Microstrip CAD Models Including Surface Wave

Coupling

Andreas R. Diewald

IEE S.A., 11, rue Edmond Reuter,

5326 Contern, Luxembourg,

e-mail: Andreas.Diewald@rwth-aachen.de

Abstract—Surface waves, especially the fundamental substrate-guided TMz

0 mode, are excited by any kind of discontinuity inRF printed circuit boards (PCBs) and planar microwave circuits.This special type of substrate-bound radiation is highly increasingwith frequency and can become a dominant coupling mechanismin planar circuits. In this paper, an efficient method is presentedto calculate correctly the coupling mechanism by surface waveradiation. The required current distribution is estimated onlywith single-port CAD models.

Index Terms—substrate, surface wave, planar circuit, radia-tion, coupling.

I. INTRODUCTION

Today, the majority of RF and microwave circuits is realized

in planar technologies like RF PCB, MIC (microwave inte-

grated circuits) and LTCC (low temperature cofired ceramics).

These techniques use planar dielectric carriers (substrates)

with metallizations, mostly one side is totally metallized as

the ground plane. The substrate can guide surface waves,

particularly the fundamental surface mode TMz0 that has a

zero cut-off frequency ( fcuto f f = 0Hz) and is always present.

The amount of power transferred into a surface wave mode

increases linearly at low frequencies, so their effects are only

negligible up to their gradual onset, depending on substrate

dielectric constant, thickness and the specific discontinuity.

Analytical models for microstrip circuit elements are available

in commercial CAD tools. To verify electromagnetic (EM)

coupling in these circuits, commercial fullwave-solvers, based

on different simulation approaches (FEM, FDTD, PEEC,

MoM, SDA, TLM, etc.) are well-proven. Most of these ap-

proaches are capable to account for surface waves implicitely

(except PEEC), but all of them are very time-consuming.

The above mentioned analytical CAD models are not able to

handle coupling by surface waves. The power of this kind

of guided radiation decreases along the surface with 1/rin contrast to freespace-radiation (1/r2). Therefore, surface

wave radiation has a far reaching effect, causes performance

perturbation and is the main cause responsible for coupling

phenomena [1].

Surface wave radiation was occasionally investigated in the

last decades. The transmission coefficient of a microstrip

line open end was estimated using the field impedances of

the strip and surface wave mode [2] and also measured

experimentally [3]. The overall radiated power of microstrip

lines and resonators [4], but also the surface wave excitation

by fundamental [5] and higher microstrip and resonator modes

[6] were investigated with spectral domain approaches, while

the radiation of horizontal current dipoles placed on the

air/dielectric interface has been explained in [7].

The current distribution and the full radiated spectrum, sep-

arated into surface and space wave, have been calculated for

the microstrip open end [8] and other planar discontinuities

like radial stub, microstrip bends [9]. The authors show, that

for purely planar microstrip discontinuities without vias, the

amount of surface and space wave power are nearly equal.

In contrast to that, in [10] the radiation, also separated into

space and surface waves has been presented for a single

horizontal current element connecting the substrate surface to

ground, showing that the amount of surface wave power can

be much higher than the space wave power. First far-field cou-

pling calculations of purely planar microstrip discontinuities

for shielded circuits were presented by [11] and qualitative

statements about the coupling in fully open structures are given

in [12]. Although there were some efforts in this field, the final

step for the integration of surface wave radiation and coupling

in segmentation-based CAD is missing.

In [13], [14] or alternatively [15] a very fast method is

developed to calculate correctly the surface wave coupling

between one-port microstrip structures. The novel approach

applied on the raw current distribution of a fullwave solution

(CST Microwave Studio) is presented in [16] and shows

excellent agreement with the coupling determined by the

fullwave solution itself. In this paper, we shortly present the

method applied on microstrip open ends and via grounds, for

which the current distribution is estimated from common CAD

models [18] [17].

II. ESTIMATION OF CURRENTS

For a realistic microstrip line, in contrast to patch antennas,

the main part of current is flowing on the edges, thus the half-

side I(x)/2 current average can be located on

ycur =±wef f

4=±

h

4ZL

ωμ0

β

as a good approximation. For low frequencies, it is not

important if the current is represented as one or two filaments,

but for higher frequencies the phase shift of both filaments can

be noticed in the surface wave characteristic. For wide lines

multiple filaments can be necessary.

6th European Conference on Antennas and Propagation (EUCAP)

978-1-4577-0919-7/12/$26.00 ©2011 IEEE 398

A. Microstrip open end

The horizontal current distribution of a microstrip open end

at x= 0 can directly be estimated by the reflection coefficient.

I(x) = Iinc.(−l) ·(

e−jkStrip(x+l)−Γ(−l) · e+jkStrip(x+l))

with the reflection coefficient

Γ =1− jωC ·ZL1+ jωC ·ZL

The capacitance can be computed by the formula of Hammer-

stad [18]. In this approximation evanescent currents caused

by the discontinuity are neglected because they are hardly

contributing to surface wave radiation [15].

