Chapter - 2
Application of EM- Simulators for Extraction of
Line Parameters
2. 1
Introduction
The EM-simulators-2D, 2.5D and 3D, are powerful tools for the analysis of the planar
transmission lines structure. Fig.(2.1) shows structures to which these simulators are
normally used. The EM-simulators are used to obtain equivalent circuits and equivalent
transmission line parameters. Thus, this chapter presents the process of extraction of line
parameters of different planar transmission lines using the EM-simulators. The results
obtained using three EM-simulators are compared among themselves. The method of
excitations and de-embedding techniques, in each one of the EM-simulators, are
explained.
(a)
(b)
(c)
Fig.(2.1): EM-simulators classified by geometrical dimensionality:(a) 2D cross-section, (b) 2.5D mostly
planar, and (c) 3D fully arbitrary.
The main objective in this chapter is to realize different planar transmission lines in EMsimulators and compare their line parameters (de-embedded and non de-embedded)
against results from experiments and analytical models. The study has been done in this
13
Application of EM-Simulators
thesis for microstrip, CPW, CPS and slotline on six different substrates with permittivity
ranges from 2.5 - 37 in the frequency range 0.1 GHz – 200 GHz and conductor thickness
ranges from 0.25µm – 9µm. This chapter also computes the RLCG parameters of planar
lines using the EM-simulators.
2.2 EM Simulators for Extracting Data
In this thesis, mainly three EM-simulators are used– 1) Ansoft HFSS [15], 2) CST
Microwave Studio [28] and 3) Sonnet Professional Suite [115]. In this section, we will
briefly review issues that are common with these simulators. These special issues include
method of excitation and de-embedding. Both aspects are essential for detailed study of
the planar transmission lines.
Table - 2.1: Characteristics of EM-simulators
Ansoft HFSS [15]
CST Microwave Studio [28]
3D Arbitrary geometry solver
Numerical method: FEM
Arbitrary geometry and resolution
Tetrahedral edge elements; closed
box formulation
Eigenmode-solver
3D Arbitrary geometry solver
Numerical method: FIT (FDTD)
Conformal approx. in 3D
Transient solver, eigenmode solver, modal analysis simulator
2D eigenmode - solver for port
modes
Optimization capability
Built in parametric sweep and
optimization
Code is multithreaded
True surface object modeling
Perfectly matched layers (PMLs)
Eigenmode - solver supports two
processors on PC
Second order absorbing boundary
conditions (ABCs)
Dual processor support
Well integrated
interface
14
ACIS-based
Sonnet Pro Suite [116]
2.5D Planar solver
Numerical method: MoM
Closed box formulation
Suitable basis functions
Diagonal elements, dielectric
bricks and calibrated internal
ports
Fast sweep
Support modules for viewing
currents
rd
3 party module for viewing
geometry in 3D
Optimization and parametric
analysis
Bulk
conductivity
for
semiconductor substrates
Application of EM-Simulators
The main characteristics of each EM-simulator are summarized in Table-2.1. All of these
simulators approximate the true fields or currents in the problem space by subdividing the
problem into basic “cells” or “elements” that are roughly 1/10 to 1/20 of a guide
wavelength in size.
2.2.1 Method of Excitation
The boundary conditions are important to understand and are fundamental to solution of
Maxwell’s equations. These conditions enable to control the characteristics of planes,
faces, or interfaces between objects. An excitation port is a type of boundary condition
that permits energy to flow into and out of a structure. A port is a 2D surface on which
the fields will be solved according to Maxwell’s equations to determine appropriate RF
modal excitations into the 3D model volume. It can be assigned to any 2D object or 3D
object face. Before the full three-dimensional electromagnetic field inside a structure can
be calculated, it is necessary to determine the excitation field pattern at each port. The
method of excitations in each one of the EM-simulators, are discussed in this section.
•
Ansoft HFSS – There are two types of method of excitation available in Ansoft
HFSS, as shown in Fig.(2.2):
(i) Wave Ports are applied to the structure to indicate the area where the energy enters
and exits the conductive shield. The HFSS port solver assumes that the wave port
defined is connected to a semi-infinitely long waveguide that has the same crosssection and material properties as the port, then solves for the Eigen modes. This
mode solution is a key point. Each wave port is excited individually and each mode
incident on a port contains 1 Watt of time-averaged power. The wave ports calculate
characteristic impedance, complex propagation constant and generalized Sparameters.
15
Application of EM-Simulators
It also solves for the port impedance based on one of the three definitions using
combinations of power, voltage or current, i.e. Zpi, Zpv and Zvi. Ansoft HFSS always
calculates Zpi. The impedance calculation using power and current is well defined for
a wave port. The wave ports permit de-embedding to remove excess uniform input
transmission lengths.
(ii)
Lumped Ports are applied to model internal ports within a structure. They excite
simplified field distributions to permit S-parameter outputs, where wave ports are not
feasible and support only uniform field distributions. They must contact two surfaces
that constitute a transmission line and definition includes a line which is parallel to
the direction of current. They are normally defined on a 2D object (a rectangle). The
proportions of this rectangle should not have a huge aspect ratio. These ports do not
calculate characteristic impedance and propagation constants. The impedance and
calibration line assignments are required for lumped port assignments. A terminal
line may still be defined, but only one per port. As impedance is supplied by the user
and not computed, no alternate definitions (Zpi, Zpv, Zvi) are supplied. Since
propagation constants are not computed, lumped port S-parameters may not be deembedded to remove or add uniform input transmission lengths.
(a)
(b)
Fig.(2.2): Types of Method of Excitation in Ansoft HFSS:(a) Wave Port, and (b) Lumped Port.
16
Application of EM-Simulators
•
CST Microwave Studio – In this simulator, generally two different types of ports
exist for the transient and frequency domain analyses, as shown in Fig.(2.3):
(i)
Waveguide Ports simulate an infinitely long wave guide connected to the structure
and are definitely the most accurate way to terminate a waveguide. The waveguide
modes travel out of the structure towards the boundary planes and thus leave the
computation domain with very low levels of reflections. The transient analysis only
