Plasma Effect on TM01

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International Journal of Engineering and Innovative Technology (IJEIT) Volume 3, Issue 2, August 2013



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 TM ₀₁ Mode Rectangular Microstrip Antenna for Space Telemetry and

Telecomands Subsystems Applications

Abdulkareem A. A. Mohammed¹ and Dhirgham K. Naji²

1Head ofAtmosphere 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: ¹[email protected]

,

²[email protected]

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Volume 3, Issue 2, August 2013 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:

−𝑞𝐸𝑒^𝑗𝜔𝑡 = 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

Ee^jωt= 𝑁𝑞²

𝑚(vc+ 𝑗𝜔) (3) 𝜎𝑐= 𝜎^′− 𝑗𝜎^′′=𝑁𝑞²

𝑚𝜀0∙ 𝜀0vc

𝑣𝑐2+ 𝜔²− 𝑗𝑁𝑞² 𝑚𝜀0∙ 𝜀0𝜔

𝑣𝑐2+ 𝜔² (4) The quantity (𝑁𝑞² 𝑚𝜀₀)is the natural angular frequency specific to the electrons which is given by 𝜔𝑝= 2𝜋𝑓𝑝.Where 𝑓_𝑝 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, 𝑘_𝐵 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

ε_c=𝜀^′+ 𝑗𝜀^′′ = 𝜀₀+^𝜎^𝑐

𝑗𝜔 (7) For convenience, two dimensionless quantities, the normalized electron density 𝑋 and the normalized collision frequency 𝑍 are introduced:

𝑋 = ^𝜔^𝑝 𝜔

2 (8𝑎)

𝑍 = ^𝑣^𝑐 𝜔

2 (8𝑏)

So

𝜎^′= 𝜀0𝜔 𝑋𝑍

1 + 𝑍² (9𝑎) 𝜎′^′= 𝜀0𝜔 𝑋

1 + 𝑍² (9𝑏) And

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

𝜀^′= 𝜀0 1 + 𝑋

1 + 𝑍² (10𝑎) 𝜀^′′ = 𝜀0 𝑋

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 (𝜀 = −∞) for the lowest frequency to (𝜀 = 1) for high frequencies, passing through (𝜀 =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

𝜀0

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^′ 𝜔𝜀^′ 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^′ 𝜔𝜀^′≫ 1 and dielectric media 𝜎^′ 𝜔𝜀^′≪ 1 . In the case of plasma, this condition can be calculated as:

𝜎^′

𝜔 𝜀^′ = 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 21 2

(15𝑎)

𝑘1= −1 2𝑟 +1

2 𝑟²+ 1 − 𝑟²∙𝑣𝑐

𝜔

21 2 1 2

(15𝑏)

where

𝑟 = 1 − 𝜔𝑝2

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 (𝑣_𝑐 << 𝜔_𝑝 ), three frequency regions may be defined as follow:

 Low Frequencies Case 𝜔 < 𝑣_𝑐 , we observe that 𝑛1, 𝑘₁ are nearly equal. Expanding in the limit (𝜔 <<

𝑣𝑐 , 𝑣𝑐2<< 𝜔𝑝2 ) , one can obtained the following indexes equations:

𝑛1≈ 𝜔𝑝2

2𝜔𝑣𝑐 1 2

1 − 𝜔

2𝑣𝑐 (19𝑎)

𝑘1≈ 𝜔𝑝2

2𝜔𝑣𝑐 1 2

1 + 𝜔

2𝑣𝑐 (19𝑏)

 Intermediate Frequencies Case (𝑣_𝑐 < 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<< 𝜔𝑝2 ) 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 >> 𝜔_𝑝). Here, the plasma becomes a relatively low loss dielectric. in the limit (𝑣_𝑐²<< {𝜔²-𝜔_𝑝²} and υc2 << 𝜔²{𝜔²-𝜔_𝑝²}² /𝜔_𝑝⁴ ) the following indexes equations are obtained:

𝑛1≈ 1 − 𝜔² 𝜔𝑝2

1 2

(21𝑎)

𝑘1≈𝑣𝑐𝜔_𝑝²

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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Volume 3, Issue 2, August 2013

