pack styles
(Conductor length = 1, conductor with = 7 mil, and wire-nrap
diameter = 10 mi)

etn
en
‘oni oar F781
Bee.
ee

Sih ot 70

ia
EB worn

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‘Peden 2 Ga tegen ae
PORRREE SA Rat J Seow ie

“ek

the constants fy fy Cn Cy Co Aer in eg 2), (ned). igure 3,
‘hover that this method of esting he ote temperature vise
‘agree with experimental resale,

‘Similar plots have verified that thie method of estimating the
‘transient temperature tae also agrocs with experimencal regults fo all
ther eases of interest inthis paper.

V. SOME APPLICATIONS
5.1 Staady atts temperature rises

“The sreay-stneLemperacure rises of fine-line printed conduccors,
or mize-wrap conductors, ean be readily compuled from eq, (7). The
‘equired values of chermal ress, Rp, are listed in Table Il for «
conductor lengeh of 1 fe, printed eondcior width of 7 mil and wire-
wrap diameter of 10 mil, Also, Uhe required value of the clectrical
Felbans fin bs cma

= 7% prick conductor a
Reo 2 (printed conductor), an)
2, = 22 (wicearap conductor an

r 7 c

FPNE-LINE PRINTED CONDUCTORS 1363
Teas
SRR |

Eg pemne alten ans empente eT, oe cps

where

p= (O.s757H)10-[1 + nonsasT, — 201) ome,
‘1, = ambient temperature, °C

‘L = lengeh of conductor = 1 ft (12,000 mi)

14 = thickness of conductor, mil

W = wide of conductor = 7 ail

1D diameter of wire-werap conductor = 10 mil

‘Asan example, considera double-sided (epoxy) cr ly. From Txble
IL we ceo that H, — 1871°C/W. From eq (10), for L = 12,000 mils
= Lé mils (Loz cu), W = 7 mil and T, = 20°C, we find that Ry
(O.88128, For a curment flaw of f= 25 A, ea. (7) then yiekds AT. =
989°C,

‘For conductor lengths otber than L ~ 1 ft one ean use the sealing
law Hy ~ 1/L to sale tho valucs of Zr tisted in Table UL Also, Hin
sentially independent of Wasi shown hy oq, (15) of Refs 4

Tet us now campute the maximum wealyotate lemperatare ree,
max QT when the same current-carrying conductor i nicked or
‘constricted. The maximum tampreatare rise of auch conductors was
‘meated in Ref, 4. Ie was shown that the key parumeter was Ube value

1994 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBEN 1261