Microwave and Radar Engineering_M. Kulkarni

Scilab Textbook Companion for Microwave and Radar Engineering by M. Kulkarni1 Created by Chandawar Saichander ECE Electronics Engineering SASTRA UNIVERSITY College Teacher N. Raju Cross-Checked by K. V. P. Pradeep June 13, 2014

1 Funded

by a grant from the National Mission on Education through ICT, http://spoken-tutorial.org/NMEICT-Intro. This Textbook Companion and Scilab codes written in it can be downloaded from the ”Textbook Companion Project” section at the website http://scilab.in

Book Description Title: Microwave and Radar Engineering Author: M. Kulkarni Publisher: Umesh Publications, New Delhi Edition: 3 Year: 2008 ISBN: 81-88114-00-6

1

Scilab numbering policy used in this document and the relation to the above book. Exa Example (Solved example) Eqn Equation (Particular equation of the above book) AP Appendix to Example(Scilab Code that is an Appednix to a particular Example of the above book) For example, Exa 3.51 means solved example 3.51 of this book. Sec 2.3 means a scilab code whose theory is explained in Section 2.3 of the book.

2

Contents List of Scilab Codes

4

3 Transmission Lines

7

4 Microwave Transmission Lines

18

5 Cavity Resonators

45

6 Microwave Components

50

7 Microwave Measurements

60

8 Microwave Tubes and Circuits

64

9 Solid State Microwave Devices

83

10 Microwave Communication Systems

95

11 Radars

107

3

List of Scilab Codes Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa

3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13 4.14 4.15 4.16 4.17 4.18

Terminating Impedance . . . . . power . . . . . . . . . . . . . . . phase velocity . . . . . . . . . . power . . . . . . . . . . . . . . . VSWR and Reflection coefficient point of attachment . . . . . . . Terminating Impedance . . . . . VSWR and Impedance . . . . . Reflection loss . . . . . . . . . . Characteristic Impedance . . . . Characteristic Impedance . . . . attenuation and phase constants breakdown power . . . . . . . . . Characteristic Impedance . . . . Characteristic Impedance . . . . ratio of areas . . . . . . . . . . . breadth of the guide . . . . . . . guide wavelength . . . . . . . . . guide wavelength . . . . . . . . . area . . . . . . . . . . . . . . . . possible modes . . . . . . . . . . guide wavelength . . . . . . . . . frequency . . . . . . . . . . . . . guide wavelength . . . . . . . . . possible modes . . . . . . . . . . Characteristic Impedance . . . . guide wavelength . . . . . . . . . proof . . . . . . . . . . . . . . . 4

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

7 8 9 10 11 12 13 14 15 16 18 19 20 21 22 23 25 26 27 29 30 31 32 33 34 35 36 37

Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa

4.19 4.20 4.21 4.22 4.23 4.24 5.1 5.2 5.3 5.4 6.2 6.3 6.4 6.5 6.6 6.7 6.9 6.10 6.11 6.12 6.13 7.1 7.2 7.3 7.4 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 8.10 8.11 8.12 8.13

amount of attenuation . . . . . . max power handling capacity . . maximum power . . . . . . . . . peak value of electric field . . . . breakdown power . . . . . . . . . breakdown power . . . . . . . . . minimum distance . . . . . . . . lowest resonant frequency . . . . resonant frequency . . . . . . . . resonant frequency . . . . . . . . distance to be shifted . . . . . . Scattering parameters . . . . . . powers in the remaining ports . . power . . . . . . . . . . . . . . . Reflected power . . . . . . . . . Scattering matrix . . . . . . . . Scattering matrix . . . . . . . . output powers . . . . . . . . . . coupling isolation directivity . . VSWR . . . . . . . . . . . . . . phase shift . . . . . . . . . . . . measured distance . . . . . . . . VSWR and Reflected power . . . VSWR . . . . . . . . . . . . . . Reflected power . . . . . . . . . electron velocity and etc . . . . . power and etc . . . . . . . . . . efficiency and etc . . . . . . . . . electron velocity and etc . . . . . efficiency and etc . . . . . . . . . electronic efficiency and etc . . . efficiency and etc . . . . . . . . . cyclotron frequency and etc . . . phase velocity and anode voltage electron velocity and etc . . . . . dc electron velocity and etc . . . gap transit angle . . . . . . . . efficiency and etc . . . . . . . . . 5

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

38 39 40 41 42 43 45 46 47 48 50 51 52 53 53 54 55 56 57 57 58 60 61 62 62 64 65 66 67 69 70 72 73 74 75 76 77 78

Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa

8.14 8.15 8.16 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 9.10 9.11 9.12 9.13 10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 10.9 10.10 10.11 10.12 10.13 11.1 11.2 11.3 11.4 11.5 11.6

cyclotron angular frequency efficiency and etc . . . . . . repeller voltage and etc . . frequency . . . . . . . . . . threshold electric field . . . power gain . . . . . . . . . breakdown voltage and etc Avalanche zone velocity . . power gain . . . . . . . . . minimum voltage . . . . . . rational frequency . . . . . efficiency and etc . . . . . . drift time . . . . . . . . . . breakdown voltage and etc max power gain and etc . . gain and etc . . . . . . . . radio horizon . . . . . . . . value of factor . . . . . . . power . . . . . . . . . . . . power . . . . . . . . . . . . antenna beam angle . . . . round trip time . . . . . . . figure of merit . . . . . . . CNR . . . . . . . . . . . . system noise temperature . HPBW . . . . . . . . . . . gain . . . . . . . . . . . . . gain . . . . . . . . . . . . . power gain . . . . . . . . . max range . . . . . . . . . max range . . . . . . . . . RCS . . . . . . . . . . . . . Duty cycle and etc . . . . . max range . . . . . . . . . factor . . . . . . . . . . . .

6

and etc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

80 81 81 83 84 84 85 86 87 88 88 89 90 91 92 93 95 96 97 98 99 100 101 102 102 103 104 105 106 107 108 109 110 111 112

Chapter 3 Transmission Lines

Scilab code Exa 3.1 Terminating Impedance 1 2

3 4 5 6 7 8 9 10

// c h a p t e r −3 p a g e 47 e x a m p l e 3 . 1 // ================================================================== clc ; clear ; Z0 =100; // C h a r a c t e r i s t i c Impedance i n ohms S =5; // V o l t a g e S t a n d i n g Wave R a t i o (VSWR)

//CALCULATION Zm = Z0 * S ; // T e r m a i n a t i n g i m p e d a n c e a t a max o f t h e v o l t a g e s t a n d i n g wave 11 Zl = Zm ; // L o a d i n g Impedance 12 13 14 15 16

//OUTPUT mprintf ( ’ T e r m i n a t i n g i m p e d a n c e a t a maximum o f t h e v o l t a g e s t a n d i n g wave i s Z l= %3 . 0 f ohms ’ , Zl ) ; //====================END OF PROGRAM ======================================== 7

Scilab code Exa 3.2 power 1 2

// c h a p t e r −3 p a g e 48 e x a m p l e 3 . 3 // ==================================================================

3 clc ; 4 clear ; 5 6 R =8; // R e s i s t a n c e o f a t r a n s m i s s i o n l i n e i n ohm/km 7 L =0.002; // I n d u c t a n c e o f a t r a n s m i s s i o n l i n e i n h e n r y

/km 8 C =0.002*(10^( -6) ) ; // C a p a c i t a n c e o f a t r a n s m i s s i o n 9

l i n e in Farads G =0.07*(10^( -6) ) ; // C o n d u c t a n c e o f a t r a n s m i s s i o n l i n e i n s i e m e n s /km f =2000; // F r e q u e n c y i n Hz w =2*( %pi ) * f ; // A n g u l a r F r e q u e n c y i n r a d / s e c Vs =2; // I n p u t V o l t a g e i n v o l t s l =500; // Length o f T r a n s m i s s i o n l i n e i n km

10 11 12 13 14 15 //CALCULATIONS 16 Z0 = sqrt (( R +( w * L *( %i ) ) ) /( G +( w * C *( %i ) ) ) ) ; // 17 18 19 20 21 22 23 24 25

C h a r a c t e r i s t i c Impedance x = real ( Z0 ) ; y = imag ( Z0 ) ; disp ( ’ C h a r a c t e r i s t i c Impedance i n ohms i s ’ ) ; disp ( Z0 ) ; g = sqrt (( R +( w * L *( %i ) ) ) *( G +( w * C *( %i ) ) ) ) ; // P r o p a g a t i o n Constant a = real ( g ) ; // A t t e n u a t i o n C o n s t a n t i n NP/km b = imag ( g ) ; // Phase C o n s t a n t i n r a d /km Is = Vs / Z0 ; I0 = Is * exp ( -( g * l ) ) ; // Load c u r r e n t 8

26 m = sqrt (( real ( I0 ) ) ^2+( imag ( I0 ) ^2) ) ; 27 P =( m ^2) * x ; // Power d e l i v e r e d t o t h e l o a d i n w a t t s 28 29 //OUTPUT 30 mprintf ( ’ \ n A t t e n u a t i o n C o n s t a n t i s a=%1 . 6 f NP/km \

nPhase C o n s t a n t i s b=%1 . 6 f r a d /km \ nPower d e l i v e r e d t o t h e l o a d i s P=%1 . 6 f w a t t s ’ ,a ,b , P ) ; 31 32

//===============END OF PROGRAM ================================

Scilab code Exa 3.3 phase velocity 1 2

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

// c h a p t e r −3 p a g e 48 e x a m p l e 3 . 3 // ================================================================== clc ; clear ; w =4*( %pi ) ; // A n g u l a r F r e q u e n c y i n r a d / s e c b =0.02543; // Phase C o n s t a n t i n r a d /km //CALCULATION Vp = w / b ; // Phase V e l o c i t y i n km/ s e c //OUTPUT mprintf ( ’ Phase V e l o c i t y i s Vp=%3 . 2 f km/ s e c ’ , Vp ) ; //=========END OF PROGRAM=========================

//NOTE:CHECK THE CALCULATION PART GIVEN IN THE TEXTBOOK 18 //GIVEN ANSWER 4 9 4 . 2 2 KM/SEC 19 //GETTING ANSWER 4 9 4 . 1 6 KM/SEC 9


3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

// c h a p t e r −3 p a g e 48 e x a m p l e 3 . 4 // ================================================================== clc ; clear ; f =37.5*10^6; // F r e q u e n c y i n Hz c =3*10^8; // V e l o c i t y o f L i g h t i n m/ s e c l1 =10; // Length o f l i n e i n met Vg =200; // G e n e r a t o r V o l t a g e i n v o l t s ( rms ) Zint =200; // I n t e r n a l R e s i s t a n c e o f G e n e r a t o r i n ohms Z0 =200; // C h a r a c t e r i s t i c Impedance i n ohms Zl =100; // Load i m p e d a n c e i n ohms //CALCULATIONS w = c / f ; //Wave Length i n met b =2*( %pi ) / w ; l1 =(5/4) * w ; // For L o s s l e s s L i n e Zi = Z0 *(( Zl +( Z0 *( %i ) * tan ( b * l1 ) ) ) /( Z0 +( Zl *( %i ) * tan ( b * l1 ) ) ) ) ; // I n p u t Impedance a t G e n e r a t o r end Vs = Vg *( Zi /( Zi + Z0 ) ) ; // V o l t a g e i n l i n e i n v o l t s Is = Vg /( Zi + Z0 ) ; // C u r r e n t i n L i n e drawn from G e n e r a t o r i n amps Ps = Vs * Is ; // Power drawn i n l i n e Pl = Ps ; // For L o s s l e s s L i n e s Power d e l i v e r e d t o l o a d i s e q u a l t o t h e Power drawn i n l i n e Il = sqrt (( Pl / Zl ) ) ; // C u r r e n t f l o w i n g i n t h e l o a d m = real ( Il ) ; // Magnitude o f C u r r e n t f l o w i n g i n t h e load p = imag ( Il ) ; // Phase o f C u r r e n t f l o w i n g i n t h e l o a d

