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SAMSO ltr dtd 19 Jan 1972

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AIR FORCE REPORT NO. AERO5PACE REPORT NO,SAMSO-TR-69-242 TR-006 (5220-10)-i

(FORMERLY TR.0200(4220-10)-3)

UReentry Plasma Attenuation for00 S-Band Telemetry Systems

Prepared by K. E. GOLDENPlasma Research Laboratory

69 AUG 15

DDCSE/

Lbortory Operations 15 796

AEROSPACE CORPORATION

Prepared for SPACE AND MISSILE SYSTEMS ORGANIZATIONAIR FORCE SYSTEMS COMMAND

LOS ANGELES AIR FORCE STATIONLos Angeles, California

THIS DOCUMENT IS SUBJECT TO SPECIAL EXPORTCONTROLS AND EACH TRANSMITTAL TO FOREIGNGOVERNMENTS OR FOREIGN NATIONALS MAY BE MADEONLY WITH PRIOR APPROVAL OF SAMSO(SMTAE).THE DISTRIBUTION OF THIS REPORT IS LIMITED BE.CAUSE IT CONTAINS TECHNOLOGY RESTRICTED BYMUTUAL SECURITY ACTS,

Air Force Report No. Aerospace Report No.SAMSO-TR-69-242 TR-0066(4220. 10)-i

(Formerly TR-0Z00(4220-10).3)

REENTRY PLASMA ATTENUATION FOR

S-BAND TELEMETRY SYSTEMS

Prepared by

K. E. GoldenPlasma Research Laboratory

69 AUG 15

Laboratory OperationsAEROSPACE CORPORATION

Prepared for

SPACE AND MISSILE SYSTEMS ORGANIZATIONAIR FORCE SYSTEMS COMMAND

LOS ANGELES AIR FORCE STATIONL,,s Angeles, California

This document is subject to special export controlsand each transmittal to foreign governments orforeign nationals may be made only with priorapproval of SAMSO(SMTAE). The distribution ofthis report is limited because it contains technologyrestricted by mutual security acts.

FOREWORD

This document is published by The Aerospace Corporation,

El Segundo, California, under Air Force Contract No. F04701-69-C-0066.

This report, which documents research carried out during January

1969, was submitted on 19 June 1969 to Lieutenant Edward M. Williams, Jr.,

SMTAE, for review and approval.

Approved

R. X. Meyer, DirectorPlasma Research Laboratory

Publication of this report does not constitute Air Force approval

of the report's findings or conclusions. It is published only for the

exchange and stimulation of ideas.

Edward M. WiLliams, Il7r.

Znd Lt., United States Air ForceProject officer

-ii-

-li-

Il

I

ABSTRACT

The performance of a slot telemetry antenna is analyzed,

including the effects of an inhomogeneous plasma sheath on

aperture admittance, radiation pattern distortion, antenna win-

dow absorption, reflection zad absorption losses of ihe fe,;d

network, and total antenna gain. The change in broadside

antenna gain induced by the reentry plasma sheath is compared

with plane wave signal attenuation calculations. Various

antenna matching conrl..tions sr evaluated for free-space andreentry-plasma conditions.

o,iii-

CONTENTS

iI FOREW ORD ....................................... ii

ABSTRACT .................. v........ . . . . . . if

L. INTR.ODUCTION .. .. . .. ... . .. ....... *. .*.*. *** I

SL APLATURE ADMITTANCE............ 5

IL ANTENNA GAIN ....... .. ... ................. 9

.V. FEED NETWORK .... . ...... .................. 13

V. NUMERICAL RESULTS . . .. ... .......... .- *.. 15

A. Aperture Admittance .......... . . 15

C. Feed Calculations. . .. .. o . . .# . . o o. . . . .. . . *o 18

D. Absorption Effects in the WaveguideAntenna Window ............................ Z7

E. Matching to a Plasma Environment ................ 33

IV. CONCLUSIONS o . .... ... .... ... . .... ... .... 37

REFERENCES ...... .. ... ... ..... ... ........ . 39

-9'

*1

.9

'n.[-

FIGURES

i. Slot Geometry . . . . ....... ...... . . . . . 22. Feed Network ....... . . .. ...................... 3

