seminar on magic tee or microwave tees

1. SEMINAR REPORT
On
MAGIC TEE
In partial fulfillment of the requirements for the award of the degree of
BACHELOR OF TECHNOLOGY
IN
ELOCTRONICS AND COMMUNICATION ENGINEERING
(West Bengal University of Technology)
Submitted by:-
Kazi md saidur rahaman
Roll No: 11900313072
Reg. No:131190120010 of 2014-2015
Under the guidance of
Ms. Dia Ghosh
Assistant Professor of ECE
DEPARTMENT OF ELOCTRONICS AND COMMUNICATION ENGG.
SILIGURI INSTITUTE OF TECHNOLOGY
PO: SUKNA, SILIGURI, PIN: 734009, WEST BENGAL
1

2. 2014-2015
DEPARTMENT OF ELECTRONICS & COMMUNICATION
ENGINERRING
CERTIFICATE
This is to certify that the Seminar report entitled ‘MAGIC TEE’ submitted in partial fulfillment
of the requirement for the award of Bachelor of Technology in ELECTRONICS &
COMMUNICATION ENGINEERING of the WEST BENGAL UNIVERSITY OF
TECHNOLOGY, KOLKATA during the year 2014-2015, is a faithful record of the bonafide
work carried out by KAZI MD SAIDUR RAHAMAN with Roll No. 11900313072, under my
guidance and supervision.
------------------------------------------------ --------------------------------------------------
(Miss. DIA GHOSH) (Dr. GAUTAM DAS)
Assistant Professor Associate Professor
Seminar Guide Head of the Department
Dept. of Electronics & comm. Engg. Dept. of Electronics & comm. Engg.
Siliguri Institute of Technology Siliguri Institute of Technology
West Bengal West Bengal
2

3. ACKNOWLEDGEMENT
I would like to express my sincere thanks to everyone who has helped me in the completion of
the seminar report. In particular, I would like to express my deep gratitude to my seminar guide
Miss. DIA GHOSH, Assistant Professor & Seminar Co-Ordinator Mrs. SHARMISTHA
MONDAL ECE Dept. and Dr. GAUTAM DAS, Associate Professor H.O.D, ECE Dept. for
their moral support and guidance throughout the preparation.
I would also like to thank my subject teachers and friends for their support and valuable
suggestions which has helped me a lot. Also thanks to MICROSOFT CORPORATION for
creating easy and powerful software like Microsoft Word 2010, without which it is very difficult
to complete the seminar report. Last but not the least I wish to express my gratitude to God
almighty for his abundant blessings without which this seminar would not have been a success.
3
Kazi md saidur rahaman
3rd year, ECE
ROLL: 11900313072
Reg. No: 131190120010

4. CONTENTS Page No.
 List of figures……………………………………………………… V
 Chapter-1…………………………………………………………. 1
 Introduction
 Chapter-2………………………………………………………… 2
 What is Magic tee
4
2.1: operation
2.2: structure
 Chapter-3…………………………………………………………. 4
Background Information on Magic Tees
 3.1: Simulation Scenarios
 3.2: Simulation Results
 Chapter 4………………………………….................................. 8
Tee Junction
 4.1.:Scattering matrix
 4.2:E-plane tee(series tee)
 4.2.1Scattering matrix
 4.3:H-plane tee (shunt tee)
 4.3.1:Scattering matrix:-
 4.4:Magic Tees (HybridTees)
 4.4.1:Characteristics:-
 4.4.2:Scattering matrix
 Chapter 5…………………………………………………........... 21
Advantages or Disadvantages
 Chapter 6…………………………….………………………… 22
Application