10

27 28

29 30

//CALCULATIONS mprintf ( ’ \ n C u r r e n t drawn from G e n e r a t o r i s I s=%1 . 3 f amps \ nMagnitude o f C u r r e n t f l o w i n g i n t h e l o a d i s m=%1 . 3 f \ nPhase o f C u r r e n t f l o w i n g i n t h e l o a d i s p=%2 . 2 f deg \ nPower d e l i v e r e d t o l o a d i s Pl= %2 . 2 f w a t t s ’ ,Is ,m ,p , Pl ) ; //=========================END OF PROGRAM ==============================================================

Scilab code Exa 3.5 VSWR and Reflection coefficient 1 2

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

// c h a p t e r −3 p a g e 50 e x a m p l e 3 . 5 // ================================================================== clc ; clear ; Z0 =50; // C h a r a c t e r i s t i c Impedance i n ohms f =300*10^6; // F r e q u e n c y i n Hz Zl =50+(50*( %i ) ) ; // T e r m i n a t i n g l o a d i m p e d a n c e i n ohms w =((3*10^8) / f ) ; //Wave Length //CALCULATIONS p =(( Zl - Z0 ) /( Zl + Z0 ) ) ; // R e f l e c t i o n C o e f f i c i e n t ( Complex Form ) y = real ( p ) ; z = imag ( p ) ; x = sqrt ( y ^2+ z ^2) ; // R e f l e c t i o n C o e f f i c i e n t V a l u e s =((1+ x ) /(1 - x ) ) ; // V o l t a g e S t a n d i n g Wave R a t i o (VSWR) //OUTPUT mprintf ( ’ \ n R e f l e c t i o n C o e f f i c i e n t i s x=%1 . 4 f \ 11

n V o l t a g e S t a n d i n g Wave R a t i o (VSWR) i s s=%1 . 2 f ’ ,x , s); 20 21

//===================END OF PROGRAM =====================================

Scilab code Exa 3.6 point of attachment 1 2


3 clc ; 4 clear ; 5 6 Zl =100; // Pure Load r e s i s t a n c e

o f a d i p o l e antenna in ohms 7 Z0 =600; // C h a r a c t e r i s t i c Impedance o f a w i r e f e e d e r i n ohms 8 f =100*10^6; // F r e q u e n c y i n Hz 9 c =3*10^8; // V e l o c i t y o f L i g h t i n m/ s e c 10 11 //CALCULATIONS 12 w = c / f ; //Wave Length i n met 13 l =(( w /(2*( %pi ) ) ) * atan ( sqrt ( Zl / Z0 ) ) ) ; // The p o s i t i o n

o f t h e Stub i n met 14 x = atand ( sqrt (( Zl * Z0 ) ) /( Zl - Z0 ) ) ; 15 y =180+ x ; // I n D e g r e e s 16 l1 =(( w /(2*( %pi ) ) ) * y ) ; // Length o f S h o r t C i r c u i t e d

Stub i n met 17 l0 = l1 *(( %pi ) /180) ; 18 19 20

//OUTPUTS mprintf ( ’ \ nThe P o i n t o f Attachment i s l=%1 . 3 f met \ nLength o f SC Stub i s l 1=%1 . 2 f met ’ ,l , l0 ) ; 12

21 22

//=========================END OF PROGRAM ==============================================================

Scilab code Exa 3.7 Terminating Impedance 1 2


3 clc ; 4 clear ; 5 6 Z0 =50; // C h a r a c t e r i s t i c Impedance i n ohms 7 S =3.2; // V o l t a g e S t a n d i n g Wave R a t i o (VSWR) 8 9 // I t i s p o s s i b l e t o m e a s u r e t h e l o a d i m p e d a n c e

10 11 12 13 14 15 16 17 18 19

if t h e l i n e i s assumed l o s s l e s s , by m e a s u r i n g t h e VSWR, w a v e l e n g t h and t h e d i s t a n c e from t h e l o a d t o t h e n e a r e s t v o l t a g e minimum //CALCULATIONS w =1; // Assume Wavelength i n met Xmin =0.23* w ; // D i s t a n c e from t h e l o a d t o t h e n e a r e s t v o l t a g e minimum i n met b =(2*( %pi ) ) / w ; Zl = Z0 *((1 -( S *( %i ) * tan ( b * Xmin ) ) ) /( S -(( %i ) * tan ( b * Xmin ) ) ) ) ; // Load i m p e d a n c e i n ohms disp ( ’ Load i m p e d a n c e i n ohms i s ’ ) ; disp ( Zl ) ;

//=========================END OF PROGRAM ===================================================

13

20 21

// Note : Check t h e a n s w e r g i v e n i n Text book o n c e . I t h i n k i t i s wrong i n t e x t book . .

Scilab code Exa 3.8 VSWR and Impedance 1 2

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

// c h a p t e r −3 p a g e 51 e x a m p l e 3 . 8 // ================================================================== clc ; clear ; Z0 =50; // C h a r a c t e r i s t i c Impedance i n ohms Zl =100; // Load i m p e d a n c e i n ohms f =300*10^3; // F r e q u e n c y i n Hz Pl =0.05; // Load Power i n w a t t s c =3*10^8; // V e l o c i t y o f L i g h t i n m/ s e c //CALCULATIONS w = c / f ; //Wave Length i n met p =(( Zl - Z0 ) /( Zl + Z0 ) ) ; // R e f l e c t i o n C o e f f i c i e n t S =((1+ p ) /(1 - p ) ) ; // V o l t a g e S t a n d i n g Wave R a t i o (VSWR) // S i n c e Zl >Z0 , f i r s t Vmax i s l o c a t e d a t t h e l o a d and f i r s t Vmin i s l o c a t e d a t Wavelength /4 x1max =0; // P o s i t i o n o f f i r s t Vmax ( l o c a t e d a t t h e l o a d ) from l o a d i n met x1min = w /4; // P o s i t i o n o f f i r s t Vmin from l o a d i n met Vmax = sqrt ( Pl * Zl ) ; // V a l u e o f maximum v o l t a g e i n v o l t s Vmin = Vmax / S ; // V a l u e o f minimum v o l t a g e i n v o l t s Zmax = Z0 * S ; // Impedance a t Vmax i n ohms Zmin = Z0 / S ; // Impedance a t Vmin i n ohms //OUTPUTS 14

26

27 28

mprintf ( ’ \ n V o l t a g e S t a n d i n g Wave R a t i o (VSWR) i s S=%1 . 0 f \ n P o s i t i o n o f f i r s t Vmax from l o a d i s x1max= %d met ( l o c a t e d a t t h e l o a d ) \ n P o s i t i o n o f f i r s t Vmin from l o a d i s x1min=%3 . 0 f met \ nValue o f maximum v o l t a g e i s Vmax=%1 . 2 f v o l t s \ nValue o f minimum v o l t a g e i s Vmin=%1 . 2 f v o l t s \ nImpedance a t Vmax i s Zmax=%3 . 0 f ohms \ nImpedance a t Vmin i s Zmin=%2 . 0 f ohms ’ ,S , x1max , x1min , Vmax , Vmin , Zmax , Zmin ) ; //=========================END OF PROGRAM ==============================================================

Scilab code Exa 3.9 Reflection loss 1 2

3 4 5 6 7 8 9 10 11 12 13 14 15

// c h a p t e r −3 p a g e 52 e x a m p l e 3 . 9 // ================================================================== clc ; clear ; Z0 =600; // C h a r a c t e r i s t i c Impedance i n ohms Zs =50; // G e n e r a t o r i m p e d a n c e i n ohms l =200; // Length o f t r a n s m i s s i o n l i n e i n met Zl =500; // Load i m p e d a n c e i n ohms

//CALCULATIONS p =(( Zl - Z0 ) /( Zl + Z0 ) ) ; // R e f l e c t i o n C o e f f i c i e n t x = abs ( p ) ; Lr =10* log10 (1/(1 - x ^2) ) ; // R e f l e c t i o n l o s s i n dB La =0; // S i n c e t h e l i n e i s l o s s l e s s , a t t e n u a t i o n l o s s i s z e r o dB 16 Lt = La + Lr ; // T r a n s m i s s i o n l o s s i n dB 15

17 Lrt =10* log10 ( x ) ; // Return l o s s i n dB 18 19 //OUTPUT 20 mprintf ( ’ \ n R e f l e c t i o n l o s s i s Lr=%1 . 3 f dB \

n T r a n s m i s s i o n l o s s i s Lt=%1 . 3 f dB \ nReturn l o s s i s L r t=%2 . 3 f dB ’ ,Lr , Lt , Lrt ) ; 21 22

//=========================END OF PROGRAM ==============================================================

Scilab code Exa 3.10 Characteristic Impedance 1 2

// c h a p t e r −3 p a g e 52 e x a m p l e 3 . 1 0 // ==================================================================

3 clc ; 4 clear ; 5 6 f =1000; // F r e q u e n c y i n Hz 7 l =10000; // Length o f open w i r e t r a n s m i s s i o n 8 9 10 11 12 13 14 15 16 17

l i n e in

met z1 =2930; // Magnitude o f a s h o r t c i r c u i t i m p e d a n c e i n ohms p1 =26; // Phase o f a s h o r t c i r c u i t i m p e d a n c e i n deg z2 =260; // Magnitude o f a open c i r c u i t i m p e d a n c e i n ohms p2 = -32; // Phase o f a open c i r c u i t i m p e d a n c e i n deg //CALCULATIONS Zsc =(( z1 * cosd ( p1 ) ) +(( %i ) *( z1 * sind ( p1 ) ) ) ) ; Zoc =(( z2 * cosd ( p2 ) ) +(( %i ) *( z2 * sind ( p2 ) ) ) ) ; Z0 = sqrt ( Zsc * Zoc ) ; // C h a r a c t e r i s t i c Impedance i n ohms disp ( ’ C h a r a c t e r i s t i c Impedance i n ohms i s ’ ) ; [ ro , theta ]= polar ( Z0 ) 16

18 disp ( ro ) ; 19 disp ( theta *180/ %pi ) ; 20 g =((1/ l ) *( atanh ( sqrt ( Zsc / Zoc ) ) ) ) ; // P r o p a g a t i o n

Constant 21 disp ( g ) 22 b = imag ( g ) ; // Phase C o n s t a n t 23 w =2* f *( %pi ) ; // A n g u l a r F r e q u e n c y i n r a d / s e c 24 Vp = w / b ; // Phase V e l o c i t y i n m/ s e c 25 disp ( Vp ) 26 //OUTPUT 27 mprintf ( ’ \ nPhase V e l o c i t y i s Vp=%5 . 2 f m/ s e c ’ , Vp ) ; 28 29 //=========================END OF PROGRAM

============================================================== 30 31 32

// Note : Check t h e c a l c u l a t i o n o n c e

17

Chapter 4 Microwave Transmission Lines


3 4 5 6 7 8 9 10 11 12 13

// c h a p t e r −4 p a g e 141 e x a m p l e 4 . 1 // ================================================================== clc ; clear ; d =0.0049; // D i a m e t e r o f i n n e r c o n d u c t o r i n met D =0.0110; // I n n e r D i a m e t e r o f o u t e r c o n d u c t o r i n met er =2.3; // P o l y e t h y l e n e d i e l e c t r i c c =3*10^8; // V e l o c i t y o f L i g h t i n m/ s e c