uses so-called waveguide ports.
(ii)
Discrete Ports are sometimes more convenient to use than waveguide ports. They
consist of a current source with an internal resistor and have two pins with which
they can be connected to the structure. This kind of port is often used as feeding
point source for antennas or as the termination of transmission lines at very low
frequencies. At higher frequencies (e.g. the length of the discrete port is longer than
a tenth of a wavelength) the S-parameters may differ from those when using
waveguide ports because of the improper match between the port and the structure.
For transient or frequency domain analyses, discrete ports can be used in the same
way as waveguide ports.
(a)
(b)
Fig.(2.3): Types of Method of Excitation in CST Microwave Studio:(a) Waveguide Port and
(b) Discrete Port.
17
Application of EM-Simulators
•
Sonnet Pro Suite - There are five types of ports used in Sonnet and all ports are twoterminal devices. The default normalizing impedance for a port is 50 Ohms. There is
no limit on the number of ports and the number of ports has a minimal impact on the
analysis time needed for de-embedding. By default, the ports are numbered by the
order in which they are created. With this default method, all ports are positive and
unique. However, there are some applications that require the ports to have duplicate
or even negative, numbers. Each type of port is described below and is shown in
Fig.(2.4).
(i) Standard Box wall port is a grounded port, with the positive terminal attached to a
polygon edge coincident with a box wall and the negative terminal attached to
ground. It can be de-embedded and can also have reference planes. This type of port
is the most commonly used.
(ii) Co-calibrated ports are used in the interior of a circuit. Co-calibrated internal ports
are identified as part of a calibration group with a common ground node connection.
The ground node connection can be defined as floating or the Sonnet box. When the
simulator performs the electromagnetic analysis, the co-calibrated ports within a
group are simultaneously de-embedded using a high accuracy de-embedding
technique; thus, coupling between all the ports within a calibration group is removed
during de-embedding. This type of port is the most commonly used internal port. The
reference planes may be used as well.
(iii) Via port has the negative terminal connected to a polygon on a given circuit level
and the positive terminal connected to a second polygon on another circuit level.
This port can also have the negative terminal connected to the top or bottom of the
box. Unlike co-calibrated ports, EM simulation cannot de-embed via ports. The most
common case where a via port would be used is to attach a port between two
adjacent levels in the circuit and to connect a port to the interior of a polygon, which
18
Application of EM-Simulators
is not allowed for co-calibrated ports. The reference planes cannot be applied to via
ports, since it is not possible for EM simulation to de-embed them.
(a)
(b)
(c)
(d)
(e)
Fig.(2.4): Types of Method of Excitation in Sonnet Pro Suite :(a) Standard Box-Wall Port, (b) CoCalibrated Internal Port, (c) Via Port, (d) Auto-Grounded Port and (e) Ungrounded Internal
Port.
19
Application of EM-Simulators
(iv) Automatic-grounded port is a special type of port used in the interior of a circuit
similar to a co-calibrated internal port. This port type has the positive terminal
attached to the edge of a metal polygon located inside the box and the negative
terminal attached to the ground plane through all intervening dielectric layers. Autogrounded ports can be de-embedded by the analysis engine. It is used in place of a
co-calibrated port to reduce the de-embedding processing time at the cost of less
accuracy. But the de-embedding for auto-grounded ports does not take into account
the coupling between the auto-grounded ports. The reference planes may be used
here as well.
(v) Ungrounded internal port is located in the interior of a circuit and has its two
terminals connected between abutted metal polygons. These ports can be deembedded by EM; however a reference plane or calibration length may not be set.
These ports are not as accurately de-embedded as co-calibrated internal ports, but
they do not require any space between the two polygons as is required for a cocalibrated port. Ungrounded internal ports are not allowed on the edge of a single
polygon because this would leave one terminal of the port unattached. Also, care
should be taken in interpreting the results for circuits which use these ports since all
the ports do not access a common ground.
2.2.2 De-embedding
At RF and microwave frequencies, it is often impractical to measure the impedance,
admittance, or S-parameters of an active device directly at the device terminals. Instead
the device is typically “embedded” in some form of test fixture and measurements are
made at a reference plane some distance away from the actual device as shown in
Fig.(2.5) [29]. Depending upon the nature of the analysis, this may or may not be
desirable. De-embedding is the mathematical process of removing the embedding
networks and determining the true parameters of the device under test (DUT) [68, 69].
20
Application of EM-Simulators
Fig.(2.5): Typical measurement situation.
It is a useful laboratory technique and an equally powerful tool when applied to EMsimulators. Each port in a circuit analyzed by EM simulator, introduces a discontinuity
into the analysis results. In addition, any transmission lines that might be present
introduce phase shift, and possibly, impedance mismatch and loss. Thus, it is required to
remove the discontinuities at numerical ports and to remove lengths of line from
numerical fixture. The de-embedding in active device and EM-simulators is shown in
Fig. (2.6).
(a)
(b)
Fig.(2.6): Typical de-embedding problems:(a) Measurement-based Active Device De-embedding, and
(b) EM- Simulator-based De-embedding; to remove port discontinuity.
The de-embedding is achieved through a calibration process in which the S-parameters of
two error boxes, shown in Fig.(2.7), are quantified. The error box represents errors in the
S-parameters due to cables and connectors connecting the device to the external circuit
ports [76]. The S or [ABCD] parameters representation of the device at device ports (1’-
21
Application of EM-Simulators
2’) along with the error boxes is shown in Fig. (2.7). The circuit network is the device
under test (DUT).
Fig.(2.7): Calibration process in measurement of S-parameters of a device.
The measured Am Bm Cm Dm – parameters are related to the device A’ B’ C’ D’ –
parameters as follows,
 A'
 '
C
B'   A
=
D '  C
B
D 
−1
 Am
 m
C
Bm 