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]

𝑓_𝑚𝑛 ≈2𝜋^𝑘^𝑚𝑛𝜀𝑟 (22)

where 𝑚, 𝑛 = 0, 1, 2…

𝑘𝑚𝑛 = Wave number at m, n mode 𝑐 = Velocity of light

𝜀_𝑟 = Relative dielectric constant And

𝑘_𝑚𝑛 ≈ 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 𝑓_𝑟. Taking into account the effect of fringing field, the effective dielectric constant for TM₀₁ mode is derived using [9,11]

𝐿 = 𝑐

2𝑓𝑟 𝜀𝑟− 2∆𝑙 (24) Hence

𝑓𝑟 𝑒𝑓𝑓 = 𝑐

2 𝐿 + 2∆𝑙 𝜀𝑟 (25) with

𝜀𝑒𝑓𝑓 =𝜀_𝑟+ 1

2 +𝜀_𝑟− 1

2 1

1 + 10ℎ/𝑊 (26) and

∆𝑙 = 0.412ℎ 𝜀_𝑒𝑓𝑓+ 0.3 𝑊/ℎ + 0.264

𝜀𝑒𝑓𝑓 − 0.258 𝑊/ℎ + 0.813 (27) where

∆𝑙 = Line extension

𝜀_𝑒𝑓𝑓 = 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 𝐸_𝑧 satisfies the two dimensional form of partial differential equation, the so-called wave equation

𝜕²𝐸_𝑧

𝜕𝑥 +𝜕²𝐸_𝑧

𝜕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= 𝐸0cos 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}

2𝜋𝑟 𝐸0 𝑖𝜃 𝐸𝑥 𝜉, 𝜂 cos 𝜑 + 𝐸_𝑦 𝜉, 𝜂 sin 𝜑 + 𝑖_𝜑 −𝐸_𝑥 𝜉, 𝜂 sin 𝜑 cos 𝜃 + 𝐸_𝑦 𝜉, 𝜂 cos 𝜑 cos 𝜃 (32) where

𝐸_𝑥 = ℎ𝐸₀ −1 − −1 ^𝑚 ∙ 𝑗 sin 𝜉𝑊

2 + 1 − −1 ^𝑚 ∙ ∙ cos 𝜉𝑊

2 ∙𝐿

2𝑠𝑖𝑛𝑐 𝜉𝑎 ∙ 𝑗^𝑛 ∙ 𝑠𝑖𝑛𝑐(𝜉𝐿 2 +𝑛𝜋

2) + −1 ^𝑛𝑠𝑖𝑛𝑐(𝜉𝐿

2 −𝑛𝜋

2) (33𝑎) W

L

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𝐸𝑦 = ℎ𝐸0 −1 − −1 ^𝑛 ∙ 𝑗 sin 𝜉𝐿

2 + 1 − −1 ^𝑛 ∙ ∙ cos 𝜉𝐿

2 ∙𝑊

2 𝑠𝑖𝑛𝑐 𝜉𝑎 ∙ 𝑗^𝑚∙ 𝑠𝑖𝑛𝑐(𝜉𝑊 2 +𝑛𝜋

2) + −1 ^𝑚𝑠𝑖𝑛𝑐(𝜉𝑊

2 −𝑛𝜋

2) (33𝑏) Then the far field components are

𝐸𝜃 =𝑗𝑘𝑒^{−𝑗𝑘𝑟}

2𝜋𝑟 𝐸𝑥cos 𝜑 + 𝐸𝑦sin 𝜑 (34𝑎) 𝐸_𝜑 =𝑗𝑘𝑒^{−𝑗𝑘𝑟}

2𝜋𝑟 −𝐸_𝑥sin 𝜑 cos 𝜃 + 𝐸_𝑦cos 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

ℎ𝐸_𝑧 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

𝑅 + 𝑗𝜔𝑐 +1 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

2𝑃_𝑇 (38) where

𝑃𝑇 = 𝑃𝑟+ 𝑃𝑐+ 𝑃𝑑 (39) 𝑉 = Terminal voltage

𝑃_𝑇= Total power dissipated by the antenna The radiated power outside the antenna surface is

𝑃𝑟 = 1

2𝑍₀ 𝐸𝜗 2+ 𝐸𝜑 2

𝑟²sin 𝜗𝑑𝜗𝑑𝜑

𝜋 2 𝜗 =0 2𝜋

𝜑=0

(40) where

𝑍₀ = Characteristic impedance of free space.

