1. ISSN: 2277 – 9043
International Journal of Advanced Research in Computer Science and Electronics Engineering
Volume 1, Issue 4, June 2012
THEORETICAL CHARACTERIZATION OF
COPLANAR WAVEGUIDE USING CONFORMAL
MAPPING
Mukesh kumar, Rohini Saxena, Anil Kumar, Pradyot Kala, Reena Pant
Abstract:-In this paper we present the estimation of the STRUCTURE AND FORMULATION
characteristic impedance and the effective dielectric There exist two main types of coplanar lines: the
constant of Coplanar Waveguide(CPW) using first, called coplanar waveguide (CPW), is composed
conformal mapping theory and performances are
of a median metallic strip separated by two narrow
predicted using theoretical analysis. Numerically
efficient and accurate formulae based on the conformal slits from a infinite ground plane, which is shown in
mapping method for the analysis of coplanar waveguide the figure 1.
structures are presented. The analysis formulas for
Coplanar Waveguides are derived and verified with
Matlab. Characteristic Impedance of CPW for different
dielectric material as well as for different thickness of
the substrate material is under consideration in this
work. With the help of CPW transmission techniques,
substantial amount of efficiency has been achieved.
Keywords: - Coplanar Waveguide, Conformal Mapping
Method, quasi-TEM.
INTRODUCTION
Coplanar waveguide (CPW) have been used
extensively in microwave as well as transmission line
for wide range application. Transmission system Figure: 1 Coplanar waveguide line
usually requires a portable and a probable system
suited to less or lossless energy transmission. A CPW The characteristic dimensions of a CPW are the
consisting of a center conductor and two ground central strip width W and the width of the slots s .
planes printed on the same surface of a dielectric slot The structure is obviously symmetrical along a
is one of the best suited system to meet requirement vertical plane running in the middle of the central
with many other attractive features such as active strip. The other coplanar line; called a coplanar slot
device can be mounted on top of circuit, it has very (CPS) is the complementary of that topology,
high frequency response, immediate access to adjust consisting of two strips running side by side, which is
power plane, low conduction and dispersion loss, shown in the figure 2.
continuous, lower cross talk as well as CPW design
technique allows to reduce the circuit size by about s W s
30% .CPW is an appropriate transmission line and
has ability to generate elliptical polarized magnetic
fields with two modes of propagation namely quasi-
TEM and non-TEM mode for CPW, closed form
design equation obtained by conformal mapping
method which is the simplest and most often used
quasi-static method consist of complete elliptic
integral which are difficult to calculate even with
computers, hence approximate formulas are proposed
Figure: 2 Coplanar slot line
for the calculation of elliptical integral by conformal
mapping.
Manuscript received May, 2012.
Mukesh kumar, ECE Deptt., SHIATS-DU, Allahabad,India- ANALYSIS BY CONFORMAL MAPPING:
211007, Rohini Saxena, ECE Deptt., SHIATS-DU, A CPW can be quasi-statically analyzed by the use of
Allahabad,India-211007,Anil Kumar, ECE Deptt., SHIATS-DU, conformal mappings. It consists in transforming the
Allahabad,India-211007 Pradyot Kala, Shree Ganpati Institute of
Technology Ghaziabad, India-201302, Reena Pant, IETMJP geometry of the PCB into another conformation,
Rohilkhand university bareilly,India-201001
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All Rights Reserved © 2012 IJARCSEE