5. Chapter 7……………………………………………………
5
Conclusion
Refference

6. LIST OF FIGURES Page No.
 Figure 3.1:CADFEKO magic tee model …………………..……………………………...04
 Figure 3.2: Sigmaport driven Standing wave patterns ……………………....……….....05
6
 (a) Horisontal plane plotted
 (b) Vertical plane plotted
 Figure 3.3: Delta port driven - standing wave patterns …………………………...........06
 (a) Horisontal plane plotted
 (b) Vertical plane plotted
 Figure 3.4: S-parameter phase comparison between ports 3 and 4.................................07
 (a) Sigma port driven
 (b) Delta port driven
 Figure 4.1:E-plane tee…………………………………………………..…………………..10
 Figure 4.2:E-plane tee……………………………………………………………………....10
 Figure 4.3:H-plane tee………….……………………………………………………..…....11
 Figure 4.5Magic Tees…………………………………………………………………........13
 Figure 4.6 Magic Tees……………………………………………………………………...13
 Figure 6.1:Imedence bridge using magic tee……………………………………………..17
 Figure 6.2: Magic tee antenna duplexer………………………………………………….18
 Figure 6.3: Balanced mixer……………………………………………………………......19
 Figure 6.4:circulators………………………………...…………………………………...20

7. 7
Chapter:1
INTRODUCTION
Waveguide magic tee is an important element in microwave and millimeter wave engineering
especially in monopulse antenna systems. However,because of the complicated structure and
small size,go od performance magic tees at millimeter wave wavelength such as at W band or
higher frequencies is very difficult to realize. On the other hand,a rigorous field analysis on
waveguide magic tee is also difficult. So far as we know only a little papers have been published
on the analysis. Sieverding and Arndt analyzed the magic tee with the full wave modal S-matrix
by mode-matching method in 1993 . Later Ritter and Arnd presented a new method,named “a
combined finitedifference time-domain/matrix-pencil method”,to analyze and design magic tee .
In 2002,Shen et al. introduced another method,a hybrid finite-element/modal expansion
Method,for the rigorous analysis.
Waveguide junctions are used when power in a waveguide needs to be split or some extracted.
There are a number of different types of waveguide junction that can be use, each type having
different properties - the different types of waveguide junction affect the energy contained within
the waveguide in different ways.
When selecting a waveguide junction balances between performance and cost need to be made
and therefore an understanding of the different types of waveguide junction is usedful.The main
idea behind the "Magic Tee" is to combine a TE and a TM waveguide splitter. In this particular
case port 1 and port 4 are de-coupled, so one can expect S14 and S41 to have very low values.
Viewing the electric fields gives a better understanding how the "Tee" works.
Chapter:2

8. 8
WHAT IS MAGIC TEE:-
A magic tee (or magic T or hybrid tee) is a hybrid or 3 dB coupler used in microwave systems.
It is an alternative to the rat-race coupler. In contrast to the rat-race, the three-dimensional
structure of the magic tee makes it less readily constructed in planar technologies such
asmicrostrip or stripline.
The magic tee was originally developed in World War II, and first published by W. A. Tyrell (of
Bell Labs) in a 1947 IRE paper. Robert L. Kyhl and Bob Dicke independently created magic tees
around the same time.
2.1:STRUCTURE:-
The magic tee is a combination of E and H plane tees. Arm 3 forms an H-plane tee with arms 1
and 2. Arm 4 forms an E-plane tee with arms 1 and 2. Arms 1 and 2 are sometimes called
the side or collinear arms. Port 3 is called the H-plane port, and is also called the Σ port, sum
port or the P-port (for "parallel"). Port 4 is the E-plane port, and is also called theΔ
port, difference port, or S-port (for "series"). There is no one single established convention
regarding the numbering of the ports.
To function correctly, the magic tee must incorporate an internal matching structure. This
structure typically consists of a post inside the H-plane tee and an inductive iris inside the E-plane
limb, though many alternative structures have been proposed. Dependence on the matching
structure means that the magic tee will only work over a limited frequency band.
2.2:OPERATION:-
The name magic tee is derived from the way in which power is divided among the various ports.
A signal injected into the H-plane port will be divided equally between ports 1 and 2, and will be
in phase. A signal injected into the E-plane port will also be divided equally between ports 1 and
2, but will be 180 degrees out of phase. If signals are fed in through ports 1 and 2, they are added
at the H-plane port and subtracted at the E-plane port. Thus, with the ports numbered as shown,
and to within a phase factor, the full scattering matrix for an ideal magic tee is