3. Reentry Plasma Sheatl . ........................... 164. Aperture Admittance ............................. 17

5. E-Plane Antenna Gain . . * . . * . . . . .. . . . . . . . 19

6. H-Plane Antenna Gain & * . . o 207. Feed Network Insertion Loss........................ 22

8. Reflection Loss vs Electron Density ................... 23

9. Change in Antenna Gain with ApertureMatched to Free Space . . . .. . .. .. .. .. .. ............ Z5

10. Input VSWR with Aperture Matched to Free Space . ...... . . 26

I. Plane Wave Attenuation EcrDr . .. . . . . . . . . . . . . . . . . . . . . 28

12. Thin Sheath Limit for Change in Antenna Gainwith Aperture Matched to Free Space . ................ 29

13. Thin Sheath Limit for Input VSWR with ApertureMatched to Free Space as o a a # o o o * o a o * # 30

14. Reduction in Antenna Gain Caused byby Window Absorption . o..*............ . . . ...o e e 31

15. Reflection Loss vs Window Absorption ...... .......... 32

16. Input Admittance for Various Matching Conditions. ......... 34

17. Change in Antenna Gain for VariousMatching Conditions ...... .. ... o. . ... . . . . .. .. . . 35

18. Input VSWR for Various Matching Conditions .. .... ..... ... 36

TABLES

1. Physical Dimensions of Waveguide Window .............. 15

2. Matching Conditions ............................ 33

VI-vi-

I. INTRODUCTION

The antenna gain characteristics of a simple S-band telemetry

antenna system radiating through an inhomogeneous plasma sheath have

been analyzed. Aperture admittance, radiation pattern, signal attenu-

ation, matching network, and resulting antenna gain calcula'tions are

presented herein for thick and thin plasma sheath conditions. The

rectangular aperture is assumed to be terminated in an infinite groundplane and dielectrically filled as shown in Fig. 1. The inhomogeneous

plasma covering the ground plane is approximated by a number of

equivalent slabs.

The equivalent circuit representing the antenna matching network

is shown in Fig. Z. The lossy waveguide section approximates the

antenna window; the ideal transformer and tuning reactance represents

a coax-to-waveguide transition. The probe antenna is assumed to be thin

and loosely coupled to the waveguide cavity. A similar pr blem was con-

sidered by Adams (Ref. 1) for free-space conditions only. The actu.:l

circuit parameters required for various tuning conditions may not be

realizable from a practical standpoint; however, the results illustrate the

magnitude of the feeding network effects.

I,

x

PLASMAe (z) REGION

Figure 1. Slot Geometry

-ine

Pref P

d, 2(FEED NETWORK

~ef P20

Y9 YOPV 20

(b) FREE EXCITATION

Figure Z. Feed Network

-3

II

'V:

_ _ _ _ __ _ _ _ -

II. APERTURE ADMITTANCE

The aperture admittance was calculated for various plasma conditions

for the aperture configuration shown in Fig. 1. If the reaction concept(Ref. 2) and the dominant model approximation are used, the aperture

admittance can be written as

Y __,T(Z=0) X F.(=

Y f[ Y 0 T o (1)

where ET(z=0) is the tangential aperture electric field, HT(z=0 ) is the

tangential aperture magnetic field, Y0 is the characte~istic admittance of

free space, and V 0 is the dominant mode voltage. For the aperture

orientation shown in Fig. 1, the dominant mode aperture electric field ic

E T(Z=O) = V(,(1/ab)1/2 cos(ny/b)a (2,)

where a is the height of the ap, rture, b is the aperture width, and "i is

the unit vector in the x direction. The above integral can be transformed

by Parseval's theorem to a two-dimensional integral in Fourier transform

space. If the transfcrm fields are separated into TE z and TMz components,

the resulting aperture-adnittance expression is

I =0o V'-oY o 3

YN k 2 + YN k ZY TE y YTM xYx kZ + Nk

y x

I5

II

where S(k ,k ) is the dominant mode aperture electric field FourierT x Ntransform, yN is the input TE admittance function, and Y is theITE z TM

input TM admittance function. The aperture Fourier transform for az

rectan.gular aperture is

S V b0 /2 sin ul /sin u 2 sin u3

where

u= 0. 5 (kxa) (5a)

u= . 5 (kb + rr) (5b)

= 0. 5 (kyb -rr) (5c)

The TE and TM a xnittance functions for collisional plasma sheaths

were evaluated using a multislab approximation and standard transmissio!'

line theory (Ref. 3).thThe resulting input admittances to the n slab are given by

'yn (n-1I n nT (YTE/Y 0 ) cos(kzAn) + j(kz/k 0 ) sin(kzn)

Y n n- n nA(6a)YO cos(k n) + j(YTM ko/YokZ )

YO cos(kn.n + "'ynYc kon/YkoC n ) sin)+-6z n TM z 00n

where kn is defined as

kn k ( 2 /k 2 k2/k 2 1/2 (7)z 0 n k0 ky/k0)