D m 
A
C

B
D 
(2.1)
The de-embedded device A’ B’ C’ D’ –parameters are converted to the de-embedded Sparameters of the device. The de-embedded S-parameters are further converted to Z and
Y- parameters. Thus any two port device can be characterized though measurements
using the suitable parameters - S, Z, or Y. The above mentioned concept of de-embedding
of the device S- parameters at the devices port is applicable to the EM simulators - both
2.5D and 3D simulators [29-30, 76]. Every simulator vendors have developed their own
de-embedding algorithms. These are usually not known. In next section, we examine deembedding of S-parameters of several planar transmission lines using EM-simulators.
22
Application of EM-Simulators
2.3 Comparison of De-embedded and Non De-embedded Results
The investigator should examine the EM-simulator satisfactorily before adopting it for
the data generation of the structure. The de-embedding process of an EM-simulator
determines the accuracy of results on the S-parameter and the extracted line parameters.
Thus, comparison of the de-embedded and non de-embedded results obtained from EMsimulators - HFSS, Sonnet and CST are to be examined in this section.
Let us first examine, using all the three EM-simulators, the S-parameters of the
conventional planar transmission lines without and with de-embedding i.e. the Sparameters at the external circuit ports and at the internal device ports. The S11 and S 22
are identical and also S21 and S12 are identical. Fig. (2.8a) –Fig. (2.8d) show S11 and
S21 parameters for the microstrip line ( ε r =12.9, w/h=5), CPW ( ε r =9.8, w=20 µm, s=15
µm), CPS ( ε r =3.78, w=4.5 µm, s=7.5 µm) and slotline ( ε r =2.5, w/h=0.5) in frequency
range 1 GHz – 100 GHz for substrate thickness h = 635 µm, conductor thickness t = 6
µm and line length of 500 µm is carried out at the de-embedding distance, L=15 µm. As
frequency increases from 2 GHz, the de-embedded and non de-embedded curves
experience a gradually depart from each other for both S11 and S21 in all the four cases.
This is due to the increase in discontinuity at the ports with frequency, resulting in higher
insertion loss. The de-embedded S21 results show less frequency dependence as
compared to original S21 -parameters. The HFSS shows some error in results for CPW
and slotline above 60 GHz. The slotline is treated as the limiting case of the CPW with its
central conductor width 1µm. Some error in results are seen for the CPS around 10 GHz.
The CST de-embedded results are much smoother. Overall, the de-embedded S21
parameters obtained from HFSS show more frequency dependency w.r.t. Sonnet and
CST. There is small increase in the de-embedded S11 with frequency for all the four
lines in all the three EM-simulators.
23
Application of EM-Simulators
(a)
(b)
(c)
(d)
Fig.(2.8): |S11| and |S21| from EM-simulators of conventional transmission lines: (a) microstrip line,
(b) CPW, c) CPS and d) slotline before and after de-embedding.
The de-embedded results should not be dependent on the de-embedding line length. It is
examined in Fig.(2.9). The figure shows the comparison of effect of de-embedding length
on effective relative permittivity and total loss of microstrip line, on GaAs substrate,
using EM-simulators. A both negative and positive value of de-embedded distance has
been considered. Unlike HFSS and CST, Sonnet doesn’t have provision to incorporate
negative de-embedding distance. In Fig.(2.9a), at f = 10 GHz and 20 GHz, ε eff of the line
24
Application of EM-Simulators
obtained from EM-simulators is compared against Finlay et. al. [53]. It has been observed
that Sonnet provides nearly length independent values with 0.8% deviation, whereas deembedding does improve the results obtained from HFSS and CST with less than 0.1%
deviation. However, improvement is distance dependent in both HFSS and CST.
(a)
(b)
Fig.(2.9): Effect of de-embedding length on: (a) Effective relative permittivity and (b) Loss of microstrip
line.
Similarly, in Fig.(2.9b), at f = 15 GHz and 40 GHz, loss α T obtained from EMsimulators is compared against Goldfarb et. al. [86]. The de-embedded result obtained
from HFSS, Sonnet and CST is within 0.9% average deviation against experimental
results. In this case also, Sonnet de-embedded α T is the most independent of deembedding distance. However, it is not constant at 40 GHz. The results of HFSS are
fluctuating with distance. Its de-embedded results are not constant. Thus it is difficult to
fix a proper de-embedding distance to remove effect of port discontinuity. It appears 2
mm to 3 mm distance is appropriate. Next we compare results of three simulators; CST