//CALCULATIONS x = log ( D / d ) ; L =(2*10^( -1) * x ) ; // I n d u c t a n c e p e r u n i t l e n g t h s i n microH /m 14 C =(55.56*( er / x ) ) ; // The C a p a c i t a n c e p e r u n i t l e n g t h s i n p i c o F /m 15 R0 =( x *(60/ sqrt ( er ) ) ) ; // The C h a r a c t e r i s t i c Impedance i n ohms 16 V =( c / sqrt ( er ) ) /(10^3) ; // The V e l o c i t y o f p r o p a g a t i o n 18

i n Km/ s 17 18 19

20 21

//OUTPUT mprintf ( ’ \ n I n d u c t a n c e p e r u n i t l e n g t h s i s L=%1 . 5 f microH /m \ nThe C a p a c i t a n c e p e r u n i t l e n g t h s i s C= %2 . 2 f p i c o F /m \ nThe C h a r a c t e r i s t i c Impedance i s R0=%2 . 2 f ohms \ nThe V e l o c i t y o f p r o p a g a t i o n i s V= %6 . 2 f Km/ s ’ ,L ,C , R0 , V ) ; //=========================END OF PROGRAM ===================================================

Scilab code Exa 4.2 attenuation and phase constants 1 2


3 clc ; 4 clear ; 5 6 R =0.05; // R e s i s t a n c e i n ohm/m 7 L =0.16173*10^( -6) ; // I n d u c t a n c e p e r u n i t 8 9 10 11 12 13 14

lengths in H /m C =0.15802*10^( -6) ; // The C a p a c i t a n c e p e r u n i t l e n g t h s i n F/m V =197814.14; // The V e l o c i t y o f p r o p a g a t i o n i n Km/ s l =50; // Length o f C o a x i a l L i n e i n met Pin =480; // I n p u t Power t o t h e System i n w a t t s f =3*10^9; // F r e q u e n c y i n Hz c =3*10^5; // V e l o c i t y o f L i g h t i n Km/ s e c e0 =8.854*10^( -12) ; // P e r m i t t i v i t y i n f r e e s p a c e i n F/ m

15

19

16 17 18 19 20 21 22 23 24 25 26

27 28

//CALCULATIONS Z0 = sqrt ( L / C ) ; A =( R /(2* Z0 ) ) ; // A t t e n u a t i o n C o n s t a n t i n NP/m w =(2*( %pi ) * f ) ; // A n g u l a r F r e q u e n c y i n r a d / s e c B =( w * sqrt ( L * C ) ) ; // Phase C o n s t a n t i n r a d /m Vp =(1/ sqrt ( L * C ) ) /(10^3) ; // Phase V e l o c i t y i n Km/ s er =((( c / V ) ^2) / e0 ) ; // R e l a t i v e P e r m i t t i v i t y Pl =(2* Pin * l ) ; // Power L o s s i n w a t t s //OUTPUT mprintf ( ’ \ n A t t e n u a t i o n C o n s t a n t i s A=%1 . 4 f NP/m \ nPhase C o n s t a n t i s B=%4 . 3 f r a d /m \ nPhase V e l o c i t y i s Vp=%4 . 3 f Km/ s \ n R e l a t i v e P e r m i t t i v i t y i s e r= %12 . 2 f \ nPower L o s s i s Pl=%5 . 0 f w a t t s ’ ,A ,B , Vp , er , Pl ) ; //=========================END OF PROGRAM ===========================================

Scilab code Exa 4.3 breakdown power 1 2


3 clc ; 4 clear ; 5 6 // For an a i r f i l l e d c o a x i a l c a b l e 7 f =9.375*10^9; // o p e r a t i n g f r e q u e n c y i n Hz 8 c =3*10^10; // V e l o c i t y o f L i g h t i n cm/ s e c 9 disp ( ’ Assuming a r a t i o o f ( b/ a ) =2.3 and ( b+a ) <(w/ p i )

t o e x c l u d e h i g h e r o r d e r modes and a dominant mode p r o p a g a t i n g ’ ) ; 10 a =0.36432; // l e n g t h o f c o a x i a l c a b l e i n cm 20

11 x =2.3; // r a t i o o f b / a 12 13 //CALCULATION 14 w0 =( c / f ) ; // f r e e s p a c e w a v e l e n g t h i n cm 15 Pbd =(3600*( a ^2) * log ( x ) ) ; // Breakdown power o f a

c o a x i a l c a b l e i n kW 16 17 18 19 20

//OUTPUT mprintf ( ’ \ nBreakdown power o f a c o a x i a l c a b l e i s Pbd =%3 . 0 f kW ’ , Pbd ) ; //=========================END OF PROGRAM ===============================



3 clc ; 4 clear ; 5 6 b =0.3175; // D i s t a n c e b e t w e e n g r o u n d p l a n e s

of strip l i n e i n cm 7 d =0.0539; // D i a m e t e r o f c i r c u l a r c o n d u c t o r i n cm 8 er =2.32; // D i e l e c t r i c C o n s t a n t 9 c =3*10^8; // V e l o c i t y o f L i g h t i n m/ s e c 10 11 //CALCULATION 12 Z0 =((60/ sqrt ( er ) ) * log ((4* b ) /( d *( %pi ) ) ) ) ; //

C h a r a c t e r i s t i c Impedance i n ohms 13 V =( c / sqrt ( er ) ) /(10^3) ; // The V e l o c i t y o f p r o p a g a t i o n i n Km/ s 14

21

15 16

17 18

//OUTPUT mprintf ( ’ \ n C h a r a c t e r i s t i c Impedance i s Z0=%2 . 2 f ohms \ nThe V e l o c i t y o f p r o p a g a t i o n i s V=%5 . 2 f Km/ s ’ , Z0 , V ) ; //=========================END OF PROGRAM ===================================================



3 clc ; 4 clear ; 5 6 // For a m i c r o s t r i p t r a n s m i s s i o n l i n e 7 er =9.7; // r e l a t i v e d i e l e c t r i c c o n s t a n t o f an a l u m i n a

substrate 8 x1 =0.5; //w/h r a t i o i n f i r s t t r a n s m i s s i o n l i n e 9 x2 =5; //w/h r a t i o i n s e c o n d t r a n s m i s s i o n l i n e 10 c =3*10^8; // V e l o c i t y o f L i g h t i n m/ s e c 11 12 //CALCULATION 13 disp ( ’ For c a s e 1 : w/h =0.5 ’ ) ; 14 disp ( ’ S i n c e x1 =0.5 <1 , f o r t h i s we u s e h i g h i m p e d a n c e

a n a l y s i s ’ ); Eeff1 =((( er +1) /2) +(( er -1) /2) *(1/(( sqrt (1+(12/ x1 ) ) ) +(0.04*(1 - x1 ) ^2) ) ) ) ; // E f f e c t i v e d i e l e c t r i c constant 16 Zo1 =((60/ sqrt ( Eeff1 ) ) * log ((8/ x1 ) +( x1 /4) ) ) ; // C h a r a c t e r i s t i c i m p e d a n c e i n ohms 17 V1 =( c / sqrt ( Eeff1 ) ) /10^8; // V e l o c i t y o f p r o p a g a t i o n i n 15

22

1 0 ˆ 8 m/ s e c 18 mprintf ( ’ \ n E f f e c t i v e d i e l e c t r i c c o n s t a n t i s E e f f 1=%1 . 2 f \ n C h a r a c t e r i s t i c i m p e d a n c e i s Zo1=%2 . 2 f ohms \ n V e l o c i t y o f p r o p a g a t i o n i s V1=%1 . 1 f ∗ 1 0 ˆ 8 m/ s e c ’ , Eeff1 , Zo1 , V1 ) ; 19 20 21 22

disp ( ’ For c a s e 2 : w/h=5 ’ ) ; disp ( ’ h e r e x2 >1 ’ ) ; Eeff2 =((( er +1) /2) +(( er -1) /2) *(1/( sqrt (1+(12/ x2 ) ) ) ) ) ; // E f f e c t i v e d i e l e c t r i c c o n s t a n t 23 Zo2 =((120*( %pi ) / sqrt ( Eeff2 ) ) *(1/( x2 +1.393+(0.667* log (1.444+ x2 ) ) ) ) ) ; // C h a r a c t e r i s t i c i m p e d a n c e i n ohms 24 V2 =( c / sqrt ( Eeff2 ) ) /10^8; // V e l o c i t y o f p r o p a g a t i o n i n 1 0 ˆ 8 m/ s e c 25 mprintf ( ’ \ n E f f e c t i v e d i e l e c t r i c c o n s t a n t i s E e f f 2=%1 . 2 f \ n C h a r a c t e r i s t i c i m p e d a n c e i s Zo2=%2 . 2 f ohms \ n V e l o c i t y o f p r o p a g a t i o n i s V2=%1 . 2 f ∗ 1 0 ˆ 8 m/ s e c ’ , Eeff2 , Zo2 , V2 ) ; 26 27

//=========================END OF PROGRAM ===============================

Scilab code Exa 4.6 ratio of areas 1 2


3 clc ; 4 clear ; 5 6 //To c a l c u l a t e

the r a t i o o f c i r c u l a r waveguide cross −s e c t i o n a l area to the r e c t a n g u l a r waveguide cross section 7 disp ( ’ Assuming t h a t b o t h t h e s e w a v e g u i d e s have 23

s i m i l a r or equal c u t o f f f r e q u e n c i e s / wavelengths ’ ) ; 8 9 10

11

12 13 14 15 16 17 18 19

20

disp ( ’ Case1 : When TE wave i s p r o p a g a t e d ’ ) ; disp ( ’ For s t a n d a r d r e c t a n g u l a r w a v e g u i d e s a=2b and For TE11 dominant mode i n c i r c u l a r w a v e g u i d e wc1 =(2( p i ) r ) / 1 . 8 4 1 ’ ) ; disp ( ’ where r i s t h e r a d i u s o f t h e c i r c u l a r w a v e g u i d e and wc1 i s t h e c u t o f f w a v e l e n g t h f o r c i r c u l a r waveguide ’ ); disp ( ’ I t i s g i v e n wc1=wc2 where wc2 i s t h e c u t o f f wavelength f o r r e c t a n g u l a r waveguide ’ ); disp ( ’ For TE10 ( dominant mode ) o f p r o p a g a t i o n i n r e c t a n g u l a r w a v e g u i d e wc2=2a ’ ) ; disp ( ’ S i n c e wc2 =(2 ab ) / ( s q r t ( ( mb) ˆ2+( nb ) ˆ 2 ) ) a s m=1; n =0 f o r TE10 wc2=2ab /b=2a ’ ) ; disp ( ’ By e q u a t i n g wc1=wc2 , we g e t a = 1 . 7 0 6 4 5 r ’ ) ; disp ( ’ For a s t a n d a r d w a v e g u i d e a=2b t h e r e f o r e , b=a /2 ’ ); disp ( ’Now t h e a r e a o f r e c t a n g u l a r w a v e g u i d e=a ∗b=a ∗ a / 2 = 1 . 7 0 6 4 5 r ∗ 1 . 7 0 6 4 5 r / 2 = 1 . 4 5 6 r ˆ2 ’ ) ; disp ( ’ Area o f r e c t a n g u l a r w a v e g u i d e = 1 . 4 5 6 r ˆ2 , Area o f c i r c u l a r w a v e g u i d e =( p i ) ∗ r ˆ2 ’ ) ; disp ( ’ R a t i o o f a r e a o f c i r c u l a r t o a r e a o f r e c t a n g u l a r w a v e g u i d e =( Area o f c i r c u l a r w a v e g u i d e / Area o f r e c t a n g u l a r w a v e g u i d e ) =( p i ∗ r ˆ 2 ) / ( 1 . 4 5 6 r ˆ2) =2.1576873=2.2 ’ ); disp ( ’ T h i s c l e a r l y shows t h a t t h e s p a c e o c c u p i e d by a r e c t a n g u l a r w a v e g u i d e s y s t e m i s l e s s compared t o t h a t f o r a c i r c u l a r w a v e g u i d e s y s t e m . Hence c i r c u l a r w a v e g u i d e s a r e n o t p r e f e r r e d i n some a p p l i c a t i o n s ’ );