2. ISSN: 2277 – 9043
International Journal of Advanced Research in Computer Science and Electronics Engineering
Volume 1, Issue 4, June 2012
whose properties make the computations r 1
straightforward.  re  (3)
2
z
dz and the impedance:
w   30 K ' k1 
z0 z  W 2 z  W 2  2  Z  (4)
 re K k1 
W/2 s
A B
C D
Figure: 4 Parallel plate capacitor filled
Figure: 3 Infinitely deep substrate of CPW
with dielectric substrate
The CPW of negligible thickness located on top of an In practical cases, the substrate has a finite thickness
infinitely deep substrate, as shown in the Figure 3, h Figure 4. To carry out the analysis of this
can be mapped into a parallel plate capacitor filled conformation, a preliminary conformal mapping
with dielectric ABCD using the conformal function transforms the finite thickness dielectric into an
as shown in the Figure 4.To further simplify the infinite thickness one Figure 3. Only the effective
analysis, the original dielectric boundary is assumed permittivity is altered, it becomes:
to constitute a magnetic wall, so that BC and AD
 r  1 K k 2  K ' k 1 
become magnetic walls too and there is no resulting
fringing field in the resulting capacitor. With that
 re  1   ' 
K k 2  K k 1 
assumption, the capacitance per unit length is merely (5)
2
the sum of the top (air filled) and bottom (dielectric
filled) partial capacitances. Capacitance of dielectric Finally, let us consider a CPW over a finite thickness
filled bottom of the substrate and the dielectric backed by an infinite ground plane. In this
case, the quasi-TEM wave is a hybrid between
capacitance of top of the substrate is given by
microstrip and true CPW mode. The equations then
the formula: become:
K k1   re  1  q   r  1
Cd  2   0   R  (6)
K ' k1 
(1)
Where q , called filling factor.The impedance of this
K k 1  line amounts to:
Ca  2   0 
K ' k 1 
(2)
60  1
 
In both formulae K k and K k  represent the
' Z
 re

K k 1  K k 3 
(7)

K ; k 1  K ' k 3 
complete elliptic integral of the first kind and its
W
complement, and k1  '
.with k being the
W  2s RESULTS & DISCUSSION
complementary modulus: k  1  k . Where
' 2
the accuracy of the above formulae is close a) CHARACTERISTIC IMPEDANCE Vs
5 6 NORMALIZED STRIP WIDTH FOR DIFFERENT
to 10 to 3  10 . It can be considered as exact
DIELECTRIC MATERIALS OF CPW:
for any practical purposes. The total line capacitance
1.1 For Infinite Substrate Thickness
is thus the sum of C d and C a . The effective
It is observed that the characteristic impedance of
permittivity is therefore: CPW decreases as normalized strip width increases.
49
All Rights Reserved © 2012 IJARCSEE

