 Open Access
 Total Downloads : 143
 Authors : P. Ujjvala Kanthi Prabha, G. S. N Raju
 Paper ID : IJERTV5IS030797
 Volume & Issue : Volume 05, Issue 03 (March 2016)
 DOI : http://dx.doi.org/10.17577/IJERTV5IS030797
 Published (First Online): 23032016
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Impedance Characteristics Hplane Tee Junction using L band Wave Guide

Ujjvala Kanthi Prabha1
1Department of ECE, MVGR college of Engineering
Vizianagaram535005.
G. S. N. Raju 2
2Honorary Distinguished Professor Andhra university,
Visakhapatnam530003.
Abstract – In all radar and communication applications antennas play an important role, for transmitting and receiving purposes. For certain special applications, it is essential to radiate with desired polarization. Wave guide junction radiators are preferred for this purpose. In HPlane Tee junctions, the Tee arm is commonly coupled to the main wave guide by a longitudinal slot. The analysis of such structures is reported in the literature. However, the coupling can be done by inclined slot in the narrow wall of main wave guide. This structure acts as a radiator to produce vertically polarized waves with polarization limits. The knowledge of admittance characteristics of this new coupling system provides additional design parameters for the array designer.
In the present work, the analysis is made to obtain variation of conductance, susceptance, coupling and VSWR as a function of frequency after determining the resonant slot length of L band Hplane Tee junction wave guide. The results are numerically computed for varied slot width and slot inclinations. The concepts of selfreaction and discontinuity in modal currents of the main guide as well as Tee arm are used in the analysis. The data presented are extremely useful for the design of small and large arrays of L band HPlane Tee junction radiators, which are more suitable in navigations, GSM mobile phones, and in military applications. They are also used to measure the soil moisture of rain in forests.
Key words: Admittance, wave guide junction, shunt Tee, H plane Tee

INTRODUCTION:
Basically the HPlane Tee junction is a three port device. The main guide containing two ports and the coupled arm contains third port. The main wave guide is in shunt with the coupled arm. In power division applications Shunt Tees are usually preferred, to divide the power equally into two main ports when fed through shunt port. In the present work HPlane Tee junctions are used as radiators with vertical polarization. For this purpose, the power is fed at the input port of main guide with the corresponding output port matched terminated. The power is radiated through the coupled arm. The Tee arm is coupled to the main guide usually by a longitudinal slot. However, the coupling can be made by inclined slot in the narrow wall of main guide. This structure is also useful to produce vertically polarized waves. For the array designer additional design parameter will be provided by this coupling system i.e. waveguide dimensions and slot dimensions. Literature on Longitudinal slot coupled Shunt Tee wave guides is available, but no one
reported on inclined slot coupled wave guide Shunt Tee. The rectangular waveguides are used due to their compact size and space considerations .Radiation pattern will be distorted in case of open ended slot arrays because of mutual coupling exists between the slots. In array applications, cross polarized components can be suppress by Slot coupled Shunt Tees which in turn reduces mutual coupling between slots.
The analysis of different slots is presented by many researchers [14]. Results on studies of impedance characteristics of slots are reported. Raju and Das have reported how To obtain a desired radiation pattern for a wave guide array by suppressing cross polarization [5] and to reduce mutual coupling between the slots[6]. Pandharipande et al [7] derived an expression for the equivalent network of long axial slot in the case of Hplane T junction coupled through longitudinal slot in the narrow wall of primary wave guide. Oliner[8] presented impedance properties of different types of slots using equivalent circuit and variational method. The results include with thickness and without thickness. Marcuvitz[9] has developed concept that Discontinuities in Waveguides walls produce fields. Discontinuity Electric and Magnetic Fields equivalent represents Discontinuity in modal Currents. Hsu. [10] obtained some admittance properties of the inclined slots in the narrow wall and investigated on the possible resonant length. Raju [11] has reported on variation of resonant length as a function of slot width and Admittance of inclined Slots in narrow wall of rectangular waveguide that are sufficiently wide as a function of frequency. Very useful investigations on slot coupled waveguide junctions and slot radiators carried out by Watson [12]. The coupled slots are either in the narrow wall or broad wall of a rectangular waveguide. Das [13] derived an equivalent circuit for waveguide T junction using variational technique considering the slot thickness. Raju[14] and Das [15]have obtained admittance characteristics and resonant length of inclined slots in the narrow wall of a rectangular waveguide by using selfreaction and discontinuity in modal current approach . The variation of resonant length as a function of inclination of the slot is given using variational analysis as well as method of moments. Cheng Geng jan [16] has reported the analysis of side wall inclined slots using method of moment technique.

