Volume 3, Issue 2, August 2013 Plasma Effect on … 3/Issue 2/IJEIT1412201308_22.pdfVolume 3, Issue 2, August 2013 119 Abstract —A operating in dominant mode TMsingle rectangular

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ISO 9001:2008 Certified International Journal of Engineering and Innovative Technology (IJEIT)

Volume 3, Issue 2, August 2013

119

Abstract—A single rectangular microstrip patch antenna

operating in S band at resonance frequency near 2.15 GHz has

been studied in the existence of cold plasma as a layer covering the

patch antenna. Microwave Office Package is used to design the

rectangular microstrip antenna and to analyze some plasma

parameters at different conditions. Cavity model is also used in the

microstrip antenna to study the plasma when it is considered as a

medium between the patch and ground. Expressions of cold

plasma and their coefficients in the conditions of plasma

interaction operating microwave frequencies are investigated and

presented in details. The radiation pattern, input impedance and

resonance frequency for dominant TM01 mode are calculated for

different plasma conditions. The results presented in this research

may be useful when designing antennas in case of existing plasma

conditions in space system.

Index Terms— Cavity model, Cold Plasma, Rectangular

Microstrip Antenna, TT&C.

I. INTRODUCTION

Antennas have been an essential reciprocal device

employed in telemetry and telecomands (TT&C) space

systems. Microstrip patches are one of suitable elements for

array antennas because of their low weight, better

aerodynamic properties, easy covered by protection layer and

low fabrication cost for aerospace vehicle, like satellites and

reusable space shuttles [1], [2]. However, during re-entry

into earth's atmosphere, a plasma sheath is formed around the

vehicles. A major problem confronting the aerospace

engineers in the space mission is the estimation of the effect

of plasma on the radiation properties of an antenna mounted

on aerospace vehicles or satellites. The plasma sheath may be

seriously affects system performance. Sometimes these

conditions caused interruption of communication link

because of changing the input impedance of the antenna and

may be highly mismatch occurrence. Due to the interaction of

electromagnetic field with plasma in certain parameters value

for plasma frequency, collision frequency and plasma

thickness may be add another effect on such interruptions.

In this work a detailed theoretical formulation on the

isotropic cold plasma, which is normally occurred in space

applications and its interaction with electromagnetic radio

frequencies is presented. A rectangular microstrip antenna

operating in dominant mode TM01, is taken as an important

element in studying the plasma effects. Cavity model

analysis is taken in this report for studying some plasma

conditions on the patch antenna input impedance.

The existence of plasma near conformal microstrip

antennas in flight vehicles operates and below plasma

frequency gives special performance conditions. In

hypersonic missile flight, high temperature generation is

produced. So that, a slap of ceramic material covers the

conductive patch antenna for protection purposes. The

ceramic materials properties at X band are illustrated in Table

I. The plasma effects on receiver antenna are also taken into

account. Different computed and published results are

demonstrated and discussed to illustrate some important

parameters contribution in the antenna.

Table I: Representative values for ceramic materials at X band

Material Relative

permittivity 𝜺′ Loss tangent

𝐭𝐚𝐧 𝜹

Alumina 9.4 - 9.6 0.0001 -0.0002

Boron nitride 4.2 – 4.6 0.0001-0.0003

Beryllia 4.2 0.0005

Borosilicate glass 4.5 0.0008

Pyroceram 5.54 -5.65 0.0002

Rayceram 4.7 -4.85 0.0002

Slip cast fused silica

(SCFS) 3.30 – 3.42 0.0004

Woven (3D) quarts 3.05 – 3.1 0.001-0.005

Silicon nitride

(HPSN) 7.8 – 8.0 0.002-0.004

Silicon nitride

(RSSN) 5.6 0.0005-0.001

Nitroxyceram 5.2 0.002

Reinforced celasin 6.74 0.0009

Plasma Effect on TM01 Mode Rectangular

Microstrip Antenna for Space Telemetry and

Telecomands Subsystems Applications Abdulkareem A. A. Mohammed

1 and Dhirgham K. Naji

2

1Head of

Atmosphere and Space Science Center, Directorate of Space & Communication, Ministry of Science

and Technology, Baghdad, Iraq

2Department of Electronic and Communications Engineering, College of Engineering, Alnahrain University,

Baghdad, Iraq

E-mail: [email protected], [email protected]

mailto:[email protected]

mailto:[email protected]

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II. THEORETICAL FORMATION

A. Electromagnetic Interaction with Plasma

The approach presented here follows closely the material

developed in some published texts [3-5]. By using the cold

plasma approximation, the equation of motion of an electron

mass m and charge 𝑞 in electric field of amplitude 𝐸 and

angular frequency 𝜔, with collision frequency vc acting as

damping force and when the electron velocity equal to v:

−𝑞𝐸𝑒𝑗𝜔𝑡 = 𝑚𝑑𝑣

𝑑𝑡+ 𝑚𝑣𝑐𝑣 (1)

The current density 𝐽 per unit volume is given by

𝐽 = −𝑁𝑞𝑣 (2)

The complex conductivity of the medium is equal to the ratio

of the current density to field

𝜎𝑐 =𝐽

Eejωt=

𝑁𝑞2

𝑚(vc + 𝑗𝜔) (3)

𝜎𝑐 = 𝜎 ′ − 𝑗𝜎′′ =𝑁𝑞2

𝑚휀0∙

휀0vc

𝑣𝑐2 + 𝜔2

− 𝑗𝑁𝑞2

𝑚휀0∙

휀0𝜔

𝑣𝑐2 + 𝜔2

(4)

The quantity (𝑁𝑞2 𝑚휀0) is the natural angular frequency

specific to the electrons which is given by 𝜔𝑝 = 2𝜋𝑓𝑝 . Where

𝑓𝑝 is called plasma frequency and practically defined by

𝑓𝑝 = 8970𝑁−1 2 (5)

where 𝑓𝑝 in [Hz] and N is the number of electrons per cm-3.

The collision frequency vc is given by

vc = 𝑛𝑛𝜎 𝑘𝐵𝑇𝑚 (6)

where 𝑛𝑛 is the number density of neutral species, 𝜎 is the

collision cross section, 𝑘𝐵 is the Boltzmann’s constant, and

m is the electron mass.

