MTD Microwave Techniques and Devices MODULE I&II PART2

8/7/2019 MTD Microwave Techniques and Devices MODULE I&II PART2

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Fig.G.G E-plane Tee.When TEIOmode is made to propagate into port ti),the two outputsat port ~ and $ will have a phase shift of 180. as shown in Fig. 6.7.Since the electric field lines change their direction when they come outof port ~ and $, it is called a E-plane Tee. E-plane Tee is a voltage orseries junction symmetrical about the central arm. Hence any signalsthat is to be split or any two signal that are to be combined will be fedfrom the E arm. .


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1. (8) is a 3 X3 matrix since there are 3 ports:[

81i 812 813

](8) = 821 822 823831 832 8332~ The Scattering coefficient823 =- 813 ...(6.20)Since outputs at ports (i)and e are out of ph~se by 180. withan input at port 6).

-3. If port 6)is perfectly matched to the junction.833 = 0

4. From symmetricproperty 8u = 8jj:. 812 = 821

813 = 831823 = 832 ...(6.22)

With the above properties (Eq. 6.21 and 6.22), (8) becomes,

[811 \ 812 813

][8J = 812 822 -813

813 -813' 0-5. From unitary property, [8].[8J*= [n

[811 812 813

]

-

[8~1 8~2 S~3

]

-[l

812 822 813 812 822 813 - 0* *813 813 0 813 813 0, 0

181112+ 181212+ 181312 = 1181212+ 182212+181312 = 1

181312+ 181312 = 1

i.e.,

R1C1 :R2C2:R3C3: * *R3 C1 : 813.811 - 813 812 = 0Equating Eqs. 6.24and 6.25we get

811 = 822From Eq. 6.26, 1813 = ~

or

* *From Eq. 6.27,813 (811- 812) = 0 or 811 = 812,=.822Using these values (Eqs. 6.28 to 6.30) in Eq. 6.24

181112+ISl112~l = 11 - 12181112::::- or 811::::-2 2

...(6.21)

...(6.23)

0 0

]1 00 1

...(6.24)

...(6.25)

...(6.26)...(6.27)...(6.28)...(6.29)...(6.30)

...(6.31)


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Substituting the values from Eq. 6.29 to 6.31, the [8] matrix ofEq.6.23 becomes,

...(6.32)

We know, (from Eq. 6.3)[b]= [8] [a]

[

bl

]

~ ~ i[

al

l1 1 -1b2 = "2 "2 ~ a2

ba i ~ 0 aa1 1 1bl = - al + - a2 + - aa2 2 ...f21 1 1b2 = -al+-a2--aa2 2 ...f2

.. ...(6.33)

.. ...(6.34)...(6.35)

ba = ~al-~a2...f2 ...f2 ...(6.36)Case 1 : al = a2 = 0, aa "# 0

1 1bl = ~ aa ; b2 = - ~ aa ; ba = 0

i.e., An input at port EDequally divides between (i),and @but introducesa phase shift of 180. between the two outputs. Hence E-plane Tee alsoacts as a 3 dB splitter.Case 2 : al = a2 = a,aa= 0

Substituting again in Eqs. 6.34 to 6.36, we geta a a a 1 1

/' bl = "2+"2 ; b2 = "2+"2 ; ba = 12 a - ~ a = 0i.e., equalinputs at port (i)and port ~ result in no output at port G>Case 3 : al "# 0, a2 = 0, aa = 0 LLHence b - al. b - al . b -~ .{,

, I - 2 ' 2 - 2' a - ...f2/~...

1 1 1- -2 21 1 -1[8] = 1-21 -1 0


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6.3.3 E-H Plane {Hybrid or Magic} TeeHere rectangular slots are cut both along the width and breadth of along waveguide and side arms are attached as 5hown in Fig. 6.8a. Ports~ and @are collinear arms, port @is the H-arm, and port @is the E-arm.