ANALYSIS FOR ADMITTANCE CHARACTERISTICS:
It is well known that a vertical slot in narrow wall of rectangular waveguide does not radiate. The electric field in such a slot is horizontally directed. But in applications where vertically polarized fields are required from inclined slots, it is possible to obtain them by coupling the slot into shunt Tee arm forming a Shunt Tee. In the present paper, the admittance characteristics of inclined slot in narrow wall of L band Shunt Tee is determined from selfreaction and discontinuity in modal current [8]. The analysis

FORMULATION:

Selfreaction equations in H plane Tee junction coupled through inclined slot:
The Electric field in aperture plane of slot is replaced by an equivalent magnetic current. The total selfreaction <a,a>T of this magnetic current, with magnetic Fields produced by This Magnetic currents. The admittance seen by primary guide can be expressed as
consists of two parts: first part consists of evaluation of selfreaction for the feed guide. This in turn consists of
Y = (IIs)
T
T
<a,a>T
, where
is discontinuity in
evaluation of selfreaction of horizontal and vertical components of the magnetic current. The second part consists of evaluation of selfreaction for the Tee arm.
modal current. (1)
Expression for self reaction is given by [3]
In the present work, the analysis is carried out to obtain variation of slot conductance and susceptance as a function
< a, a >T= HS.
S dv. —– (2)
of resonant slot length. The result is numerically obtained for varied slot widths and slot inclination. Consider a L band waveguide shunt Tee coupled through an inclined slot of length 2L and width 2w, on the narrow wall as shown in Fig.1.
The analysis for admittance characteristics is obtained using selfreaction and discontinuity in modal current. The admittance characteristics in the coupled waveguide radiator are evaluated using TE and TM mode field concepts. In the present work the equivalent network parameter is obtained [14]. It is assumed that slot is inclined at an angle from the vertical axis and coupling takes place through inclined slot in narrow wall of the primary feed waeguide.
As shown in fig (1) a and are narrow wall and broad wall dimensions of primary and secondary rectangular wave guide. An inclined slot in the narrow wall of coupled junction of two different standard waveguides with slot length 2L and width 2W . is the angle of inclination of slot from vertical axis. The slots admittance characteristics are analyzed using selfreaction and discontinuity in modal current. Using TE and TM mode field concepts, slot radiators are analyzed.
where H S is magnetic field and M S is magnetic current. V is the coupled volume.
The equivalent network parameter is given by [9] the expression of the form [5].In present work Self reaction <a, a>T is determined separately for the two guides. The self reaction , in primary guide is longitudinal component of magnetic current, the self
reaction , in primary guide is transverse component of magnetic current, the selfreaction
, in secondary guide, obtained from the modal expansion of the magnetic field in the coupled guide, is given by [14]., The shunt impedance loading on the
primary guide due to the slot coupled shunt Tee can be expressed as the total selfreaction is equal to the sum of selfreactance, , , and
, .Hence, the equivalent network parameter will
be
<a, a>T = , + , + ,
The expression for shunt impedance loading on the primary guide due to slot coupled matched terminated Tee arm will be
= , = , , , — (3)
=1+2+3
Fig.1 Inclined slot coupled waveguide shunt Tee junction