shows variation of 0.3 % in ε eff at 20 GHz and 0.2 % variation at 10 GHz. Whereas
HFSS shows 0.2 % and 0.6 % variation at 10 GHz and 20 GHz respectively due to deembedding distance.
25
Application of EM-Simulators
2.4 Comparison of Different EM Simulators
In this section, we compare accuracy of computation of ε eff and α T using HFSS, Sonnet
and CST. In case of microstrip line, CPW and CPS results are compared against the
experimental results. In case of the slotline results are compared against the results of
mode matching method (MMM).amongst each other. Table- 2.2a–2.2d presents %
deviation in line parameters obtained from EM-simulators for the microstrip line, CPW,
CPS and slotline respectively on GaAs dielectric substrate.
Table-2.2a shows comparison of dispersive ε eff of microstrip line against experimental
results of Finlay et. al. [53] over frequency range 2 GHz - 22 GHz. The loss α T of the
microstrip line is also compared in Table-2.2a against experimental results of Goldfarb et.
al.[86] over frequency range 1 GHz – 40 GHz. The % average deviation in results
obtained for ε eff and α T from HFSS, Sonnet and CST are (2.3%, 4.3%), (2.2%, 4.2%)
and (2.6%, 5.1%) respectively.
Table-2.2b shows comparison of ε eff and α T of CPW against experimental results of
Papapolymerou et. al. [64] over frequency range 2 GHz - 118 GHz. The % average
deviation in results obtained for ε eff and α T from HFSS, Sonnet and CST are (4.9%,
8.8%), (8.5%, 6.2%) and (8.2%, 11%) respectively.
Table-2.2c shows comparison of ε eff and α T of CPS against experimental results of
Kiziloglu et. al. [74] over frequency range 2 GHz - 18 GHz. The % average deviation in
results obtained for ε eff and α T from HFSS, Sonnet and CST are (2.3%, 3.7%), (2.2%,
2%) and (2.6%, 1.2%) respectively.
26
Application of EM-Simulators
Table-2.2a: Comparison of εeff and αT of microstrip line from EM-simulators against
experimental results [53] and [86] on GaAs substrate with σ=3.33x107S/m respectively:
[53]
w= 30 µm, h=200µm, t= 6 µm & [86] w=20 µm, h=100µm, t=3µm.
Freq.
f
Exp.
[53]
HFSS
Sonnet
CST
Freq.
f
%
error
%
error
%
(GHz)
2
8.26
4
8.29
6
8.32
8
8.35
10
8.37
12
8.39
14
8.41
16
8.43
18
8.45
20
8.48
22
8.5
% av. deviation
0.5
0.4
0.8
1.4
1.6
2.6
2.6
3.1
4.3
4.1
4.2
2.3
0.2
1.1
1.7
2.4
2.5
2.6
2.6
2.6
2.7
2.6
2.7
2.2
error
1.5
0.6
0.4
1.2
2.3
3.0
3.8
4.0
4.1
4.0
4.0
2.6
% max.
deviation
4.3
2.7
4.1
(GHz)
εeff (f)
Exp.
[86]
HFSS
Sonnet
CST
αT
(dB/cm)
%
error
%
error
%
error
0.24
0.43
0.6
0.77
0.88
1.03
1.1
1.16
1.23
4.2
2.3
1.7
2.6
5.7
5.8
6.4
4.3
5.7
4.6
4.7
5.0
2.6
2.3
3.9
4.5
6.0
4.1
4.2
7.0
6.7
3.9
6.8
2.9
4.5
4.3
5.7
% av. deviation
4.3
4.2
5.1
% max. deviation
6.4
6.0
7.0
1
5
10
15
20
25
30
35
40
Table-2.2b: Comparison of εeff and αT of CPW from EM-simulators against experimental results
[64] on GaAs substrate: w= 45 µm, s=50µm, h=525µm, t =1µm, σ=3.33x107S/m.
Freq.
f
HFSS
Sonnet
CST
Freq.
f
%
error
%
error
%
(GHz)
2
7.38
10
7.24
20
7.19
30
7.19
40
7.18
50
7.18
60
7.19
70
7.20
80
7.21
90
7.21
100
7.22
110
7.22
118
7.23
% av. deviation
0.2
4.4
4.2
4.3
4.0
3.7
3.4
2.9
2.3
1.1
7.6
11.3
13.9
4.9
2.5
2.1
2.0
2.0
1.7
1.4
8.6
9.1
9.7
10.9
16.8
20.5
23.1
8.5
error
3.2
1.3
1.1
1.2
1.9
2.2
2.5
2.9
3.6
12.8
21.5
25.1
27.8
8.2
% max. deviation
13.9
23.1
27.8
Exp.
[64]
(GHz)
εeff (f)
Exp.
[64]
HFSS
Sonnet
CST
αT
%
error
%
error
%
error
2
0.78
10
0.96
20
1.23
30
1.42
40
1.58
50
1.77
60
1.96
70
2.1
80
2.29
90
2.46
100
2.64
110
2.82
118
2.93
% av. deviation
4.9
6.1
8.0
8.3
9.0
8.3
9.8
8.6
7.7
5. 8
12.2
10.8
15.3
8.8
5.7
4.2
5.5
7.4
6.8
6.7
6.0
5.4
6.2
7.3
11.7
11.5
22.6
6.2
4.3
6.8
8.6
9.3
9.1
10.9
9.7
10.9
10.6
12.1
15.8
16.8
18.0
11.0
% max. deviation
15.3
22.6
16.8
(dB/cm)
27
Application of EM-Simulators
Table-2.2c: Comparison of εeff and αT of CPS from EM-simulators against experimental results
[74] on GaAs substrate: w= 4 µm, s= 8µm, h=670µm, t=0.5µm, σ=4.1x107S/m.
Freq.
f
Exp.
[74]
Exp.
[74]
HFSS
Sonnet
CST
αT
%
error
%
error
%
error
2
0.90
3
1.02
4
1.08
5
1.1
6
1.13
7
1.15
8
1.17
9
1.19
10
1.21
11
1.21
12
1.22
13
1.23
14
1.24
15
1.26
16
1.27
17
1.29
18
1.30
% av. deviation
8.7
6.2
2.7
4.4
3.6
3.5
4.6
3.4
3.1
3.7
4.1
3.3
3.2
2.0
2.6
2.1
1.8
3.7
5.4
2.3
1.5
2.6
1.8
1.8
2.1
1.7
2.2
2.9
2.5
1.6
1.6
1.2
1.3
1.0
1.0
2.0
3.2
1.3
1.9
0.1
0.9
0.8
0.4
0.8
1.1
0.5
0.0
0.8
0.9
1.9
1.3
1.8
2.1
1.2
% max. deviation
8.7
5.4
3.2
HFSS
Sonnet
CST
Freq.
f
%
error
%
error
%
error
(GHz)
2
7.48
3
6.93
4
6.95
5
7.07
6
8.25
8.21
7
8
7.77
9
7.55
10
7.67
11
7.64
12
7.84
13
7.54
14
7.68
15
7.37
16
7.65
17
7.83
18
7.32
% av. deviation
6.6
4.0
6.9
6.7
6.2
3.8
1.1
0.3
2.8
3.8
0.3
4.2
0.8
3.0
0.2
0.3
7.6
3.4
3.2
4.8
1.1
2.1
9.4
10.2
9.4
5.0
3.9
5.4
6.1
6.1
4.0
5.7
1.4
9.6
5.1
5.4
3.1
1.4
4.3
0.9
8.0
10.6
1.2
1.8
1.0
9.8