21 22 23

disp ( ’ Case2 : When TM wave i s p r o p a g a t e d ’ ) ; disp ( ’ For TM01 mode wc1 =(2∗ p i ∗ r ) / (Pnm) min =(2∗ p i ∗ r ) / Pnm=(2∗ p i ∗ r ) / 2 . 4 0 5 where r i s t h e r a d i u s o f c i r c u l a r w a v e g u i d e wc1 = 2 . 6 1 5 5 r ’ ) ; 24 disp ( ’Now i f wc2 i s t h e w a v e l e n g t h f o r TM11 wave 24

25

26 27

28

29 30

propagating in a standard r e c t a n g u l a r waveguide wc2=wc1 but wc2 =(2 ab ) / s q r t ( aˆ2+b ˆ 2 ) ’ ) ; disp ( ’ For s t a n d a r d w a v e g u i d e s , we know a=2b , wc2 =(2∗2 b∗b ) / s q r t ( 4 bˆ2+b ˆ 2 ) =(4b ˆ 2 ) / s q r t ( 5 b ˆ 2 ) =4b/ s q r t ( 5 ) ’ ); disp ( ’ By e q u a t i n g wc1=wc2 , we g e t 2 . 6 1 5 5 r =4b/ s q r t ( 5 ) =>b = 1 . 4 6 2 1 r ’ ) ; disp ( ’ Area o f r e c t a n g u l a r w a v e g u i d e=b∗b=b ˆ2 but b = 1 . 4 6 2 1 r , s o Area o f r e c t a n g u l a r w a v e g u i d e = ( 1 . 4 6 2 1 r ) ˆ 2 = 2 . 1 3 2 r ˆ2 and Area o f c i r c u l a r w a v e g u i d e= p i ∗ r ˆ2 ’ ) ; disp ( ’ R a t i o o f a r e a o f c i r c u l a r t o a r e a o f r e c t a n g u l a r w a v e g u i d e =( Area o f c i r c u l a r w a v e g u i d e / Area o f r e c t a n g u l a r w a v e g u i d e ) =( p i ∗ r ˆ 2 ) / ( 2 . 1 3 2 r ˆ 2 ) =1.5 ’ ) ; //=========================END OF PROGRAM ===============================

Scilab code Exa 4.7 breadth of the guide 1 2


3 clc ; 4 clear ; 5 6 // For a r e c t a n g u l a r w a v e g u i d e 7 disp ( ’ For a r e c t a n g u l a r w a v e g u i d e t h e dominant mode

i s t h e TE10 mode . TE10 mode can p r o p a g a t e a t a l o we r f r e q u e n c y ’ ); 8 f =9*10^9; // f r e q u e n c y i n Hz 9 wg =4; // g u i d e w a v e l e n g t h i n cm 10 c =3*10^10; // V e l o c i t y o f L i g h t i n cm/ s e c 25

11 disp ( ’ For TE10 mode wc=2a ’ ) ; 12 13 //CALCULATION 14 w0 =( c / f ) ; // f r e e s p a c e w a v e l e n g t h i n cm 15 wc =( w0 / sqrt (1 -( w0 / wg ) ^2) ) ; // C u t o f f w a v e l e n g t h f o r 16 17 18 19 20 21 22 23 24 25 26 27

TE10 mode i n cm disp ( ’ F r e e s p a c e w a v e l e n g t h w0 i n cm i s ’ ) ; disp ( w0 ) ; disp ( ’ C u t o f f w a v e l e n g t h wc i n cm i s ’ ) ; disp ( wc ) ; disp ( ’ S i n c e wc>w0 , t h e wave p r o p a g a t e s ’ ) ; a =( wc /2) ; // l e n g t h o f t h e g u i d e i n cm b =( wc /4) ; // b r e a d t h o f t h e g u i d e i n cm //OUTPUT mprintf ( ’ \ n l e n g t h o f t h e g u i d e i s a=%1 . 0 f cm \ n b r e a d t h o f t h e g u i d e i s b=%1 . 1 f cm ’ ,a , b ) ; //=========================END OF PROGRAM ===============================

Scilab code Exa 4.8 guide wavelength 1 2

3 4 5 6 7 8 9 10

// c h a p t e r −4 p a g e 147 e x a m p l e 4 . 8 // ================================================================== clc ; clear ; a =10; // b r e a d t h o f a r e c t a n g u l a r w a v e g u i d e i n cm f =2.5*10^9; // F r e q u e n c y i n Hz i n TE10 mode c =3*10^10; // V e l o c i t y o f L i g h t i n cm/ s e c //CALCULATION 26

11 12 13 14 15 16 17 18 19

20 21

wc =2* a ; // C u t o f f w a v e l e n g t h f o r TE10 mode i n cm w0 =( c / f ) ; // F r e e s p a c e w a v e l e n g t h i n cm x = sqrt (1 -( w0 / wc ) ^2) ; wg =( w0 / x ) ; // Guide w a v e l e n g t h i n cm Vp =( c / x ) /10^5; // Phase V e l o c i t y i n Km/ s e c Vg =(( c ^2) / Vp ) /10^10; // Group V e l o c i t y i n Km/ s e c //OUTPUT mprintf ( ’ \ n C u t o f f w a v e l e n g t h f o r TE10 mode i s wc=%2 . 0 f cm \ nGuide w a v e l e n g t h i s wg=%2 . 0 f cm \ nPhase V e l o c i t y i s Vp=%7 . 2 f Km/ s e c \ nGroup V e l o c i t y i s Vg=%6 . 2 f Km/ s e c ’ ,wc , wg , Vp , Vg ) ; //=========================END OF PROGRAM ===============================


3 4 5 6 7 8 9 10 11 12

// c h a p t e r −4 p a g e 147 e x a m p l e 4 . 9 // ================================================================== clc ; clear ; f =8.6*10^9; // f r e q u e n c y i n Hz c =3*10^10; // V e l o c i t y o f L i g h t i n cm/ s e c a =2.5; // Length o f a Waveguide i n cm b =1; // Width o f a Waveguide i n cm

//CALCULATION disp ( ’ The c o n d i t i o n f o r t h e wave t o p r o p a g a t e a l o n g a g u i d e i s t h a t wc>w0 . ’ ) ; 13 w0 = c / f ; // f r e e s p a c e w a v e l e n g t h i n cm 14 disp ( ’ F r e e s p a c e w a v e l e n g t h w0 i n cm i s ’ ) ; 27

15 disp ( w0 ) ; 16 disp ( ’ For TE waves , wc=(2 ab / s q r t ( ( mb) ˆ2+( na ) ˆ 2 ) ) ’ ) ; 17 disp ( ’ For TE01 waves ’ ) ; 18 m1 =0; 19 n1 =1; 20 wc1 =((2* a * b ) /( sqrt (( m1 * b ) ^2+( n1 * a ) ^2) ) ) ; // C u t o f f 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43

w a v e l e n g t h f o r TE01 mode i n cm disp ( ’ C u t o f f w a v e l e n g t h f o r TE01 mode i n cm i s ’ ) ; disp ( wc1 ) ; disp ( ’ S i n c e wc f o r TE01=2cm i s n o t g r e a t e r t h a n w0 TE01 , w i l l n o t p r o p a g a t e f o r TE01 mode . ’ ) ; disp ( ’ For TE10 waves ’ ) ; m2 =1; n2 =0; wc2 =((2* a * b ) /( sqrt (( m2 * b ) ^2+( n2 * a ) ^2) ) ) ; // C u t o f f w a v e l e n g t h f o r TE10 mode i n cm disp ( ’ C u t o f f w a v e l e n g t h f o r TE10 mode i n cm i s ’ ) ; disp ( wc2 ) ; disp ( ’ S i n c e wc TE10 > w0 TE10 i s a p o s s i b l e mode . ’ ) ; fc =( c / wc2 ) /10^9; // C u t o f f f r e q u e n c y i n GHz disp ( ’ For TE11 and TM11 waves ’ ) ; m3 =1; n3 =1; wc3 =((2* a * b ) /( sqrt (( m3 * b ) ^2+( n3 * a ) ^2) ) ) ; // C u t o f f w a v e l e n g t h f o r TE11 mode i n cm disp ( ’ C u t o f f w a v e l e n g t h f o r TE11 and TM11 modes i n cm i s ’ ) ; disp ( wc3 ) ; disp ( ’ As wc f o r TE11 and TM11 i s < w0 b o t h TE11 and TM11 do n o t p r o p a g a t e a s h i g h e r modes . ’ ) ; wg =( w0 / sqrt (1 -( w0 / wc2 ) ^2) ) ; // Guide w a v e l e n g t h i n cm disp ( ’ From t h e a b o v e a n a l y s i s we c o n c l u d e t h a t o n l y TE10 mode i s p o s s i b l e ’ ) ; //OUTPUT mprintf ( ’ \ n C u t o f f f r e q u e n c y i s f c=%1 . 0 f GHz \ nGuide w a v e l e n g t h i s wg=%1 . 3 f cm ’ ,fc , wg ) ;

44

28

45

//=========================END OF PROGRAM ===============================

Scilab code Exa 4.10 area 1 2


3 clc ; 4 clear ; 5 6 // For an a i r

f i l l e d c i r c u l a r Waveguide i n t h e dominant mode 7 c =3*10^10; // V e l o c i t y o f L i g h t i n cm/ s e c 8 disp ( ’ For an a i r f i l l e d c i r c u l a r Waveguide TE11 i s t h e dominant mode i e p r o p a g a t e d ’ ) ; 9 wc =10; // c u t o f f wave l e n g t h i n cm 10 11 //CALCULATION 12 r =((1.841* wc ) /(2*( %pi ) ) ) ; // r a d i u s 13 14 15 16 17 18 19 20

of circular Waveguide i n cm A =( %pi ) * r ^2; // C r o s s s e c t i o n a l a r e a o f t h e g u i d e i n s q . cms fc =( c / wc ) /10^9; // C u t o f f f r e q u e n c y f o r TE11 mode i n GHz disp ( ’ C u t o f f f r e q u e n c y f o r TE11 mode i n GHz i s ’ ) ; disp ( fc ) ; disp ( ’ F r e q u n c y a b o v e 3GHz can be p r o p a g a t e d t h r o u g h the waveguide ’ ); //OUTPUT mprintf ( ’ \ n C r o s s s e c t i o n a l a r e a o f t h e g u i d e i s A=%2 . 2 f s q . cms ’ ,A ) ;

21

29

22

//=========================END OF PROGRAM ===============================

Scilab code Exa 4.11 possible modes 1 2

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

// c h a p t e r −4 p a g e 149 e x a m p l e 4 . 1 1 // ================================================================== clc ; clear ; // For a r e c t a n g u l a r w a v e g u i d e f =5*10^9; // f r e q u e n c y i n Hz c =3*10^10; // V e l o c i t y o f L i g h t i n cm/ s e c a =4; // Length o f R e c t a n g u l a r Waveguide i n cm b =3; // Width o f R e c t a n g u l a r Waveguide i n cm //CALCULATION disp ( ’ The c o n d i t i o n f o r t h e wave t o p r o p a g a t e a l o n g a g u i d e i s t h a t wc>w0 . ’ ) ; w0 = c / f ; // f r e e s p a c e w a v e l e n g t h i n cm disp ( ’ F r e e s p a c e w a v e l e n g t h w0 i n cm i s ’ ) ; disp ( w0 ) ; disp ( ’ For TE waves , wc=(2 ab / s q r t ( ( mb) ˆ2+( na ) ˆ 2 ) ) ’ ) ; disp ( ’ For TE01 waves ’ ) ; m1 =0; n1 =1; wc1 =((2* a * b ) /( sqrt (( m1 * b ) ^2+( n1 * a ) ^2) ) ) ; // C u t o f f w a v e l e n g t h f o r TE01 mode i n cm disp ( ’ C u t o f f w a v e l e n g t h f o r TE01 mode i n cm i s ’ ) ; disp ( wc1 ) ; disp ( ’ S i n c e wc f o r TE01=6cm i s n o t g r e a t e r t h a n w0 TE01 , w i l l n o t p r o p a g a t e f o r TE01 mode . ’ ) ; disp ( ’ For TE10 waves ’ ) ; 30

