Substrate Material Selection and its Importance
Chapter 3
Chapter 3
3. Substrate Material Selection and its importance
The first step in designing an antenna is to choose an appropriate substrate. The
substrate in micro strip antennas is principally needed for the mechanical support of
the antenna. To provide this support, the substrate should consist of a dielectric
material, which may affect the electrical performance of the antenna, circuits and
transmission line. A substrate must, therefore, simultaneously satisfy the electrical
and mechanical requirements, which is sometimes difficult to meet.
3.1 Criteria for Substrate Selection:
The following parameters should be considered while selecting the substrate material
in the design of antennas
a) Surface wave excitation
b) Dispersion of the dielectric constant and loss tangent of the substrate
c) Copper loss
d) Anisotropy of the substrate
e) Effects of temperature, humidity and aging
f) Mechanical requirements: conformability, machinability, solderability,
weight, elasticity etc.
g) Cost
The first three factors are of special concern in the millimetre wave range (f>=30
GHz).
3.2 Surface wave Excitation
Surface waves can be excited at the dielectric-to-air interface. Surface waves give
rise to end fire radiation. In addition they can lead to unwanted coupling between
array elements. The phase velocity of surface waves is strongly dependent on the
dielectric constant εr and thickness h of the substrate. The excitation of surface waves
in a dielectric slab backed by a ground plane has been well studied (Collin, Field
Theory of Guided Waves). The lowest order TM mode, TM0, has no cut-off
frequency. The cut-off frequencies for higher order modes (TMn and TEn) are given
by
31
Substrate Material Selection and its Importance
f c( n ) 
Chapter 3
n.c
, n  1,2.....
4h  r  1
(13)
Where ‘c’ is the speed of light. The cut-off frequencies for the TEn modes are given
by n=1, 3, 5 ... and the cut-off frequencies for the TMn modes are given by the even
n. For the TE1 mode the calculated values of h/λc (1) are 0.217 for duroid (εr = 2.32),
0.0833 for alumina (εr = 9.2). Where
h
c
(1)
are [c
(1)

c
f
(1)
c
,
h
c
(1)