-6-

- _ _ _ _ _ __ _ _ _ _ _ __ _ _ _

:1h

I "

and e is the complex relative dielectric constant of the n slab, I is

the thickness of the nth slab, and k 0 is the free space wavenumber. If

the radiation condition is imposed, the admittances at the outer plasma

surface are

Y0E/Yo - k°/ko (8a)

0 = k0/k0 (8b)YTM/Y0

0where k isz

k 0 0 . 0 ( 2 2 2 21/2z Oz " =k kx/k - /k 0 )(9)

The TE and TM admittances of the aperture surface were evaluated by

starting at the outer plasma boundary and transforming the load admittances

given in Eqs. (8) through the N-plasma slabs using Eqs. (6). A more

detailed description of the analysis and the numerical integration of Eq. (3)

is given in Ref. 3. A summary of self- and mutual-admittance calculations

compared with plasma simulation measurements is given in Ref. 4. The

actual numerical resuits are precented in Section V.

When the thin sheath approximation is valid, the aperture admittance

can be approximated by (Refs. 3 and 5)

y =yO + y (10)

00~ap ap (10

where Y is the aperture admittance in free space, and Y is the equivalentap

plasma surface admittance VIi

SN (z)dz

Ys k k C (p e a k ) Ne(peak) (11)

The electron density is Ne (z), and the relative dielectric constant at the

peak electron density conditions in the sheath is C (peak).

p[

III. ANTENNA GAIN

For purposes of this discussion the antenna gain of a slot antenna

radiating through a plasma sheath is defined as21T r 2Y0ii g(e, P. =2rY 0 {e(r, 08,0)12 + fE O(r, e, 0)P (12)inc

where Pinc is the forward or incident power to the a.tenna-feed system,

Ee is the far field theta component of the electric field, and E is the far

field phi component of the electric field. The spherical coordinates aredenoted by r, 8, and 0,, It is well known that the far field radiation from

a siot antenna can be related to the Fourier transform of the aperture field.

In the case of a plasma or dielectric covered antenna, the far field is

related to the Fourier transform of the electric field at the outer plasma

surface. The far field components are obtained using saddle-point

integration techniques, resulting in

.2 NE0(r, .0) j .cos. exp(-jk 0 r) exp(+jk 0coser z) (13a)

T-0 TMx( 0xs ksys) 0 011bn

E0(r, e, 0= -j sin0 cos e GT(k k exp(-jk0 r) exp(+jk 0 n0 1Exsy

where Fourier transform functions are evaluated at

k xS= k 0 sine cosO (14a)

k ys = k 0 sine sinO (14b)

-n = sin2 )1/2 (14c)zs n

II

The resulting gain expression is

g(O 0)8kZab Y0

g(e, 0) = T3 IV ap/VinY' Pe(e, 0) (15)

c

where the radiation pattern Pe (0, 0) is given by

+i s-3- sO in-0cos 0 ] (16)e(0, 0)Z~ [ UlsT ( T, + ) e), + sG~~ein

and the aperture voltage, incident voltage, and characteristic admittance

of the feed transmission line are denoted by Vap, Vinc, and Y c' respectively.

The functions uls, u2 s, and u3s are defined in Eqs. (5) with

k =k andk =kx xs y ys

U1 = 0. 5 (k0 a sine cos0) (17a)

U2 = 0.5 (kob sine sin0+ T) (17b)

U3 = 0. 5 (k0 b sine sinO - T) (17c)

The radiation pattern is normalized to unity at broadside (0 = 0) when the

slot is radiating into free space.

The TE and TM components of the aperture electri: field Fourierstransform gT(k ,k , z = 0) were transformed to the outvr plasma surface

by the plasma distortion functions GTE and GTM , respectively.

-10-

:7

The distortion functions are defined asN

GE ETE, ,(z O)l/ETE. Tz)a

N

GTM [ TM ax ( - Oj/ TM" T - ) (18b)

where "iTE and aTM are the TEz and TMz mod3 unit vectors

5 TE= (5xky - Rk x)/(k2 + kZ) i Z (19a)

Z 1/2(lb(TM (xkx + ayky)/(k + k) (19b)

TM x y x y

The transverse electric field Fourier transform at the outer plasma surfaceN

is denoted by 9T(z =E 1tn) . For the multislab approximation the distortion

functions areN

GTEe [cos (kn TE + 0'k/Y k n) sin(kn L1 (20aTE n=I co s n TE0 zs n O

N, r.n-l n,,] inkh~ ) ZbGTM( e) =H cos(k n. A + j(yTM kns/Yok0¢n J (20b)TM n = z )T 6n nd

The admittance functions are defined in Eqs. (6).