Referring to Maxwell equations the complex dielectric

constant related to conductivity by the expression

εc = 휀′ + 𝑗휀 ′′ = 휀0 +𝜎𝑐

𝑗𝜔 (7)

For convenience, two dimensionless quantities, the

normalized electron density 𝑋 and the normalized collision

frequency 𝑍 are introduced:

𝑋 = 𝜔𝑝

𝜔

2

(8𝑎)

𝑍 = 𝑣𝑐

𝜔

2

(8𝑏)

So

𝜎 ′ = 휀0𝜔𝑋𝑍

1 + 𝑍2 (9𝑎)

𝜎′′ = 휀0𝜔𝑋

1 + 𝑍2 (9𝑏)

And

Fig. 1. Real dielectric constant of plasma at different collision

frequency 𝒗𝒄.

휀′ = 휀0 1 +𝑋

1 + 𝑍2 (10𝑎)

휀′′ = 휀0𝑋

1 + 𝑍2 (10𝑏)

In the absence of any collisions 𝑍 = 0 and the relative

dielectric constant is real and equal to (1 − 𝑋). It varies with

frequency (i.e. it is dispersive medium) from (휀 = −∞) for

the lowest frequency to (휀 = 1) for high frequencies, passing

through (휀 =0) for 𝑋 = 1, Fig. 1.

In the case of plane wave, the propagation constant 𝛾 ,

wave number 𝐾 and the dielectric constant are related by the

following relationship:

𝛾 = 𝛼 + 𝑗𝛽 = 𝑗2𝜋

𝜆 εc

휀0

1 2

= 𝑗 𝐾𝜔

𝑐=

𝐾

𝑗 (11)

While the skin depth, the depth which the incident wave is

attenuated by factor (1/𝑒), of plasma media computed by:

𝑃𝑝 =1

𝛼 (12)

It is important to determine the conditions under which the

plasma can be considered as a conductor, and those under

which it can be considered a dielectric. From the ratio of

conduction current to displacement current 𝜎′ 𝜔휀′ the

nature of material can be determined. The point at which

these two currents are equal is generally considered as the

boundary between conductive media 𝜎′ 𝜔휀′ ≫ 1 and

dielectric media 𝜎′ 𝜔휀′ ≪ 1 . In the case of plasma, this

condition can be calculated as:

𝜎 ′

𝜔 휀′ =

𝑋𝑍

1 − 𝑋 + 𝑍2 (13)

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Fig. 2. Boundary between conducting plasma and dielectric

plasma.

Fig. 2 shows the curve representing the boundary between

conductive plasma and dielectric plasma. The behaviour of

plasma as a function of frequency, from the point of view of

refractive index, can now be described briefly. The complex

refractive index defined

𝑛 = 𝑛1 − 𝑗𝑘1 = −𝑗𝛾𝑐

𝜔= 𝐾 (14)

where 𝑛1 and 𝑘1 are the real refractive index and attenuation

index, respectively, and they defined as[3]

𝑛1 = 1

2𝑟 +

1

2 𝑟2 + 1 − 𝑟 2 ∙

𝑣𝑐

𝜔

2

1 2

1 2

(15𝑎)

𝑘1 = −1

2𝑟 +

1

2 𝑟2 + 1 − 𝑟 2 ∙

𝑣𝑐

𝜔

2

1 2

1 2

(15𝑏)

where

𝑟 = 1 −𝜔𝑝

2

𝜔2 + 𝑣𝑐2 (16)

and the dielectric constant of the plasma

εc = ε0 ∙ 𝑛2 (17)

and the intrinsic impedance of non magnetized plasma

medium is

ηc = 𝜇0

εc

(18)

In case of low loss plasma (𝑣𝑐 << 𝜔𝑝 ), three frequency

regions may be defined as follow:

Low Frequencies Case 𝜔 < 𝑣𝑐 , we observe that 𝑛1,

𝑘1 are nearly equal. Expanding in the limit (𝜔 << 𝑣𝑐 , 𝑣𝑐

2 << 𝜔𝑝2 ) , one can obtained the following

indexes equations:

𝑛1 ≈ 𝜔𝑝

2

2𝜔𝑣𝑐

1 2

1 −𝜔

2𝑣𝑐 (19𝑎)

𝑘1 ≈ 𝜔𝑝

2

2𝜔𝑣𝑐

1 2

1 +𝜔

2𝑣𝑐 (19𝑏)

Intermediate Frequencies Case (𝑣𝑐 < 𝜔 < 𝜔𝑝) . In

this region the propagate an electromagnetic wave is

forbidden due to plasma, where the waveguide below

cutoff. Expanding in the limit (𝑣𝑐2 << 𝜔2 << 𝜔𝑝

2 )

we obtained the following indexes equations:

𝑛1 ≈𝑣𝑐𝜔𝑝

2𝜔2 1 −

5𝑣𝑐2

8𝜔2+

𝜔2

2𝜔𝑝2 (20𝑎)

𝑘1 ≈𝜔𝑝

𝜔 1 −

3𝑣𝑐2

8𝜔2−

𝜔2

2𝜔𝑝2 (20𝑏)

High Frequencies Case (𝜔 >> 𝜔𝑝 ). Here, the plasma

becomes a relatively low loss dielectric. in the limit

(𝑣𝑐2 << {𝜔2 -𝜔𝑝

2} and υc2 << 𝜔2{𝜔2 -𝜔𝑝

2 }2 /𝜔𝑝

4 )

the following indexes equations are obtained:

𝑛1 ≈ 1 −𝜔2

𝜔𝑝2

1 2

(21𝑎)

𝑘1 ≈𝑣𝑐𝜔𝑝

2

2𝜔3 1 −

𝜔2

𝜔𝑝2 (21𝑏)

Note that the refractive index is quite insensitive to

collisional damping and the attenuation for the assumed

conditions.

B. Theoretical Formulation of Microstrip Antenna

A microstrip patch antenna consists of a very thin metallic

patch placed a small fraction of wavelength above a

conducting ground-plane. The patch and the ground-plane

are separated by a dielectric layer. The dielectric substrate is

usually non-magnetic and low loss material, (see Fig. 3).