10.2
3.3
0.7
2.4
3.0
0.4
8.6
4.2
% max. deviation
7.6
10.2
10.6
(GHz)
εeff (f)
(Np/cm)
Table-2.2d: Comparison of εeff and αT of slotline from EM-simulators against MMM results
[132] on GaAs substrate: s= 40µm, h=600µm, t=6µm, σ=3x107S/m.
Freq.
f
MMM
[132]
(GHz)
εeff (f)
10
6.68
20
6.62
30
6.54
40
6.59
50
6.65
% av. deviation
% max. deviation
HFSS
Sonnet
CST
Freq.
f
%
error
%
error
%
error
(GHz)
6.6
4.0
6.9
6.7
6.2
3.4
3.2
4.8
1.1
2.1
9.4
5.4
3.1
1.4
4.3
0.9
8.0
4.2
6.9
9.4
8.0
MMM
[132]
HFSS
Sonnet
CST
αT
%
error
%
error
%
error
10
0.04
20
0.07
30
0.08
40
0.09
50
0.11
% av. deviation
4.5
0.5
2.5
5.5
4.5
3.5
3.6
2.0
4.1
7.3
7.6
4.9
5.1
2.6
3.7
8.6
7.0
5.4
% max. deviation
5.5
7.6
8.6
(dB/mm)
28
Application of EM-Simulators
Table-2.2d shows comparison of ε eff and α T of slotline against MMM based results of
Heinrich [132] over frequency range 10 GHz - 50 GHz. The % average deviation in
results obtained for ε eff and α T from HFSS, Sonnet and CST are (3.4%, 3.5%), (5.4%,
4.9%) and (4.2%, 5.4%) respectively.
Next we compare the performance of microstrip, CPW, CPS and slotline over frequency
1 GHz - 60 GHz using three simulators. For this purpose, the characteristic impedance Z0
is kept constant at 50 Ω,75 Ω and 90 Ω for ε r = 9.8, t = 6µm, tan δ = 0.0002, σ = 4.1 x
107 S/m. The results on ε eff and α T are shown in Fig.(2.10a)-(2.10f). It has been
observed that the microstrip is the most dispersive line, followed by slotline, CPS and
CPW. The dispersion is technically present at all frequencies. However, it becomes
significant above 4 GHz. The total loss is observed to be more in CPW, followed by CPS,
slotline and microstrip line. The losses are frequency dependent in the same order. In all
the four lines, with increasing Z0 from 50 Ω to 90 Ω, there is subsequent increase in ε eff
and decrease in α T .
Finally, Table-2.3 compares % average and % maximum deviation in computation for all
the three cases of Z0, in Sonnet and CST w.r.t. HFSS for microstrip line, CPW, CPS and
slotline. The results of CST and HFSS are in closer agreement for computation of ε eff .
However results of Sonnet and HFSS show better agreement for computation of α T . In
general, we can say results of simulations for ε eff can deviate between 1.1 % to 4.3 %
i.e. about 2.5 % on average. The results for computation of α T can deviate between 2.7
% - 5.8 % i.e. about 4.5 % on average.
29
Application of EM-Simulators
(a)
(b)
(c)
(d)
(e)
(f)
Fig.(2.10): Comparison of characteristics of different planar transmission lines keeping Z0 constant at
50 Ω, 75 Ω and 90 Ω.
30
Application of EM-Simulators
Table-2.3: Percentage deviations of EM-simulators w.r.t. HFSS for all the four lines
ε r = 9.8, t = 6µm, tan δ = 0.0002, σ = 4.1 x 107 S/m.
2.5 Comparison of Characteristics of Transmission Lines
In this section, line parameters of microstrip line obtained from EM-simulators, are
compared against results from experiments and analytical models available in open
literature. The same methodology for study of characteristics of CPW, CPS and slotline
has been carried out in Chapter-5, 6 and 7 respectively. The line parameters considered
for study are effective relative permittivity ( ε eff ), characteristic impedance (Z0), total
loss ( α T ) and quality factor (Q) factor. The study has been done for different line
geometries of all the four lines on six different substrates – PTFE/glass ( ε r = 2.5);
Quartz ( ε r = 3.78);
Alumina ( ε r = 9.8);
Gallium Arsenide, GaAs
( ε r = 12.9);
Zirkonate ( ε r = 20), and Barium Tetratitanate, BaTi4O9 ( ε r = 37) in the frequency range
0.1 GHz – 200 GHz and conductor thickness (t) of gold (σ = 4.1 x 107 S/m) ranges from
0.25µm – 9 µm. The gold is not a practical conductor for all cases; however for
comparison we have used it in all cases of simulation.
31
Application of EM-Simulators
Microstrip line is the most commonly used transmission medium in RF and microwave
circuits, due to its quasi-TEM nature and excellent layout flexibility. A cross-sectional
view of a microstrip line is shown in Fig. (1.1b). The important parameters for designing
these transmission lines are the characteristic impedance, effective relative permittivity,
attenuation constant, discontinuity reactances, frequency dispersion, surface-wave
excitation and radiation. Several methods to determine these parameters are summarized
in the open literature [3, 36,51, 56-58, 73,87].
Our study of effective relative permittivity, characteristic impedance and losses of
microstrip line w.r.t. frequency, conductor thickness and w/h ratio are based on the
following models:
•
Effective relative permittivity (LDM) [9]
ε eff ( f , t ) =
•
εr
1 + Me − K ( f / f1 )
R
 17