The power losses inside the dielectric is

𝑃𝑑 =𝜔0𝜀0𝜀𝑟tan 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

𝑃_𝑐= 2𝑅𝑠

2 𝐻_𝑥²+ 𝐻_𝑥𝑦² 𝑑𝑥𝑑𝑦 (42) where

𝑅𝑠= 𝜔𝜇0𝜇𝑟

2𝜎 (43) 𝑅𝑠= Surface resistance

𝐻_𝑥 = 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 = 𝑄_𝑇

2𝜋𝑅𝑓𝑟 (45𝑏) The total quality factor 𝑄_𝑇 is

𝑄𝑇= 𝑅 𝐿

𝐶 (46𝑎) In other meaning

𝑄𝑇=𝜔𝑊_𝑇

𝑃𝑇 (46𝑏)

𝑊_𝑇 =𝜀0𝜀𝑟

2 𝐸_𝑧 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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Volume 3, Issue 2, August 2013 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, 𝜀, 𝜇) = 1

𝜂0 𝑍𝑎(𝑛𝜔, 𝜀, 𝜇0) (48) In case of gaseous plasma, 𝜇 = 𝜇0 and 𝜀 = 𝑛²𝜀0 the expression become [3].

𝑍𝑎(𝜔, 𝑛²𝜀0) =1

𝑛 𝑍𝑎(𝑛𝜔, 𝜀0) (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 𝑁_𝑜𝑢𝑡 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

𝐺𝑘_𝐵𝑇₀𝐵₀ (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 +𝑇_𝑅

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 + 𝑇_𝐿𝐿 (56) where

𝑇𝐿𝑁𝐴 = Antenna radiation efficiency (0 ≤ 𝜂𝐴≤ 1) 𝑇_𝐿= 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 𝜀′ and t 𝑎𝑛𝛿 . 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

(7)

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 (f_p=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 0

Attenuation by collissional absorbtion at radiating Freq =2.15GHz

Collision Frequency,Hz

tan delta

plasma frequency

=2.0GHz

=2.05 GHz

=2.10 GHz

=2.125GHz

(8)

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, 𝜺_𝒓=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, 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. 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 80 100

tan delta

Plasma frequency =2.5 GHz =4.0 GHz =8.0 GHz

10⁸ 10⁹ 10¹⁰ 10¹¹

0 2 4 6 8 10 12 14 16

Alph [neper/meter]

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 -5

Beta [rad/meter]

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

Real and Imaginary of Z (ohm)

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

VSWR

(9)

2 2.05 2.1 2.15 2.2

Frequency (GHz) -20

0 20 40 60

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(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(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, 𝜺_𝒓=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, 𝜀𝑟 = 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 (𝜀𝑟< 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 𝜀_𝑟=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 1.01.0-1.0 10.0

10.0

-10.0

5.0

-5.0

2.0

-2.0

3.0

-3.0

4.0

-4.0

0.2

-0.2

0.4

-0.4

0.6

-0.6

0.8

-0.8

Swp Max 2.2GHz

Swp Min 1.9GHz

0 1.01.0-1.0 10.0

10.0

-10.0

5.0

-5.0

2.0

-2.0

3.0

-3.0

4.0

-4.0

0.2

-0.2

0.4

-0.4

0.6

-0.6

0.8

-0.8

Swp Max 2.2GHz

Swp Min 1.9GHz

0 1.01.0-1.0 10.0

10.0

-10.0

5.0

-5.0

2.0

-2.0

3.0

-3.0

4.0

-4.0

0.2

-0.2

0.4

-0.4

0.6

-0.6

0.8

-0.8

Swp Max 2.2GHz

Swp Min 1.9GHz

0 1.01.0-1.0 10.0

10.0

-10.0

5.0

-5.0

2.0

-2.0

3.0

-3.0

4.0

-4.0

0.2

-0.2

0.4

-0.4

0.6

-0.6

0.8

-0.8

Swp Max 2.2GHz

Swp Min 1.9GHz

0 1.01.0-1.0 10.0

10.0

-10.