n
].
4 r 1
Thus, the lowest order TE1 mode is excited at 41 GHz for 1.6 mm thick duroid
substrate, and at about 39 GHz for 0.635 mm thick alumina substrate. The substrate
h
h
is well below
( 0 is free-space
(1)
0
c
thickness is chosen so that the ratio
wavelength at operating frequency)
h
4 fu
c
 r 1
(14)
Where ‘fu ’is the highest frequency in the band of operation. Note that ‘h’ should be
chosen as high as possible under the constraint of (3), so that maximum efficiency is
achieved. Also ‘h’ has to conform to the commerciality available substrates. Another
practical formula for ‘h’ is
h
0.3c
2f u  r
(15)
The TM0 mode has no cut-off frequency and is always present to some extent. The
surface TM0 wave excitation becomes appreciable when h/λ > 0.09 (εr =2.3) and
when h/λ > 0.03 (εr =10) generally to suppress the TM0 mode, the dielectric constant
should be lower and the substrate height should be smaller. Unfortunately decreasing
εr increases the antenna size, while decreasing h leads to smaller antenna efficiency
and frequency band. Table 3.1 shows the electrical properties of some commonly
used substrate materials.
Table 3.1 Electrical properties of commonly used substrate materials for microstrip antennas
S No
1
2
3
4
5
6
7
Material
Unreinforced PTFE, Cuflon
Reinforced PTFE, RT Duroid 5880
Fused Quartz
96% Alumina
99.5% Alumina
Sapphire
Semi insulating GaAs
32
Dielectric constant
2.1
2.2 (1.5%)
3.78
9.4 (5%)
9.8 (5%)
9.4, 1.6
12.9
Loss Tangent
0.0004
0.0009
0.0001
0.0010
0.0001
0.0001
0.0020
Substrate Material Selection and its Importance
Chapter 3
 Cuflon is a microwave material consisting of pure Teflon resin electroplated
with copper using a process developed by polyflon. Longer tool life can be
expected when drilling cuflon than glass reinforced laminates.
 Reinforced PTFE, RT Duroid materials have features like lowest electrical
loss, low moisture absorption, uniform electrical properties over frequency
and excellent chemical resistance. As per the applications are concerned, they
can be used in microstrip and strip line circuits, millimetre wave applications
and in point to point digital radio antennas.
 Fused quartz or Fused silica is glass consisting of silica in non crystalline
form. The optical and thermal properties of fused quartz are superior to those
of other types of glass due to its purity. Its low coefficient of thermal
expansion also makes it a useful material for precision mirror substrates.
 96% Alumina has good electrical insulation, high mechanical strength,
excellent wear resistance, excellent corrosion resistance and low dielectric
constant value. The applications includes in the area of aerospace
components, automotive sensors, semiconductor components and in electrical
and electronic insulators.
 99.5% Alumina is one of the most widely specified, general purpose technical
ceramic materials. It has very hard and wear resistant with high compressive
strength even against extreme temperatures and corrosive environments.
Table 3.2shows the non electrical properties of the commonly used substrate
materials and Table 3.3 shows the popular Rogers Corporation substrate materials,
which are mostly used in the printed antenna technology.
Table 3.2 Non Electrical properties of commonly used substrate materials for microstrip
antennas
Properties
Temperature range
(ᵒC)
Thermal
Conductivity
(w/cm.k)
Coefficient of
thermal expansion
PTFE
Fused Quartz
Alumina
Sapphire
GaAs
-55 -260
<+1100
<+1600
-24 -370
-55 -260
0.0026
0.017
0.35-0.37
0.42
0.46
16.0-108.0
0.55
6.30-6.40
6.00
5.70
33
Substrate Material Selection and its Importance
(ppm/k)
Temperature
coefficient of
dielectric constant
(ppm/k)
Minimum thickness
(mil)
Machinability
Solderability
Dimensional
Stability
Cost
Chapter 3
+350 to 480
+13.0
136.0
110 to 140
-
4
2
5
4
4
Good
Good
Poor for
unreinforced,
Good for
others
Very Poor
Good
Very Poor
Good
Poor
Good
Poor
Good
Good
Excellent
Good
Good
Very Low
High
Low
-
Very
High
Table 3.3 Commonly used materials from Rogers Corporation
S.No
Substrate Material
1
2
3
4
5
6
7
8
9
10
RT/duroid 5870
RT/duroid 5880
RT/duroid 6002
RT/duroid 6006
RT/duroid 6010.2LM
RT/duroid 6202
RT/duroid 6002 PR
RT/duroid RO4003C
RT/duroid RO4050B
ULTRALAM® 3850
Dielectric
constant εr
2.33
2.2
2.94
6.45
10.7
2.94
2.90
3.55
3.66
2.9
Dissipation
Factor tanδ
0.0012
0.0009
0.0012
0.0027
0.0023
0.0015
0.0020
0.0027
0.0037
0.0025
Moisture
absorption
0.02
0.02
0.02
0.05
0.01
0.1
0.1
0.06
0.06
0.04
Coefficient of
thermal expansion
22,28,173 in x,y,z
31,48,237 in x,y,z
16,16,24 in x,y,z
47,34,117 in x,y,z
24,24,47 in x,y,z
15,15,30 in x,y,z
15,15,30 in x,y,z
11,14,46 in x,y,z
11,14,46 in x,y,z
17,17,150 in x,y,z
RT/duroid high frequency circuit materials are filled PTFE (random glass or
ceramic) composite laminates for use in high reliability, aerospace and defence
applications. Low electrical loss, low moisture absorption, stable dielectric constant
over frequency are the benefits from this material. It can be used in airborne and
ground based radar systems, millimetre wave applications, military radar systems,
missile guidance systems and space satellite transceivers. RT/duroid 5870 high
frequency laminates are PTFE composites reinforced with glass microfibers.
3.3 Dispersion Effects in the substrate
The dependence of the dielectric constant εr and loss tangent on the frequency is
referred to as frequency dispersion. For frequencies up to 100 GHz (The typical
ranges for printed antennas is <30 GHz), the dispersion of εr is practically negligible.
The losses, however, display noticeable changes with frequency. In general, loss
increases with frequency.
34
Substrate Material Selection and its Importance
Chapter 3
3.3.1 Dielectric loss and copper loss
The loss in the feed lines and the patches themselves are usually computed with
formulas, which were first derived for microstrip transmission lines.
3.3.2 Dielectric loss (in dB per unit length, length is in the units used for 0 )
 d  27.3
[ r ( f )  1] tan 
r
. eff
.
0
 reff ( f ) ( r  1)
(16)
Where λ0 is free space wavelength, tan δ is loss tangent and εr is dielectric constant of
the substrate material.
3.3.3 Copper loss (in dB per unit length)
2