26 m2 =1; 27 n2 =0; 28 wc2 =((2* a * b ) /( sqrt (( m2 * b ) ^2+( n2 * a ) ^2) ) ) ; // C u t o f f

w a v e l e n g t h f o r TE10 mode i n cm 29 disp ( ’ C u t o f f w a v e l e n g t h f o r TE10 mode i n cm i s ’ ) ; 30 disp ( wc2 ) ; 31 disp ( ’ S i n c e wc TE10 > w0 TE10 i s a p o s s i b l e mode . ’ ) ; 32 disp ( ’ For TE11 waves ’ ) ; 33 m3 =1; 34 n3 =1; 35 wc3 =((2* a * b ) /( sqrt (( m3 * b ) ^2+( n3 * a ) ^2) ) ) ; // C u t o f f 36 37 38 39 40

w a v e l e n g t h f o r TE11 mode i n cm disp ( ’ C u t o f f w a v e l e n g t h f o r TE11 mode i n cm i s ’ ) ; disp ( wc3 ) ; disp ( ’ As wc TE11 < w0 TE11 d o e s n o t p r o p a g a t e . ’ ) ; //=========================END OF PROGRAM ===============================



3 clc ; 4 clear ; 5 6 // For an a i r

f i l l e d c i r c u l a r Waveguide i n t h e dominant mode 7 D =4; // I n n e r d i a m e t e r o f an a i r f i l l e d c i r c u l a r Waveguide i n cm 8 c =3*10^10; // V e l o c i t y o f L i g h t i n cm/ s e c 9 10

//CALCULATION 31

11 12 13 14 15 16

17 18 19 20 21 22

disp ( ’ The dominant mode i n t h e c i r c u l a r w a v e g u i d e would be l i k e TE11 , wc i s maximum ’ ) ; r = D /2; // r a d i u s i n cm wc =((2*( %pi ) * r ) /1.841) ; // C u t o f f w a v e l e n g t h i n cms fc =( c / wc ) /10^9; // C u t o f f f r e q u e n c y i n GHz mprintf ( ’ \ n C u t o f f w a v e l e n g t h i s wc=%1 . 4 f cms \ n C u t o f f f r e q u e n c y i s f c=%1 . 3 f GHz ’ ,wc , fc ) ; disp ( ’ S i n c e cut − o f f f r e q u e n c y i s 4 . 3 9 5 GHz , f r e q u e n c i e s h i g h e r t h a n f c w i l l be p r o p a g a t e d . Assume a s i g n a l o f f r e q u e n c y o f 5 GHz i s b e i n g propagated ’ ); f =5*10^9; // f r e q u e n c y o f s i g n a l i n Hz w0 =( c / f ) ; // f r e e s p a c e w a v e l e n g t h i n cm wg =( w0 / sqrt (1 -( w0 / wc ) ^2) ) ; // Guide w a v e l e n g t h i n cm mprintf ( ’ \nWave l e n g t h i n t h e g u i d e i s wg=%2 . 2 f cm ’ , wg ) ; //=========================END OF PROGRAM ===============================

Scilab code Exa 4.13 frequency 1 2

3 4 5 6 7 8 9 10 11

// c h a p t e r −4 p a g e 150 e x a m p l e 4 . 1 3 // ================================================================== clc ; clear ; // For a r e c t a n g u l a r w a v e g u i d e i n TE10 mode a =6; // Length o f R e c t a n g u l a r Waveguide i n cm b =4; // Width o f R e c t a n g u l a r Waveguide i n cm c =3*10^10; // V e l o c i t y o f L i g h t i n cm/ s e c x =4.55; // d i s t a n c e b e t w e e n maximum and minimum i n cm

32

12 //CALCULATIONS 13 wc =2* a ; // C u t o f f w a v e l e n g t h f o r a TE10 mode i n cms 14 wg =4* x ; // Guide Wavelength i n cm 15 w0 =( wg / sqrt (1+( wg / wc ) ^2) ) ; // // F r e e s p a c e w a v e l e n g t h

i n cm 16 f =( c / w0 ) /10^9; // F r e q u e n c y o f t h e wave i n GHz 17 18 19 20 21

//OUTPUT mprintf ( ’ \ n F r e q u e n c y o f t h e wave i s f=%1 . 3 f GHz ’ ,f ) ; //=========================END OF PROGRAM ===============================


3 4 5 6 7 8 9 10 11 12 13 14 15 16

// c h a p t e r −4 p a g e 151 e x a m p l e 4 . 1 4 // ================================================================== clc ; clear ; // For a r e c t a n g u l a r w a v e g u i d e b =2.5; // Length o f R e c t a n g u l a r Waveguide i n cm a =5; // b r e a d t h o f R e c t a n g u l a r Waveguide i n cm c =3*10^10; // V e l o c i t y o f L i g h t i n cm/ s e c w0 =4.5; // F r e e s p a c e w a v e l e n g t h i n cm

//CALCULATION disp ( ’ For a TE10 mode which i s t h e dominant mode ’ ) ; wc =2* a ; // C u t o f f w a v e l e n g t h i n cm wg =( w0 / sqrt (1 -( w0 / wc ) ^2) ) ; // Guide w a v e l e n g t h i n cm Vp =( c / sqrt (1 -( w0 / wc ) ^2) ) /10^10; // Phase V e l o c i t y i n 1 0 ˆ 1 0 cm/ s e c 17 B =((2*( %pi ) * sqrt ( wc ^2 - w0 ^2) ) /( w0 * wc ) ) ; // Phase 33

constant in radians 18 19 20

21 22 23 24 25 26 27 28

//OUTPUT mprintf ( ’ \ nGuide w a v e l e n g t h i s wg=%1 . 5 f cm \ nPhase c o n s t a n t i s B=%1 . 3 f r a d i a n s \ nPhase V e l o c i t y i s Vp=%1 . 2 f ∗ 1 0 ˆ 1 0 cm/ s e c ’ ,wg ,B , Vp ) ; //=========================END OF PROGRAM =========================================== // Note : Check t h e a n s w e r s o n c e // C o r r e c t a n s w e r s a r e // Guide w a v e l e n g t h i s wg = 5 . 0 3 9 0 3 cm // Phase c o n s t a n t i s B= 1 . 2 4 7 r a d i a n s // Phase V e l o c i t y i s Vp=3.36 ∗ 1 0 ˆ 1 0 cm/ s e c

Scilab code Exa 4.15 possible modes 1 2


3 clc ; 4 clear ; 5 6 wcTE10 =16; // C r i t i c a l w a v e l e n g t h o f TE10 mode i n cm 7 wcTM11 =7.16; // C r i t i c a l w a v e l e n g t h o f TM11 mode i n cm 8 wcTM21 =5.6; // C r i t i c a l w a v e l e n g t h o f TM21 mode i n cm 9 disp ( ’ For any wave t o be p r o p a g a t e d , t h e c o n d i t i o n 10 11 12 13 14

t o be met i s wc>wo ’ ) ; wo1 =10; // F r e e s p a c e w a v e l e n g t h i n cm wo2 =5; // F r e e s p a c e w a v e l e n g t h i n cm disp ( ’ C r i t i c a l w a v e l e n g t h o f TE10 mode i n cm i s ’ ) ; disp ( wcTE10 ) ; disp ( ’ C r i t i c a l w a v e l e n g t h o f TM11 mode i n cm i s ’ ) ; 34

15 16 17 18

19 20 21 22

disp ( wcTM11 ) ; disp ( ’ C r i t i c a l w a v e l e n g t h o f TM21 mode i n cm i s ’ ) ; disp ( wcTM21 ) ; disp ( ’ For wo1=10cm , The mode t h a t p r o p a g a t e s o n l y TE10 . B e c a u s e wcTE10>wo1 and a l l o t h e r modes t h a t i s TM11 TM21 d o n o t p r o p a g a t e ’ ) ; disp ( ’ For wo2=5cm ’ ) ; disp ( ’ wcTE10>wo2 , s o TE10 mode p r o p a g a t e s ’ ) ; disp ( ’ wcTM11>wo2 , s o TE11 mode p r o p a g a t e s ’ ) ; disp ( ’ wcTE21>wo2 , s o TE21 mode p r o p a g a t e s ’ ) ;


3 4 5 6 7 8 9 10 11 12 13

// c h a p t e r −4 p a g e 152 e x a m p l e 4 . 1 6 // ================================================================== clc ; clear ; n =120*( %pi ) ; // I n t r i n s i c Impedance a =3; // Length o f R e c t a n g u l a r Waveguide i n cm b =2; // Width o f R e c t a n g u l a r Waveguide i n cm f =10^10; // F r e q u e n c y i n Hz c =3*10^10; // V e l o c i t y o f L i g h t i n cm/ s e c

//CALCULATION wc =((2* a * b ) / sqrt ( a ^2+ b ^2) ) ; // C u t o f f w a v e l e n g t h i n TM11 mode i n cms 14 w0 =( c / f ) ; // F r e e s p a c e w a v e l e n g t h i n cms 15 ZTM =( n * sqrt (1 -( w0 / wc ) ^2) ) ; // C h a r a c t e r i s t i c Wave Impedance i n ohms 16 17 18

//OUTPUT mprintf ( ’ \ n C h a r a c t e r i s t i c Wave Impedance i s ZTM=%2 . 3 35

f ohms ’ , ZTM ) ; 19 20 21 22 23 24

//=========================END OF PROGRAM ================================= // Note : Check t h e g i v e n a n s w e r o n c e i t // c u r r e c t a n s w e r i s 1 6 3 . 2 4 2 ohms

i s wrong


3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

// c h a p t e r −4 p a g e 152 e x a m p l e 4 . 1 7 // ================================================================== clc ; clear ; c =3*10^10; // V e l o c i t y o f L i g h t i n cm/ s e c f =6*10^9; // F r e q u e n c y i n Hz //CALCULATION fc =(0.8* f ) ; // Given C u t o f f f r e q u e n c y f o r TE11 mode i n Hz wc =( c / fc ) ; // C u t o f f w a v e l e n g t h i n cms D =((1.841* wc ) /( %pi ) ) ; // D i a m e t e r o f w a v e g u i d e i n cm w0 =( c / f ) ; // F r e e s p a c e w a v e l e n g t h i n cm wg =( w0 / sqrt (1 -( w0 / wc ) ^2) ) ; // Guide w a v e l e n g t h i n cm //OUTPUT mprintf ( ’ \ n D i a m e t e r o f t h e w a v e g u i d e i s D=%1 . 4 f cm \ nGuide w a v e l e n g t h i s wg=%1 . 3 f cm ’ ,D , wg ) ; //=========================END OF PROGRAM =============================== 36

Scilab code Exa 4.18 proof 1 2


3 clc ; 4 clear ; 5 6 // For a TE10 mode 7 a =1.5; // Length o f an a i r

f i l l e d s q u a r e Waveguide i n

m 8 b =1; // b r e a d t h o f an a i r

f i l l e d s q u a r e Waveguide i n

cm 9 c =3*10^10; // V e l o c i t y o f L i g h t i n cm/ s e c 10 f =6*10^9; // I m p r e s s e d F r e q u e n c y i n Hz 11 er =4; // d i e l e c t r i c c o n s t a n t 12 13 //CALCULATION 14 wc =2* a ; // C u t o f f w a v e l e n g t h i n cm 15 fc =( c / wc ) /10^9; // C u t o f f f r e q u e n c y i n GHz 16 disp ( ’ C u t o f f f r e q u e n c y i n GHz i s ’ ) ; 17 disp ( fc ) ; 18 disp ( ’ The i m p r e s s e d f r e q u e n c y o f 6 GHz i s