Due to the simple geometry of the microstrip patch

antenna, the half-wave rectangular patch is the most

commonly used microstrip antenna. It is characterized by its

length 𝐿 , width 𝑊 and thickness ℎ . The patch is fed by

coaxial feed to excite the cavity field. The inner conductor of

the coaxial line is connected to the radiating patch while the

outer is connected to the ground-plane as shown in Figure 3.

A cavity model for the microstrip antennas is based on

considering close proximity between the microstrip antenna

and ground plane. So that E field has only the z component

and the H has only the xy-components in the region bounded

by the microstrip and the ground plane. The field in the

aforementioned region is independent of the z-coordinate for

all frequencies of interest. The electric current in the

microstrip must have no component normal to the edge at any

point on the edge, which implies that the tangential

component of H along the edge is negligible. Thus the region

between the microstrip and the ground plane may be treated

as a cavity bounded by a magnetic wall along the edge, and

by electric walls from above and below [6, 7].

10-2

10-1

100

101

102

10-1

100

101

102

Boundary between conducting plasma & dielectric plasma

(W/Wp)2

Vc/W Conductor plasma

Dielectric plasma

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Fig. 3. The rectangular microstrip geometry.

The resonance frequency of m, n order mode 𝑓𝑚𝑛 depends

on the patch size, cavity dimension, and the filling dielectric

constant [8, 9]

𝑓𝑚𝑛 ≈𝑘𝑚𝑛

2𝜋 휀𝑟 (22)

where 𝑚, 𝑛 = 0, 1, 2…

𝑘𝑚𝑛 = Wave number at m, n mode

𝑐 = Velocity of light

휀𝑟 = Relative dielectric constant

And

𝑘𝑚𝑛 ≈ 𝑚𝜋 𝑊 2 + 𝑚𝜋 𝐿 2 (23)

where

𝑊 = Width of the microstrip antenna

𝐿 = Length of the microstrip antenna

The radiating edge W, patch width, is usually chosen such

that it lies in the range (𝐿 < 𝑊 > 2𝐿), for efficient radiation.

The ratio 𝑊/𝐿 = 1.5 may give good performance according

to the side lobe appearances.

In practice the fringing effect causes the effective distance

between the radiating edges of the patch to be slightly greater

than 𝐿. Therefore, the actual value of the resonant frequency

is slightly less than 𝑓𝑟 . Taking into account the effect of

fringing field, the effective dielectric constant for TM01 mode

is derived using [9,11]

𝐿 =𝑐

2𝑓𝑟 휀𝑟

− 2∆𝑙 (24)

Hence

𝑓𝑟 𝑒𝑓𝑓 =𝑐

2 𝐿 + 2∆𝑙 휀𝑟

(25)

with

휀𝑒𝑓𝑓 =휀𝑟 + 1

2+

휀𝑟 − 1

2

1

1 + 10ℎ/𝑊 (26)

and

∆𝑙 = 0.412ℎ 휀𝑒𝑓𝑓 + 0.3 𝑊/ℎ + 0.264

휀𝑒𝑓𝑓 − 0.258 𝑊/ℎ + 0.813 (27)

where

∆𝑙 = Line extension

휀𝑒𝑓𝑓 = Effective dielectric constant

ℎ = Dielectric substrate thickness

The electric field is assumed to act entirely in the

z-direction and to be a function only of the x and y

coordinates

𝐸 = 𝑧𝐸𝑧 𝑥, 𝑦 (28)

The z-component of the electric field 𝐸𝑧 satisfies the two

dimensional form of partial differential equation, the

so-called wave equation

𝜕2𝐸𝑧

𝜕𝑥+

𝜕2𝐸𝑧

𝜕𝑦+ 𝑘2𝐸𝑧 = 0 (29)

Equation (29) cannot be solved without specifying some

boundary conditions for the patch. An obvious requirement is

that the outward current flowing on the perimeter of the patch

must be zero. It may be shown that this requirement is

approximately equivalent to

𝜕𝐸𝑧

𝜕𝑛= 0 (30)

Solving equation (29) subject to the requirement (30) and

using separation of variable, the electric field of the m and n

mode number associated with 𝑥 and 𝑦 direction in a

rectangular resonator with dimensions 𝑊 and 𝐿 can be

written in the form [9].

𝐸𝑧 = 𝐸0 cos 𝑚𝜋𝑥/𝑊 𝑛𝜋𝑦/𝐿 (31)

Now to calculate the far field, aperture model is used. The

resonator surface considered to be as a set of four slots of

width 2𝑎 [12]. By using Green's function and after many

mathematical steps, the general form of the far field for any

(𝑚, 𝑛) mode is in the following form:

𝐸 𝑟 =𝑗𝑘𝑒−𝑗𝑘𝑟

2𝜋𝑟𝐸0 𝑖𝜃 𝐸𝑥 𝜉, 𝜂 cos 𝜑 + 𝐸𝑦 𝜉, 𝜂 sin 𝜑

+ 𝑖𝜑 −𝐸𝑥 𝜉, 𝜂 sin 𝜑 cos 𝜃 + 𝐸𝑦 𝜉, 𝜂 cos 𝜑 cos 𝜃 (32)

where

𝐸𝑥 = ℎ𝐸0 −1 − −1 𝑚 ∙ 𝑗 sin 𝜉𝑊

2 + 1 − −1 𝑚 ∙

∙ cos 𝜉𝑊

2 ∙

𝐿

2𝑠𝑖𝑛𝑐 𝜉𝑎 ∙ 𝑗𝑛 ∙ 𝑠𝑖𝑛𝑐(

𝜉𝐿

2+

𝑛𝜋

2) +

−1 𝑛𝑠𝑖𝑛𝑐(𝜉𝐿

2−

𝑛𝜋

2) (33𝑎)