0

5.0

-5.0

2.0

-2.0

3.0

-3.0

4.0

-4.0

0.2

-0.2

0.4

-0.4

0.6

-0.6

0.8

-0.8

Swp Max 2.1GHz

Swp Min 1.95GHz

0 1.01.0-1.0 10.0

10.0

-10.

0

5.0

-5.0

2.0

-2.0

3.0

-3.0

4.0

-4.0

0.2

-0.2

0.4

-0.4

0.6

-0.6

0.8

-0.8

Swp Max 2.1GHz

Swp Min 1.95GHz

0 1.01.0-1.0 10.0

10.0

-10.

0

5.0

-5.0

2.0

-2.0

3.0

-3.0

4.0

-4.0

0.2

-0.2

0.4

-0.4

0.6

-0.6

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(Z[1,1]) ~ Im(Z[1,1]) ~

2 2.05 2.1 2.15 2.2

Frequency (GHz) -20

0 20 40 60

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(Z[1,1]) ~ Im(Z[1,1]) ~

(10)

(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 𝜺_𝒓=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.

REFERENCES

[1] K.-F. Lee, and K.-F. Tong, "Microstrip patch antennas-basic characteristics and some recent advances", Proceedings of the IEEE, Vol. 100, No. 7, July 2012.

[2] D. Guha and Yahia M. M. Antar, Microstrip and Printed Antennas New Trends, Techniques and Applications, New York; John Wiley & Sons, Ltd, 2011.

[3] Chen, F.F., Introduction to plasma physics, Plenum press, New York, 1974.

[4] Frankel D.S., et al "Re entry plasma induced pseudo range and attenuation effects in a GPS simulator", SPIE defense and security symposium, Orlando, FL, SPIE proceeding 5420 (12-16 April 2004). Downloaded from the physical science incorporation library.

[5] Drabowitch, S. and Anaconna C. "Antennas Volum2 Applications", Hemisphere publishing corporation, 1988.

[6] Y. T. Lo, D. Solomon and W. F. Richards “Theory and experiment on microstrip antennas,” IEEE Trans. on Antennas and Propag., vol. AP 27, no. 2, pp. 137-145, 1979.

[7] I.J. Bahl and P. Bhartia, Microstrip Antennas, Artech House, Inc. printed and bound in the U.S. A, 1980.

[8] Andersg G. Derneryd, and Anders G. Lind, “Extended analysis of rectangular microstrip resonator antennas”, IEEE Trans. on Antennas and Propag., vol. AP-27, no.6, pp. 846-849, Nov.

1979.

[9] J. R. James and P. S. Hall, “Handbook of Microstrip Antennas,” Peter Peregrinus Ltd, London, 1989.

[10] Gildas P. Gauthier and Gabriel M. Rebeiz, “Microstrip antennas on synthesized low dielectric-constant substrates,”

IEEE Trans. on Antennas and Propag., vol. 45, no. 8, pp.

1310-1313, Aug. 1997.

[11] Keith R. Carver and James W. Mink, “Microstrip antenna technology,” IEEE Trans. on Antennas and Propag.", vol.

AP-29, no.1, pp. 2-23, 1981.

[12] P. Hammer, D. Van Bouchaute, D. Verschraeven, and A. Van De Capelle. "A model for calculating the radiation field of 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 30

Rectanguler microstrip antenna of plasma substrate

F(Hz)

Input reactance

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 60

Rectanguler microstrip antenna of plasma substrate

F(Hz)

Input resistance

Apsr=0.05 =0.1 =0.2 =0.4 =0.6 =0.8 =1.0

(11)

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.

Plasma Effect on TM01

Plasma Effect on TM 01 Mode Rectangular Microstrip Antenna for Space Telemetry and

Telecomands Subsystems Applications

,

Plasma Effect on TM ₀₁ Mode Rectangular Microstrip Antenna for Space Telemetry and