For a freely excited slot antenna (Fig. Zb), the aperture voltage can

be expressed in terms of the aperture admittance. The resulting aperture

gain is given by

8k 2ab Y8k0a YO 1I + Pap 2 Pe,)(1

gap1e ) = 3 Y ap e

-11-

........-. - , -- -

where the aperture reflection coefficient is

9 ap (ZPap =Y + Y

g ap

and the waveguide characteristic admittance is

Yg9 = Y 0 leg - (TT/k 0b) Z]1/2 (23)

When the aperture is excited by a feed network (Fig. 2a) the net

antenna gain, including feed absorption and input reffections, can be

expressed as

gF(e, 0) 3 Y V 1 p P e,(4

where the reflection coefficient at the input terminals of the feed is

Y C - Y1PF Y + Y (25)

c 1

In Eq. (a) Yu is the characteristic admittance of the input transmission

line; YI is the input admittance to the feed, and is determined from a circuit

analysis of the feed. In Eq. ( 4) fV ( is the voltage transfer function of

the feed. Subscripts F and ap [Eqs. (21), (22), and (24)] designate thefeed and aperture, respectively.

When the plasma is in contact with the ground plane and the thin sheath

limit is valid, the distortion functions are equal to unity. The resulting

radiation patterns are equal to the free space patterns, and the antennagain is reduced by the reflection loss only.

y-1y

I.

IV. FEED NETWORK

The hypothetical feed equivalent circuit is shown in Fig. Za. Theaperture admittance is transformed through the heat shield to the output

terminals of an ideal transformer representing a coax-to-waveguide

transition by a length of lossy waveguide having the same cross-sectional

dimensions of the aperture. The dielectric constant and cross-sectional

dimensions of the dielectrically loaded waveguide are selected in such

a way that only the TE 0 1 mode propagates. The transformer turn ration and series reactance X s are adjusted to obtain the desired antenna

matching.The admittance at the terminal plane of the transformer looking

toward the aperture is given by

Y _ (Yap/Yo cos(kold) + j sin(kold)

Y cos 1 d) +J(Y ly 0 1 )sin(k0 d)

where the complex propagation constant and characteristic admittance of

the TEoI waveguide mode are equel to

[r zl1/zY0 [eg(l - j tan6) - (n/k 0b) (26a)

'A k0 1 k 0 g(l - tan6) - (r/k 0b) (Z6b)

Ti'e input admittance and aperture voltage were obtained from a

simple network. The results are given by

Yn 2 (27a)

1 + j Yn XS

-13-

________________ ________________

V2nj ~ v~~ Z(27b)Vi (I + j Yn Xs)G01(k01d)

G0 1 (k0 1d) = cos(k 0 1d) + j(Yap/Y01)sin(k01d) (27c)

where G0 1 (kOld) is the voltage transfer function that relates the aperture

to the voltage at the transformer end of the waveguide.

The aperture-feed combination was matched by adjusting the turn

ratio and series reactance until the reflections at the input terminals

were reduced to zero. For a specified aperture admittance, the matched

conditions were obtained by setting

n2 = Real(Y c/Y) (28a)

jmagY)= + Ral(Y)(Z~b)

c

where the characteristic impisdance of the input transmi ssion line isZc = y The matching equations were obtained by setting Y 1 = Yc in

Eq. (77a).

-14-

V. NUMERICAL RESULTS

The antenna admittance, antenna gain, input voltage standing wave

ratio (VSWR), and plane wave attenuation computations are presented for

various plasma conditions at S-band frequencies.

The dimensions of the aperture, dielectric properties of the window,

and length of the waveguide window are given in Table 1.

Table 1. Physical Dimensions of Waveguide Window

Case koa kob £ tan6 d/Xg Z .ohm

1 0.45 2.10 4.0 0.01 0.5 50

2 0.45 2.10 4.0 0.04 0.5 50

The physical dimensions are typical of proposed S-band telemetry antenna

systems.

The normalized electron density profile used in the calculations is

shown in Fig. 3. The peak electron density was varied from 2. 5 x 101l12 -3to 7. 2 X 10 cm . The plasma was approximated by eight equivalent slabs

that provided adequate numerical accuracy at S-band frequencies. The

collision frequency was assumed to be constant and equal to 6 X 109

collisions per second.