9. (the signs of the elements in the fourth row and fourth column of this matrix may be
reversed, depending on the polarity assumed for port 4).
9

10. 10
Chapter:3
Background Information on Magic Tees:
FEKO provides microwave engineers with the tools to simulate waveguide problems, enhancing
understanding of real world problems. These tools have been applied to simulate a magic tee for
the WR-90 waveguide band (X-band). Figure 1 depicts an annotated CADFEKO model for the
magic tee.
The magic tee is a four-port, 180° hybrid splitter, realised in waveguide. Like all of the coupler
and splitter structures, the magic tee can be used as a power combiner or a divider. It is ideally
lossless, so that all power into one port can be assumed to exit the remaining ports. A signal
incident on the sigma port (port 1) splits equally between ports 3 and 4, with the resulting signals
being in phase. On the other hand, a signal incident on the delta port (port 2) also splits equally
between ports 3 and 4, but the resulting signals are 180° out of phase. Ports 3 and 4 are
sometimes called the co-linear ports as these are the only two ports that are in line with each
other.
Figure 3.1: CADFEKO magic tee model

11. 11
3.1:Simulation Scenarios:
The magic tee depicted in Figure 1 was simulated in FEKO for two scenarios:
 Driving the sigma port (port 1) with a FEM modal excitation.
 Driving the delta port (port 2) with a FEM modal excitation.
The results that are presented below depict the following for both scenarios:
 Standing wave patterns with phase indicated by arrows.
 S-parameter plots depicting the phase difference between ports 3 and 4.
3.2:Simulation Results
Sigma port driven
Figure 3.2: Sigma port driven - standing wave patterns
(a) Horisontal plane plotted (b) Vertical plane plotted
Animate Animate

12. Inspection of the phase of the standing waves in Figure 2(a) shows that the energy flowing out of
ports 3 and 4 are indeed in phase. Figure 2(b) illustrates that almost no energy is transmitted to
the delta port when the sigma port is driven.
12
Delta port driven
Figure 3.3: Delta port driven - standing wave patterns
(a) Horisontal plane plotted (b) Vertical plane plotted
Animate Animate

13. Inspection of the phase of the standing waves in Figure 3(a) shows that the energy flowing out of
ports 3 and 4 are indeed out of phase. Figure 3(a) also shows that almost no energy flows to the
sigma port while the delta port is driven as indicated in Figure 3(b).
13
S-parameters
Figure 3.4: S-parameter phase comparison between ports 3 and 4
(a) Sigma port driven (b) Delta port driven
Inspection of Figure 4(a) reveals that ports 3 and 4 are always in phase when the sigma port is
driven, while inspection of Figure 4(b) reveals that ports 3 and 4 are indeed always 180° out of
phase when the delta port is driven.

14. 14
Chapter:4
Tee Junction:-
In microwave circuits a wave guide or co-axial line junction with three independent ports is
commonly referred toa as a tee junction. From the s parameter theory of a microwave junction it
is evident that a tee junction should be characterizied by a matrix of third order containing nine
elements, six of which should be independent. The characteristics of a three port junction can be
explained by three theroems of the teejunction.Thesetheroems are derived from the equivalent
circuit representation of the tee junction.
1.A short circuit may always be in one of the arms of a three port junction in such a way that no
power can be transferred through the other two arms.
2.If the junction is symmetric about one of its arms, a short circuit can always be placed in that
arm so that no refectionsoccour in power transmission between the other two arms.
3.It is impossible for a general three port junction of arbitrary symmetry to present matched
impedences at all three arms.
4.1:Scattering matrix:-
Tee is a three port device, so the scattering matrix in general be written as
S11 S12 S13
[S]= S21 S22 S23
S31 S32 S33
Since [S] is symmetric, we haveS12=S21, S13=S31, S23=S32 and more ever tee is
symmetric about port 1 and 2 (symmetric arms) S1=S22m using these properties of tee
junction would become