Selfreaction due to longitudinal component of magnetic current in primary wave guide , :
The Electric field in aperture plane of slot of fig 1 is related to equivalent magnetic Current by the relation
= ——– (4)
where is unit vector normal to the aperture plane
The field distribution in the slot is assumed to be of form
given by [6]
= ( )—— (5)
for  + and 
is wave length. a and b are narrow wall and broad wall dimensions of feed guide.
=Lcos , = Wcos with respect to xcomponent of magnetic current.
2 2 Corresponding magnetic current is
where is maximum Electric field, is unit vector along x direction and K=2/. is wave length. 2L is length of slot and 2W is width of slot.
= —— (8)
From the fig.1 that = . Hence the magnetic current
The magnetic current is along xdirection in present case
due to slot is in z direction. From the knowledge of magnetic field and magnetic current, it is possible to evaluate self reaction required for obtaining expression for equivalent network. The self reaction has been defined in
(2) in the form of volume integral. Since magnetic current is distributed over the surface, the volume integral in the
= ( )
for  and  +
selfreaction reduced to surface integral. Taking the image 2 2
in the wall y=b into account, the expression for self
reaction
Takes the form < , >= .2
By integrating and simplifying the above expression
< , >
By using selfreaction expressions given by [3]
< , >= .
As the magnetic current distributed over the surface, the volume integral reduces to surface integral
sin () +
= 2 2 2 cos 2 cos () [cos  (
2
2
402
2
< , > = .
—– – (9)
)  cosh ( ) ]
By further Simplifying the expression for self reaction for the longitudinal component of the slot magnetic current in primary wave guide will be reduced to
By integrating and simplifying the expression for Self reaction given by [9 ]
24
sin() 2
2 2
, =
2. 2 [ ]
,
= [2
15
=0 =1
(2 + 2)
2 ()
2402
2
2
[0.5(1 + 2 sin ) cos() 2 sin cos( sin ) + sin( sin )] —–2
2
(6)
( ) ] 2 2 [
2
2]
2()
[coscos
2 422 2]—– (10)
where = sin
and m=0, n=1.(In the above
] [
2
It should be noted that the integral .
is
expression summation is done for except m=0,n=0 and
m=1,n=0.) and
= [()2
+ ()2
1
()2 2
performed at y=b plane. Because the magnetic current
is the surface current and extended in x direction from
]
2
2
2
2

Selfreaction due to transverse component of magnetic current in primary wave guide < , >:
The field distribution in the slot is assumed having length
2Lt and widtpWt given by
= ( )——– (7)
for  and  +
+ and in z direction . Selfreaction of magnetic current along to xcomponent of magnetic
current can be obtained by replacing by Lcos , by W cos and E m by V cos .
With modification Selfreaction due to transverse component of magnetic current in primary wave guide
2 2 < , >= . —— (11)
where is maximum Electric field, is unit vector and K=2/ .
, =
= [(0) + (0) ] — (16)
22
2. 2 [ 1
2
] [ ()
60
=0
2
=1 (012)
2 2()2
cos()] [2 + 2 1 ]—(12)
Here (0) (0) are characteristic admittance
of TE and TM modes. and are modal vector

Selfreaction in coupled/ secondary wave guide
, :
For the coordinates shown in fig.2 the variables are related as
x= + () and z= + ();
2 2
k=2/. ——– (13)
From formulation given by [3] and using the relations
functions for transvers component of magnetic field .
Since magnetic current is in ground plane y'=0, The total magnetic current considering its image in the ground plane is given by
= 2
The electrical field distribution in the aperture plane of slot can represent by an equivalent magnetic current. The selfreaction , of the magnetic
current. in coupled guide given by
above (13) the normalized vectors for electric ( ) and magnetic ( ) are found. The electric and
, = . —— (17)
magnetic voltages are given
The self reaction , is reduced to
, = 2 =0 1(0)
( )2 + 2 =0 1(0)
( )2 (18)
=
=
=
2
where (0) =
; (0) =
and = [() +
1
]
]
()2 ()2 2
Âµ0
=
—— (14)


xpression for discontinuity in modal current:
The expression for discontinuity in modal current IS is given by [8] and it is expressed as
where is maximum Electric field, and K=2/ . is wave length. a and b are narrow wall and broad
wall dimensions of feed and coupled guide. From the
I jY
an E h
sin
z jh
cos
zds —– (19)
knowledge of [6] the expressions for modal voltages are obtained.
S 01
slot
S 01 01
Z 01 01
The field distribution in the aperture plane of slot is assumed having length 2Lt and width 2wt given by
= ( ) —— (15)
Here h01 and hz01 are transverse and longitudinal modal vector functions respectively. Y01 is characteristic wave admittance and 01 is propagation constant.
These are given by
1
h 2 2 sin y a — (20)
01 ab b x
for L  and W 
1
2 2
m ——– (21)
where is maximum Electric field, is unit
h Z01 = j ab
cos a
b b z
vector along x direction and
01
K=2/. is wave length. 2L is length of slot and
For a slot on the narrow wall the expression
1
h Z01 is
2W is width of slot and V=2WEm
turns to
h Z01
2 2
j
j
ab b
—— (23)
The transvers component of magnetic field in y=0 plane of guide 2 is of the form
01
Since the slot is located at y=b plane, h01 = 0 and h02 takes the form of (21). Using the equations (20),(22)
The VSWR in terms of reflection coefficient is given by [9]
and evaluating the integral in the equation (19)
The expression for discontinuity in modal current [9]
VSWR 1
1
——– (22)
reduces to the form


