Available via license: CC BY 4.0
Content may be subject to copyright.
Acta Electrotechnica et Informatica, Vol. 18, No. 2, 2018, 3–10, DOI: 10.15546/aeei-2018-0010 3
ISSN 1335-8243 (print) © 2018 FEI TUKE ISSN 1338-3957 (online), www.aei.tuke.sk
DETERMINING PCB TRACE CAPABILITY AND FUSING, USED IN SWITCH MODE
POWER SUPPLIES, BASED ON MODELING AND SIMULATION WITH THE FINITE
ELEMENT METHOD
Borislav DIMITROV*, Andrew CRUDEN**, Suleiman SHARKH***
Faculty of Engineering and the Environment, University of Southampton, Southampton, UK,
E-mail: *B.H.Dimitrov@soton.ac.uk, **A.J.Cruden@soton.ac.uk, ***S.M.Abu-Sharkh@soton.ac.uk
ABSTRACT
PCB fuses are used widely in small power and small size electronic devices such as switch mode power supplies, chargers etc.
They offer small size and low cost but their dependency of the track’s geometry make them imprecise. The aim of this research is to
show an approach for improving the design procedure, leading to improved parameters and operation of the fuse. The suggested
design is based on modeling with finite element method and numerical simulation. Experimental results validating this work are
presented.
Keyword: PCB fuse, switch mode power supply, electronic device, finite element method, simulation, experiments
1. INTRODUCTION
Modern PCB fuses have their application in
contemporary low power electronic devices such as switch
mode power supplies for battery chargers, LED lamps,
different mobile applications etc. Their major advantage is
compactness i.e. small mass and size, and lower cost,
compared to ordinary fuses with fusible plugs. The PCB
fuses are applicable only in unserviceable units with
relatively small power and consequently small size. These
characteristics helped designers to reduce entire devices’
size and cost. In addition, these types of fuses have a
significant disadvantage – they are not precise enough,
because the accuracy depends on the geometrical
characteristics of the tracks. The experimental results
show that when they blow under short circuit this often
causes the switching-off of the central circuit breaker or
fuse, which is an unacceptable event. This problem has
been mentioned with several electronic devices available
on the market. Experiments conducted with ten identical
boards (switch mode power supply for battery charging,
offered from the same manufacturer) showed that four of
them caused switching of the central switch before the
PCB fuse.
Numerous literature sources are focused on PCB trace
current and heat ability and showed results in a different
directions. Some of them are focused on application of the
numerical methods in the design procedure of the PCB
trace. Papers [1, 2, 3] show research of the PCB track
capability and application of contemporary mathematical
apparatus. Paper [4] used modelling with numerical
methods in order to determine their temperature under
steady state conditions. A lot of research has been
conducted regarding general issues as traces current
abilities, calculation of the losses, high frequency ability
and noise on the PCB boards etc. [5, 6, 7, 8]. The design
procedure is given in [9, 10, 11] and design standards [12]
is describes in detail in [3, 13]. The use of the traces as
fuses is given in [14] where the modeling procedure and
the final experiments with them as part of the electronic
device are not presented.
The aim of this research is to show a new approach,
leading to improved precision of the fuse and eventually
to improve the design procedure of the entire electronic
device. This approach is based on modeling with
numerical methods (Finite Element Method FEM) which
are included in established analytical procedures, in order
to complement and improve them. The result should give
a more correct definition of the mass and geometric
characteristic of the tracks, used as PCB fuse.
2. ANALYSIS
Generally, ordinary fuses used in switch mode power
supplies are selected according to their let-through
current, or It rating. This characteristic is provided from
manufacturers in graphical and numerical manners, which
make their selection methodology easy and strongly
defined. Working with PCB fuses still requires a lot of
experimental activity, design changing in order to alter the
characteristics of the fuses, which are resources
consumable.
The electrical circuit presented in fig.1, shows the
connection between the circuit breaker, as part of the
electrical installation, and electronic device protected with
a PCB fuse. The major requirement on this schematic is:
short circuit in the electronic device should cause the
blowing of the PCB fuse and not the operation of the
circuit breaker.