A. APERTURE ADMITTANCE

The aperture admittance calculations were obtained by numerically inte-

grating Eq. (3). The results are normalized to the free admittance Y0 and are

plotted on the Smith chart shown in Fig. 4. Thin sheath results using Eq. ,(10)

are also plotted in Fig. 4 for various equivalent surface resistances. The

thin sheath results approximate thin, highly overdense, collision-dominated

plasma sheaths typically encountered at low altitudes on slender conical

-15-

io i II I_

i0-I

10-2

zY6xIO9 cps

3.8 cm10-4 N0 (PEAK) =2.25x I0II TO

7.2 xI0 12 cm3

I01-5 .

0 0.2 04 0.6 0.8 1.0:1 z/8

Figure 3. Reentry Plasma Sheath

-16-

*1 -o

- PLASMA1

SPACE CLOTH OR THIN SHEATH- -FREQUENCY 2 25 GHz

k0a O.45

k00 :2.10Eg 4.0

iv7

Figure 4. Aperture Admnittance

vehicles. The thin sheath results also approximate the results obtained if

the antenna aperture is covered with a resistive cloth, commonly called space

cloth. The numbers adjacent to the ,ight slab calculations (Fig. 4) denote

peak electron density; the numbers adjacent to the thin sheath results denote

the additive surface resistance. Because of the small size of the aperture,

the open-ended waveguide aperture behaves as an open circuit in free space

and as a short circuit in the plasma.

B. FREE EXCITATION ANTENNA GAIN

The antenna gain can be calculated using Eqs. (21 ) through (23)

when the aperture is waveguide-fed with an isolator absorbing the aperture

reflections. The E-plane (0 = 00) results are plotted in Fig. 5. The

aperture is loaded with a dielectric having a dielectric constant equal

to 4. 0 and tan6 = 0. The H-plane calculations are shown in Fig. 6. The

angle theta is measured from the aperture normal or z-axis (Fig. I).

The numbers adjacent to the curves (Figs. 5 and 6) denote the peak electron-3density conditions in units of cm . The radiation pattern distortions

induced by the plasma are evident by comparing the free space gain

with the corresponding antenna gain calculations in the presence of the

plasma. However, the most predominant plasma-antenna effect shown

in Figs. 5 and 6 is signal attenuation.

C. FEED CALCULATIONS

The insertion loss ratio of the feed network is defined as

Insertion loss P Pz/P20 (29a)

-18-

V.---- -___ _________-

II

0Ne=2.25 x lol FREE SPACE

-10 - Ne = 4.50 x loll

-20 Ne: 9.00 x 1011

-30 Ne 1.80 x 1012

-40

7<0 Ne 3.60 x 1012I--

S-60 -

" -70 -Ne 7.20 x 1012

-80 FREQ- 2.25GHzkoo = 0.45kob = 2.10

-90 Eg = 4.0

0 10 20 30 40 50 60 70 806, deg

Figure 5. E-Plane Antenna Gain

-19-

it

0 7'

Ne = 2.25 x l FREE SPACE-I0 - Ne = 4.50 x loll

-20 Ne 9.00 x 1011

1 -30 r Ne_ 1.80 x 1012

a 40 -

z , Ne :3.60 x 1012LU -50

IJ -60

-70 - Ne 720 x .1012

-80 FREQ : 2.25 GHzkoa = 0.457kob = 2.10

-90 - g = 4.01

-1000 10 20 30 40 50 60 70 80 i

8, deg

Figure 6. H-Plane Anterna Gain

-zo-

where

P 2 Real(Y a) Ivz( (

inc c

P 20 Real(Ya2)-1 + Pa (z9c)

inc g

The insertion loss wt be reduced to

= s (30)

The above nomenclature is defined in Fig. 2. This particular definition

of insertion loss is useful since the net antenna, including the feed, is

expressed as

gF(,1 (P 2 /P 2 0 ) gap (0,) (31)

The results of the insertion loss calculations are shown in Fig. 7. The

antenna-feed system was matched to free space conditions. The results

for two loss tangent values are presented. The reflection loss for the

same matching conditions are plotted in Fig. 8. The reflection loss

shown in Fig. 8 is defined as

Reflection loss 1 IPFI2 (32)

-?.l

,I, , .-i

-10

IJ

tan 8:0.01

-8

t, o n 8 ........................

-6

MATCHED TO FREE SPACE

-4 FREQUENCY -25GHzc,, k a= 0.45

kob =2.10-2 Eg = 4.0

d =0.5XoI

o II I I I I

Iol 1012 o13

Ne (PEAK) cm-3

Figure 7. Feed Network Insertion Loss

-2zz-

____ ________ _ !

I " I I!