15. S11 S12 S13
[S]= S12 S11 S23
S13 S23 S33
15
4.2:E-plane tee(series tee):-
An E- plane tee is a wave guide tee in which the axis of its side arm is parallel to the E field of
the main guide. If the collinear arms are symmetric about the side arm, there are two different
transmission characteristics. If the E plane tee is perfectly matched with the aid of tuners or
inductive or capacitive windows at the junction, the diagonal components of scattering matrix,
S11,S22,and S33, are zero because there will be no reflection.
4.2.1Scattering matrix:-
E-type T-junction is the three port device, the scattering matrix will be the order of 3*3
S11 S12 S13
[S]= S21 S22 S23
S31 S32 S33
If an input energy is fed at port,(3) than o/p at ports (1) and (2) are out of phase by 180 deg.
The scattering coefficient S23 = -S13
From symmetric property Sij = Sji
S12 = S21, S13 = S31, S23 = S32

16. By substituting the above properties in [s] matrix, we get
S11 S12 S13
[S] = S12 S22 S13 …………4.1
S13 S13 0
S33 = 0, if the port (3) is perfectly matched.
Now by using unitary property [S].[S]* = [I]
S11 S12 S13 S*11 S*12 S*13 1 0 0
[S] = S12 S22 S13 S*12 S*22 S*13 = 0 1 0
S13 S13 0 S*13 S*13 0 0 0 1
16
Multiplying we get
R1C1(Row 1: column 1): S11.S*11+S12. S*12+S13. S*1
| S11| ² + | S12 | ²+ |S13 |² = 1 ………..…..4.2
R2*C2: |S12|² +|S22|² + |S13|² =1 ………..….4.3
R3*C3: |S13|² + |S13|² =1 ………...…4.4
R3*C1:S13*S*11 – S13*S*12= 0 ………….4.5
By equation (2) and (3), we get
S11 = S22 ………….4.6
By equation (4)
2|S13|² = 1
|S13|² =1/2
S13=( 1/√2 ) …….……..4.7

17. 17
From equation (5)
S13(S*11 –S*12) = 0
since S13≠ 0, S*11 –S*12 = 0
S11=S12=S22 …….……..4.8
By putting the value from equation (6, 7 and 8) in the equation (2)
|S11|² + |S11|² + ½ = 1
2|S11|² = ½ or S11 = 1/2 …………4.9
By substituting the value from (7,8 and 9) in equation (1)
1/2 1/2 1/√2
[S]= 1/2 1/2 - 1/√2
1/√2 - 1/√2 0
Since ΙbΙ=[s][a]
B1 1/2 1/2 1/√2 [ a1]
B2 = 1/2 1/2 1/√2 [a2]
B3 1/√2 - 1/√2 0 [a3]
B1=1/2* a1+1/2* a2+1/√2 *a3
B2=1/2* a1+1/2* a2+1/√2 *a3
B3= 1/√2 *a1+1/√2 *a2

18. Figure 4.1: E-plane tee
Figure 4.2: E-plane tee
18

19. 19
4.3:H-plane tee (shunt tee):-
An H-plane tee is a wave guide tee in which the axis of its side arm is “shunting” the E- field or
parallel to the H field of the main guide.
Figure 4.3: H-plane tee
Figure 4.4: H-plane tee
It can be seen that if two input waves are fed into port-1 and port-2 of the collinear arm, the
output wave at port-3 will be in phase and additive. On the other hand, if the input is fed into
port-3,the wave will split equally into port-1 and port-2 in phase and in the same magnitude.
Therefore the S matrix of the H plane tee is similar.