(b)
Wheeler’s incremental inductance rule [6]
αc =
•
(a)
Characteristic impedance [103]
R
Z 0 ( f , t ) = Z 0 (0 )  13
 R14
•
− E∆ε eff ( f )
27.29
λ0
ε eff ( ε r , w, h , f , t )
∆Z ( ε r = 1, w , h , f , t ,δ s )
dB/m
Z 0 ( ε r = 1, w , h , f , t )
(c)
Holloway and Kuester model [24,157]
 w t

ln 
− 1 

R sm
 t ∆
  Np/m
Strip conductor : α sc =
⋅

2
Z 0 ( f , t )  2π w 


32
(d)
Application of EM-Simulators
R sm  1
Ground plane : α gc =

2 Z 0 ( f , t )  wπ
2
2 ∞
 −1  w − 2 x 

−1  w + 2 x  

 + tan 
  dx Np/m
tan 
 −∞ 
 2h 
 2h 
∫
α c = α sc + α gc Np/m
•
(e)
(f)
Dielectric loss [73]
α d = 27.29
 ε eff ( f ,t ) − 1 tan δ


ε eff ( f ,t )  ε r − 1  λ0
εr
dB/m
(g)
(2.2)
The detailed definitions of the above mentioned closed-form models can be found in the
open literature [6,9,24,73,103,157].
Fig. (2.11), Fig.(2.12) and Fig.(2.13) present variation in ε eff , Z0, α T and Q-factor of
microstrip line with respect to the frequency range 0.1 GHz – 200 GHz, strip conductor
thickness 0.25 µm – 9 µm and w/h ratio 0.1 - 10 respectively. We have considered
substrate relative permittivity in the range 2.5 - 37. The closed-form model with LDM [9]
for dispersion has % average and % maximum deviation of (1.5%, 4.8%), (2.2%, 9.2%)
and (3.4%, 7.9%) against HFSS, Sonnet and CST respectively, as shown in Fig.(2.11).
With increasing permittivity, the deviation in closed-form model is evidently increasing.
The deviation is also more at higher frequencies.
Fig.(2.12) shows the effect of dispersion in Z0 of a microstrip line. The closed-form
model for the frequency-dependent Z0 a microstrip line [103] is based on power-current
definition. For ε r < 20 and 0 ≤ h. f ≤ 30 GHz-mm, the model is within 6.2% average
deviation against the results obtained from EM-simulators. The closed-form model
includes the correct asymptotic dependences on the various parameters, however outside
the specified ranges, the error increases slowly but significantly as shown in Fig.(2.12a).
When compared against each EM simulator for 2.5 ≤ ε r ≤ 20 , 0.25 µm ≤ t ≤ 9 µm and
0.1 ≤ w / h ≤ 10 , the closed-form model has % average and % maximum deviation of
33
Application of EM-Simulators
(6.9%, 13.8%), (8.2%, 15.2%) and (7.6%, 12.9%) against HFSS, Sonnet and CST
respectively, as shown in Fig.(2.12b) and Fig.(2.12c).
(a)
(b)
(c)
Fig.(2.11): Comparisons of ε eff ( f , t ) computed by the closed-form model against the EM-simulators as a
function of: (a) Frequency, (b) Conductor thickness, and (c) w/h ratio for microstrip lines on
various substrates.
The losses depend on the nature of conducting material used in the strip conductor and
ground plane of a microstrip, material of the substrate and physical structure of a
microstrip. The total loss in a microstrip structure can be obtained by adding mainly three
loss components: radiation loss ( α r ), conductor loss ( α c ) and dielectric loss ( α d ).The
34
Application of EM-Simulators
α d and α c are dissipative effects whereas α r is an essentially parasitic phenomenon
[116]. Moreover, the attenuation is usually dominated by α r for frequencies above 200
GHz. As THz frequencies have not been accounted in this study, so radiation losses have
been neglected in this thesis. The conductor loss is caused by the finite conductivity of
strip conductor and ground plane conductor, whereas the dielectric loss is caused by an
imperfect lossy substrate material.
(a)
(b)
(c)
Fig.(2.12): Comparisons of Z 0 ( f , t ) computed by the closed-form model against the EM-simulators as a
function of: (a) Frequency, (b) Conductor thickness, and (c) w/h ratio for microstrip lines on
various substrates.
35
Application of EM-Simulators
The Q or Quality factor of a microstrip [57] can be related to α T in the line by:
Qu =
π ε eff ( f )
β
=
2α T
α T λ0
(2.3)
where Qu is the total or unloaded Q of the line, β is the phase coefficient and λ0 is the
free-space wavelength. Unloaded Q – factors are of great importance in resonant circuit
applications (e.g. matching networks and filters) which indicate the selectivity, the
performance of the resonator and the losses of the resonator. It is expressed as
1
1
1
1
=
+
+
Qu Qr Qc Qd
(2.4)
where Qr is the radiation Q due to α r , Qc is the conductor Q due to α c and Qd is the
dielectric Q due to α d . In this study, Qu is computed from EM- simulators and closedform model (both ε eff and α T ), using equation-(2.3).
Fig.(2.13) shows the characteristics of the total loss α T and unloaded Q – factors in a
microstrip line on different substrates with ε r = 3.78, 9.8 and 12.9; w/h =1, h = 635 µm
and t = 3 µm as a function of frequency. Two closed-form models are used for the
conductor loss computation of the lines in our study: Wheeler’s incremental inductance
rule [13] and perturbation method with the concept of the stopping distance by Holloway
[24]. Holloway’s model along with the closed-form model for dielectric loss [73] are
used for the computation of α T and compared against the EM-simulators in Fig.(2.13a)
with 6.7% average deviation till 0 ≤ h. f ≤ 30 GHz-mm condition is getting satisfied and
beyond that, error increases steadily for high permittivity substrate at higher frequencies
with % average deviation reaching upto 19.3%. The deviation at frequencies above 50