RESULTS:
I 2 jY
1
1
V
V
2
2
2
2 2
1
cos
L cos k
L sin 01 w —
2
2
Using the expressions of normalized admittance
S 01
a b
b 2 k 2
01 2
2 w
—— (19)
1 1
1 01 01
01 2
presented above, the variations of normalized conductance, normalized susceptance with the length
Here
01
and
;
2
2
of the slot is numerically computed at the central
Y01
01
k 2
frequency of Lband wave guide. For the slot
01
V=2Em W
b1
inclination of =300,350, 400,450,500 the resonant lengths of the slot 2L= 10.6cm, 11.0cm, 11.4cm,
3.3. Expression for admittance loading:
The normalized shunt admittance is related to normalized impedance by the relation and can be calculated from the knowledge of selfreaction and discontinuity in modal current
11.8cm, 12.0cm are obtained respectively. The variation of conductance, susceptance, coupling and VSWR as a function of frequency for slot widths of 2W=0.05cm, 0.1cm,0.15cm 0.2cm,0.25, 0.3cm are presented in fig.2, fig.3, fig.4, fig.5, fig.6 and fig.7
YT gn

jbn
1
zT
1
r jx
—— (20)
respectively.
From the results the variation of normalized admittance with slot width for fixed resonant length are presented in fig(89).The resonant length is
where gn the normalized conductance and bn is the normalized susceptance
3.4 Expression for Coupling and VSWR:
It has been possible to represent the radiation of present interest by the equivalent circuit which consists of admittance parameters.
The transmission matrix of the shunt admittance parameters [5] given by
obtained from variation of normalized admittance with slot length for Centre frequency of Lband. The results are presented in appendixI
+
1 + /2 /2
+
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
=3
0
=3
5
=3
0
=3
5
NORMALIZED
CONDUCTANCE
NORMALIZED
CONDUCTANCE
[ 1 ] =[ /2 1 /2] [ 2 ]
1
1
2
2
1
1
frequency i 1.5 z
frequency i 1.5 z
2
2
When port2 of guide1is terminated with matched load =0
n GH
n GH
The reflection coefficient seen by port1 is given by
1 YLN
1 YLN
where
YLN
1 YT
Using power balanced condition the radiated power coupled to free space is given by
C = 42/[(2 + )2 + 2 ] —— (21)
0.3
0.2
0.1
=30
=35 =40 =45 =50
0.3
0.2
0.1
=30
=35 =40 =45 =50
0
0
1
1.2
1.4
1.6
0
1
1.2
1.4
1.6
0
1
5 =30
=35 =40
10 =45
=50
15
1.5
1
5 =30
=35 =40
10 =45
=50
15
1.5
15
15
20
frequency in GHz
20
frequency in GHz
20
frequency in GHz
20
frequency in GHz
1.4
1.3
1.2
1.1
1
0.9
0.8
0.7
=30
=35 =40 =45
=50
1.4
1.3
1.2
1.1
1
0.9
0.8
0.7
=30
=35 =40 =45
=50
0
0
1
1
1.5
1.5
0.1
0.2 frequency in GHz
0.1
0.2 frequency in GHz
0.4
0.3
0.2
0.1
0
0.4
0.3
0.2
0.1
0
=30
=35 =40 =45