20. 20
4.3.1:Scattering matrix:-
When the i/p is fed from side arm (port-3) the wave appearing at the two ports -1 and 2 of
collinear arm will be in phase and in the same magnitude, that S13=S23 Thus its [S] matrix is
written as
S11 S12 S13
[S]= S21 S22 S23
S31 S32 S33
From the symmetric property of ‘s’ matrix,
Sij = Sji , S12=S21, S13= S31, S23 = S32, S13 = S23 , S33 = 0
By substituting the s-parameters value , we get
S11 S12 S13
[S]= S12 S22 S13
S13 S13 0
By using unitary property [S] [S]* = [I]
S11 S12 S13 S*11 S*12 S*13 1 0 0
[S]= S21 S22 S23 S*12 S*22 S*13 = 0 1 0
S31 S32 S33 S*13 S*13 0 0 0 1
R1*C1: |S11|² +|S12|² + |S13|² =1 …………….....4.10.
R2*C2: |S12|² + |S22|² + |S13|² =1 .………..............4..11
R3C1: S13S *11+ S13S *12 = 0 .………………4.12
R3*C3: |S13|² +|S13|² =1 …………..…4.13
or 2|S13|² = |S13|= 1/√2 ……………....4.14

21. 21
By using eqn (10) and (11)
|S11|² =|S22|²
S11=S22 ……………4.15.
By solving eq. (12)
S13(S*11+S*12)=0
Since S13 # 0, S*11+S*12 = 0
Or S11= -S12 or S11 = -S12 …... ..............4.16
By using these values in eqn (10), we get
|S11|² + |S11|² +| 1/√2 |² =1
Or 2 |S11|²= 1/2 …………4.17
S12= -S11 S12= -1/2 and S22 = 1/2
By putting the values of S11,S12, S13 and S22, in following
S11 S12 S13
[S]= S12 S22 S13
S13 S13 0

22. 1/2 -1/2 1/√2
[S]= -1/2 1/2 1/√2 ……….4.18
1/√2 1/√2 0
22
It is known that [b] = [S] [a]
B1 1/2 -1/2 1/√2 [ a1]
B2 = -1/2 1/2 1/√2 [a2]
B3 1/√2 1/√2 0 [a3]
b1=1/2*a1-1/2*a2+ 1/√2 *a3 …..…4.19
b2=-1/2*a1-1/2*a2+ 1/√2 *a3 ……….4.20
b3= 1/√2 *a1+ 1/√2 *a2 …........4.21

23. 23
4.4:Magic Tees (HybridTees):-
A magic tee is a combination of E-plane tee and H-plane tee. The magic tee has several
characteristics.
Figure 4.5: Magic tee
Figure 4.6: Magic tee

24. 24
4.4.1:Characteristics:-
1. If two waves of equal magnitude and the same phase are fed into port 1 and port 2, the output
will be zero at port 3 and additive at port 4
2. If a wave is fed into port 4 (H arm), it will be divided equally between port 1 and port 2 of
the collinear arms and will not appear at port 3 (E arm).
3. If a wave is fed into port 3 (E arm), it will produce an output of equal magnitude and
opposite phase at port 1 and port 2. Output at port 4 is zero i.e S43 = S34 = 0.
4. If a wave is fed into one of the collinear arms at port 1 or port 2, it will not appear in the
other collinear arm at port 2 or port 1 because the E arm causes a phase delay while the H
arm causes the phase advance. i.e S12 = S21 = 0.
Therefore the S matrix of a magic tee can be expressed asThe magic tee is commonly used
for mixing,duplexing, and impedencemeasurments. Suppose, for ex- there are two identical
radar transmitters in equipment stock. A particular application requires twice more input
power to an antenna than either transmitter can deliver. A magic tee may be used to couple
the two transmitter to the antenna in such a way that the transmitter do not load each other.
The two transmitters should be connected to ports-3and 4. Transmitter 1, connected to port 3,
causes a wave to emanate from port-1 and another to emanate from port-2;these waves are
equal in magnitude but opposite in phase. Similarly, transmitter 2, connected to port -4,gives
rise to a wave at port-1 and another at port-2, both equal in magnitude and in phase. At port-1
the two opposite waves cancel each other. At port-2 the two in phase waves add together;so
double output power at port-2 is obtained for the antenna as shown in