3. ISSN: 2277 – 9043
International Journal of Advanced Research in Computer Science and Electronics Engineering
Volume 1, Issue 4, June 2012
air=1 quartz=3.78 alumina=9.5
be at negative potential or grounded to complete the
300
circuitry. As for finite and infinite substrate thickness
shielding for different dielectric materials are not
250
Characteristic impedance in ohm
possible because dielectric or air can never be
200
grounded. As the shielded plate is grounded the
150 central strip occupies higher potential and eventually
100 can hold more energy. Hence loss will be reduced
50
and from all the graphs discussed earlier,
characteristic impedance of CPW changes which is a
0
0.1 1 10 proof for above mention postulates.
Normalize d strip width (W/s) in mm
When alumina is used as dielectric material
Graph 1.1: characteristic impedance Vs normalized strip width. whose relative permittivity is equal to 9.5 for infinite
thickness, finite thickness and ground shielded of
1.2 For Finite Substrate Thickness CPW, the electric field between central strip line and
ground plane becomes more and more dominant as
compared to dielectric material with lower
air=1 quartz=3.78 alumina=9.5 permittivity, which means there will be an increase in
300 displacement current also called leakage current from
central strip to ground plane. With large leakage
Characteristic impedance in ohm
250
200
current, conductance increases which eventually
150
corresponds into a decrement of characteristic
impedance.
100
The characteristic impedance of any type of
50
transmission line decreases with increase in relative
0
0.1 1 10
permittivity and can be expressed by using formula
Normalize d strip width (W/s) in mm from transmission line is given by
Graph 1.2: characteristic impedance Vs normalized strip width. R  jL
Z0 
G  jC
1.3 For Ground plane shielded
Hence it is observed that the graph 1.3 for alumina is Where is R  Resistance per unit length, L 
more linear as compared for air and quartz. Inductance per unit length, G  Conductance per
air=1 quartz=3.78 alumina=9.5 unit length, C  Capacitance per unit length
600 Form the above mention formula, the condition arises
R  C  L  G for distortion less transmission
Characteristic impedance in ohm
500
400
line. Since there is no wires or long conducting
300
element L and G cannot be changed so it is very
200
evident from the above condition that only R and
100
C can be inversely proportional to each other as C
0
is dependent on relative permittivity and R can be
0.1 1 10 treated as characteristic impedance it can be knuckled
Normalize d strip width (W/s) in mm
with the fact that whenever C increases R
Graph 1.3: characteristic impedance Vs normalized strip width.
decreases.
It is also observed that in the entire above graph, if
Shielding is a technique due to which losses the width of slot is fixed, then large normalized strip
in CPW is reduced. CPW provides other means for width means less strip width. It is cleared that that the
electric field to complete the path which produces characteristic impedance of CPW decreases as re-
and additional capacitance between central strip and reduce the strip width which is due to strong electric
metallic plate. As the capacitance is in parallel with field between central strip and ground.
the original capacitance, the total capacitance of the
CPW surface will increase. The main objective of a CONCLUSION
waveguide is to transmit total energy at feed to Work has been done to demonstrate the utility of
antenna without any loss. We can perform this action CPW and its advantages especially when energy is to
in CPW with the help of shielding. To feed the be transferred from feed to antenna in a very compact
energy in CPW the outer jacket of coaxial cable must
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4. ISSN: 2277 – 9043
International Journal of Advanced Research in Computer Science and Electronics Engineering
Volume 1, Issue 4, June 2012
and efficient form. A simple and inexpensive method
also known as quasi-static conformal mapping theory
has been applied for calculating the characteristic
impedance of CPW. Variation of characteristic
impedance with normalized strip width due to change
in different substrate thickness, different dielectric
materials and metallization effect is also represented.
It has been observed that characteristic impedance
decreases with advancement of normalized strip
width and increases for increasing dielectric substrate
thickness. The reason for this observation is that, the
characteristic impedance decreases when ever
permittivity of dielectric substrate increases. This
property can be applied in microwave transmission
theory to design different antenna models for
different purposes along with the advantage of
mounting active and passive component on the same
plane.
REFERENCES
[1] Gevorgian S, Linner LJP and Kollberg EL(1995), CAD
models for Shielded multilayered CPW. IEEE Trans. Microwave
Theory Tech.43, 326-334.
[2] Wen CP(1969) Coplanar waveguide: a surface strip
transmission line suitable for non-recirocal gyro magnetic device
applications, IEEE Trans. Microwave Theory Tech. MTT-17, 1087-
1090
[3] K. C. Gupta, R. Garg, I. J. Bahl, and
P. Bhartia, Microstrip Lines and Slotlines, 2nd ed.Artech House,
Inc., 1996. pp. 375
[4] Microstrip Characteristic Impedance,'' IEEE
Transactions on Microwave Theory and Techniques, vol. 27, no. 5,
p. 293, Apr. 1979.
[5] H. A. Wheeler, ``Transmission-Line Properties of
Parallel Wide Strips by a Conformal-Mapping
Approximation,'' IEEE Transactions on Microwave Theory and
Techniques, vol. 12, no. 3, pp. 280-289, May 1964.
[6] S. S. Bedair and I. Wolff, ``Fast, Accurate and Simple
Approximate Analytic Formulas for Calculating the Parameters of
Supported Coplanar Waveguides for (M)MIC's,'' IEEE
Transactions on Microwave Theory and Techniques, vol. 40, no. 1,
pp. 41-48, Jan. 1992.
[7] M. V. Schneider, ``Microstrip Lines for Microwave
Integrated Circuits,'' The Bell System Technical Journal, vol. 48,
pp. 1421-1444, May 1969.
[8] E. Hammerstad and Ø. Jensen, ``Accurate Models for
Microstrip Computer-Aided Design,'' Symposium on Microwave
Theory and Techniques, pp. 407-409, June 1980.
[9] E. Hammerstad, ``Computer-Aided Design of
Microstrip Couplers with Accurate Discontinuity
Models,'' Symposium on Microwave Theory and Techniques, pp.
54-56, June 1981.
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