=30
=35 =40 =45
0.1
0.1
1
1
1.5
1.5
0.2
0.2
frequency in GHz
frequency in GHz
5
10
5
10
=30
=35 =40 =45 =50
=30
=35 =40 =45 =50
1
1
frequency in 1.5
frequency in 1.5
GHz
GHz
1.5
1.4
1.3
1.2
1.1
1
0.9
0.8
0.7
1.5
1.4
1.3
1.2
1.1
1
0.9
0.8
0.7
=30
=35 =40 =45 =50
=30
=35 =40 =45 =50
1 frequency1i.n5 GHz
1 frequency1i.n5 GHz
VSWR
VSWR
COUPLINGe
COUPLINGe
NORMALIZED
SUSCEPTANCE
NORMALIZED
SUSCEPTANCE
COUPLING
COUPLING
NORMALIZED
SUSCEPTANCEe
NORMALIZED
SUSCEPTANCEe
VSWR
VSWR
Fig.2.Variation in conductance, susceptance, coupling and VSWR for a=
16.5 cm, b=8.2cm, slot width W=0.05 and with slot inclination =
300,350,400,450,500 Fig.3.Variation in conductance, susceptance, coupling and VSWR for a=
0.4
0.3
0.2
0.4
0.3
0.2
0.1
0
0.1
0
frequency in 1G.H5z
frequency in 1G.H5z
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
=30
=35 =40 =45 =50
=30
=35 =40 =45 =50
NORMALIZED
CONDUCTANCE
NORMALIZED
CONDUCTANCE
Normalized conductance
Normalized conductance
16.5 cm, b=8.2cm, slot width W=0.1 and with slot inclination = 300,350,400,450,500
=30
=35 =40 =45 =50
1
=30
=35 =40 =45 =50
1
1 1.5
freqency in GHz
1 1.5
frequency in GHz
0
0
1
1.5
0
1
1.5
0
1
=30
=35 =40 =45 =50
1.5
1
=30
=35 =40 =45 =50
1.5
0.4
0.3
0.2
0.1
0.4
0.3
0.2
0.1
=30
=35 =40 =45
=30
=35 =40 =45
0
0
0.1
0.1
1
1
1.2
1.2
1.4
1.4
1.6
1.6
0.2
0.2
frequency in GHz
frequency in GHz
0.4
0.3
0.2
0.1
0
0.4
0.3
0.2
0.1
0
=30
=35 =40 =45 =50
=30
=35 =40 =45 =50
1 1.5
1 1.5
0.1
0.2
0.1
0.2
frequency in GHz
frequency in GHz
5
10
5
10
15
15
20
20
frequency in GHz
frequency in GHz
5
10
5
10
=30
=35 =40 =45 =50
=30
=35 =40 =45 =50
15
20
15
20
frequency in GHz
frequency in GHz
1.5
1.4
1.3
1.2
1.1
1
0.9
0.8
0.7
1.5
1.4
1.3
1.2
1.1
1
0.9
0.8
0.7
=30
=35 =40 =45 =50
=30
=35 =40 =45 =50
1
1
frequency in 1.5
frequency in 1.5
GHz
GHz
1.5
1.3
1.1
1.5
1.3
1.1
=30
=35 =40 =45 =50
=30
=35 =40 =45 =50
0.9
0.7
0.9
0.7
1
1
frequency in G1H.5z
frequency in G1H.5z
VSWR
VSWR
TCOUPLING
TCOUPLING
Normalized susceptance
Normalized susceptance
VSWR
VSWR
COUPLING
COUPLING
NORMALIZED SUSCEPTANCE
NORMALIZED SUSCEPTANCE
Fig.4.Variation in conductance, susceptance, coupling and VSWR for a=
1
1
frequen1c.5y in GHz
frequen1c.5y in GHz
2
2
1 frequency in G1H.5z
1 frequency in G1H.5z
NORMALIZED
CONDUCTANCE
NORMALIZED
CONDUCTANCE
Normalized conductance
Normalized conductance
16.5 cm, b=8.2cm, slot width W=0.15 and with slot inclination = 300,350,400,450,500
Fig.5.Variation in conductance, susceptance, coupling and VSWR for a=
16.5 cm, b=8.2cm, slot width W=0.2 and with slot inclination = 300,350,400,450,500