W

L

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123

𝐸𝑦 = ℎ𝐸0 −1 − −1 𝑛 ∙ 𝑗 sin 𝜉𝐿

2 + 1 − −1 𝑛 ∙

∙ cos 𝜉𝐿

2 ∙

𝑊

2𝑠𝑖𝑛𝑐 𝜉𝑎 ∙ 𝑗𝑚 ∙ 𝑠𝑖𝑛𝑐(

𝜉𝑊

2+

𝑛𝜋

2) +

−1 𝑚𝑠𝑖𝑛𝑐(𝜉𝑊

2−

𝑛𝜋

2) (33𝑏)

Then the far field components are

𝐸𝜃 =𝑗𝑘𝑒−𝑗𝑘𝑟

2𝜋𝑟 𝐸𝑥 cos 𝜑 + 𝐸𝑦 sin 𝜑 (34𝑎)

𝐸𝜑 =𝑗𝑘𝑒−𝑗𝑘𝑟

2𝜋𝑟 −𝐸𝑥 sin 𝜑 cos 𝜃 + 𝐸𝑦 cos 𝜑 cos 𝜃 (34𝑏)

with

𝜉 = 𝑘 𝑠𝑖𝑛 𝑐𝑜𝑠

= 𝑘 𝑠𝑖𝑛 𝑠𝑖𝑛

𝑘 = 2𝜋/𝜆𝑜

0 =wavelength of free space

Normalizing the input voltage at the feed point (𝑥0 , 𝑦0) to

1V, one can write

ℎ𝐸𝑧 𝑥0 , 𝑦0 = 1 (35)

Using the expression of the closed-cavity resonator model,

the maximum amplitude of the field 𝐸𝑧 is

𝐸0 = ℎ ∙ cos 𝑚𝜋𝑥0

𝑊 ∙ cos

𝑛𝜋𝑦0

𝐿

−1

(36)

where

𝐸0 = Maximum amplitude of the 𝐸𝑧 field

The input impedance of the microstrip antenna fed by a

coaxial probe is 𝑍𝑖𝑛 = 𝑅𝑖𝑛 + 𝑗𝑋𝑖𝑛 . At resonance the

impedance is purely resistive (𝑋𝑖𝑛 = 0). Then the impedance

may be represented by a parallel RLC circuit

𝑍𝑖𝑛 =𝑘

1𝑅

+ 𝑗𝜔𝑐 +1

𝑗𝜔𝐿

(37)

Where at 𝑘 = 1.5, the results give excellent agreement with

the measured and microwave office package results. The

resistance of the patch can be written as

𝑅 =𝑉2

2𝑃𝑇

(38)

where 𝑃𝑇 = 𝑃𝑟 + 𝑃𝑐 + 𝑃𝑑 (39)

𝑉 = Terminal voltage

𝑃𝑇 = Total power dissipated by the antenna

The radiated power outside the antenna surface is

𝑃𝑟 =1

2𝑍0

𝐸𝜗 2 + 𝐸𝜑 2𝑟2 sin 𝜗𝑑𝜗𝑑𝜑

𝜋 2

𝜗=0

2𝜋

𝜑=0

(40)

where

𝑍0 = Characteristic impedance of free space.

The power losses inside the dielectric is

𝑃𝑑 =𝜔0휀0휀𝑟 tan 𝛿

2 𝐸. 𝐸∗𝑑𝑣

𝑣

(41)

where

= Angular operating frequency

𝑡𝑎𝑛 =Loss tangent of the dielectric layer of the patch

The power losses inside the conductor surface of radiator and

the ground plane is

𝑃𝑐 = 2𝑅𝑠

2 𝐻𝑥

2 + 𝐻𝑥𝑦2 𝑑𝑥𝑑𝑦 (42)

where

𝑅𝑠 = 𝜔𝜇0𝜇𝑟

2𝜎 (43)

𝑅𝑠 = Surface resistance

𝐻𝑥 =𝑗

𝜔𝜇 𝜕𝐸𝑧

𝜕𝑦 (44𝑎)

𝐻𝑦 =−𝑗

𝜔𝜇 𝜕𝐸𝑧

𝜕𝑥 (44𝑏)

The inductance and the capacitance of the patch are

respectively

𝐿 =𝑅

2𝜋𝑓𝑟𝑄𝑇

(45𝑎)

and

𝐶 =𝑄𝑇

2𝜋𝑅𝑓𝑟 (45𝑏)

The total quality factor 𝑄𝑇 is

𝑄𝑇 = 𝑅 𝐿

𝐶 (46𝑎)

In other meaning

𝑄𝑇 =𝜔𝑊𝑇

𝑃𝑇

(46𝑏)

𝑊𝑇 =휀0휀𝑟

2 𝐸𝑧

2𝑑𝑣

𝑣

(47)

C. Antenna Coating Material as Plasma Protector

The existence of plasma around and above conformal

antennas may appears in flight vehicles operating at and

below about 4 Mach and missiles. A high temperature

generation in hypersonic missile may use slab of Ceramic

material on conductive patch antenna. Table 1 lists

representative values for ceramic materials [13]. Most of

these materials have suitable electrical properties for high

velocity applications. For instance, Aluminium oxide, Pyroceram and Rayceram have been widely used for space

vehicles. They are hard and have fair rain erosion resistance

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but are difficult to grind to shape. Pyroceram has a higher

dielectric constant than either Rayceram or alumina, which

implies tighter mechanical tolerances in manufacture.

D. Antenna Impedance of Plasma

Immersing an antenna in an ionized medium with a

refractive index different from that of the vacuum has the

effect of modifying the impedance presented by this antenna.

The input impedance of an antenna 𝑍𝑎 in a medium of index

(𝑛) to be related to the impedance of the antenna in vacuum,

at an angular frequency (𝑛𝜔).

1

𝜂𝑍0(𝜔, 휀, 𝜇) =

1

𝜂0

𝑍𝑎(𝑛𝜔, 휀, 𝜇0) (48)

In case of gaseous plasma, 𝜇 = 𝜇0 and 휀 = 𝑛2휀0 the

expression become [3].

𝑍𝑎(𝜔, 𝑛2휀0) =1

𝑛 𝑍𝑎(𝑛𝜔, 휀0) (49)

Input impedance at real refractive index plasma: In the

case where the refractive index is real (𝑋 < 1 𝑎𝑛𝑑 𝑍 ≈0),

the angular frequency 𝑛 ω is a multiple of angular

frequency ω and the impedance at this angular frequency

is accessible both to measurement and calculation.

