Summary of a study on the TM01 radiation pattern of corrugated conical horn antennas with small flare angle

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Summary of a study on the TM01 radiation pattern of

corrugated conical horn antennas with small flare angle

Citation for published version (APA):

Scharten, T. (1970). Summary of a study on the TM01 radiation pattern of corrugated conical horn antennas with small flare angle. Technische Hogeschool Eindhoven.

Document status and date: Published: 01/01/1970

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TECHNISCHE HOGESCHOOL EIN1)HOVEN

'~~fd~ling der eiektrotechniek

Summary of a study on the TMOl radiation pattern of corrugated conical horn antennas with small flare angle.

by

ir.Th. Scharten

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Summary of·a study on the TMOI radiation pattern of corrugated conical horn antennas with small flare angle

Th. ,Scharten

This summary is based on the technical reports Nr ETA-3-1969 and Nr ETA-30-1969 (Eindhoven University of Technology)

I. The configuration and its electromagnetic description I

1.1 Corrugated cionical horn antenna

- - _ . - .

Figure I 1.2 Electromagnetic mode l perfectly conducting surface Figure 2

.~

-

_"'-\d.

1t

I

.f

aperture -/c.:Jt He assume a simple harmonic time dependence <Z

We suppose tl+t,2<<'A.!9u/de and Ro .,.>a "» A"uicle' Furthermore we suppose the flare angle to be so small that -if a TMO mode is ,excited in' the horn- the aperture field can be approxima¥ed by the TMO mode field of a circular cylindrical, corrugated waveguide with ninner radius .a , but now with a quadratic phase distribution in the -radial aperture direction. For ih~that case the longitudinal phase factor. ' of the aperture field, e/~n4 ,has to be replaced by the factor

'j3/'J (R/-A'a)

e·

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-2-2. Fields on the horn surfaces

2.1 Outer surface.

On the outer surface we-assume the wall currents to be zero; so we have

ny..£=o

nxi1=o

on S •

c

2.2 Inner surface.

The surface impedance on the 1nner horn surface is determined by 'the relation

where Z - X ~f Zgr-oove + t2. Zcl';;'i77 r.;:::) r=

t

1 +

t2,

if

Z

.

L t groova CofT 2. on S; _r

Yo

Ua)

Yo

(kdf-kd)

-::J.,

(Id+kd)

Yo

(id )

J,

(,{d.)

Yo

(i:.d+k.d)-70(kd,+k.d)Yt

(kd)

being the input impedance of a shortened radial waveguide, d ~

P

~ d. + ci J

propagating a TEM wave.

2.3

Aperture.

The aperture fields are found 'by considering a circular cylindrical waveguide (radius d) having the reactance wall condition, given abov!=, and propagating a TI10 mode (exp[+i,8"z]). Taking into account the quadratic phase distngution 've find .

Epn

= -

if3n An

00\"

f)

(2.)(,/0 ( if3n

p2/

2Ro)

'\ th

where A., is the n root of the TMOn characteristic equation

.' ). ~ (Aa) - wC.O X,..~

Old..)

='0.

In our case

ka

'» 1 ; so the surface reactance can be approximated by

It is shown that the characteristic equation has two imaginairy soluti.ons (surface wave solutions) if

and real, sigle valued solutions if

k

u..n

kd

~ 2 (1:1 .,.. C:z)

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-3-3; The radiation pattern.

The energy-flow density can now be evaluated ~n the usual way, giving

4. Results

Horn dimensions

do . /(3" p2. ., (1.co::;(J+(3,,)2

j00

..

"p)J,(4ps(.'nQ)e 2RO pdp

a

=

0,132 (m) ] d 0,009 (m) t 1= 2,5 (rom) t 2=,4,0 (mm) R

=

0,493 (m) o Q _o= 15° o dimensions of the 'equivalent' waveguide

Figure 3 Dispersion curves for the circular cylindrical, corrugated waveguide

Figure 4-10 Theoretic~l and experimental TIIOI radiation 'patterns ~n ,the frequency range 8,5 - J 1,5 GHz

Figure Ll Half beamwidth characteristics

(6)

(7)

o

10 20 30 40

o

{\

,

12 < .

\

'\

24

THO 1 radiation patterns theoretical ---- J experimental ----frequency: 8,5 GHz

.

; Figure 4

\

rY

~

\

< 1 I I I \ \ \ \ "< I I \ \

,

\ ( I

VJ

\ < I

i\~

\ . I _\ \ 36 48 60 degrees

(8)

-5-o

(\

. THO! radiation patterns

theoretical -, , experimental ----; frequency: 9 GHz Figure 5 10

,

\

,

\

20

,

"

\

"

,

'\

\ \ 30 '\ \ \ '\

"

\ \

,

I 40 ~' "

o

12 24 36 48 60 degrees

(9)

.,

o

10 20' 30 40

o

12

1\ '

\

\/,\

I 24 36

",

™OI radiation patterns theoretical -experimental ----frequency: 9,5 Gi:lz i , Figure 6 , ,

\

48 , 60 degrees

(10)

O~r\~---r---,----:r---'

THo I radiation patterns

~ theoretical . --experimental ----10

,

20 30 40

o

12 24

1

I \ \ \ i \ ,1 ~I \ 36

1',

.1 \

J

V\

48 frequency: 10 GHi Figure 7 60 degrees

(11)

-7-

-8-o

:

™OI radiation patterns theoretical

-experimental ----frequency: 10,5 GHz i " ! , !,

\

Figure 8 " ;. : ,

\

t

.

. " i ~

...

"

-

\ ; " 20 ~ j ,f , ' i

,

, ",

.,'"

,

J

e'

\....

i 30

~

} ,

~,

I ~ .r 1 I ' . .•

~

, .'

,

r

! I I ~ ,

1

I I " I 1 I ! , . I J ~ I ~ 40

o

12 24 36 48 60 degrees

(12)

,..0 '"d )..I <l.I ;3: 0 p.. <l.I :> '.-I .u <1l .-1 <l.I )..I

o

10 20 30 40

o

'\

~

\

., ;

\

l\

... 12 24

™OI radiation patterns

theoretical -experimental _..----

-frequency: 11 GHz Figure 9 ~

\:

\ t \

.,.

, I'

\J \

"t \ f.:

~\

1 1 I I \

-II

, 36 .48 60 degrees

(13)

a

'\

~

10

\

~.

l

20

\

,

\

30

,

40

o

12 24

.

"',

\

,'"

II 1

V\\

₁

1 I

\f

_\

36 48

r

'fMOI radiation patterns t'heoretical -experimental ---frequency: 11,5 GHz Figure 10