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
=30
=35 =40 =45 =50
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
=30
=35 =40 =45 =50
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
=30
=35 =40 =45 =50
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
=30
=35 =40 =45 =50
0
0
2 1
4
6
8
10
12
14
16
1.5
0
0
2 1
4
6
8
10
12
14
16
1.5
20
frequency in GHz
20
frequency in GHz
1.5
1.3
1.1
0.9
=30
=35 =40 =45 =50
1.7
1.5
1.3
1.1
0.9
0.7
0.5
=50
=45 =40 =35 =30
1.5
1.3
1.1
0.9
=30
=35 =40 =45 =50
1.7
1.5
1.3
1.1
0.9
0.7
0.5
=50
=45 =40 =35 =30
0.7
1 1.5
frequency in GHz
0.7
1 1.5
frequency in GHz
1
frequen1c.5y in GHz
2
1
frequen1c.5y in GHz
2
Fig.6.Variation in conductance, susceptance, coupling and VSWR for a=
0
0
Normalized conductance
Normalized conductance
16.5 cm, b=8.2cm, slot width W=0.25 and with slot inclination = 300,350,400,450,500
0.4
0.3
0.2
0.1
=50
=45 =40 =35 =30
0.4
0.3
0.2
0.1
=50
=45 =40 =35 =30
1 1.5
frequency in GHz
1 1.5
frequency in GHz
0.4
0.3
0.2
0.1
0.4
0.3
0.2
0.1
=30
=35 =40 =45 =50
=30
=35 =40 =45 =50
0
0
1
1
1.5
1.5
2
2
0.1
0.2 frequency in GHz
0.1
0.2 frequency in GHz
0.4
0.3
0.2
0.1
0
0.1 1
0.2
0.4
0.3
0.2
0.1
0
0.1 1
0.2
=50
=45 =40 =35 =30
=50
=45 =40 =35 =30
1.5
1.5
frequency in GHz
frequency in GHz
=50
=45 =40 =35 =30
=50
=45 =40 =35 =30
frequency in GHz
frequency in GHz
1
1
1.5
1.5
2
2
5
10
5
10
=30
=35 =40 =40 =45 =50
=30
=35 =40 =40 =45 =50
15
15
VSWR
VSWR
coupling
coupling
normalized susceptance
normalized susceptance
normalized susceptance
normalized susceptance
VSWR
VSWR
COUPLING
COUPLING
FIG.7.Variation in conductance, susceptance, coupling and VSWR for a=
0.4
0.3
0.2
0.1
0
0.4
0.3
0.2
0.1
0
normalized
conductance
normalized
conductance
16.5 cm, b=8.2cm, slot width W=0.3 and with slot inclination = 300,350,400,450,500
=30
=35 =40 =45 =50
=30
=35 =40 =45 =50
0.05
slot wi 0.25 cm
0.05
slot wi 0.25 cm
dth in
dth in
Fig 8.variation of conductance as a function of slot width at central frequency=1.3ghz ,for slot inclination = 300,350, 400, 450, 500 with resonant lengths 2L=10.6cm,11cm, 11.4cm,11.8cm and 12.0 cm respectively
0.02
0.01
0
0.01 0
0.02
0.03
0.04
0.2
0.4
0.02
0.01
0
0.01 0
0.02
0.03
0.04
0.2
0.4
slot width in cm
slot width in cm
=30
=35 =40 =45 =50
=30
=35 =40 =45 =50
normalized
susceptance
normalized
susceptance
Fig.9.variation of susceptance as a function of slot width at central frequency=1.3ghz , for slot inclination = 300,350, 400, 450, 500 at, with resonant lengths 2L=10.6cm,11cm, 11.4cm,11.8cm and 12.0 cm respectively