B. Microstrip via ground

The modeling of a via to ground is more complex than for a

microstrip open end. The following Fig. 1 shows an enhanced

network model of an via ground including the pad capacitance.

mic

rost

rip

ref. plane

LVia

RVia

IVia

IPadIin

IL

CPad GPad

Fig. 1. Network modell of microstrip via ground

When the reference plane is located in the center of the via

cylinder (x= 0), the current distribution is determined together

with the via inductance LVia and the frequency dependant

ohmic resistance RVia [17]. The vertical currents on the via

cylinder are nearly constant, so IL= Iz(z= h)≈ IVia= Iz(z= 0).The azimutal current distribution of the via cylinder is also

modeled as an equivalent current filament and is placed at

the effective location, which is estimated with the scattering

formula for a cylinder of [20]

xIz =

2π∫0

rVia cos(φ)

∣∣∣∣ ∞

∑n=−∞

(j−n ejnφ

H(2)n (kStriprvia)

)∣∣∣∣dφ

2π∫0

∣∣∣∣ ∞

∑n=−∞

(j−n ejnφ

H(2)n (kStriprvia)

)∣∣∣∣dφ

The parameter GPad (radiation caused by pad) is not zero for

large pads, but for realistic pads, this loss can be neglected.

The capacitance of the pad CPad is estimated by the formula of

Hammerstad [18], although the fringe field under the strip can

be distorted by the via to ground conductor. The capacitance

GStub is line transformed from the open end to the via center

(Δx = lStub) and the analytical capacitance of the half via

cylinder εrε0 · (πr2Via)/(2h) is substracted. Both can be done

stepwisely as shown in Fig. 2. For computation of surface

wave radiation the vertical currents are considered, but also

the horizontal microstrip line currents which are modeled in

a similar way as of the microstrip open end.

x= 0

x= xi

x = xi−1 = xi+Δx

Ai

Cx=lStubStub

x= lStub

Fig. 2. Top view of microstrip via ground and via pad

III. SURFACE WAVE RADIATION AND COUPLING

With the above presented CAD model of a microstrip

via ground an approximate current distribution is estimated.

Comparison with fullwave simulations is shown in [15] and fits

well. The radiated surface wave is computed with the methode

in [13]. To compute the radiation resistance a numerical

surface integral is evaluated in a distance of 1 m around the

via, which separates into a numerical ring integration and a

analytical integration over the via height, as the surface wave

distribution in z-direction is equal on every point (x,y). The

Fig. 3 shows the comparison between measurements, fullwave

simulation (CST MWS), our new model and the models with

pure vertical currents from Brewitt [10] and Vrba [21] .

0 5 10 15 20 25 30 35

10−3

10−2

10−1

100

101

102

Radiation resistance

f/GHz

(RSWrad+RVia)/

Ω

Measurement

CST MWS

Vrba [21]

Brewitt [10]

New model

Fig. 3. Comparison of measurement, simulation and model for h= 635 μm,εr = 6, rVia = 0.25 mm and wStrip = 1 mm

The coupling between several single-port discontinuities is

developed explicitly in [14]. The magnitude and the phase

of the S-Parameter S12 is computed as follows

|S12|=|b1|

|a2|=

√√√√(

1−|S11|2)

|a2|2Ps,1

· (1)

√2|n̂′ver|

2

16 · k3ρS2(r1,z= 0)S1(r2,z= 0) ·2π |r1− r2|

399

� S12 = � E2(r1)+ � E1(r2)−(−kρ · |r1− r2|

)(2)

IV. VERIFICATION

The approach is compared to measurements and a fullwave

simulation of a circuit mixed with two shorting vias (port 1

and 3) and with two microstrip open end (port 2 and 4) as

shown in the photograph (Fig. 4).

port

4port

3

port

2port

1

Fig. 4. Photograph of circuit with port numbering

The comparison of magnitude is shown in Fig. 6 and the

comparison of phase is shown in Fig. 5. The novel approach

shows good results for coupling to opposite discontinuities

and the agreement is much better as the fullwave simulation.

The coupling between lateral placed discontinuities (S21 and

S34) is much higher in the measurements, because in the new

approach, but also in the fullwave simulation, coupling to the

”‘on wafer pads”’ is not considered.

0 0.5 1 1.5 2 2.5 3 3.5

x 1010

−4000

−3000

−2000

−1000

0

1000

f/Hz

�S/◦

Fig. 5. Phase comparison of new approach with measurements and fullwavesimulations

The large difference between fullwave simulation and mea-

surement for lower frequencies can be explained by a draw-

back of finite elemente simulations. Because the surface wave

fields reaches higher for low frequencies, a non-negligible

portion of power is absorbed by the lossy boundaries of the

fullwave simulation, which results in a damping over the

distance.

V. CONCLUSION

An efficient and accurate semi-analytical calculation

method for the surface wave radiation and coupling from

single-port microstrip CAD models is presented here.