W'  

 32  
 
h  
Rs' 
w


,.................... for  1
1.38. hZ . 
' 2
h
0

 32   W  


 h  
c  


W' 
'

0.667
'
R Z  ( f ) W
h   ,......... for w  1
6.1 105. s 0 reff
.  '

h
h
 h W  1.444 

h



(17)
 reff ( f ) is the effective dielectric constant (generally, dispersive).
1/ 2
r  1 r 1 
h
w

.
1

12


 ,....................  1
2 
W
h
 2
 reff (0)  
1/ 2
2
  r  1   r  1 .  1  12 h   0.04 1  W   ,..... w  1



 
 2
2 
W
h  
h


(18)
Alternative expression for the quasi-static approximation of  reff can be found in [5].
The quasi-static expressions need a dispersion correction for frequencies higher than
8 GHz. One possible correction is based on an empirical formula for the dispersive
phase velocity in a microstrip line [5]. We first compute a normalized frequency
(normalized with respect to the cut-off of the TE1 mode):
35
Substrate Material Selection and its Importance
fn 
f
f
(1)
c

4h  r  1
.
0
Chapter 3
(19)
Then, the dispersive phase velocity is calculated as
f n2  reff (0)   r
1
vp 
.
.
f n2  1
 0 reff (0)
(20)
Finally,
 reff ( f )  (c / v p ) 2 .
(21)
Z0 is the characteristic impedance of the microstrip line (generally, dispersive):

120  reff
w

,................ for  1
h
 W  1.393  0.667 ln  W  1.444 



Z0   h
h

 60
W
w
 8h

.ln   0.25  ,................................ for  1
h
h
W
  reff

(22)
 is a constant dependent on the strip thickness t
 h  1.25t 1.25  4W 
w 1

ln 
1 ' 1
 , for 
  t 
h 2
 W  W

1 h 1 1.25t  1.25 ln  2t  ,..... for w  1
 W '  W
  t 
h 2

(23)
W ' is the effective strip width:
W 1.25t 
W'
1
 4 W  

1

ln
,
for






h 
h 2
 t 
W'  h

h W 1.25t 
W'
1
 2h  

1  ln    ,.... for


h
h 
h 2
 t 

(24)
Rs| is the effective surface resistance of the conductor:
 2
    2  
R  Rs 1  arctan 1.4     , 
     
 
'
s
(25)
Where Rs   f  /  is the high frequency surface resistance of the conductor. Rs
1
relates to the skin–depth  as Rs     . For a uniform surface current distribution
36
Substrate Material Selection and its Importance
Chapter 3
over a conducting rod of length l and perimeter of its cross-section P, the resultant
resistance is
Rhf  Rs .l / P, . .
Finally, the total loss is the sum of the conduction and dielectric losses:
t   d   c .
(26)
Table 5 gives the skin depth of some of the materials at 2 GHz.
Table 3.4 Skin depth of some materials
Metal
Rs [Ohm/square x 107 f]
Silver
Ag
Copper
Cu
Gold
Au
Aluminium
Al