Several different examples of PCB fuses are presented
in Fig. 2. The experiments showed in part 3 are conducted
with the same boards.
The design of the fuses with fusible plug is based on
an analytical procedure, with certain assumptions and
mathematical analysis. If the current through the plug
(trace) is over three times larger than nominal current then
all the heat energy is used to heat the plug i.e. the process
is adiabatic. The dependency between the time (t) for
reaching the melting temperature, the cross section of the
plug and its material is given from the equation:
4 Determining PCB Trace Capability and Fusing, Used in Switch Mode Power Supplies …
ISSN 1335-8243 (print) © 2018 FEI TUKE ISSN 1338-3957 (online), www.aei.tuke.sk
tK
(1)
where: K is a constant, depending on the material, for
cooper 80 000 I.secmm
; A is the cross section (m);
I is the current (A); J is the current density (Am
⁄).
Fig. 1 PCB fuse as part of electrical circuit. Points A and B –
control points before and after the PCB fuse.
After time t i.e. reaching the melting temperature,
additional energy is necessary to change the state of the
material from a solid to a liquid. This energy is equal to
the latent heat capacity of the material. The time of this
phase (t) is given by the equation:
t.
ln
K
(2)
where: ρ is the specific resistance on the melting
temperature; ρ is the resistance of the liquid metal; γ is
density; T is the latent heat; K is a constant, depending
on the material, for cooper 11 600 I.secmm
.
The sum of the equations (1) and (2) determine the
transient time of the switch-off process of the fuse (t).
More precisely this sum must contain the time of the
electrical ark extinguishing t also, or:
tttt (3)
The last component is often described experimentally,
but for practical purposes the next equation is applicable:
tK
k (4)
where: c is the experimental coefficient showing the
destruction of the fuse, commonly c3; k is the
coefficient considering the time t, commonly k
1.21.3; K is a constant, depending on the material, for
cooper 80 000 I.secmm
; K is a constant, depending
on the material, for cooper 11 600 I.secmm
;
Fig. 2 Experimental PCB fuses
The analytical design procedure is based on the
determination of the traces cross-section as a functional
dependency of temperature, according to the widely used
standard IPC-2221 [12]. Fig. 3 shows the methodology of
estimation of the temperature rise due to electrical current.
This process has two general steps, following the dashed
arrows in Fig. 3: determine the cross-section according to
the thickness of the trace; determine the temperature rise
and maximum permitted current.
The same analytical design can be based on two
equations, specified in [3, 12, 14] with the format:
Acta Electrotechnica et Informatica, Vol. 18, No. 2, 2018 5
ISSN 1335-8243 (print) © 2018 FEI TUKE ISSN 1338-3957 (online), www.aei.tuke.sk
Ik.∆T.A (5)
W here: I is the current (amps); ∆T is the change in the
temperature above ambient (C); A is the cross section
area (square mills); k, β1,β2 are coefficients.
According to the IPC standard equation (5) has the
parameters:
I0.065∆T.A. (6)
and according to [3], the same equation is specified as:
I0.040∆T.A. (7)
Although the standard IPC-2221 allows a fast and
straightforward design, the data shows that it can be used
only for the general design of the PCB trace. This standard
is not applicable for the design of fuses, because their
melting temperatures are not available.
The results of the presented equations and analytical
methodology of design have to be compared and corrected
according to results from FEM procedure in the context of
the design of the PCB fuses.
Fig. 3 Nomograph from the standard IPC-2221
3. NUMERICALMODELINGOFTHEPCBFUSE
WITHFINITEELEMENTMETHOD
Two models, showing the basic work modes, short
circuit and normal conductivity mode are prepared. The
simulation procedure is realised with a specialised product
[15] and is based on a multiphysical model including Heat
transfer and Joule heating modules. The models work with
different time constants and this requires consideration of
the boundary condition. Both models are based on direct
resistance heating theory.