Such a device became necessary because ofthe difficulty ofobtaininga completely matched three port Tee junction. This four port hybrid Teejunction combines the power dividing properties of both H-plane Teeand E-plane Tee as shown in Fig. 6.8b and has the advantage of beingcompletely matched at all its ports. This has several useful applicationsas will be seen later. Using the properties of E-H plane Tee, itsscattering matrix can be obtained as follows.

(a)--- Signal into. l E-arm

~ort 4

f f ~ort . 1 E Po~:t~ H tOutput Port 3 Output

signal/signaltSignal intoH-arm(b)

Fig. 6.8


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.~ ~ . . r. . . . . .~ r. . r.r. .1.. lS1 is a 4 x 4 matrix since tnere are 4 ports

[

811 812 813 814

][8] = 821 822 823 824831 832 833 834

841 842 843 8442. Because ofH-plane Tee section

823 = 8133. Because of E-plane Tee section

824 = -814 ...(6.39)4. Because of geometry ofthe junction an input at port @cannotcome out of port ~ since they are isolated ports and vice versa

:. 834 = 843 = 0 ...(6.40)5. From symmetricproperty, 8ij = 8ji

812 = 821 ; 813 = 831 ; 823 = 832;834 = 843; 824 = 842; 841 = 814 ...(6.41)6. If ports Ci)and ~ are perfectly matched to the junction.833 = 844 = 0 ...(6.42)Substituting the above properties from Eqs. 6.38 to 6.42 in Eq.6.37, we get

[

811 812 813[8] = 812 822 813813 813 0

814 -814 07. Fromunitary property, [8)[8]* =

i.e.,

814

]S~[1]

I81112+ I81212 + 1 81312 + I81412= 1181212+ 182212+ 181312+ 181412 = 1

18131'2+ 181312 = 1181412+ I81412 = 1

RICI:R2C2:R3C3:R4C. :From Eq. 6.46 andEq. 6.47,

...(6.37)

...(6.38)

...(6.43)

100 00 1000 0 1 0000 1

...(6.44)

...(6.45)

...(6.46)

...(6.47)

811 812 813 ,* * * *814 811 812 813 814. 1812 822 813 -814 * * * *812 822 813 -814.e.;. 1=813 813 0 0 813 813 0 0

814 -S14 0 0 814 -S14 0 0


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1. [8] is a 4 x 4 matrix since there are 4 ports

[

811 812 813 814

][8] = 821 822 823 824831 832 833 834

841 842 843 8442. Because of H-plane Tee section

823 = 8133. Because of E-plane Tee section824 = -814 ...(6.39)

4. Because of geometry ofthe junction an input at port @cannotcome out of port ~ since they are isolated ports and vice versa:. 834 = 843 = 0 ...(6.40)

5. From symmetric property, 8ij = 8ji812 = 821; 813 = 831; 823 = 832;834 = 843; 824 = 842; 841 = 814 ...(6.41)

6. Ifports


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pomparing Eqs. 6.44 and 6.45, we get811 = 822 (- ...(6.50)

Using these values from Eqs. 6.48 and 6.49 in Eq. 6.44 we get,181112+181212+~+~ = 1

181112+ 181212= 0811 = 812 = 0 ...(6.51)

:. From Eq. 6.45, 822 =:=0 ...(6.52)This means ports (i)and @are also perfectly matched to the junction".Hence in any four port junction, if any two ports are perfectly matchedto the junction, then the remaining two ports are automatically matched

to the junction. Such ajunction where in all the four ports are perfectlymatched to the junction is called a Magic Tee.The [8] of Magic Tee is obtained by substituting the scatteringparameters from Eqs. 6.48 to 6.52 in Eq. 6.43.

1 1~ ~1 112 -~

..i.e.,

[8] = 1 1~121 1~ -~ 0[8] [a] (from Eq. 6.3)

1 112 12" al1 1:J2 - \72" a2

0 0

...(6.53)0 00 0

0

0 01la3

0 0

0 01la4

0 01 1:J2121 112 - \72

} ...(6.54) .

