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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)

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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.

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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.

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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.

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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

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[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.

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[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).

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[8] LUNN, T.C.: Designing for Board level

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[9] Infineon Technologies, EMC and System-ESD

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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.