Due to the small time constant of the short circuit
mode, the heat transfer between the PCB fuse, the
environment and the board can be neglected. With this
assumption, thermal transfer with convection and
radiation are excluded from the model. The thermal
transfer is only through conductivity in the body of the
fuse. Such an adiabatic process requires thermal insulation
around the fuse.
The heat transfer in solids steady-state problem is
described with the equation:
ρC
ρCu.T.qQ (8)
qk.T (9)
Where: ρ is the density (kg/m3); C is the heat
capacity (J/(kg.K)); T is the temperature (K); u is the
velocity field vector (m/s); Q is the heat source (W/m3); q
is the heat flux vector (W/m2); k is the conductivity
(W/m.K).
The boundary condition for thermal insulation is
described as:
n.q0 (10)
Where: n is the vector potential.
If the model represents the normal continuous mode of
operation, the last condition should be replaced by
convection and radiation between the top surface of the
fuse and the environment and conduction between the
bottom surface of the fuse and the board. In this case the
process of heat transfer in the complete system (fuse track
– board – ambient environment) is described from
equation (8) with the equation:
Qpu
дt
дp
дТ
дT
S
qTu
дt
дТ
С
P
P
).(
:).().(.
(11)
Where
T
uuS 2
1 is the strain-rate tensor
(1/s), τ is the viscous stress tensor (Pa);
In the models developed from the equation (11) the
stationary mode is reduced to:
ρC
.k.TQ (12)
The necessary border condition is heat flow and
radiant heat transfer between surfaces:
4
0
4
inf0
).1(
).()().(
TJG
TGTThqTkn
(13)
6 Determining PCB Trace Capability and Fusing, Used in Switch Mode Power Supplies …
ISSN 1335-8243 (print) © 2018 FEI TUKE ISSN 1338-3957 (online), www.aei.tuke.sk
Where n is a vector normal to the corresponding
surface, G, J are the incoming and emitted flux
respectively.
The heat transfer between surface and environment is
described by the equation:
4
.amb
TG
(14)
Thus the heat flux obtained is given as:
).(. 44 TTq amb
(15)
Where: is blackness coefficient, Тamb is ambient
temperature [K], is the Stefan–Boltzmann constant.
The border condition used is heat flow through the
respective surface, identified as follows:
uTCTkq p
.
(16)
The thermal model of the PCB fuse includes the phase
change process during the melting time of the conducting
trace. The model heat transfer with phase change is based
on equations:
ρθρ1θρ; ρHθρH
1θρH (17)
Where ρ is the specific capacity, H is the specific
enthalpy, indices phase1 and phase 2 indicate the fuse in
phase 1 (before has reached the melting temperature) and
in phase 2 (during the melting temperature) respectively, θ
is the temperature difference.
The specific capacity C:
C
(18)
Eventually, the latent heat capacity C is:
CTHH
(19)
where α is the mass function:
α
(20)
Here, the transformation occurs in a temperature
interval between T∆T2
⁄ and T∆T2
⁄, where T
is the phase change temperature. The phase changing
process is described by a smoothed function (θ),
representing the fraction of phase before transition.
The Joule heating model describes the heating of the
electrical conductor from the electrical current passing
through it due to the Joule losses. The equation that
describes the dependency between the conductivity of the
material, in this case copper PCB track, and temperature
is:
σ
(21)
Where: ρΩ.mis the resistivity; α
is the
resistivity temperature coefficient; T and TK are the
current temperature and the reference temperature.
The external current density J appears in Ohm’s law
and is described by the following equations:
.JQ (22)
Jσ.E
J (23)
EV (24)
Eventually, the current conservation is:
Jσεε
.EJ (25)
Where: J is external current density
; ε,ε are
the permittivity of the free space and relative permittivity
respectively; Q
is current source, described by
equation:
Qn.JJ (26)
The electric isolation boundary condition means that
no electric current flows through the boundary i.e. leakage
between the fuse track and PCB is neglected. The
equation is:
n.J0 (27)
The materials used for the model are fiberglass (PCB
board), copper (fuse track) and air (surrounding
environment). The thermal and electrical parameters of
the copper are shown in table 1. The two other materials,
fiberglass and air, have only thermal characteristics shown
respectively in Table 2 and Table 3.