GHz and for high permittivity substrate is due to the surface-wave generation that is not
accounted for in the closed-form models. The EM-simulator accounts surface-wave loss.
36
Application of EM-Simulators
(a)
(b)
(c)
(d)
(e)
(f)
Fig.(2.13): Comparisons of the closed-form models against the EM-simulators for computation of:
α T ( f ,t ) as a function of (a) Frequency, (b) w/h ratio, (c) Conductor thickness;
Qu as a function of (e) Frequency, and (f) w/h ratio for microstrip lines on various substrates.
37
Application of EM-Simulators
Fig.(2.13b) shows the comparison of the total loss, computed using Wheeler’s model and
Holloway’s model for conductor loss, against EM-simulators as a function of w/h ratio
with % average and % maximum deviation of (7.2%,16.6%) and (3.9%,11.4%)
respectively. Both the closed-form models have 7% average deviation between each other
and deviation seems to be increasing with increase in w/h ratio. In Fig.(2.13c), both the
closed-form models for conductor loss and all the three EM-simulators are compared
against the MMM based results of Heinrich [133] for 0.25 µm ≤ t ≤ 9 µm. The % average
and % maximum deviation of Holloway’s model, Wheeler’s model, HFSS, Sonnet and
CST w.r.t. Heinrich’s results are (3.4%,5.2%), (5.4%,28%), (1.9%,2.7%), (4.4%,7.6%)
and (4.6%,7.9%) respectively. It has been observed that, for a wide range of parameters,
both the closed-form models work well. However, if the ratio
t
δs
≤ 1.1 (where δ s is the
skin depth and t is the thickness of the conductor), then Wheeler rule breaks down and
gives poor results. Fig.(2.13d) compares the closed-form model for dielectric loss against
the EM-simulators w.r.t. conductor thickness and the model is within 1.54% average
deviation.
Fig.(2.13e) shows the variation of Qu in a microstrip line on different substrates with
ε r = 3.78, 9.8 and 12.9; w/h =1, h = 635 µm and t = 3 µm in the frequency range 0.1 GHz
– 200 GHz. Fig.(2.13f) compares computation of Qu for ε r = 2.5 and 12.9; f = 60 GHz as
a function of w/h ratio. Overall, % average and % maximum deviation in the closed-form
model against EM-simulators are 8.9% and 19.5% respectively. The error in closed-form
model is observed to be increasing with increase in frequency and w/h ratio.
2.6 Comparison of R, L, C and G against EM Simulators
The planar transmission lines, which are like the TEM mode supporting two conductor
transmission lines, are described by the secondary line parameters- the complex
propagation constant γ and the characteristic impedance Z0. These secondary line
38
Application of EM-Simulators
parameters are described by the primary line constants - R, L, C, G i.e. the resistance,
inductance, capacitance and conductance per unit length (p.u.l.) of a line. The secondary
parameters are directly measurable quantities and are useful in the design. The
measurement results are analyzed by converting the measured S- parameters to ABCD
parameters of the transmission line system, from which γ and Z 0 of the lines can be
extracted. As postulated by Kiziloglu et. al. [74] based on theoretical estimations, the
quasi- TEM model can be used to describe digital circuit interconnects [149]. The
measured line parameters can be determined from γ and Z 0 .
It has been observed that the propagation characteristics of lines, obtained from EMsimulators, deviate from linearity at the lower frequency range which is due to the finite
conductivity of the strip conductor. At the lower frequencies the EM-fields penetrate to
the strip conductors that cause dispersion in ε eff and Z0 in the lower frequency range. It
really indicates increase in ε eff at the lower frequency range. Due to losses, Z0 also has
an imaginary part and shows increase at the lower frequency range.
Fig.(2.14): Circuit model applicable to planar transmission lines
The closed-form models that compute ε eff and Z0 of the planar transmission lines, do not
account for the effect of conductor loss on these parameters. This can be accounted for
with the help of the circuit model of the lines shown in Fig. (2.14). Thus, the circuit
model provides an opportunity for the interaction of the line parameters, i.e. the
39
Application of EM-Simulators
propagation constant and the characteristic impedances are influenced by the losses in the
line. The EM-simulators - HFSS, Sonnet and CST, exhibit these low frequency features
as these parameters are extracted from the frequency dependent S-parameters and also Y–
parameters and these parameters are influenced by the line structure and its losses. Either
of these forms of data can be used to extract the line parameters of structures. The
characteristic impedance Z 0 and complex propagation constant γ are related to Sparameters by the following expressions [138],
s 11 = s 22 =
(Z 02 − Z r2 )sinh (γ l )
2 Z 0 Z r cosh (γ l ) + (Z 02 + Z r2 )sinh (γ l )
s 12 = s 21 =
2Z0Zr
(
(a)
(2.5)
)
(b)
2 Z 0 Z r cosh (γ l ) + Z 02 + Z r2 sinh (γ l )
where Zr = 50 Ω is the reference impedance and l is the line length of transmission line.
The expression for complex propagation constant γ giving the attenuation constant α T
p.u.l is obtained from above equations,
1
l
1 + s11 − s 22 − s 11 s 22 + s 21 s12 