1 1b1 = ~(a3+a4); b3 = ::J2(al+a2)1 1b2 =~ (a3- a4); b4 = :.r2 (al - a2)

Using Eq. 6.54, we look at the properties of Magic Tee for someimportant cases.Case 1 : a3 'fI:0, al = a2 = a4 = 0

Substituting these in Eq. 6.54, we get,

..

Weknowthat, [b]=rb1b2

i.e., I 1=b3b4


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a3 a3bl = "::]2; b2 = ~; b3 = b4 = 0

This is the property ofH-plane Tee.Case 2 : a4 :F-0, al = a2 ::;:a3 = 0

a4 a4. . bl = ~; b2 = -12; b3 = b4 = 0This is the property of E-plane Tee.

Case 3 : al :F-0 , a2 = a3 = a4 = 0al al:. bl = 0; b2 = 0; b3 = ~; b4 = :J2

i.e., when power is fed into port (i), nothing comes out of port @eventhough they are collinear ports (Magic!!). Hence ports (i) and (2)arecalled isolated ports. Similarly an input at port @cannot come out atport (i). Similarly E and H ports are isolated ports.Case 4 : a3 = a4, al = a2 = 0

1Then bl = ~ (2 a3) ; b2 = 0; b3 = b4 = 0This is nothing but the additive property. Equal inputs at ports 6)and (4) result in an output at port (i)(in phase and equal in amplitude).

Case 5 : ' al = a2, a3 = a4 = 0 ;1

bl = 0 = b2 = b4; b3 = ~ (2al)that is equal inputs at ports (i) and ~ results in an output at port 6)(additive property) and no outputs at ports (i), @and~. This is similarto case 4.

..

6.3.4 Applications of Magic TeeA magic Tee has several applications. A few of them have beendiscussed here.(a) Measurement ofImpedance : A Magic Tee has been used in theform of a bridge, as shown in Fig. 6.9 for measuring impedance.

Microwave source is connected in arm G>and a null detector in arm~. The unknown impedance is connected in arm (2)and a standardvariable known impedance in arm (i). Using the properties of Magic Tee,the power from microwave source (a3)gets divided equally between arms(i) and (2) (~) (to the unknown impedance and standard variableimpedances). These impedances are not equal to char~cteristicimpedance Zo and hence there will be reflections from arms (i)and (2). IfPl and P2are the reflection coefficients, powers P~3 and P~ enter the


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@)

P1- refl~0 \\ .1 03j2 \\ j2

o~Unknownimpedance

CDI Z1Standard variableknown impedance

Fig. 6.9Magic Tee for measurement of impedances.Magic Tee junction from arms CDan~ as shown in Fig. 6.9. Theresultant wave into arm @ i.e., the null detector can be calculated asfollows: -

The net wave reaching the mill detector (Refer Fig. 6.9)1(1

J1(1

)1

= ~ /-12.~apl -:v2 12 aapz = 2' aa (pl - pz)For perfect balancing of the bridge (null detection) Eq. 6.55 isequated t6-~ro. .

...(6.55)

.~12' aa (pl - pz) = 0Pl - pz = 0 or Pl = pzZl - Zz - Zz - ZzZl +Zz - Zz+Zz

Zl = ZzRl + j Xl = Rz + j XzRl = Rz and Xl = Xz.

Thus the unknown impedance can be measured by adjusting thestandard variable impedance till the bridge is balanced and bothimpedances become equal.(b) Magic Tee as a Duplexer : The transmitter and receiver areconnected in ports @ and CDespectively, antenna in the E-arm or port

t.e.,or

or

..

i.e.,or

@03Pj -IT-3P2,j2coeff I Z, L 1 p,'efl coeff 01 Z,o3P1 j2 3PZ - @2

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MTD Microwave Techniques and Devices MODULE I&II PART2