19 20 21 22 23 24

l e s s than t h e C u t o f f f r e q u e n c y and h e n c e t h e s i g n a l w i l l not pass through the gu i d e ’ ); w =( c / f ) ; // Wavelength i n cm disp ( ’ A l t e r n a t i v e l y , t h e w a v e l e n g t h o f t h e i m p r e s s e d s i g n a l i n cm i s ’ ) ; disp ( w ) ; wair = w ; disp ( ’ which i s l o n g e r t h a n t h e c u t o f f w a v e l e n g t h ( 3 cm ) and h e n c e no p r o p a g a t i o n o f t h e wave ’ ) ; w1 = wair / sqrt ( er ) ; // Wavelength i n cm 37

disp ( ’ I f t h e w a v e g u i d e i s l o a d e d w i t h d i e l e c t r i c o f e r =4 , t h e n t h e w a v e l e n g t h i n cm i s ’ ) ; 26 disp ( w1 ) ; 27 disp ( ’ which i s l e s s t h a n w a i r ’ ) ; 28 disp ( ’Now t h e s i g n a l w i t h 6 GHz f r e q u e n c y w i l l p a s s through the d i e l e c t r i c loaded waveguide ’ );

25

29 30

//=========================END OF PROGRAM ===============================

Scilab code Exa 4.19 amount of attenuation 1 2


3 clc ; 4 clear ; 5 6 a =0.015; // Length o f h o l l o w R e c t a n g u l a r Waveguide i n

m b =1; // b r e a d t h o f h o l l o w R e c t a n g u l a r Waveguide i n cm f =6*10^9; // F r e q u e n c y i n Hz i n TE10 mode c =3*10^8; // V e l o c i t y o f L i g h t i n m/ s e c m =1; // V a l u e o f m i n TE10 mode n =0; // V a l u e o f n i n TE10 mode u =4*( %pi ) *10^( -7) ; // P e r m e a b i l i t y i n f r e e s p a c e i n Henry 13 e =8.854*10^( -12) ; // P e r m i t t i v i t y i n f r e e s p a c e i n F/m

7 8 9 10 11 12

14 15 //CALCULATION 16 wc =2* a ; // C u t o f f w a v e l e n g t h f o r TE10 mode i n m 17 fc = c / wc ; // C u t o f f f r e q u e n c y i n Hz 18 w =2*( %pi ) * f ; // A n g u l a r f r e q u e n c y i n r a d / s e c 19

38

// So 6GHz s i g n a l w i l l n o t p a s s t h r o u g h w a v e g u i d e but w i l l get attenuated 21 A =( sqrt (( m *( %pi ) / a ) ^2+( n *( %pi ) / b ) ^2 -( w ^2* u * e ) ) ) ; // A t t e n u a t i o n i n NP/m 22 AdB = A *(20/ log (10) ) ; // A t t e n u a t i o n i n dB/m

20

23 24 25 26 27

//OUTPUT mprintf ( ’ \Amount o f A t t e n u a t i o n i s A=%3 . 1 f NP/m \ n A t t e n u a t i o n i s AdB=%4 . 2 f dB/m ’ ,A , AdB ) ; //=========================END OF PROGRAM ===============================

Scilab code Exa 4.20 max power handling capacity 1 2

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

// c h a p t e r −4 p a g e 154 e x a m p l e 4 . 2 0 // ================================================================== clc ; clear ; a =3; // Length o f R e c t a n g u l a r Waveguide i n cm b =1; // Width o f R e c t a n g u l a r Waveguide i n cm f =9*10^9; // F r e q u e n c y i n Hz i n TE10 mode c =3*10^10; // V e l o c i t y o f L i g h t i n cm/ s e c Emax =3000; //Max p o t e n t i a l g r a d i e n t i n V/cm //CALCULATION w0 =( c / f ) ; // F r e e s p a c e w a v e l e n g t h i n cms disp ( ’ F r e e s p a c e Wavelength i n cm i s ’ ) ; disp ( w0 ) ; wc =2* a ; // C u t o f f w a v e l e n g t h i n TE10 mode i n cms wg =( w0 / sqrt (1 -( w0 / wc ) ^2) ) ; // Guide w a v e l e n g t h i n cms disp ( ’ Guide Wavelength i n cm i s ’ ) ; 39

19 disp ( wg ) ; 20 P =((6.63*10^( -4) ) *( Emax ^2) * a * b *( w0 / wg ) ) /1000; // Power

h a n d l i n g c a p a b i l i t y o f t h e w a v e g u i d e i n kW 21 22 23 24 25 26

//OUTPUT mprintf ( ’ \ nPower h a n d l i n g c a p a b i l i t y o f t h e w a v e g u i d e i s P=%2 . 3 f kW ’ ,P ) ;

//=========================END OF PROGRAM =================================

Scilab code Exa 4.21 maximum power 1 2

3 4 5 6 7 8 9 10 11 12 13

// c h a p t e r −4 p a g e 154 e x a m p l e 4 . 2 1 // ================================================================== clc ; clear ; d =5; // I n t e r n a l D i a m e t e r o f c i r c u l a r w a v e g u i d e i n cm f =9*10^9; // F r e q u e n c y i n Hz i n TE11 mode c =3*10^10; // V e l o c i t y o f L i g h t i n cm/ s e c Emax =300; //Max f i e l d s t r e n g t h i n V/cm

//CALCULATION w0 =( c / f ) ; // F r e e s p a c e w a v e l e n g t h i n cms wc =(( d *( %pi ) ) /1.841) ; // C u t o f f w a v e l e n g t h i n TE11 mode i n cms 14 wg =( w0 / sqrt (1 -( w0 / wc ) ^2) ) ; // Guide w a v e l e n g t h i n cms 15 Pmax =(0.498*( Emax ^2) *( d ^2) *( w0 / wg ) ) /1000; //Maximum power i n kWatts 16 17

//OUTPUT 40

18 19 20 21

mprintf ( ’ \nMaximum power i s Pmax=%4 . 2 f kWatts ’ , Pmax ) ;

//=========================END OF PROGRAM ===============================

Scilab code Exa 4.22 peak value of electric field 1 2


3 clc ; 4 clear ; 5 6 // For an a i r f i l l e d s q u a r e w a v e g u i d e 7 a =0.01; // Length o f an a i r f i l l e d s q u a r e Waveguide i n

m 8 b =0.01; // b r e a d t h o f an a i r 9 10 11 12 13 14 15 16 17 18

f i l l e d s q u a r e Waveguide

in m c =3*10^8; // V e l o c i t y o f L i g h t i n m/ s e c f =30*10^9; // F r e q u e n c y i n Hz i n TE11 mode Pmax =746; //Max power =1 h o r s e p o w e r in W n =120*( %pi ) ; // Impedance o f f r e e s p a c e i n ohms

//CALCULATION w0 =( c / f ) ; // F r e e s p a c e w a v e l e n g t h i n m wc =2* a ; // C u t o f f w a v e l e n g t h i n m ZTE =( n / sqrt (1 -( w0 / wc ) ^2) ) ; // Impedance i n ohms Emax =( sqrt (( Pmax *4* ZTE ) /( a * b ) ) ) /1000; // The Peak value of E l e c t r i c f i e l d occuring in the guide in kV/m 19 // From P= ( 1 / 2 ) ∗ I n t e g r a t i o n ( Re (E∗H) ) da 20 // and Pmax= ( 1 / ( 4 ∗ZTE) ) ∗Emaxˆ2∗ a ∗b 41

21 22 23 24 25

//OUTPUT mprintf ( ’ \ nThe Peak v a l u e o f E l e c t r i c f i e l d o c c u r i n g i n t h e g u i d e i s Emax=%3 . 2 f kV/m ’ , Emax ) ; //=========================END OF PROGRAM ===============================



3 clc ; 4 clear ; 5 6 // For an a i r f i l l e d r e c t a n g u l a r w a v e g u i d e 7 a =0.023; // Length o f an a i r f i l l e d Rectangular 8

Waveguide i n m b =0.01; // b r e a d t h o f an a i r f i l l e d R e c t a n g u l a r Waveguide i n m c =3*10^8; // V e l o c i t y o f L i g h t i n m/ s e c f =9.375*10^9; // F r e q u e n c y i n Hz i n TE11 mode w0 =0.01; // F r e e s p a c e w a v e l e n g t h i n m wc =0.02; // C u t o f f w a v e l e n g t h i n m Pmax =746; //Max power =1 h o r s e p o w e r in W

9 10 11 12 13 14 15 //CALCULATION 16 wo =( c / f ) ; // F r e e s p a c e w a v e l e n g t h i n cm 17 Pbd =(597* a * b * sqrt (1 -( wo /(2* a ) ) ^2) ) ; // The breakdown

power f o r t h e dominant mode i e TE11 i n W 18 wg =( w0 / sqrt (1 -( w0 / wc ) ^2) ) ; // Guide w a v e l e n g t h i n m 19 Emax =( sqrt (( Pmax * wg ) /(6.63*10^( -4) * w0 ) ) ) /1000; //Max e l e c t r i c f i e l d i n kV/m 42

20 21 22

23 24

//OUTPUT mprintf ( ’ \ nThe breakdown power f o r t h e dominant mode i e TE11 i s Pbd=%1 . 5 f W \nMax e l e c t r i c f i e l d i s Emax=%1 . 4 f kV/m ’ ,Pbd , Emax ) ; //=========================END OF PROGRAM ===========================================

25 26 27 28 29

// Note : Check t h e a n s w e r s o n c e // C o r r e c t a n s w e r s a r e // The breakdown power f o r t h e dominant mode i e TE11 i s Pbd = 0 . 0 9 8 6 4 W 30 //Max e l e c t r i c f i e l d i s Emax = 1 . 1 3 9 8 kV/m


3 4 5 6 7 8 9 10 11 12 13

// c h a p t e r −4 p a g e 156 e x a m p l e 4 . 2 4 // ================================================================== clc ; clear ; a =2.5; // R a d i u s o f c i r c u l a r w a v e g u i d e i n cm d =5; // I n t e r n a l D i a m e t e r o f c i r c u l a r w a v e g u i d e i n cm f =9*10^9; // F r e q u e n c y i n Hz i n TE11 mode c =3*10^10; // V e l o c i t y o f L i g h t i n cm/ s e c

//CALCULATION w0 =( c / f ) ; // F r e e s p a c e w a v e l e n g t h i n cms wc =(( d *( %pi ) ) /1.841) ; // C u t o f f w a v e l e n g t h i n TE11 mode i n cms 14 fc =( c / wc ) ; // C u t o f f f r e q u e n c y i n Hz 43

15 Pbd =(1790*( a ^2) * sqrt (1 -( fc / f ) ^2) ) /1000; // Breakdown

Power i n TE11 mode i n kW 16 17 18 19 20

//OUTPUT mprintf ( ’ \ nBreakdown Power i n TE11 mode i s Pbd=%5 . 3 f kW ’ , Pbd ) ; //=========================END OF PROGRAM ===============================

44

Chapter 5 Cavity Resonators

Scilab code Exa 5.1 minimum distance 1 2


3 clc ; 4 clear ; 5 6 // For a c i r c u l a r w a v e g u i d e 7 a =3; // r a d i u s i n cm 8 f0 =10*10^9; // r e s o n a n t f r e q u e n c y o f a c i r c u l a r 9

r e s o n a t o r i n Hz disp ( ’ Given t h e mode o f o p e r a t o r i s TM011 s o h e r e n =0 ,m=1 , p=1 ’ ) ; c =3*10^10; // V e l o c i t y o f l i g h t i n cm/ s e c m =1; n =0; p =1; Pnm =2.405; // dominant mode v a l u e [ TM01 ]