The result of the simulation procedure is shown on
figures 4 and 5, respectively with nominal and short
circuit current.
The last model, based on short circuit, does not require
the environment and the PCB board to be included in it,
because the time is too short for any thermal conducting in
the entire system. This means that only fuse track needs to
be modelled. This approach saves computer resources,
calculation time and consequently reduces the time for the
design.
Fig. 6 shows zig-zag trace fuses, modelled in short
circuit mode. The same geometry is shown on Fig. 2 and
is widely used in electronic devices, as it gives an option a
bigger length to be allocated on a limited place. The
simulation shows the temperature difference between the
angle and the linear part of the trace. It can be expected
that the melting process will begin from the linear part,
which shows the similar thermal operation as linear
geometry.
Acta Electrotechnica et Informatica, Vol. 18, No. 2, 2018 7
ISSN 1335-8243 (print) © 2018 FEI TUKE ISSN 1338-3957 (online), www.aei.tuke.sk
Table 1 Electrical and thermal parameters of the cooper,
used for the fuse.
Electrical conductivity 5.9E7 (/)
Heat capacity 385 (
/.)
Heat latent capacity 207 (
/.
Density 8700 (/)
Thermal conductivity 400 (/.)
Reference resistivity 1.72E-8 (Ω.)
Resistivity temp. coefficient 0.0039 (1/)
Reference temperature
Melting temperature
298
1358
(K)
(K)
Table 2 Thermal parameters of the fiberglass, used for the
board.
Thermal conductivity 0.04 (/.)
Heat capacity 400 (
/.)
Density 100 (/)
Electrical conductivity 0 S/m
Table 3 Thermal parameters of the surrounding air at 20oC.
Thermal conductivity 0.0257 (/.)
Heat capacity 1.005 (
/.)
Density 1.205 (/)
Kinematic viscosity 15.1110-6 (m/s)
Expansion coefficient 3.4310-3 (1/)
Prandtl’s Number 0.713
Fig. 7 shows the phase changing process during the
entire melting time. Generally, that time depends on two
parameters: the heat latent capacity (Table 1) and the
geometric characteristic of the fuse. This simulation
shows how the phase changing time can be altered during
the design procedure with changing the thinness, the
length and the width of the fuse. Here, the first thinness
(0.6 mm) is bigger than the second (0.5 mm) and the third
(0.4 mm). Such reducing of the overall volume reduces
the phase change time.
It must be considered that the time for the phase
change process is not equal to the entire switched-off time
of the fuse. After this process consequently start two
processes of evaporating and arc extinguish. This feature
requires a series of conducting conformation experiments.
Fig. 4 Thermal field as result of FEM simulation procedure.
Established of the process with nominal current through the
PCB fuse track.
Fig. 5 Thermal field as result of FEM simulation procedure.
Temperature with short circuit current.
4. EXPERIMENTALRESULTS
Experimental results are provided according to the
schematic on Fig. 1 with 10 different PCB fuses, produced
according to the shown FEM models – linear, zigzag and
spiral shapes. The major requirements are:
During a short circuit of the electronic device only
the PCB fuse should blow.
The circuit breaker must not switched-off and the
other loads powered with it must not be affected.
The current breaker is rated of 16A class C.
The PCB fuse must not blow during the transient
switch-on process of the electronic device due to
inrush current.
8 Determining PCB Trace Capability and Fusing, Used in Switch Mode Power Supplies …
ISSN 1335-8243 (print) © 2018 FEI TUKE ISSN 1338-3957 (online), www.aei.tuke.sk
The major problem is presented in Fig. 8, which is
found with a battery charger available on the market.