MATCHED TO FREE SPACEFREQUENCY: 2.25 GHz

-20 ( =O :0.45

k0b =2.100"0., = 4.0

00

P-10w-I0

ton 000

01 1 A I I

Ne (PEAK), cm"3

Figure 8. Reflection Loss vs Electron Density

i-23-

The total antenna-feed system degradation caused by the reentry

plasma is best illustrated by comparing inhomogeneous plane wave

attenuation predictions with the change in broadside antenna gain induced

by the plasma. The change in antenna gain is defined as

AGain =g (6 O)/g0O = 0) (33)

where g(FO( 0) is the total antenna gain in the plasma environment and

gF(O = 0) is the free space antenna gain. The turn ratio and series reactance

were selected to match the system to a free space environment. The

relative gain expression given in Eq. (33) was therefore a measure of the

telemetry link degradation caused by the plasma and!or changing the

matching conditions. In Fig. 9 the plane wave attenuation and AGain

calculations are shown as a function of peak electron density. The most

important effect to note is the large difference between the antenna

calculations and the commonly used plane wave calculations. The signal

attenuation associated with the reflection and absorption losses in the

feed are indicated by the difference between the feed results and the free

excitation results.

The VSWR at the input terminals is

vswR =-- +lIPb/( -I P'FI

where the reflection coefficient is given in Eq. (25). The results of the

VSWR calculations are shown in Fig. 10, assuming the antenna is matched to

free space conditions. The results indicate the absorption effects in

the window as the loss tangent is increased.

Since plane wave analyses are commonly used to predict signal

attenuation in telemetry link margin computations, the difference between

the plane wave attenuation and relative gain calculations shown in Fig. 9

-24-

F, ~ _____

21 ____ _ _ _ __ _ _ _ _

mton 8 001

5 jI -in8 00

EXCIATI- ANTENNA (8 SLABS)- - PLANE WAVE(18 SLABS)

MATCHED TO FREE SFYACEFREQUENCY: 2.25 9izkoo =045k0b =2.10

IE=4.0

d 0. o

-lo

ol iI + 2

e(PEAK) Cm-3

Figure 9. Change in Antenna Gain with Aperture Matched to Free Space

I

1_ ___i01 _n =0. / 25

:0:

10 .J I '

SFREQUENCY =225 GHzho a = 0.45

ko b =2.10eg =4.0i

d =t0.5 X01

i0l 10 12 1013Ne(PEAK) , cm-3

Figure 10. Input VSWR with Aperture matched to ree Space

FQ C 25

"Zb2.I"16 g :4.

is plotted in Fig. 11. The plane wave error is defined as

Error = tt'*/AGain

where tt'r is the plane wave transmission coefficient. These results

indicate that the plane wave predictions can underestimate signal

attenuation by at least 5 to 15 dB. The plane wave analysis does not

properly approximate the absorption and reflection losses of the feed

and surface wave effects in the plasma.

The thin sheath resul.t. are plotted in Figs. 12 and 13. In these 1cases the aperture admittance was calculated using the asymptotic

expression shown in Eqs. (10) and (11). The equivalent surface

susceptance was assumed to be zero and the conductance varied from

0. 001 mho to 0. 1 mho. The results are applicable for low-altitude

turbulent plasma sheaths surrounding slender conical vehicles.

D. ABSORPTION EFFECTS IN THE WAVEGUIDE

ANTENNA WINDOW

The decrease in anLenna gai,, caused by increased window

absorption due to temperature effects was obtained by parametrically

varying the loss tangent of the waveguide window from 0. 01 to 0. 16,

keeping the turn ratio and series reactance fixed. The feed network

was matched to free space conditions with a loss tangent of V. 01.

Figure 14 shows the decrease in antenna gain for various plasmra

conditions. In addition to increased absorption, the reflection lossdecreases as the window losses increase (Fig. 15). The decrease in

reflection losses from window absorption ultimately limits antenna

matching techniques in a reentry environment.

-27-

10 2

MATCHED TO FREE SPACEFRE]UENCY =225 GHz

koa =0.45kob=2.10

:4.0d;:0.5kom~

0ton 8 =0.01I ~~~"'I0I :.5

10 ton 8 =0.04

10 0112 1 J3i0 10 103

Ne (PEAK),cm-3

Figure 11. Plane Wave AttenuationxError

-28-

K iiI!

11'211

U7

-10I

- ANTENNA AGAIN--- PLANE WAVE ATTENUATION

loe MATCHED TO FREE SPACEFREQUENCY :2.25 GH zk a =015k0a = 2.10Eg= 4.O

:11

-29-

2 10.