Input impedance at complex refractive index plasma: In

the case of complex n, the frequency 𝑛𝑓 is also complex

[5]. It is, however, well defined mathematically, and if

there is an analytical formula for impedance in vacuum,

the impedance of the antenna in plasma can be deduced

from it.

E. Effect of Plasma Layer on Receiving Antenna

Noise generated by the receiver is characterized by its

noise figure, 𝑁. The ratio of the maximum available noise

power at the output of the receiver 𝑁𝑜𝑢𝑡 to the maximum

noise power that there would be if there were no noise source

other than the generator connected to the receiver input at

standard reference temperature 𝑇0 = 290 °𝐾 (i.e. 𝐺𝑘𝐵𝑇0𝐵0)

is called as noise factor [ 14 ].

𝑁𝐹 =𝑁𝑜𝑢𝑡

𝐺𝑘𝐵𝑇0𝐵0

(50)

where

𝐺 = Maximum usable power gain of the receiver.

𝐵 =Noise equivalent bandwidth at the receiver.

𝑘𝐵 =Boltzmann constant, 1.38 ∗ 10−23 [𝐽𝐾−1].

The noise figure is the noise factor expressed in dB. If the

actual source has noise temperature of 𝑇0 at the input, the

maximum noise power at the output is given by

𝑁𝑜𝑢𝑡 = 𝐺𝑘𝐵𝑇0𝐵0 + 𝐺𝑘𝐵𝑇𝑅𝐵 (51)

which gives

𝑁𝐹 = 1 +𝑇𝑅

𝑇0

(52)

This expression only applied for particular terminating

impedance at the receiver input. All matter emits radiant

energy, when picked by an antenna; this radiation is

superimposed on the usable signal as background noise. If

𝑁0 is the power spectral density of such noise (expressed in

watt/Hz) the antenna temperature (expressed in Kelvin) is

such that:

𝑁0 = 𝑘𝐵𝑇𝐴 (53)

The antenna temperature is affected by:

The temperature and absorbance of external radiators.

The antenna gain and its orientation relative to these

external radiators.

In cascade subsystems of two stages the noise factor is related

to the noise temperatures by following formula

𝑁𝐹 = 𝑁𝐹1 +𝑁𝐹2 − 1

𝐺1

(54)

then

𝑇 = 𝑇1 +𝑇2

𝐺1

(55)

From these relationships, note that if the gain of the first

stage is sufficiently high, (particularly relevant in low-noise

receiving system were the first stage is low noise amplifier

LNA and the second stage the microwave receiver) the first

stage essentially sets the overall system noise performance.

The existence of a layer (like plasma) having power loss L

can seriously degrade system noise temperature. The system

noise temperature is

𝑇 = 𝑇𝐿𝑁𝐴 + 1 − 𝜂𝐴 𝑇0 + 𝜂𝐴 𝑇𝐴 1 − 𝐿 + 𝑇𝐿𝐿 (56)

where

𝑇𝐿𝑁𝐴 = Antenna radiation efficiency (0 ≤ 𝜂𝐴 ≤ 1)

𝑇𝐿 = Physical temperature of the plasma layer (°𝐾)

𝐿 = Noise temperature of LNA

𝜂𝐴 = Plasma power transmission loss factor (0 ≤ 𝐿 ≤ 1)

III. COMPUTATIONAL RESULT

The isotropic plasma may be considered as dielectric

media or conductive media depending on the propagating

frequency value with respect to plasma and collision

frequency. Fig. 2 represents the boundary between

conductive and dielectric plasma.

A propagating frequency 2.1 GHz is taken as interested

frequency, this frequency is used in TT&C space system, in

calculating the plasma parameters 휀′ and t𝑎𝑛𝛿 . Table II

illustrate the values at three plasma frequencies 0.5, 1.0 and 2

GHz. The contribution effect of collision frequency on these

parameters are demonstrated in the table via five values of

collision frequencies (𝑣𝑐=0, 0.2, 2.0, 4.0 and 8.0 GHz).

The skin depth parameter Pp is computed since the

plasma has conductive properties. Fig. 4 shows the variation

of Pp (m) for multi plasma frequencies (fp= 1.0, 2.0, 5, 10

and 15 GHz) since all calculations are taken in collision

frequency equal to 1 GHz. The loss parameter 𝑡𝑎𝑛𝛿 is

computed at propagating frequency 2.15 GHz for deferent

ISSN: 2277-3754



125

Table II: Plasma dielectric constants at 2.1 GHz at different

plasma and collision frequency.

Plasma

Frequency

[GHz]

Collision

Frequency

[GHz]

Real

relative 𝜺′

of Plasma

𝐭𝐚𝐧 𝜹 of

Plasma

0.5 0 0.9438 0

1.0 0 0.7732 0

2.0 0 0.0933 0

0.5 0.2 0.9438 0.0057

1.0 0.2 0.7753 0.0276

2.0 0.2 0.1011 0.8466

0.5 2.0 0.9703 0.0292

1.0 2.0 0.8811 0.1285

2.0 2.0 0.5240 0.8638

0.5 4.0 0.9878 0.0236

1.0 4.0 0.9500 0.0981

2.0 4.0 0.8040 0.4643

0.5 8.0 0.9963 0.014

1.0 8.0 0.9854 0.0565

2.0 8.0 0.9415 0.2366

plasma frequencies (fp= 2.0, 2.05, 2.10 and 2.125 GHz),

with respect to collision frequency as mentioned in Fig. 5.

While this 𝑡𝑎𝑛𝛿 parameter is computed, at same

propagating frequency f another plasma frequencies

(fp= 2.5, 4.0 and 8.0 GHz) as shown in Fig. 6. The absorption parameter α (Neper/m) at propagating

frequency 2.15 GHz is computed for many plasma

frequencies (fp= 2.15, 2.0, 1.5 and 1.0 GHz) with respect to

collision frequency as illustrated in Fig. 7. The absorption

parameter α (dB/m) is computed for the same variables and

drawings as in Fig. 8.