CONCLUSIONS:

It is evident from the results that the maximum conductance in all cases is found to appear slightly away from resonant frequency. The shift is to the left of resonant frequency fr and. normalized susceptance is found to have change of sign at fr. These observations are irrespective of slot angle and slot width.
Coupling is found to vary from 6dB to 16dB and VSWR has a variation between 1 to 1.5.It is interesting to note that normal conductance does not exhibit any peak as a function of slot width. But variation of susceptance is different as a function of slot width. In some cases it has polarity changes and in some cases there no such cross over.
From the results presented in appendixI, the variation of normalized admittance with slot length is similar to that of variation with frequency i.e. Conductance has peak and susceptance has a cross over from positive to negative.
REFERENCES:
[1]. R.F. HarringtonTime Harmonic Electromagnetic Fields, Mc GrawHill New York, 1961 [2]. Raju.G.S.N.,Microwave Engineering, IK International Publishers, New Delhi, 2007. [3]. Collin, R.E and Zucker,P.J .(1968). Antenna theory,Vol 1,Mc GrawHill, new York. [4]. R.S.Elliot, ANTENNA THEORY AND DESIGN, PrenticeHall Inc.,1981.
[5]. G.S.N. Raju., DAS. B.N., Ajay Chakraborty,design of cross polarization suppressed wave guide array for desired radiation pattern, IEEE Transactions on Antennas and Propagation symposium,pp6770,vol.1,june1988 [6]. Edelberg.S, oliver.A.A.,Mutual coupling effects in large antenna arrays: partIslot arrays,IRE Transactions on Antennas & Propagation, May 1960, pp.286297. [7]. Pandharipande.V.M., Das.B.N.,Equivalent circuit of a narrowwall waveguide slot coupler, IEEE Transactions on MTT, vol.27, No.09, Sept. 1979, pp. 800804. [8]. Oliner A A ,The Impedance Properties of Narrow – Radiating Slots in the Broad face of Rectangular Waveguide, Part I & II, IEEE Trans. on Antennas & Propagation, 1957 Vol. AP5, No.1 pp. 520. [9]. N. Marcuvitz & J.Schwinger,On the Representation of Electric and Magnetic Fields produced by Current and Discontinuities to Wave Guides,Journal APPL.PHYS., vol. 22. ,no.6., pp806 819 , june1951. [10]. P.HSU & S.H.CHEN.,Admittance and Resonant Length of Inclined Slots in the Narrow Wall of a Rectangular Wave Guide,IEEE TRAS.A&P,vol.37,no.1,Jan 1989. [11]. Raju.G.S.N., Ajoy Chakraborty, Das.B.N.,Studies on wide inclined slots in the narrow wall of rectangular wave guide, IEEE Transactions on Antennas and Propagation, vol.38, No.1, Jan. 1990, pp. 2429. [12]. W.H. Watson,Resonant Slots, JIEE (London), Vol.93, Part 3A, pp.747777, 1946. [13]. B.N. Das, N.V.S. Narsimha Sarma and A. Chakraborty, A rigorous variational and Techniques, Vol.38, No.1, January 1990, pp 9395 [14]. Raju.G.S.N., Das.B.N., Ajoy Chakraborty, Analysis of long slot coupled HPlane Tee junction, Journal of Electromagnetic waves and applications,1980. [15]. Das.B.N., Janaswamy Ramakrishna,Resonant conductance of inclined slots in the narrow wall of a rectangular waveguide, IEEE Transactions on Antennas & Propagation, vol.AP32, No.7, July 1984, pp. 759761. [16]. ChengGeng Jan, RueyBeei Wu and Powen Hsu,Variational analysis of inclined slots in the narrow wall of a rectangular waveguide, IEEE transactions on Antennas and Propagation, Vol. 42, No. 10 October 1994, pp. 14551458.
normalized admittance
normalized admittance
AppendexI
0.2
0.15
0.1
0.05
conductan
ce susceptanc e
0.2
0.15
0.1
0.05
conductan
ce susceptanc e
0
0.05 4
0.1
6
8
0
0.05 4
0.1
6
8
slot length in cm
slot length in cm
normalized admittance
normalized admittance
Variation of conductance and susceptance as a function of slot length, at f=1.3 Ghz . for a= 16.5 cm , b= 8.25 cm and = 300, The resonant length obtained is 10.6 cm
0.2
0.15
0.1
0.05
0
0.05 4
0.1
0.15
conductan
ce susceptan ce
0.2
0.15
0.1
0.05
0
0.05 4
0.1
0.15
conductan
ce susceptan ce
6
6
8
8
slot length in cm
slot length in cm
Variation of conductance and susceptance as a function of slot length, at f=1.3 Ghz . for a= 16.5 cm , b= 8.25 cm and = 350, The resonant length obtained is 11 cm
0.3
0.2
0.1
0
0.1 4
0.2
conductan
ce susceptan ce
0.3
0.2
0.1
0
0.1 4
0.2
conductan
ce susceptan ce
slot length in cm
slot length in cm
6
6
8
8
0.3
0.2
0.1
0.3
0.2
0.1
conducta
nce suscepta nce
conducta
nce suscepta nce
normalized admittance
normalized admittance
normalized admittance
normalized admittance
Variation of conductance and susceptance as a function of slot length, at f=1.3 Ghz . for a= 16.5 cm , b= 8.25 cm and = 400, The resonant length obtained is 11.4 cm
Variation of conductance and susceptance as a function of slot length, at f=1.3 Ghz . for a= 16.5 cm , b= 8.25 cm and = 450, The resonant length obtained is 11.8cm
0.4
0.3
0.2
0.1
0
0.1 4
0.2
conducta
nce
suscepta nce
0.4
0.3
0.2
0.1
0
0.1 4
0.2
conducta
nce
suscepta nce
slot length in cm
slot length in cm
slot length in cm
slot length in cm
normalized admittance
normalized admittance
Variation of conductance and susceptance as a function of slot length, at f=1.3 Ghz . for a= 16.5 cm , b= 8.25 cm and = 500, The resonant length obtained is 12.0 cm
0
0
0.1
0.2
4
6
8
0.1
0.2
4
6
8