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ECCTD’01 - European Conference on Circuit Theory and Design, August 28-31, 2001, Espoo, Finland

Simulation of the Coupling of an External ElectromagneticField to the PCB Traces in SPICE Simulator

Andrzej Dobrzański* and Wojciech Bandurski*

Abstract – In the paper the response of PCB structureto an electromagnetic field has been investigated.Employing active transmission line model the analyticalexpressions were derived for waveforms of currentsources. An illustrative example of trace on PCBterminated by ECL gates and illuminated by doubleexponential has been presented.

1 Introduction

Various time-domain models exist for predictingthe induced voltages and currents by coupling ofelectromagnetic waves to Printed Circuit Board(PCB). The more exact of these are based on 3-Danalysis (e.g. FT-DT) of electromagnetic field,however they still require great computationalresources if applied to practical problems.

Hence the coupling phenomenon of an externalelectromagnetic field to a PCB is usually modeled byelectromagnetic plane wave incident on a system oftransmission lines, with PUL parameters calculatedfrom PCB structure, placed in free-space aboveperfectly conducting plane. Next incident electricfield is converted to distributed voltage and currentsources located along the line e.g. [1]. Such a line wecold Active Lossy Transmission Line (ALTL). Itappears however [2] that such an approach is toosimple some times and can provide erroneous results.

Recently in [3] was proposed the method forsolving this problem. Basing on the general theory ofplanarly layered media, were derived analyticalfrequency-domain expressions describing horizontalelectric field component on the substrate surface andvertical electric field component in the substrate.These expressions were simplified by low-frequencyapproximation and next transform to the time-domain. Such an approach permits for taking intoaccount distortion of electromagnetic wave in treelayer medium (air, substrate, and conductor) andtherefore more realistic simulation [2].

Different versions of SPICE are equipped in modelsof losslees and lossy, single and multiconductortransmission lines. However there is no widely andeasily accessible transmission line model withindependent distributed voltage and current sourcesin SPICE family simulators.

* Poznań University of Technology, Inst. of Electronics andTelecommunication, 60-965 Poznań, ul. Piotrowo 3a,Poland, E-mail: Wojciech.Bandurski@put.poznan.pl

The aim of this paper is to propose a subcircuit,modeling an ALTL in SPICE, consisting of a model ofPassive Lossy Transmission Line (PLTL) and twocurrent sources connected in parallel to the input andoutput PLTL ports. Moreover we give, basing on [3],a procedure of conversion of an external electro-magnetic field incident on PCB traces into functionsdescribing the current sources.

2 Theory

Our approach will be explained, for simplicity, on thecase of single lossy TL, but it can be extended for thecase of the multiconductor TL. In the ALTL model inFig.1 current i1 (t) and i2 (t), which are the sums of

u (t)2

Y c

u (t) 1

j (t)1

j (t)2

i (t) 1i (t)2

2Sj (t)

j (t)1S

Yc

ALTL

PLTL

Figure 1: Model of the ALTL as connection of PLTLand current source j1 (t) and j2 (t).

j1(t), j2(t) and respectively input and output PLTLmodel currents, have to control the internal PLTLcurrent sources j1s (t), j2s (t) (eqs. (2), (4)). Therefore itis impossible to use own SPICE models of PLTL.Hence we have to create such a model also. It wasdone on the base of method described in [5].

2.1. Model of an active lossy transmissionline The telegrapher’s equations, for an active transmissionline has the following form

jtuCRu

zie

tiLRi

zu

−∂∂+=

∂∂−−

∂∂+=

∂∂− , (1)

Eqs. (1) can be solved by the method of successiveapproximation [5]. The solution can be written in theform:

),(2),1()(1),0()(2),1(

),(1),1()(2),0()(1),0(

ττττττττττττ

jiSiSi

jiSiSi+−∗++∗=+

−−∗++∗=− (2)

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In (2) S1(τ), S2(τ) are scattering parameters of the lineand i-, i+ are backward and forward current wavesrespectively. Functions j1, j2 represent distributedcurrent and voltage sources. For the case oftransmission line with the small loses ( R l Zc/ 2 < ππππ)first order approximation of the solution (2) is simple,exact enough [5] and poses the form

[ ]

.),,0(),0(),0(),,0(),0(),0(

,)1,()(

,),()(

),1()(,)2()(2

)(

1

0

)1(2

1

01

21

etcivYiivYi

djej

djej

eSeb

S

c

c

a

a

aa

ττττττ

ξξτξτ

ξξτξτ

τδττττ

ξ

ξ

τ

+=−=

+−∫=

−∫=

−=−−=

+

−

+−−

−−

−− 11

(3)

where( ) ( )