10 11 12 13 14 15 16 //CALCULATION 17 d =(( p *( %pi ) ) /( sqrt ((2*( %pi ) * f0 / c ) ^2 -( Pnm / a ) ^2) ) ) ; //

45

The minimum d i s t a n c e b e t w e e n t h e two end p l a t e s i n cms 18 19 20

21 22

//OUTPUT mprintf ( ’ \ nThe minimum d i s t a n c e b e t w e e n t h e two end p l a t e s o f a c i r c u l a r w a v e g u i d e i s d=%1 . 2 f cms ’ ,d ) ; //=========================END OF PROGRAM ===============================

Scilab code Exa 5.2 lowest resonant frequency 1 2

3 4 5 6 7 8 9 10

11 12 13 14 15 16 17

// c h a p t e r −5 p a g e 174 e x a m p l e 5 . 2 // ================================================================== clc ; clear ; // For a r e c t a n g u l a r c a v i t y r e s o n a t o r a =2; // b r e a d t h i n cm b =1; // h e i g h t i n cm l =3; // l e n g t h o f r e c t a n g u l a r w a v e g u i d e i n cm disp ( ’ Lowest r e s o n a n t f r e q u e n c y i s o b t a i n e d f o r t h e dominant mode TE10 [ f=c /w where w i n c r e a s e s a s f d e c r e a s e s . I n dominant mode wc i s maximum ] ’ ) ; disp ( ’ So t h e dominant mode i s TE101 s o h e r e m=1 , n =0 , p=1 ’ ) ; c =3*10^10; // V e l o c i t y o f l i g h t i n cm/ s e c m =1; n =0; p =1; //CALCULATION 46

18 f0 =(( c /2) * sqrt (( m / a ) ^2+( n / b ) ^2+( p / l ) ^2) ) /10^9; // The

resonant frequency of a rectangular cavity r e s o n a t o r i n GHz 19 20 21 22 23

//OUTPUT mprintf ( ’ \ nThe r e s o n a n t f r e q u e n c y o f a r e c t a n g u l a r c a v i t y r e s o n a t o r i s f 0=%1 . 0 f GHz ’ , f0 ) ; //=========================END OF PROGRAM ===============================

Scilab code Exa 5.3 resonant frequency 1 2


3 clc ; 4 clear ; 5 6 // For a c i r c u l a r r e s o n a t o r 7 D =12.5; // d i a m e t e r i n cm 8 l =5; // l e n g t h o f c i r c u l a r w a v e g u i d e i n cm 9 disp ( ’ Given t h e mode o f o p e r a t o r i s TM012 s o h e r e n

=0 ,m=1 , p=2 ’ ) ; c =3*10^10; // V e l o c i t y o f l i g h t i n cm/ s e c m =1; n =0; p =2; Pnm =2.405; // dominant mode v a l u e [ TM01 ]

10 11 12 13 14 15 16 //CALCULATION 17 a = D /2; // r a d i u s i n cm 18 f0 =(( c /(2*( %pi ) ) ) * sqrt (( Pnm / a ) ^2+(( p *( %pi ) ) / l ) ^2) )

/10^9; // The r e s o n a n t f r e q u e n c y o f a c i r c u l a r 47

r e s o n a t o r i n GHz 19 20 21 22 23

//OUTPUT mprintf ( ’ \ nThe r e s o n a n t f r e q u e n c y o f a c i r c u l a r r e s o n a t o r i s f 0=%1 . 2 f GHz ’ , f0 ) ; //=========================END OF PROGRAM ===============================

Scilab code Exa 5.4 resonant frequency 1 2

3 4 5 6 7 8 9 10

// c h a p t e r −5 p a g e 175 e x a m p l e 5 . 4 // ================================================================== clc ; clear ; // For a c i r c u l a r r e s o n a t o r a =3; // r a d i u s i n cm b =2; // d i m e n s i o n i n cm l =4; // l e n g t h o f c i r c u l a r w a v e g u i d e i n cm disp ( ’ Given t h e mode o f o p e r a t o r i s TE101 s o h e r e m =1 , n =0 , p=1 ’ ) ; c =3*10^10; // V e l o c i t y o f l i g h t i n cm/ s e c m =1; n =0; p =1;

11 12 13 14 15 16 //CALCULATION 17 f0 =(( c /2) * sqrt (( m / a ) ^2+( n / b ) ^2+( p / l ) ^2) ) /10^9; // The

r e s o n a n t f r e q u e n c y o f a c i r c u l a r r e s o n a t o r i n GHz 18 19 20

//OUTPUT mprintf ( ’ \ nThe r e s o n a n t f r e q u e n c y o f a c i r c u l a r 48

r e s o n a t o r i s f 0=%1 . 2 f GHz ’ , f0 ) ; 21 22

//=========================END OF PROGRAM ===============================

49

Chapter 6 Microwave Components

Scilab code Exa 6.2 distance to be shifted 1 2

// Chapter −6 , Example 6 . 2 , Page 234 // ==================================================================

3 4

// I n p u t p a r a m e t e r s // [ s ] = [ 0 , ( 0 . 3 + ( %i ) ∗ ( 0 . 4 ) ) ; ( 0 . 3 + ( %i ) ∗ ( 0 . 4 ) ) , 0 ] ; / / s c a t t e r i n g m a t r i x o f a two p o r t // C a l c u l a t i o n s // t o f i n d l s u c h t h a t S12 and S21 w i l l be r e a l when p o r t 1 i s s h i f t e d lm t o t h e l e f t // l e t p o r t 1 be s h i f t e d by p h i 1 d e g r e e t o t h e l e f t and p o r t 2 p o s i t i o n be r e m a i n e d unchanged i . e . , p h i 2=d e l t a // Then [ p h i ] = [ e ˆ−( j ∗ p h i 1 ) , 0 ; 0 , 1 ] // [ S ’ ] = [ p h i ] ∗ [ s ] ∗ [ p h i ] // f o r S12 and S21 t o be r e a l phi1 =53.13; // i n d e g r e e s phi1 = phi1 *( %pi /180) ; // p h i i n r a d i a n s b =34.3; // me a s u r e d i n r a d /m l =( phi1 ) / b ; // d i s t a n c e o f s h i f t i n m // Output

5 6 7

8 9 10 11 12 13 14 15

50

mprintf ( ” d i s t a n c e t h a t t h e p o s i t i o n o f p a r t 1 s h o u l d be s h i f t e d t o t h e l e f t s o t h a t S21 and S12 w i l l be r e a l numbers i s %1 . 4 f m” ,l ) 17 //=================================END OF PROGRAM ============================== 16

Scilab code Exa 6.3 Scattering parameters 1 2

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

// Chapter −6 , Example 6 . 3 , Page 236 // ================================================================== clc ; // I n p u t p a r a m e t e r s D =30; // d i r e c t i v i t y i n dB VSWR =1; //VSWR a t e a c h p o r t u n d e r matched c o n d i t i o n s C =10; // c o u p l i n g f a c t o r // C a l c u l a t i o n s S41 = sqrt (0.1) ; S14 = S41 ; // u n d e r matched and l o s s l e s s c o n d i t i o n s S31 = sqrt ((( S41 ) ^2) /(10) ^( D /10) ) ; S13 = S31 ; S11 =( VSWR -1) /( VSWR +1) ; S22 = S11 ; S33 = S22 ; S44 = S33 ; // l e t i n p u t power i s g i v e n a t p o r t 1 // p1=p2+P3+p4 S21 = sqrt (1 -( S41 ) ^2 -( S31 ) ^2) ; S12 = S21 ; S34 = sqrt ((0.5) *(1+( S12 ) ^2 -0.1 -0.0001) ) ; S43 = S34 S23 = sqrt (1 -10^ -4 -( S34 ) ^2) S32 = S23 ; S24 = sqrt (1 -0.1 -( S34 ) ^2) 51

26 S42 = S24 ; 27 [ S ]=[ S11 , S12 , S13 , S14 ; S21 , S22 , S23 , S24 ; S31 , S32 , S33 , S34 28 29 30 31

; S41 , S42 , S43 , S44 ]; // Output mprintf ( ” The s c a t t e r i n g m a t r i x i s ” ) ; disp ([ S ]) //=================================END OF PROGRAM ==============================

Scilab code Exa 6.4 powers in the remaining ports 1 2


3 4 5 6 7 8 9

clc ; // I n p u t p a r a m e t e r s a1 =32*10^ -3; // power i n w a t t s a2 =0; a3 =0; // C a l c u l a t i o n s [ S ]=[0.5 , -0.5 ,0.707; -0.5 ,0.5 ,0.707;0.707 ,0.707 ,0]; // S−m a t r i x f o r H−p l a n e t e e // [ B] = [ b1 , b2 , b3 ] [ B ]=[ S ].*[ a1 ,0 ,0;0 ,0 ,0;0 ,0 ,0]; b1 =(0.5) ^2* a1 ; // power a t p o r t 1 b2 =( -0.5) ^2* a1 ; // power a t p o r t 2 b3 =(0.707) ^2* a1 ; // power a t p o r t 3 // Output mprintf ( ” Thus b1 , b2 , b3 a r e %g W, %g W, %g W r e s p e c t i v e l y ” ,b1 , b2 , b3 ) ; //=================================END OF PROGRAM ==============================

10 11 12 13 14 15 16 17

52


3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

// Chapter −6 , Example 6 . 5 , Page 239 // ================================================================== clc ; // I n p u t p a r a m e t e r s [ S ]=[0.5 , -0.5 ,0.707; -0.5 ,0.5 ,0.707;0.707 ,0.707 ,0]; R1 =60; // l o a d a t p o r t 1 i n ohms R2 =75; // l o a d a t p o r t 2 i n ohms R3 =50; // c h a r a c t e r i s t i c i m p e d a n c e i n ohms P3 =20*10^ -3; // power a t p o r t 3 i n Watts // c a l c u l a t i o n s p1 =( R1 - R3 ) /( R1 + R3 ) ; p2 =( R2 - R3 ) /( R2 + R3 ) ; P1 =0.5* P3 *(1 -( p1 ) ^2) ; // power d e l i v e r e d t o t h e p o r t 1 i n Watts P2 =0.5* P3 *(1 -( p2 ) ^2) ; // power d e l i v e r e d t o t h e p o r t 2 i n Watts // Output mprintf ( ” Thus power d e l i v e r e d t o t h e p o r t 1 and p o r t 2 a r e %g W, %g W r e s p e c t i v e l y ” ,P1 , P2 ) ; //=================================END OF PROGRAM ==============================

Scilab code Exa 6.6 Reflected power 1 2


53

3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

clc ; // I n p u t p a r a m e t e r s p1 =0.5; // r e f l e c t i o n c o e f f i c i e n t a t p o r t 1 p2 =0.6; // r e f l e c t i o n c o e f f i c i e n t a t p o r t 2 p3 =1; // r e f l e c t i o n c o e f f i c i e n t a t p o r t 3 p4 =0.8; // r e f l e c t i o n c o e f f i c i e n t a t p o r t 4 // [ S ]=[0 ,0 ,0.707 ,0.707;0 ,0 ,0.5 , −0.707;0.707 ,0.707 ,0 ,0; −0.707 ,0.707 ,0 , S m a t r i x o f magic Tee // s o l v i n g f o r b1 , b2 , b3 , b4 we g e t i t a s // c a l c u l a t i o n s b1 =0.6566; b2 =0.7576; b3 =0.6536; b4 =0.0893; P1 =( b1 ) ^2; // power a t p o r t 1 i n w a t t s disp ( P1 ) ; P2 =( b2 ) ^2; // power a t p o r t 2 i n w a t t s disp ( P2 ) ; P3 =( b3 ) ^2; // power a t p o r t 3 i n w a t t s disp ( P3 ) ; P4 =( b4 ) ^2; // power a t p o r t 4 i n w a t t s disp ( P4 ) ; //=================================END OF PROGRAM ==============================