Curve 1 and 2 are AC voltage respectively before (point
A, Fig. 1) and after (point B) the PCB fuse. Curve 3 is the
current through the entire schematic: circuit breaker, fuse
and electronic device. In the moment of short circuit, the
fuse blows together with the shutting down of the circuit
breaker. This is depicted in curve 1 which also stops after
the short circuit.
Fig. 6 A: Zig-zag PCB fuse, FEM simulation procedure; B:
temperature distribution on the angle; C: temperature
distribution on the linear part. The color temperature line is the
same as Fig. 4.
The first correction of the design is shown in Fig. 9.
For these experiments 10 different PCB fuses are used as
well as numerical and physical models, with different
geometrical characteristics: thickness between 0.2 and 1.1
mm and length of 20 mm. Fig. 8 shows that the voltage is
continued after the short circuit but only for a half period,
which is an unsuccessful result.
This problem is solved with several geometrical
corrections of the PCB fuse, based on analytical
calculations and modeling with FEM. The result is shown
on Fig.10. In the moment of short circuit only the fuse
interrupts the current and disconnects the circuit – curve 2.
This event does not affect the work of the circuit breaker
and curve 1 is not interrupted.
Eventually, the design algorithm is shown in Fig.11.
The geometrical parameters of the PCB fuse are corrected
according to the interaction procedure, based on presented
FEM simulations and experiments.
Fig. 7 A melting process of the PCB fuse during its short
circuit. The results are based on a FEM model.
Fig 8 Short circuit of the PCB fuse. The fuse is working
incorrectly, because it causes shut down of the circuit breaker.
Curve 1 – voltage before PCB fuse, 2 – voltage after PCB fuse, 3
– current through the fuse.
Acta Electrotechnica et Informatica, Vol. 18, No. 2, 2018 9
ISSN 1335-8243 (print) © 2018 FEI TUKE ISSN 1338-3957 (online), www.aei.tuke.sk
Fig. 9 Short circuit of the PCB fuse /first correction of the
geometrical parameters/. Curve 1 – voltage before PCB fuse, 2 –
voltage after PCB fuse, 3 – current through the fuse.
Fig. 10 Short circuit of the PCB fuse. The fuse is working
correctly, because it does not cause shut down of the circuit
breaker. Curve 1 – voltage before PCB fuse, 2 – voltage after
PCB fuse, 3 – current through the fuse.
Fig. 11 The design procedure of PCB fuses based on FEM
modeling and simulations.
5. CONCLUSION
Established design methodologies, based on
analytical methods, are precise enough for fuses with a
fusible plug, but they do not show the desirable precision
for PCB fuses. This can cause the shutdown of the main
supply circuit breaker, before the fuse under short circuit
condition. The problem is seen even on switch mode
power supplies available on the market.
The standard design procedure used for standard PCB
track (Fig. 3, standard IPC-2221A) is not applicable for
PCB fuses. Shoed modelling with FEM during the design
procedure helps to improve and adapt the design of the
PCB fuses.
Conducted experiments and models showed that the
phase change time (Fig.7) can be taken as first assumption
around 1/3 of the AC period during the short circuit
current. For 50 Hz input voltage that time is 0.006-0.007
sec. In this conditions the designed PCB fuse can meet the
requirements showed above and will work correctly (Fig.
10) as part of the entire installation (Fig. 1).
ACKNOWLEDGMENTS
This paper is developed in the frames of project
“ELEVATE - ELEctrochemical Vehicle Advanced
TEchnology”, EP/M009394/1.
REFERENCES
[1] COONROD, J.: Keeping a Gauge on PCB Thermal
Effects, High Frequency, pages 32-42; March 2014.
[2] GUOQUAN, R. – BEN, L. – DONGWEI, L. –
YINGQI, J.: Modal Analysis of the Printed Circuit
Board on Finite Element Method. International
Conference on Computer Science and Electronic
Technology, ICCSET 2014, pp. 150 - 154, 2014.