.),(),(),.(,,

,10,,

,,,

,21,2

1

1

ττττ

yjyeYyjlengthlinelTt

lzyLClT

LC

ZY

parameterslineCGLR

lRYcGZcblRYcGZca

c

cc

!! =

−=

≤=≤===

−

−=+=

−

Functions j1(τ), j2(τ) (3) are specified current wave-forms of the two independent current sources shown inFig.1. Controlled current sources marked in Fig.1 as j1s (τ), j2s (τ) has the form

).,1()(),0()()(),,1()(),0()()(

122

211

ττττττττττ

iSiSj

iSiSj

s

s

−+

−+

∗+∗=∗+∗=

(4)

Relationships (4), in which the stars denote con-volution, can be easily modeled in SPICE by means oflossless transmission lines and first order circuits.Basing on eqs. (2), (4) and Fig.1 an equivalent circuitfor ALTL has been created in SPICE. The separateproblem are formulas describing conversion ofexternal electromagnetic field into current sourcesj1(τ), j2 (τ), we will discuss this in the next point.

2.2 External electomagnetic field

Distributed sources ek(z,t), jk(z,t), for k-th conductor,depend on electric field vector and are described byknown formulas e.g.[4] in following manner:

∫=

∫−=

k

k

x

kxk

x

kxkkzk

xdtzyxEtCtzj

xdtzyxEztzyxEtze

0

0

,),,,(),(

,),,,(),,,(),(

∂∂

∂∂

(5)

wherez k kE x y z t( , , , ) - horizontal component of the electric

field for k-th conductor, x kE x y z t( , , , ) - vertical component of the electricfield for k-th conductor.For simplicity of calculation, the externalelectromagnetic field is usually considered as a generaluniform plane wave of the form

( )

−−

−−

−−⋅

⋅++=

z

o

y

o

x

o

omzzyyxx

vzz

vyy

vxx

t

fEaeaeaetzyxE""""

),,,(

(6)

where

( ) ( )( ) ( ) ( ) ( ) ( )( ) ( ) ( ) ( ) ( )

e

e

e

x E p

y E p p E p

z E p p E p

= −

= − −

= − +

sin sin ,

sin cos cos cos sin ,

sin cos sin cos cos ,

θθθθ θθθθ

θθθθ θθθθ φφφφ θθθθ φφφφ

θθθθ θθθθ φφφφ θθθθ φφφφ

( ) ( ) ( )

( ) ( ).sinsin

,cossin

,cos

ppz

ppy

px

vv

vvvv

φθ

φθθ

−=

−=−=

The angles are with reference to Fig.2. The electricfield components zE and xE were calculated for the

Figure 2: Nonhomogeneous structure - PCB.

configuration of conductors (traces) shown in Fig.2 onthe basis of closed form formulas derived in [3]. Next,basing on formulas (6), (5) and (3) we derivedformulas for current source j1(t), j2(t) :

[ ]

[ ]),(),(*)(

),(),(*)(

212

111

tTGBtTGAeTT

lEtj

tTFBtTFAeTT

lEtj

hTT

at

z

m

hTTat

z

m

z

z

ε

ε

+−

=

++

=

≥−−

+−

(7)

where

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*- denotes convolution,

,)(

)()()(),(

,)(

)()()(),(

apo

aozpozop

apzo

azopoop

eTTtf

eTtfTTtfTtftTG

eTTTtf

eTTtfTtftftTF

−

−

−

−

−−+

−−−−−−=

−−−+

−−−−−=

−

−

=,

)sin(

)sin()sin()cos()cos()cos(2

1

r

pr

pEpEp

cYA

εθε

φθφθθ

),sin()sin()sin( 2

2/1 pE

prr

o

z

oc v

vvv

YB θθ

θεε −

±

=

.,)sin(2,2 2

zzpr

ooh v

lTvhT

vhT =−== θεε

3 Results

As a test we consider an example of structure shown inFig.1. The traces possessing coordinates y3=-300,y2=0, y1=100 x1= x2= x3=625 with thickness t1=t2=t3=30 and widths w1=60 w2=100 w3=100 [µm] havelengths of 20 cm. They are placed on commonsubstrate with εr =4.7 and conductance of the traces isσ =5.6E7 [m-1 Ω-1]. The traces are excited by double-exponential pulse (EMP) with parameters Em =-3kV/mand time constants of 1 ns and 20 ns. ECL gates andtheir pull-down networks (see Fig.3) terminate thetraces.

Figure 3: The traces terminated by ECL gates and theirpull-down networks, Rbb=600Ω, Vbb=-2V.