The phase constant β (radian/m) at propagating

frequency 2.15 GHz is calculated for many plasma

frequencies (fp=2.15, 2.0, 1.5, 1.0 and 0.5 GHz) with

respect to collision frequency as illustrated in Fig. 9. For a

single patch microstrip antenna, the well-known work

published by Lo [9, 11] was studied where the experimental

data of impedance locus and the radiation pattern were in

good agreement with the theory. The patch has the

dimensions of 11.43cm x 7.62cm and fed with a 50

coaxial probe at resonance frequency of 1187 MHz

operating with (0, 1) transverse magnetic TM01 mode. This

work has been investigated with the aid of MW-Office

package. The antenna was simulated in such a way that the

package conditions were: (a) the number of divisions=64,

(b) the division cell size was x=0.714cm, y=0.476cm, and

(c) the top dielectric layer of the enclosure was set to have

the properties of air with 2 cm in thickness; the antenna was

Fig. 4. The computational skin depth at different plasma

frequency.

Fig. 5. The tan loss of plasma as a function of collision frequency

for plasma frequencies blow and near propagating frequency

2.15 GHz.

fed with excitation port of 50 . There is good agreement

between the computed and the published results [6]. The

radiation pattern for both E and E in the same operating

(0, 1) mode has been computed for each of the two cuts,

=0 Fig. 9(a) and =90 Fig. 9(b). It is seen that there is

excellent agreement between the published radiation

patterns of the two cuts one as shown in Fig. 9(c) and Fig.

9(f), respectively.

Accordingly, the MW-Office package is used to design

rectangular microstrip patch antenna of dimensions of 4.96

cm x 3.3 cm printed on dielectric substrate (εr=4.45 and

𝑡𝑎𝑛𝛿 =0.0005) of thickness 1.6 mm and fed with a 50

coaxial probe at resonance frequency of 2.15 GHz operating

with (0, 1) transverse magnetic mode TM01. Some antenna

characteristics, the input impedance, VSWR and radiation

pattern are shown in Fig. 10.

For space application when cold plasma is generated

around spacecraft or space launcher the GPS or TT&C

antenna required ceramic cover to protect the conformal

antenna. A ceramic layer of 1 and 2 mm is tested when it

support directly above the patch antenna. The input

impedance of TM01 mode single rectangular patch operating

108

109

1010

1011

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0Attenuation by collissional absorbtion at radiating Freq =2.15GHz

Collision Frequency,Hz

tan d

elta

plasma frequency

=2.0GHz

=2.05 GHz

=2.10 GHz

=2.125GHz

ISSN: 2277-3754



126

0

-45

-90

-135

180

135

90

45

Mag Max

1

Mag Min

0

0.25

Per Div

E_Theta[0,1] E_Theta[90,1]

0

-45

-90

-135

180

135

90

45

Mag Max

1

Mag Min

0

0.25

Per Div

E_Phi[0,1] E_Phi[90,1]

Fig. 6. The tan loss of plasma as a function of collision frequency

for plasma frequencies above propagating frequency 2.15 GHz.

Fig. 7. Absorption coefficient as a function of collision

frequency for plasma frequencies above propagating

frequency 2.15 GHz.

Fig. 8. Phase shift in plasma as a function of collision frequency

for plasma frequencies below propagating frequency 2.15 GHz.

(a) (b)

(c) (d)

Fig. 9. Radiation patterns (E ( =90) and E ( =0)) for

published [12] and calculated results for TM01 mode of a

rectangular microstrip antenna with W=11.43 cm, L=7.62 cm

operating at resonance frequency 1.187GHz. (a) Published E,

(b) calculated E, (c) published E and (d) calculated E .

(a) (b)

(c) (d) Fig. 10. The input impedance (a), VSWR (b) and radiation

pattern E- and H-plane (c) and (d) of TM01 mode single

rectangular patch operating 2.15 GHz resonance frequency,

(patch size 4.96 cm x 3.3 cm, substrate thickness=1.6 mm,

𝜺𝒓=4.45 and 𝒕𝒂𝒏𝜹=0.0005).

at 2.15 GHz resonance frequency, (patch size

4.96 cm×3.3 cm, substrate thickness=1.6 mm, 휀𝑟=4.45 and

𝑡𝑎𝑛𝛿 =0.0005), and when the patch is covered ceramic

layer of 휀𝑟 =5.2 and 𝑡𝑎𝑛𝛿 =0.002 for thickness. Results

illustrates that there is no big changes with essential antenna

as shown in Fig. 11.

108

109

1010

1011

-80

-60

-40

-20

0

20

40

60

80



tan d

elta

Plasma frequency

=2.5 GHz

=4.0 GHz

=8.0 GHz

108

109

1010

1011

0

2

4

6

8

10

12

14



Alp

h [

neper/

mete

r]

Plasma Frequency

=2.15 GHz

=2.00 GHz

=1.50 GHz

=1.00 GHz

108

109

1010

1011

-50

-45

-40

-35

-30

-25

-20

-15

-10

-5Attenuation by collissional absorbtion at radiating Freq =2.15GHz


Beta

[ra

d/m

ete

r]

Plasma frequency

=2.15 GHz

=2.00 Ghz

=1.50 GHz

=1.00 GHz

=0.50 Ghz

2 2.05 2.1 2.15 2.2

Frequency (GHz)

-20

0

20

40

60

Re

al

an

d I

ma

gin

ary

of

Z (

oh

m)

Re(Z[1,1]) ~

Im(Z[1,1]) ~

2 2.05 2.1 2.15 2.2

Frequency (GHz)

0

2

4

6

8

10

12

14

16

18

20

VS

WR

ISSN: 2277-3754



127

2 2.05 2.1 2.15 2.2

Frequency (GHz)

-20

0

20

40

60

Re

al

an

d I

ma

gin

ary

of

Z (

oh

m)

Re(Z[1,1]) ~

Im(Z[1,1]) ~

2 2.05 2.1 2.15 2.2

Frequency (GHz)

-10

0

10

20

30

Re

al

an

d I

ma

gin

ary

of

Z (

oh

m)

Re(Z[1,1]) ~

Im(Z[1,1]) ~

2 2.05 2.1 2.15 2.2

Frequency (GHz)

-20

-10

0

10

20

30

Re

al

an

d I

ma

gin

ary

of

Z (

oh

m)

Re(Z[1,1]) ~

Im(Z[1,1]) ~

(a) (b) (c) Fig. 11. The input impedance of TM01 mode single rectangular

patch operating 2.15 GHz resonance frequency, (patch size 4.96

cm x 3.3 cm, substrate thickness=1.6 mm, 𝜺𝒓=4.45 and

𝒕𝒂𝒏𝜹=0.0005), and when the patch is covered ceramic layer of

𝜺𝒓=5.2 and 𝒕𝒂𝒏𝜹=0.002 for thickness (a) 1mm, (b) 2mm and (c)

3mm.