25. Figure 4.7: Magic tee
25
4.4.2:Scattering matrix:-
A hybrid tee is a four port device so in general [S] matrix is
S11 S12 S13 S14 …… …………4.22
[S]= S21 S22 S23 S24
S31 S32 S33 S34
S41 S42 S43 S44
S24 = -S14 ( E-plane Tee section)
S23 = S13(H-plane Tee section)
S34 = S43 = 0
Sij = Sji ( Symmetric property)
S12= S21, S13= S31, S23 = S32, S34= S43 S24=S42 S41=S14
S33 = S44 =0 (port (3) and port (4) are perfectly matched, to the junction)
Substituting the values in eqn (28)
S11 S12 S13 S14 ……..………………4.23
[S]= S12 S22 S13 -S14
S13 S13 0 0
S14 -S14 0 0
[S][S]* =[I] (By unitary property)

26. S11 S12 S13 S14 S*11 S*12 S*13 S*14 1 0 0 0
[S]= S12 S22 S13 -S14 S*12 S*22 S*13 -S*14 = 0 1 0 0
S13 S13 0 0 S*13 S*13 0 0 0 0 1 0
S14 -S14 0 0 S*14 - S*14 0 0 0 0 0 1
26
Solving above matrix eqn, we get
R1*C1 = |S11|² +|S12|² + |S13|² +|S14|² =1 ………………….4.24
R1*C2 = |S12|² +|S22|² + |S13|² +|S14|² =1 ………………….4.25
R3*C3 = |S13|² +|S13|² = 1 …………………..4.26
R4*C4 = |S14|² +|S14|² = 1 …………………..4.27
From the above eqn (26) and (27)
S13= 1/√2 ………………….4.28
S14= 1/√2 ………………….4.29
By eqn (24) and (25) S11= S22 …………………..4.30
By putting all there values in eqn (24)
|S11|² +|S12|²+ ½+1/2=1
|S11|² +|S12|² =0
S11=S12 =0
S22 =0

27. 27
Chapter: 5
Advantages of Magic tee:
1. Power delivered to one of the output ports becomes independent of the
termination at the other o/p port because of the decoupling property of the o/p
ports.
2. In three port junction’s devices such as the E- or H- plane tees, power division
between ports depends on termination existing at the respective o/p ports,
whereas in case of magic tees all the o/p ports are perfectly matched. Hence
power division between the ports is independent of the terminations.
DisAdvantages of Magic tee:
When a signal is applied to any arm of a magic tee, the flow of energy in the o/p
arms is affected by reflections. Reflections are caused by impedence mismatching at the
junctions. These reflections are the cause of the two major disadvantage of the magic tee.
1. The reflections represent a power loss since all the energy fed into the junction
doesnot reach the load which the arms feed.
2. The reflections produce standing waves that can result in internal arcing.
Thus the maximum power a magic tee can handle is greatly reduced.

28. 28
Chapter: 6
Application:-
1.Impedence bridge
2. Antenna duplxer
3.Balanced mixer
4. Four port circulators in magic tee
5.1.Impedence bridge:-
A magic tee is frequently employed in microwave impedence measuring bridges.These bridges
are similar to low freq. wheatstone bridge: power from a matched source is fed in the H- arm(3)
of the magic tee. A standard variable impedence is connected to port-1 as reference impedence
and arm -2 is terminated in the impedence to be measured. A matched detector is connected to
prt-4 (E arm) to receive power reflected from arms 1 and 2. These powers will be out of 180
phase. The reffernceimpedence is adjusted so as to have no signal in the detector. Under this
condition the power reflected from the reference impedence and reaching the detector(half of the
reflected power) equals the power reflected from the unknown impedence reaching the detector.
Because the two powers are out of 180 phase and the lengths of the two ports are equal(on in
other words, when the bridge is balanced)

29. Figure 6.1: Imedencebridge using magic tee
29
5.2.Antenna duplexer:-
A duplxer system couples two circuits to the same load but avoids mutual coupling. The same
antenna is used for the transmitter as well as receiver but the transmitter power is kept out of the
receiver and vice versa. In this system the matched generator and matched detector and
connected to arms 1 ans 2 respectively. H arm(3) is terminated in a matched load and E arm (4)
is connected to the matched antenna . In this case, power received by the antenna is coupled to
the detector.Due to the coupling properties of the magic tee. In this tee, since half of power is
transmitted, it is useful at low power levels.