This PCB structure is illuminated by an electro-

magnetic plane wave incident at the different angles.The greatest electromagnetic noise can be observed inthree cases. In the first case, referred as endfireexcitation [4], angles are θp = 90o, φp = -90o, θE = 90o

and resulting output voltages of the lines v(4), v(5),v(6) (see Fig.3) are shown on the lower plot of theFig.4. The upper plot of this figure shows outputvoltages of ECL gates v(41), v(51), v(61) (see Fig.3).

In the second case, referred as sidefire excitation [4],angles are θp = 180o, φp = 0o, θE = 0o and resultingoutput voltages of the lines v(4), v(5), v(6) (see Fig.3)are shown on the lower plot of the Fig.5. The upperplot of this figure shows output voltages of ECL gatesv(41), v(51), v(61) (see Fig.3).

In the third case, referred as broadside excitation [4],angles are θp = 90o, φp = 0o, θE = 90o and resultingoutput voltages of the lines v(4), v(5), v(6) (see Fig.3)are shown on the lower plot of the Fig.6. The upperplot of this figure shows output voltages of ECL gatesv(41), v(51), v(61) (see Fig.3).

Voltages from the range (-1V, -1.2V) representslogical “1” and from range (-1.6V, -2V) logical “0”.The voltage at the level –1.4V is intermediate non-stable state. In all cases electromagnetic noise causesswitching phenomena between logical “0” and “1” atthe output of the ECL gates or introduce the gate inintermediate state.

4 Conclusions

This paper present a simple SPICE model fortransient analysis of the coupled transmission linesexcited by an external field. The main result of thepaper are derived formulas (3) and (7) describing thelumped current sources j1(t), j2(t) connected to theinput and output ports of lossy PLTL. In theseformulas function fo(t), which describes the timedependence of the electric field may be arbitrary.Hence not only double-exponential pulse excitationmay be con-sidered. The advantages of SPICEenvironment together with proposed model of theALTL permits for simulation and investigation ofpractical problems, which arise in electromagneticenvironment. The obtained results permit for the firsttime the more exact SPICE modeling and simulationof nonhomogeneous structures (PCB) illuminated byelectromagnetic plane wave. As it was mentioned inintroduction low-frequency approximation of electricfield was adopted from [3], actually we work on fullrange frequency approximation, which can be includedto time-domain simulation and the results arepromising.

ECL

ECL

ECL

ECL

ECL

ECL

Rb

bR

bb

Rb

b

Vbb

Vbb

Vbb

V4

V5

V6MTL line

ε(t,r)

V1

V2

V3 V61

V51

V41

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T im e

2 n s 3 n s 4 n s 5 n s 6 n s 7 n s 8 n s 9 n s 1 0 n sV (4 ) V (5 ) V (6 )

-2 .5 V

-2 .0 V

-1 .5 V

-1 .0 VV (6 1 ) V (4 1 ) V (5 1 )

-1 .6 V

-1 .4 V

-1 .2 V

Figure 4: Output voltages for the endfire case.

T im e

2 n s 3 n s 4 n s 5 n s 6 n s 7 n s 8 n s 9 n s 1 0 n sV ( 4 ) V ( 5 ) V ( 6 )

- 2 .5 V

- 2 .0 V

- 1 .5 V

- 1 .0 VV ( 6 1 ) V ( 4 1 ) V ( 5 1 )

- 1 .6 V

- 1 .4 V

- 1 .2 V

Figure 5: Output voltages for the sidefire case.

T im e

2 n s 3 n s 4 n s 5 n s 6 n s 7 n s 8 n s 9 n s 1 0 n sV ( 4 ) V ( 5 ) V ( 6 )

- 2 . 5 V

- 2 . 0 V

- 1 . 5 V

- 1 . 0 V

S E L > >

V ( 6 1 ) V ( 4 1 ) V ( 5 1 )- 1 . 6 V

- 1 . 4 V

- 1 . 2 V

Figure 6: Output voltages for the broadside case.

References

[1] Maio I., Canavero G.F., “Analysis of crosstalkand field coupling to lossy MTL’s in a SPICEenvironment”, IEEE Tran. on EMC, vol. 38, No.3, August 1996, pp.221-229.

[2] Lapohos T., Vetri J.L., Seregelyi J., “Externalfield coupling to MTL networks with nonlinearjunctions: numerical modeling and experimentalvalidation”, IEEE Tran. on EMC, vol. 42, No. 1,February 2000, pp.16-28.

[3] Leone M., Singer H.L., “On the coupling of anexternal electromagnetic field to a PCB trace”,IEEE Tran. on EMC, vol. 41, No. 4, November1999, pp. 418-424.

[4] Paul C.R., Analysis of multiconductortransmission lines, John Wiley & Sons, 1994.

[5] W.Bandurski, “Simulation of single and coupledtransmission lines using time-domain scatteringparameters”, IEEE Tran. Circuit Syst., vol.47,pp. 1224-1234, Aug. 2000.