(a) (b)

(c) (d) Fig. 12. The input impedance of TMo1 mode single rectangular

patch operating 2.15 GHz resonance frequency, (patch size 4.96

cm x 3.3 cm, substrate thickness=1.6 mm, 𝜺𝒓=4.45 and

tanδ=0.0005) with thin air layer of thickness=5 mm at (a)

𝒕𝒂𝒏𝜹=0, (b) 𝒕𝒂𝒏𝜹=0.005, (c) 𝒕𝒂𝒏𝜹=0.05 and (d) 𝒕𝒂𝒏𝜹=0.5

To explain the effect of dielectric plasma existence near

patch antenna, we simulate this plasma as a thin air layer has

a dielectric constant contain an imaginary part correspond to

the collision frequency in plasma conditions. The input

impedance of TM01 mode of single rectangular patch

operating at 2.15 GHz resonance frequency, (patch size of

4.96𝑐𝑚 × 3.3 𝑐𝑚, substrate thickness=1.6 mm, 휀𝑟 =4.45 and 𝑡𝑎𝑛𝛿 =0.0005) with thin air layer of thickness=5

mm at tanδ=0, 0.005, 0.05 and 0.5 is shown in Fig. 12. A

high collision simulated plasma (𝑡𝑎𝑛𝛿 = 0.5) is taken in

two different thicknesses 5.0 mm and 10 mm to compute the

input impedance of the antenna. Results are shown in Fig.

13 which shows that the high thickness gives very little

differences in both resistive and reactive element. Another procedure of simulation is used to study the

plasma effect on microstrip antenna. By designing TM01

mode single rectangular patch operating at 2.15 GHz

resonance frequency when the dielectric substrate is air (

dielectric plasma) has a sensitive loss factor (collision

frequency). Computations are done for 𝑡𝑎𝑛𝛿 = 0, 0.005,

0.05 and 0.5. At resonance patch size 10.46 𝑐𝑚 𝑥 6.97 𝑐𝑚

for air substrate thickness=1.6 mm. The input impedance cal

(a) (b) Fig. 13. The input impedance of TMo1 mode single rectangular

patch operating 2.15 GHz resonance frequency, (patch size

4.96 cm x 3.3 cm, substrate thickness=1.6 mm, 𝜺𝒓=4.45 and

tanδ=0.0005) with thin air layer of 𝒕𝒂𝒏𝜹=0.5 thickness (a) 5 mm

and (b) 10 mm.

(a) (b)

(c) (d) Fig.14. The smith chart input impedance of TM01 mode single

rectangular patch designed to operating at 2.15 GHz resonance

frequency, (patch size 10.46 cm x 6.97 cm, substrate

thickness=1.6 mm, 𝜺𝒓=1 and (a) 𝒕𝒂𝒏δ=0, (b) 𝒕𝒂𝒏𝜹=0.005, (c)

𝒕𝒂𝒏δ=0.05 and (d) 𝒕𝒂𝒏𝜹=0.5).

culations are illustrated in Fig. 14. Results shows that the

t𝑎𝑛𝛿 increases highly affect the values of both the reactive

and resistive impedance. The effect amount is clearly

explained in Fig. 14(b).

Because of the MW-Office package limitations on taking

substrate of dielectric constant (휀𝑟 < 1), a cavity model is

used. A MATLAB algorithm is programmed according to

the theory that mentioned in the previous section. The input

impedance of TM01 mode of single rectangular patch

designed to operating at 2.15 GHz resonance frequency,

(patch size of 10.46𝑐𝑚 × 6.97 𝑐𝑚, substrate thickness=1.6

mm, tanδ=0.0005) at different plasma simulated values of

휀𝑟=1, 0.8, 0.6, 0.4, 0.2, 0.1 and 0.05 are computed and

demonstrated in Fig. 15. An important mentioned result for

this trial is the bandwidth enhancement with the lower

dielectric value is achieved.