30. Figure 6.2:Magic tee antenna duplexer
30
5.3.Balanced mixer:-
A balanced microwave mixer is used in superohetrodynerecievers to balance out the local
oscillator noise at the i/p of the intermediate amplifier.Thesuperoheterodyne mixer receives
signals from both the antenna and local oscillator of the receiver but the local oscillator power is
prevented from reaching the antenna by the isolation properties of E and H arms.

31. Figure 6.3: Magic teeBalanced mixer
5.4 Four port circulators in magic tee:-
A circulator is a multiport device that has property that a wave incident in port 1 is coupled
into port 2 only, a wave incident in port 2is coupled into port 3 only, and so on. The ideal
circulator is also a matched device with all ports except one terminated in matched loads, the
i/p impedence of the remaining port is equal to the characteristics impedence of its i/p line ,
and hence presents a matched load.
31

32. A four port circulator may be constructed from two magic tee or hybrid junctions and a
gyrator. The gyrator produces an additional phase shift of 180 for propagation in the
direction from a to b. For propogation from b to a, and also from c to d or d to c, the
electrical path lenths are equal.
Figure 6.4: Four port circulator
32

33. 33
Chapter-7
Conclusion:
The magic tee is a four-port, 0° or 180° hybrid splitter, realized in waveguide. An
incident signal at the sigma port (H-arms) splits equally between the co-linear ports
with the resulting signals in phase. On the other hand, a signal incident on the delta
port (E-arms) also splits equally between collinear ports, but the resulting signals are180° out of
phase. Typical operatingbandwidth of magic-T can cover 20%. If, by means of a suitable internal
structure, the E-plane (difference) and H-plane (sum) ports are simultaneously matched, then
by symmetry, reciprocity and conservation of energyit may be shown that the two collinear ports
are also matched, and are magically isolated from each other.
The E-field of the dominant mode in each port is perpendicular to the broad wall of
the waveguide. The signals in the E-plane and H-plane ports therefore have orthogonal
polarizations, and so (considering the symmetry of the structure) there can be no communication
between these two ports.
For a signal entering the H-plane port, a well-designed matching structure will prevent any of the
power in the signal being reflected back out of the same port. As there can be no communication
with the E-plane port, and again considering the symmetry of the structure, then the power in this
signal must be divided equally between the two collinear ports.
Similarly for the E-plane port, if the matching structure eliminates any reflection from this port,
then the power entering it must be divided equally between the two collinear ports.
Now by reciprocity, the coupling between any pair of ports is the same in either direction (the
scattering matrix is symmetric). So if the H-plane port is matched, then half the power entering
either one of the collinear ports will leave by the H-plane port. If the E-plane port is also
matched, then half power will leave by the E-plane port. In this circumstance, there is no power
'left over' either to be reflected out of the first collinear port or to be transmitted to the other
collinear port. Despite apparently being in direct communication with each other, the two
collinear ports are magically isolated.

34. REFERENCES
1.http://www.radio-electronics.com/info/antennas/waveguide/waveguide-junctions-e-
34
h-type-magic.php
2. www.elmika.com/magic_tee.html
3. www.google.com
4. www.ece.unm.edu/summa/notes/CESDN/CESDN51.pd
5.www.miwavetechno.com/waveguide-bends-tees.htm
6. ramnikmota.webs.com/documents/microwave%20hybrid%20circuits.ppt
7. nurhidayahmoktar.weebly.com/uploads/6/4/8/7/6487407/2_2.ppt
8. educypedia.karadimov.info/library/423micro.ppt
9.Fundamental of microwave and radar engineering by k.k sharma