J ~tan =0,04

MATCHED TO FREE SPACEFREQUENCY= 2.25 GHz

40

d=0.5kXl

10, I0 10-2 0 -G5, mhos

I41 Figure 13. Thin Sheath Limit for Input VSWR with Aperture

Matched to Free Space

-30-

I'-6 -i. PEAK~ ELECR N NT

MATCHED TO FREE SPACE 2.25X 0 cm-3

WITH ton & =0.01-5 FREQUENCY 225 GHzko a = 0.45

k b: 2.10 4.50x.0 II cm3

z0,[ ' 4 - = :4.0/

d 0.5X

C0

1.80 x I0dl cm3

12,,, 3.60 x 101 crn",i "- 2 -7.20x1 12 cm. 3

-I

7.2 x 102crr

10-2 I0-1 100TAN 8

Figure 14. Reduction in Antenna Gain Caused by Window Absorption

-31-

-30'

MATCHED TO FREE SPACE2 FREQUENCY =225 GHz

-25 koa =0.45

kob=2.10Eg =4.0

-207 d: 0.5X,01

-J .0 l2c'c"~-15 PEAK ELECTRON DENSITY

a: -0 ....... 1.80 x 10i2 -

9.00xlOII cm 3

-5 4.50x I I c 3

2.25x1& cm-3

0 1, ,1I

00- 1 i0- I0o

TAN 8

Figure 15. Reflection Loss vs Window Absorption

-32-

F

E. MATCHING TO A PLASMA ENVIRONMENT

The antenna feed performance under various matching conditions

is shown in Figs. 16 through 17, assuming a loss tangent of 0. 004.

The calculations were performed with the antenna matched to free space11 -3conditions, a waveguide load, and Ne(peak) = 5 X 10 cm . The turn

ratio and series reactancc were determined, in matching the coax-to-

waveguide transition to a nonreflecting waveguide load,by silbstituting

Y = Y into Eqs. (28). The turn ratio and series reactance required

to match the slot antenna to various conditions are tabulated in Table 2.

The input admittance results are plotted in Fig. 16. The resulting

LGain calculations are shown in Fig. 17, and the corresponding VSWR

results are plotted in Fig. 18. When the antenna was matched to

Ne(peak) = 9 x 1011cm-3, the antenna gain in free space decreased by4 eI1 -3

5. 8 dB, while the gain at the 9 x 10 cm electron density increased

by 5. 8 dE. As the waveguide window absorption loss increased, the

gain improvement decreased. The potential gain improvement resuting

from the match at the 9. 0 x 1011cm 3 electron density was 10. 7 dB for

a waveguide window loss tangent of 0. 01. When the loss tangent wasincreased to 0. 04 the potential gain improvement was decr-eased to 5.8 dB.

Table 2. Matching Conditions

Antenna Matched to tan6 Turn Ratio X /Z Z ohm

Free space 0.01 4.22 -1.54 50

Free space 0.04 4. 29 -0. 729 50

Waveguide load 0.01 2.38 -0. 0113 50

Waveguide load 0. 04 2. 38 -C. 0453 5011 -39x 10 cm 0.01 1.07 -,. 72 50

9 x 10 cm'3 0,04 1.37 -1.59 50

-33-

0 MATCHED TO Y0, (1) Ne 2.25 x 1011 cm-3A MATCHED TO FREE SPACE (2) Ne 4.50 x 1011 cm -30 MATCHED TO Ne:= 9 x 1011 cm- 3 (3) Ne: 9.00 x 1011 cm -3

FREQUENCY z 2.256 GHz (4) Ne :1.80 x 1012 cm-3ko a =O.45 (5) Ne :3.60 X 1012 CM-3k0b 2 10 '(6) Ne 7 20 X1012 CM 3