[3] ADAM, J.: New Correlations Between Electrical
Current and Temperature Rise in PCB Traces.
Semiconductor Thermal Measurement and
Management Symposium 2004. Twentieth Annual
IEEE, 2004.
10 Determining PCB Trace Capability and Fusing, Used in Switch Mode Power Supplies …
ISSN 1335-8243 (print) © 2018 FEI TUKE ISSN 1338-3957 (online), www.aei.tuke.sk
[4] JOHANNES, A.: Thermal Management of Boards
and Current-Carrying Capacity of Traces, Bodo´s
Power Systems, http://www.bodospower.com/ 2011,
(actual on 12/06/2017).
[5] AMY, R. – AGLIETTI, G. – RICHARDSON, G.:
Accuracy of simplified printed circuit board finite
element models. Microelectronics Reliability 50, pp.
86-97. Elsevier. 2010.
[6] HAIYU, QI – GANESAN, S. – PECHT, M.: No-
fault-found and intermittent failures in electronic
products. Microelectronics Reliability 48, 663-674.
Elsevier, 2008.
[7] LOHAN, J. – TIILIKKA, P. – RODGERS, P. –
FAGER, C. – RANTALA, J.: Using Experimental
Analysis to Evaluate the Influence of Printed Circuit
Board Construction on the Thermal Performance of
Four Package Types in both Natural and Forced
Convection. Seventh Intersociety Conference on
Thermal and Thermomechanical Phenomena in
Electronic Systems, May 23-26, 2000.
[8] LUNN, T.C.: Designing for Board level
Electromagnetic Compatibility. Freescale
Semiconductor application note NA2321, Rev. 1,
10/2005, 2005.
[9] Infineon Technologies, EMC and System-ESD
Design Guidelines for Board Layout. Infineon
application note AP24026, 2016 www.infineon.com
(actual on 12/06/2017).
[10] BURKHARDT, A. – GREGG, C. – STANIFORTH,
A.: Calculation of PCB Track Impedance. Polar
instruments application note, Polar Instruments:
https://www. polarinstruments.com/, 1999, (actual on
12/06/2017).
[11] BROOKS, D.: Temperature Rise in PCB Traces.
UltraCad Desing Inc., Application note:
www.UltraCAD.com , 1998, (actual on 12/06/2017)
[12] IPC-2221A Generic Standard on Printed Board
Design IPC 2215 Sanders Road Northbrook, Illinois
60062-6135, May 2003.
[13] http://www.ultracad.com/, (actual on 12/06/2017).
[14] BROOKS, B. – ADAM, J.: Fusing Currents in
Traces, http://www.ultracad.com/, UltraCad Desing
Inc., Application note, 2015. (actual on 12/06/2017).
[15] http://comsol.com.
Received February 21, 2018, accepted April 27, 2018
BIOGRAPHIES
Borislav Dimitrov received the
M.Sc and PhD degrees in Electrical
Engineering from Technical
University of Varna in 2000 and
2008, respectively. Currently he is
working as a researcher at the
University of Southampton, UK.
Andrew Cruden received the
B.Eng. degree in electronic and
electrical engineering, the M.Sc.
degree in electrical power
engineering, and the Ph.D. degree in
the field of optical current sensing
from the University of Strathclyde,
Glasgow, U.K. In 2012 he became
the Professor of Energy Technology
at the University of Southampton, and is the Co-Director
of the EPSRC CDT in Energy Storage and its
Applications.
Suleiman M. Sharkh received the
B.Eng. and Ph.D. degrees in
electrical engineering from the
University of Southampton,
Southampton, U.K., in 1990 and
1994, respectively. He is Professor
of Power Electronics, Machines and
Drives, and Head of the
Mechatronics Research Group at the
University of Southampton. He is also the Managing
Director of HiT Systems Ltd. He has published over 160
papers in academic journals and conferences. His main
research interests are in the area of control, electrical
machine and power electronics with applications to
electric vehicles, marine propulsion, exhaust energy
recovery and submersible pumps.