Skin-depth at 2 GHz[  m]
1.4
7
=6.1x10 S/m
=5.8x10
7
S/m
1.5
=4.1x10
7
S/m
1.7
=3.5x10
7
S/m
1.9
3.4 Composite material Substrates
Material manufacturers tried to combine the characteristics of different materials to
get desired electrical and mechanical properties. The resulting materials are called
the composite materials. Different wide varieties of materials are available with
permittivity range from 2.1 to 10 and loss tangent from 0.0005 to 0.002 at 10 GHz.
Table 3.5 shows the characteristics of some of the laminates. All these substrate
materials are available in large sizes with good mechanical properties for fabrication
of printed circuits. The dielectric constant and loss tangent of some known composite
materials are listed in Table 3.6.
Table 3.5 Characteristics of Laminates at 10 GHz
S.No
1
2
3
4
5
6
7
Laminate/Substrate
Cross-linked
Polystyrene quartz
Cross -linked
polystyrene quartz,
Woven
Cross-linked
polystyreneCeramic, powder
filled
Teflon glass,
reinforced
Teflon-Ceramic,
reinforced
Teflon-quartz,
reinforced
Teflon-Ceramic,
Dielectric
Constant
Loss
Tangent
Dimensional
Stability
Chemical
Resistance
Temperature
range
2.6
0.0005
Good
Good
-27 to +110
2.65
0.0005
Good
Good
-27 to +110
3 to 15
0.0005
to
0.0015
Fair to Good
Fair
-27 to +110
Medium to
high
2.55
0.0015
Good
Excellent
-27 to +260
Medium
2.3
0.001
Fair to Good
Excellent
-27 to +260
Medium to
high
2.47
0.0006
Good
Excellent
-20 to +260
High
10.3
0.002
Good
Excellent
-27 to +260
Low
37
Relative
cost
Medium to
high
Medium to
high
Substrate Material Selection and its Importance
8
9
10
11
12
13
filled
Irradiated
polyolefin-glass,
reinforced
Polyolefin-Ceramic,
Powder filled
2.42
0.001
Fair
Excellent
-27 to +100
Medium
3 to 10
0.001
Poor
Excellent
-27 to +100
High
7.5
0.002
Excellent
Excellent
-27 to +593
Medium to
high
3 to 25
0.0005
to 0.004
Fair to Good
Good
-27 to +268
Medium
6
0.017
Excellent
Excellent
-27 to +205
Medium
1.07
0.0009
_
_
_
_
Glass-bonded mica
Silicon resinCeramic, powder
filled
Polyester-Ceramic
powder filled glass,
reinforced
Polymethacrylate
foam, Rohacell 51
Chapter 3
Table 3.6 Composite materials characteristics at 10 GHz
S.No
1
2
3
4
5
6
7
8
9
10
11
12
13
Material
RT/Duroid 5870
RT/Duroid 5880
RT /Duroid 6002
RT/Duroid 6006
RT/Duroid 6010.5
Ultralam 2000
RO 3003
TMM-3
TMM-4
TMM-6
TMM-10
Trans-Tech D-MAT
Trans-Tech S-145
Dielectric Constant
2.33  0.02
2.2
2.94
6.0  0.15
10.5  0.25
2.5  0.05
3.0  0.04
3.25
4.5
6.5
9.8
8.9-14
10.0
Loss Tangent
0.0012
0.0009
0.0012
0.0019
0.0024
0.0022
0.0013
0.0016
0.0017
0.0018
0.0017
<0.0002
<0.0002
3.5 Low loss and Low cost Substrates
General microstrip patch antennas at microwave frequencies use substrates such as
quartz, PTFE and honeycomb for good radiation efficiency. The electrical
performance of these materials is quite good but cost is high to place them for
commercial applications like mobile communication, direct broadcasting satellite
reception so on. Generally cost of printed antennas depends on substrate material and
connectors only. FR4 is one of the commercially available low cost materials for
printed antennas above 1 GHz range. Substrate manufacturers introduced so many
materials with good electrical performance at reasonable cost. Some of the low cost
materials are listed in the Table 3.7.
Table 3.7 Low loss and Low cost substrate materials
S. No
Material
1
R03003
Dielectric
Constant at