1 eg =4.0

TAN 8 : 0.04d :0.5X0 ,

~Ll

-34

FREQUENCY 2.25 GHz MATCHED TO FREE SPACEk0u 0.45k0b 2.I10

-20 - d -5 j

0o 2 4 6 810Ne (PEAK), CM3 X 1O11

Figure 17. Change in Antenna Gain for Various Matching Conditions

-35-

t -I In - t' irf'yC .n

15- FREQUENCY 2.25 GHz

131k05 FRQEC 0.4 5 H MATCHED TO FREE SPACE13 kob:2.I0eg = 4.0

Tan8= 0.04I d 0.5X0

Cr9- MATCHED TO 11 --INe(PEAK)=9xlO cm

7-

5 MATCHED TO YO,

0 2 4 6 8 10Ne (PEAK), cm-3x l0l

Figure 18. Input VSWR for Variouz Matching Conditions

-36-

-~ -

VI. CONCLUSIONS

Antenna gain calculations, including absorption and reflection

losses of the feed network are useful in estimating plasma-induced

signal attenuation. Plane wave calculations underestimate .:ignal

attenuation by 3 to 15 dB at S-band frequencies. As the anten.a

aperture increases in size, the difference between antenna gain calcu-

lations and nlane wave predictions decreases. When reflection losses

can be neglected in both the plane wave and antenna gain calculations,

the attenuation results of both analyses are the same, provided the

antenna absorption losses are zero.

The antenna gain in a plasma can be improved by matching the

antenna to peak plasma conditions, but at the expense of the free space

gain if preset matching is used. As the losses from window absorption

losses increase, the amount of gain improvement obtainable by

matching decreases. Matching the coax-to-waveguide transition to

the characteristic admittance of the waveguide window provides antenna

matching midway between ti.e open-circuit conditions of free space and

short-circuit conditions of reentry.

-37-

Ii REFERENCES

1. At T. Adams, "Flush Mounted Rectangular Cavity Slot Antenna -

Theory and Design, " IEEE Trans. Antennas and Propagation AP-15,

34Z (May 1967).

2. R. F. Harrington, Time Harmonic Electromagnetic Fields, McGraw-Hill Book Co., Inc. New York (1969). p. 4Z8.

3. K. E. Golden and G. E. Stewart, Self and Mutual Admittances of

Rectangular Slot Antennas in the Presence of an Inhomogeneous

Plasma Laver, TR-0Z00(4220-10)-i, Aerospace Corporation,

El Segundo, Calif. (March 1969).

4. K. E. Golden and G. E. Stewart, "Admittancce and Isolation of Slot

Antennas in the Presence of an Inhomogeneous Plasma Layer,"

IEEE Sum. Digest, presented 1968 International Antennas and

Propagation Symposium, Boston, Mass. (9-11 September 1968).

5. R. L. Fante, "Mutual Admittances of Infinite Slot Antennas,"

Proc. IEEE 55, 1754 (October 1967).

-39-

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DOCUIMENT CONTROL DATA - R&D3 (Security Clasifictimn of tile. 6wdj of abetutee an" lndeabd anotfa in be enfterd vous ow *esae sh toI IC88481400

~I. ORIGINATING ACTIVITY (Coopsme!aueh*) 20. REPORT 819CUmgY C LAGOM~CATION

F The Aerospace Corporation UnclassifiedEl Segundo, California 264 emoub

3. REPORT TITLE

Reentry Plasma Attenuation for S-Band Telemetry Systems

4- DESCRIPTIVE NOTES (Tv,. of -61001 W an Mt...lv dose)

S AUTHOR(S) MLeet nan.. JIM6 name, ZF1100

Golden, Kurt E.

f. REPORT 0ATW7.TTLN.OPAHaorp$

69 AUG 15 4Ga. CONTRACT OR GRANT No. 90. OR1qSNATOR'S 09PORT WiSKU~S)

F04701-69-C-0066 TR-0066(5220-1O)-l6. PROJ6CT NO. (omryT-2042-0-

10 AVA ILASILITY/LIMITATION NOMIESThis document is subject to special export controls and each transmittal toforeign governments or foreign nationals may be made only with prior approvalof SAMSO(SMTAE)._________ _______

11. SUPPLEMENTARY NOTES 12. SPONSORING MILITARY ACYIVtTY* Space and Missile Systems Organization

Air Force Systems Command____ ___ ___ ___ ____ ___ ___ ___ U.S. Air Force

12. ASSYRACT

The performance of a slot telemetry antenna is analyzed, including the

effects of an inhomogeneous plasma sheath on aperture admittance,

radiation pattern distortion, antenna window absorption, reflection and

absorption losses of the feed network, and total antnna. gain. The

* change in broadside antenna gain induced by the reentry pLsma sheath ir.

compared with plane wave signal attenuation calculatio-ts. Various antenna

matching conditions are evaluated for free-space and reentry-plasma

conditions.

noD FORMA 14n3UCASFEIFACSIMILK) UCASFE

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1 4.i KEY WOMO$

Slot antenna gainReentry plasmaFeed network performanceAntenna matchingReentry telemetry antenna

I.

Abstract (Continued)

10. Cont.The distribution of this report is limited because it contains technologyrestricted by mutual security acts.

*11

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