0 1.0

1.0

-1.0

10.0

10.0

-10.0

5.0

5.0

-5.0

2.0

2.0

-2.0

3.0

3.0

-3.0

4.0

4.0

-4.0

0.2

0.2

-0.2

0.4

0.4

-0.4

0.6

0.6

-0.6

0.8

0.8

-0.8

Swp Max

2.2GHz

Swp Min

1.9GHz

0 1.0

1.0

-1.0

10.0

10.0

-10.0

5.0

5.0

-5.0

2.0

2.0

-2.0

3.0

3.0

-3.0

4.0

4.0

-4.0

0.2

0.2

-0.2

0.4

0.4

-0.4

0.6

0.6

-0.6

0.8

0.8

-0.8

Swp Max

2.2GHz

Swp Min

1.9GHz

0 1.0

1.0

-1.0

10.0

10.0

-10.0

5.0

5.0

-5.0

2.0

2.0

-2.0

3.0

3.0

-3.0

4.0

4.0

-4.0

0.2

0.2

-0.2

0.4

0.4

-0.4

0.6

0.6

-0.6

0.8

0.8

-0.8

Swp Max

2.2GHz

Swp Min

1.9GHz

0 1.0

1.0

-1.0

10.0

10.0

-10.0

5.0

5.0

-5.0

2.0

2.0

-2.0

3.0

3.0

-3.0

4.0

4.0

-4.0

0.2

0.2

-0.2

0.4

0.4

-0.4

0.6

0.6

-0.6

0.8

0.8

-0.8

Swp Max

2.2GHz

Swp Min

1.9GHz

0 1.0

1.0

-1.0

10.0

10.0

-10.0

5.0

5.0

-5.0

2.0

2.0

-2.0

3.0

3.0

-3.0

4.0

4.0

-4.0

0.2

0.2

-0.2

0.4

0.4

-0.4

0.6

0.6

-0.6

0.8

0.8

-0.8

Swp Max

2.1GHz

Swp Min

1.95GHz

0 1.0

1.0

-1.0

10.0

10.0

-10.0

5.0

5.0

-5.0

2.0

2.0

-2.0

3.0

3.0

-3.0

4.0

4.0

-4.0

0.2

0.2

-0.2

0.4

0.4

-0.4

0.6

0.6

-0.6

0.8

0.8

-0.8

Swp Max

2.1GHz

Swp Min

1.95GHz

0 1.0

1.0

-1.0

10.0

10.0

-10.0

5.0

5.0

-5.0

2.0

2.0

-2.0

3.0

3.0

-3.0

4.0

4.0

-4.0

0.2

0.2

-0.2

0.4

0.4

-0.4

0.6

0.6

-0.6

0.8

0.8

-0.8

Swp Max

2.1GHz

Swp Min

1.95GHz

2 2.05 2.1 2.15 2.2

Frequency (GHz)

-10

0

10

20

30

Re

al

an

d I

ma

gin

ary

of

Z (

oh

m)

Re(Z[1,1]) ~

Im(Z[1,1]) ~

2 2.05 2.1 2.15 2.2

Frequency (GHz)

-20

0

20

40

60

Re

al

an

d I

ma

gin

ary

of

Z (

oh

m)

Re(Z[1,1]) ~

Im(Z[1,1]) ~

2 2.05 2.1 2.15 2.2

Frequency (GHz)

-20

0

20

40

60

Re

al

an

d I

ma

gin

ary

of

Z (

oh

m)

Re(Z[1,1]) ~

Im(Z[1,1]) ~

ISSN: 2277-3754



128

(a)

(b)

Fig. 15. The input resistance (a) and input reactance (b) of TM01

mode of single rectangular patch designed to operate at 2.15

GHz resonance frequency, (patch size of 10.46cm x 6.97 cm,

substrate thickness=1.6 mm, 𝒕𝒂𝒏𝜹 =0.0005) for different

plasma simulated values of 𝜺𝒓=1, 0.8, 0.6, 0.4, 0.2, 0.1 and 0.05.

IV. CONCLUSION

The plasma generation around antenna in space system is an

important subject must be considered in primary design

stages. Normal system measurements are taken in the

laboratory and may be a free space atmosphere is available

to adjust and tuning the front end of the antenna. In plasma

condition this adjustment is not enough since the plasma

change the input impedance. So that we suggest two

antennas system must be used as a redundancy system to

overcome such problem. The existence of collision plasma

absorbs microwave energy depending on plasma thickness

and density distribution. The plasma effects open very

important window on TT&C and GPS antennas which now

a days are widely used. Finally this report give the essential

windows in plasma affect on antenna system for continuous

researches in different actual importance in this field.

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[9] J. R. James and P. S. Hall, “Handbook of Microstrip

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[12] P. Hammer, D. Van Bouchaute, D. Verschraeven, and A. Van

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microstrip antennas", IEEE Trans. on Antennas and Propag.,

vol. 27, no.2, pp 267-270, Mar. 1979.

[13] Kokako, D.J. "Analysis of radome-enclosed antennas" Artech

house, 1997.

[14] Maral,G. and Bousquat, M. "Satellite Communications

Systems ", John Wiley & Sons, 1980.

AUTHOR BIOGRAPHY

Abdulkareem A. A. Mohammed was born in AL

Nassiria, Iraq, in 1958. He received his BSc in electrical engineering (1980) from Sulaimania

University, Sulaimania, Iraq, postgraduate diploma

in communications (1982) and MSc in communication (1984) from the University of

Technology, Baghdad, Iraq. From 1984 to 1988 he

was working with the Electromagnetic Wave Propagation Department, Space and Astronomy

Research Center, Scientific Research Council,

Baghdad, Iraq. From 1988 to 1993 he was working with the Space

Technology Department, Space Research Center, Baghdad, Iraq. On 1994,

he joined the Physics department, college of science, Saddam University,

Baghdad, Iraq where he obtained his PhD (1997) in electromagnetic, microstrip microwave antennas. From 1997 to 2003 he was working with the

1.5 2 2.5 3

x 109

-30

-20

-10

0

10

20

30Rectanguler microstrip antenna of plasma substrate

F(Hz)

Input

reacta

nce

Apsr=0.05

=0.10

=0.20

=0.40

=0.60

=0.80

=1.00

1.5 2 2.5 3

x 109

0

10

20

30

40

50

60Rectanguler microstrip antenna of plasma substrate

F(Hz)

Input

resis

tance

Apsr=0.05

=0.1

=0.2

=0.4

=0.6

=0.8

=1.0

ISSN: 2277-3754



129

Al-Battany Space Directorate as a researcher and head of group in the field

of microwave system. Since 2004 he is the head of Space and Atmosphere

Research Center in Iraqi ministry of science and technology. Now he leads group of atmosphere remote sensing for dust storm monitoring and detection

by using different space tools. Since January 2011 he joined a post doctorate

in Systems Engineering Department, University Arkansas at Little Rock in the field of dust storm monitoring.

Dhirgham K. Naji was born in AL Nassiria, Iraq, in 1973. He received his BSc degree in Electrical

Engineering from Baghdad University, Baghdad,

Iraq, in 1995, and MSc degree in Communications Engineering from Baghdad University, Baghdad,

Iraq, in 1998, and PhD degree in Modern

Communications Engineering from Alnahrain University, Baghdad, Iraq, in 2013. His current

research interests include fractal antennas, RFID

antenna miniaturization and Electromagnetic optimization.

Documents

Volume 3, Issue 2, August 2013 Plasma Effect on … 3/Issue 2/IJEIT1412201308_22.pdfVolume 3, Issue 2, August 2013 119 Abstract —A operating in dominant mode TMsingle rectangular