Post on 18-Dec-2016
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
[1] R.K. Hoffmann, Handbook of microwave integrated circuits, Norwood,MA, Artech House, Inc., 1987.
[2] J.R. James and P.H. Ladbrooke, ”Surface-wave phenomena associatedwith open-circuited stripline terminations”, Electronics Letters, vol. 9,pp. 570–571, 1973.
[3] R.J. Collier and P.D. White, ”Surface Waves in Microstrip Circuits”, 6thEuropean Microwave Conference, vol. 9, pp. 632–636, 1976.
[4] L.J. van der Pauw ”The Radiation of Electromagnetic Power by Mi-crostrip Configurations”, Microwave Theory and Techniques, IEEE Trans-actions on, vol. 25, pp. 719–725, 1977.
[5] J. Boukamp, ”Spectral Domain Investigation of Surface Wave Excitationand Radiation by Microstrip Lines and Microstrip Disk Resonators”,Microwave Conference, 1983. 13th European, pp. 721–726, Sept. 1983.
[6] A.A. Oliner and K.S. Lee, ”Surface Waves in Microstrip Circuits”,Microwave Symposium Digest, 1986 IEEE MTT-S International, vol. 9,pp. 632–636, 1986.
[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.
[10] C.R. Brewitt-Taylor, ”Radiation from Via-Holes in MMICs”, MicrowaveConference, 17th European, pp. 433–436, 1987.
[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.
[18] E. Hammerstad and O. Jensen, ”Accurate Models for MicrostripComputer-Aided Design”, Microwave symposium Digest, 1980 IEEEMTT-S International, pp. 407–409, 1980.
[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