1 GHz
3.00
Loss Tangent at 1 GHz
Manufacture
r
0.0013
Rogers Corp
38
Substrate Material Selection and its Importance
Chapter 3
2
3
4
R03006
R03010
R04003
6.15
10.2
3.38
0.0013
0.0013
0.0022
5
TLC-32
3.2
0.003
6
HT-2
4.3
0.0033
7
Polyguide
2.32
0.0005
8
Epoxy/glass(
FR4)
4.4
0.01
Rogers Corp
Rogers Corp
Rogers Corp
Taconic
Plastics
HewlettPackard
Shawinigan
Research
-
3.6 Design Considerations and Specifications of basic Rectangular patch
Antenna
The main objective is to design a basic microstrip antenna with rectangular shaped
patch operating at a specific frequency. Selecting suitable geometry according to the
substrate material dielectric constant, loss tangent and thickness is crucial in this
process. When substrate material dielectric constant is low, fringing fields around the
patch will increase and thus the radiated power. Antenna efficiency will decrease
with high loss tangent value.
Patch width will affect less on resonating frequency and radiation pattern, but it
affects the bandwidth considerably. Increase in patch width leads to increment in
bandwidth and radiation efficiency. The patch width should be taken more than patch
length without exciting undesired modes. The patch length can be calculated as
L
c
2 fr  r
--------
(27)
Fields are not entirely confined to the patch. A fraction of fields lie outside the
physical dimensions of the patch, which is called as fringing fields. The fringing field
effect can be included with effective dielectric constant  reff .
L
c
2 f r  reff
--------
(28)
Mainly three essential parameters are required to design the rectangular patch
antenna.
1. Resonant frequency: The designed antenna should operate at that particular
frequency
2. Dielectric Constant of Substrate: Performance deciding factor
3. Substrate Height: Bandwidth improvement factor
39
Substrate Material Selection and its Importance
Chapter 3
The design procedure for rectangular microstrip patch antenna at a particular
frequency with suitable substrate material is as follows
1. For the case of coaxial feeding, center of the patch should be considered as origin
and feed location will be represented as (Xf, Yf) from origin. Feed point should be
selected on the patch with input impedance of 50 ohms at a particular location for the
resonating frequency.
2. The width of the antenna can be calculated using the equation
W
2 f0
c
 r 1
2
--------
(29)
3. The effective dielectric constant can be calculated using the equation
 reff 
 r 1  r 1
h

(1  12 ) 0.5
2
2
w
---------
(30)
4. The effective length can be calculated using the equation
Leff 
c
2 f 0  reff
----------
5. Active length is given by L  Leff  2L
(31)
----------
(32)
6. Ground width and length are given by
Lg  6 h  L
---------
Wg  6 h  W
(33)
7. Finding feed point location for perfect impedance matching once by calculating
the dimensions of the antenna using commercial EM tool, the design and simulation
will be carried out. Nowadays almost all the tools are providing wide range of
substrate material library for choosing particular material. Once after getting
simulation results, then optimization of the model will be done with the tool before
going for the fabrication. Seven substrate materials are considered in this work to
examine the performance of different antennas. These materials dielectric constant
and loss tangent values are provided in Table 1.2 of chapter 1.
40