2 s 21


γ = α T + jβ = cosh −1 
(2.6)
The S-parameters obtained from the software are first converted to the ABCD-parameters.
Next we get expression for γ from the ABCD-parameters. We can also convert the Sparameters to the Y-parameters and then obtain expression for the complex propagation
constant γ in terms of it [81],

yc
2
tanh − 1 
l
 4 yd
where , 4 y d = y 11 −
γ =




y 12 − y 21 + y 22
y c = y 11 + y 12 + y 21 + y 22
40
(a )
(b )
(c )
(2.7)
Application of EM-Simulators
In this section we present the comparison of low frequency features in the line parameters
of planar transmission lines using different EM-simulators. In circuit model, the
resistance and inductor of the equivalent circuits are in series; whereas the conductance
and capacitors are connected in shunt. Their expressions in per unit length (p.u.l.) are
summarized below,
Resistance p.u.l. :
Conductanc e p.u.l. :
R(f, t) = 2 Z 0 ( f , t ) α c ( f , t )
2 α d ( f ,t )
G(f, t) =
Z 0 ( f ,t )
Capacitanc e p.u.l. :
C (f, t) =
Inductance p.u.l. :
L (f, t) =
ε eff ( f , t )
cZ 0 ( f , t )
Z 0 ( f , t ) ε eff ( f , t )
c
(a)
(b)
(2.8)
(c)
(d )
where, c is the free-space velocity of the EM wave. The ε eff ( f ,t ), Z 0 ( f ,t ), α d ( f ,t )
and α c (f, t) of the lines are computed using the closed-form models. The complex
characteristic impedance Z 0* (f, t) and complex propagation constant γ * (f, t) are
computed from above primary line constants as follows:
Z *0 ( f , t ) =
R( f , t ) + jω L( f , t )
G( f ) + jω C( f , t)
γ * ( f , t ) = α T ( f , t ) + jβ ( f , t ) =
(a)
(R( f , t ) +
jω L( f , t ))(G( f , t ) + jω C( f , t ))
(2.9)
(b)
The extracted line parameters of the microstrip line, using HFSS, Sonnet, CST and
LINPAR, are compared against each other on substrates with
2.5 ≤ ε r ≤ 37 ,
0.25µm ≤ t ≤ 9µm , 0.1 ≤ w / h ≤ 5 and σ = 4.1 x 107 S/m. The frequency range is 0.01
GHz – 10 GHz. This frequency range is selected to emphasize the dispersion in the lower
frequency and also to examine changes in other line parameters.
41
Application of EM-Simulators
(a)
(b)
Fig.(2.15): Extraction of RLCG parameters of lossy microstrip line using circuit model and EM-simulators.
Fig.(2.15) and Fig.(2.16) show the characteristics of microstrip line on the substrate with
ε r = 3.78, w/h = 2 , h = 635µm and t = 3 µm. In Fig.(2.15a), resistance R increases as a
function of frequency and the value of conductance G also increases with increasing
frequency in EM simulators. The capacitance C remains relatively constant till 1 GHz,
then onwards there is gradual decrease in the value and the inductance L of the microstrip
line saturates gradually 1 GHz onwards as shown in Fig.(2.15b). The results of LINPAR
are higher than those of the EM-simulators. The results of the circuit model follow results
of EM-simulators closely, especially to CST.
Then we obtain frequency dependent effective relative permittivity ε eff , characteristic
impedance- real and imaginary parts, and total loss from the RLCG parameters. These
results obtained from the circuit models are presented in Fig.(2.16) and compared against
the results of EM-simulators. The results of circuit model follow results of EMsimulators; whereas results of our previous closed-form individual models do not follow
EM-simulators, especially at lower end of frequency. It is true for all parameterseffective relative permittivity, losses and characteristic impedance.
42
Application of EM-Simulators
Fig. (2.16a) shows that ε eff of the microstrip line has marginal increase in value with
decrease in frequency, which is supported by the results obtained from the EMsimulators. There is continuous rise in attenuation with increase in frequency, as shown
by results from all the three softwares in Fig.(2.16a). All the EM- simulators show slower
decrease in loss. In Fig. (2.16b) the real part of Z0 of the microstrip line also increases
marginally with decrease in the frequency below 1 GHz. The imaginary part of Z0
remains nearly constant throughout the frequency range. The circuit model accurately
predicts and improves the dispersive nature of the microstrip line at the lower frequency
range for computation of ε eff ( f , t ) , Z0 ( f , t ) and α T ( f , t ) with average and maximum
deviation of (3.3%, 7.2%), (3.9%, 6.5%) and (4.6%, 7.2%) respectively.
(a)
(b)
Fig.(2.16): Comparison of circuit model, closed-form model against EM-simulators for line parameters of
lossy microstrip line in respect of ε eff ( f ,t ) and αT ( f ,t ) , Re( Z *0 ( f ,t )) and Im( Z *0 ( f ,t )).
The detailed study of the circuit models of CPW, CPS and slotline on planar and curved
surfaces and comparison against experimental results will be discussed in Chapter-5, 6
and 7 respectively.
43