The results show a very good agreement with rigorous

fullwave simulations and measurements.

The method presented here is a further step towards a

surface wave coupling model connecting separate single-port

microstrip discontinuities in segmentation based CAD.

REFERENCES

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[7] J.R. Mosig and F.E. Gardiol, ”Analytical and numerical techniques inthe Green’s function treatment of microstrip antennas and scatterers”,Microwaves, Optics and Antennas, IEE Proceedings H, vol. 130, pp. 175–182, 1983.

[8] T.-S. Horng and S.-C. Wu and H.-Y. Yang and N.G. Alexopoulos, ”Ageneralized method for distinguishing between radiation and surface-wavelosses in microstrip discontinuities”, Microwave Theory and Techniques,IEEE Transactions on, vol. 38, pp. 1800–1807, 1990.

[9] W.P. Harokopus and L.P.B. Katehi and W.Y. Ali-Ahmad and G.M. Re-beiz, ”Surface wave excitation from open microstrip discontinuities”,Microwave Theory and Techniques, IEEE Transactions on, vol. 39, pp.1098–1107, 1991.

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[11] R.H. Jansen and L. Wiemer, ”Full-wave theory based development ofmm-wave circuit models for microstrip open end, gap, step, bend andtee”, Microwave Symposium Digest, 1989., IEEE MTT-S International,vol. 2, pp. 779–782, 1989.

[12] D. Vanhoenacker and I. Huynen, ”Prediction of surface wave radiationcoupling on microwave planar circuits”, Microwave and Guided WaveLetters, IEEE, vol. 5, pp. 255–257, 1995.

[13] A.R. Diewald, R.H. Jansen and J. Vrba ”Excitation Mechanism for Sur-face Waves in PCBs and Microstrip Circuits”, Antennas and Propagation,IEEE Transactions on, vol. xx, pp. xxx–xxx, submitted for publication.

[14] A.R. Diewald and R.H. Jansen ”Surface Wave Coupling Mechanismin PCBs and Microstrip Circuits”, Antennas and Propagation, IEEETransactions on, vol. xx, pp. xxx–xxx, submitted for publication.

[15] A.R. Diewald, ”‘Anregungs- und Kopplungsmechanismen von Sub-stratwellen in HF- und Mikrowellenschaltungen”’, PhD-thesis, RWTHAachen, Chair of Electromagnetic Theory, 2012, in final review.

[16] A.R. Diewald and R.H. Jansen, ”Surface Wave Excitation and CouplingMechanisms in PCBs and Microstrip Circuits”, Microwave Conference(GeMIC), 7th German, vol. 7, 2012, accepted for publication

[17] M.E. Goldfarb and R.A. Pucel, ”Modeling via hole grounds in mi-crostrip”, Microwave and Guided Wave Letters, IEEE, vol. 1, pp. 135–137, 1991.

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[19] Das, N.K. and Pozar, D.M., ”A Generalized Spectral-Domain Green’sFunction for Multilayer Dielectric Substrates with Application to Mul-tilayer Transmission Lines”, Microwave Theory and Techniques, IEEETransactions on, vol. 3, pp. 326–335, 1987.

[20] C. A. Balanis, Advanced engineering electromagnetics, Wiley, 1989.[21] J. Vrba jun., ”Investigation of the EM field of microstrip via structures

including radiation into space and coupling to substrate modes formultilayer substrates”, Master thesis, RWTH Aachen, 2006.

400

0 0.5 1 1.5 2 2.5 3 3.5

x 1010

10−4

10−3

10−2

10−1

100

0 0.5 1 1.5 2 2.5 3 3.5

x 1010

10−4

10−3

10−2

10−1

100

0 0.5 1 1.5 2 2.5 3 3.5

x 1010

10−4

10−3

10−2

10−1

100

0 0.5 1 1.5 2 2.5 3 3.5

x 1010

10−4

10−3

10−2

10−1

100

0 0.5 1 1.5 2 2.5 3 3.5

x 1010

10−4

10−3

10−2

10−1

100

0 0.5 1 1.5 2 2.5 3 3.5

x 1010

10−4

10−3

10−2

10−1

100

f/Hz

f/Hz

f/Hzf/Hz

f/Hz

f/Hz

|S|

|S|

|S|

|S|

|S|

|S|

S12 (CST)

S12 (Meas.)

S12 (Model)

S21 (Model)

S13 (CST)

S13 (Meas.)

S13 (Model)

S31 (Model)

S14 (CST)

S14 (Meas.)

S14 (Model)

S41 (Model)

S23 (CST)

S23 (Meas.)

S23 (Model)

S32 (Model)

S24 (CST)

S24 (Meas.)

S24 (Model)

S42 (Model)

S34 (CST)

S34 (Meas.)

S34 (Model)

S43 (Model)

Fig. 6. Magnitude comparison of new approach with measurements and fullwave simulations

401