Scilab code Exa 6.7 Scattering matrix 1 2


3 clc ; 4 // I n p u t p a r a m e t e r s 5 ins =0.5; // i n s e r t i o n

l o s s i n db 54

6 7 8 9 10 11 12 13 14

iso =30; // i s o l a t i o n l o s s i n db // C a l c u l a t i o n s S21 =10^ -( ins /20) ; // i n s e r t i o n l o s s =0.5=−20∗ l o g [ S21 ] S12 =10^ -( iso /20) ; // i s o l a t i o n l o s s =30=−20∗ l o g [ s 1 2 ] S11 =0; S22 =0; [ S ]=[ S11 , S12 ; S21 , S22 ]; disp ( S ) ; //=================================END OF PROGRAM ==============================

Scilab code Exa 6.9 Scattering matrix 1 2

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

// Chapter −6 , Example 6 . 9 , Page 241 // ================================================================== clc ; // I n p u t p a r a m e t e r s ins =0.5; // i n s e r t i o n l o s s i n db iso =20; // i s o l a t i o n l o s s i n db S =2; //VSWR // C a l c u l a t i o n s S21 =10^ -( ins /20) ; // i n s e r t i o n l o s s =0.5=−20∗ l o g [ S21 ] S13 = S21 ; S32 = S13 ; S12 =10^ -( iso /20) ; // i s o l a t i o n l o s s =30=−20∗ l o g [ s 1 2 ] S23 = S12 ; S31 = S23 ; p =( S -1) /( S +1) ; S11 = p ; S22 = p ; S33 = p ; [ S ]=[ S11 , S12 , S13 ; S21 , S22 , S23 ; S31 , S32 , S33 ]; disp ( S ) ; 55

21 22 23 24 25

// f o r a p e r f e c t l y matched , non−r e c i p r o c a l , l o s s l e s s 3− p o r t c i r c u l a t o r , [ S ] i s g i v e n by // [ S ] = [ 0 , 0 , S13 ; S21 , 0 , 0 ; , 0 , S32 , 0 ] // i . e . , S13=S21=S32=1 // [ S ] = [ 0 , 0 , 1 ; 1 , 0 , 0 ; 0 , 1 , 0 ] //=================================END OF PROGRAM ==============================

Scilab code Exa 6.10 output powers 1 2

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

// Chapter −6 , Example 6 . 1 0 , Page 242 // ==================================================================

clc ; clear ; close ; In_loss =0.5; // i n s e r t i o n l o s s ( i n dB ) C =20; // c o u p l i n g c o e f f i c i e n t i n dB D =35; // d i r e c t i v i t y i n dB Pi_Pf =10^( C /10) ; Pi =90; // i n Watts Pf = Pi / Pi_Pf ; Pf_Pb =10^( D /10) ; Pb = Pf / Pf_Pb ; P_rec =( Pi - Pf - Pb ) ; // Power r e c e i v e d ( i n Watts ) P_rec_dB =10* log ( Pi / P_rec ) / log (10) ; P_rec_eff = P_rec_dB - In_loss ; // E f f e c t i v e power r e c e i v e d ( i n dB ) disp ( Pf , ’ Output power t h r o u g h c o u p l e d p o r t ( i n Watts )= ’ ) ; disp ( Pb , ’ Output power t h r o u g h i s o l a t e d p o r t ( i n Watts )= ’ ) ; 56

disp ( P_rec_dB , ’ Power r e c e i v e d ( i n dB )= ’ ); 21 disp ( P_rec_eff , ’ E f f e c t i v e power r e c e i v e d ( i n dB )= ’ ) ;

20

22 23 24

//=================================END OF PROGRAM ==============================

Scilab code Exa 6.11 coupling isolation directivity 1 2

// Chapter −6 , Example 6 . 1 1 , Page 242 // ==================================================================

3 clc ; 4 // C a l c u l a t i o n s 5 S13 =0.1*( cos (90* %pi /180) +( %i ) * sin (90* %pi /180) ) ; // 6 7 8 9 10 11 12

13

c o n v e r s i o n from p o l a r t o r e c t a n g u l a r S13 = abs ( S13 ) ; C = -20* log10 ( S13 ) ; // c o u p l i n g c o e f f i c i e n t i n dB S14 =0.05*( cos (90* %pi /180) +( %i ) * sin (90* %pi /180) ) ; // c o n v e r s i o n from p o l a r t o r e c t a n g u l a r S14 = abs ( S14 ) ; D =20* log10 ( S13 / S14 ) ; // d i r e c t i v i t y i n dB I = -20* log10 ( S14 ) ; // i s o l a t i o n i n dB mprintf ( ” Thus c o u p l i n g , d i r e c t i v i t y and i s o l a t i o n a r e %1 . 0 f dB , %1 . 2 f dB and %2 . 2 f dB r e s p e t i v e l y ” ,C ,D ,I); //=================================END OF PROGRAM ==============================

Scilab code Exa 6.12 VSWR 57

1 2


3 clc ; 4 clear ; 5 6 x =3.5; // d i s t a n c e b e t w e e n two minimas i n cm 7 y =0.25; // d i s t a n c e b e t w e e n t w i c e minimum power p o i n t s

i n cm 8 9 //CALCULATION 10 wg =2* x ; // g u i d e d w a v e l e n g t h i n cm 11 S =( wg /( y *( %pi ) ) ) ; // V o l t a g e S t a n d i n g Wave R a t i o (VSWR) 12 13 //OUTPUT 14 mprintf ( ’ \ n V o l t a g e S t a n d i n g Wave R a t i o (VSWR) i s S=%1

. 4 f ’ ,S ) ; 15 16

//=========================END OF PROGRAM ===============================

Scilab code Exa 6.13 phase shift 1 2


3 clc ; 4 clear ; 5 6 wg =7.2; // g u i d e w a v e l e n g t h i n cm 7 x =10.5; // P o s i t i o n o f r e f e r e n c e n u l l w i t h o u t t h e

w a v e g u i d e component i n cm o f r e f e r e n c e n u l l with the

8 y =9.3; // P o s i t i o n

58

w a v e g u i d e component i n cm 9 10 //CALCULATION 11 z =x - y ; // Path d i f f e r e n c e

i n t r o d u c e d due t o t h e component i n cm 12 p =(2*( %pi ) *( z / wg ) ) ; // Phase d i f f e r e n c e i n t r o d u c e d i n rad 13 Pd =( p *180) /( %pi ) ; // Phase s h i f t i n t r o d u c e d i n deg 14 15 16

17 18

//OUTPUT mprintf ( ’ \ nPhase s h i f t i n t r o d u c e d i s Pd=%2 . 0 f deg ’ , Pd ) ; //=========================END OF PROGRAM ===============================

59

Chapter 7 Microwave Measurements

Scilab code Exa 7.1 measured distance 1 2


3 4 5 6 7 8 9

clc ; clear ;

a =4; // Length o f Waveguide i n cm b =2.5; // b r e a d t h Waveguide i n cm f =10^10; // F r e q u e n c y i n Hz x =0.1; // d i s t a n c e b e t w e e n t w i c e minimum power p o i n t s i n cm 10 c =3*10^10; // V e l o c i t y o f L i g h t i n cm/ s e c 11 12 13 14 15 16

//CALCULATION wc =2* a ; // C u t o f f w a v e l e n g t h i n TE10 mode i n cms w0 =( c / f ) ; // F r e e s p a c e w a v e l e n g t h i n cms wg =( w0 / sqrt (1 -( w0 / wc ) ^2) ) ; // Guide w a v e l e n g t h i n cms S =( wg /( x *( %pi ) ) ) ; // V o l t a g e S t a n d i n g Wave R a t i o (VSWR) f o r d o u b l e minimum method

17

60

18 19 20 21

//OUTPUT mprintf ( ’ \ nFor d o u b l e minimum method , V o l t a g e S t a n d i n g Wave R a t i o (VSWR) i s S=%2 . 1 f ’ ,S ) ; //=========================END OF PROGRAM ===============================

Scilab code Exa 7.2 VSWR and Reflected power 1 2


3 clc ; 4 clear ; 5 6 x =3; //O/P i n c i d e n t power from

first

directional

c o u p l e r i n mW 7 y =0.1; //O/P r e f l e c t e d power from s e c o n d d i r e c t i o n a l c o u p l e r i n mW 8 9 10 11 12 13 14 15 16

17 18

//CALCULATION Pi = x *100; // I n c i d e n t Power i n mW Pr = y *100; // R e f l e c t e d Power i n mW p = sqrt ( Pr / Pi ) ; // R e f l e c t i o n C o e f f i c i e n t S =((1+ p ) /(1 - p ) ) ; // V o l t a g e S t a n d i n g Wave R a t i o (VSWR) //OUTPUT mprintf ( ’ \ n V o l t a g e S t a n d i n g Wave R a t i o (VSWR) i n t h e main w a v e g u i d e i s S=%1 . 2 f \ n R e f l e c t e d Power i s Pr =%2 . 0 f mW’ ,S , Pr ) ; //=========================END OF PROGRAM ===============================

61

Scilab code Exa 7.3 VSWR 1 2


3 clc ; 4 clear ; 5 6 Pi =2.5; // I n c i d e n t Power from one d i r e c t i o n a l

coupler i n mW 7 Pr =0.15; // R e f l e c t e d Power from o t h e r d i r e c t i o n a l c o u p l e r i n mW 8 9 //CALCULATION 10 p = sqrt ( Pr / Pi ) ; // R e f l e c t i o n C o e f f i c i e n t 11 S =((1+ p ) /(1 - p ) ) ; // V o l t a g e S t a n d i n g Wave R a t i o (VSWR) 12 13 //OUTPUT 14 mprintf ( ’ \ n V o l t a g e S t a n d i n g Wave R a t i o (VSWR) i n t h e

w a v e g u i d e i s S=%1 . 2 f ’ ,S ) ; 15 16

//=========================END OF PROGRAM ===============================

Scilab code Exa 7.4 Reflected power 1 2


3 clc ;

62

4 5 6 7 8 9 10 11 12

clear ; S =2; // V o l t a g e S t a n d i n g Wave R a t i o (VSWR) C =30; // C o u p l i n g Power o f a D i r e c t i o n a l C o u p l e r i n dB Pf =4.5; // C o u p l e r I n c i d e n t S a m p l i n g Power i n mW

//CALCULATION p =(( S -1) /( S +1) ) ; // R e f l e c t i o n C o e f f i c i e n t Pi = Pf *10^( C /10) ; // I n c i d e n t Power i n mW [ From C=10 l o g ( Pi / Pf ) ] 13 Pr =( Pi *( p ^2) ) /10^3; // R e f l e c t e d Power i n W [ From p= s q r t ( Pr / Pi ) ]

14 15 16 17 18

//OUTPUT mprintf ( ’ \ nValue o f R e f l e c t e d Power i s Pr=%1 . 2 f W’ , Pr ) ; //=========================END OF PROGRAM ===============================

63

Chapter 8 Microwave Tubes and Circuits

Scilab code Exa 8.1 electron velocity and etc 1 2

3 4 5 6 7 8 9 10 11 12 13

// c h a p t e r −8 p a g e 336 e x a m p l e 8 . 1 // ================================================================== clc ; clear ;

// For a f o u r c a v i t y K l y s t r o n V0 =14500; //Beam v o l t a g e i n V I =1.4; //Beam c u r r e n t i n A f =10^10; // O p e r a t i o n f r e q u e n c y i n Hz p0 =10^( -6) ; // dc e l e c t r o n c h a r g e d e n s i t y i n C/mˆ3 p =10^( -8) ; //RF c h a r g e d e n s i t y i n C/mˆ3 V =10^5; // V e l o c i t y p e r t u r b a t i o n s i n m/ s e c e0 =8.854*10^( -12) ; // P e r m i t t i v i t y o f f r e e s p a c e i n F/ m 14 R =0.4; 15 16 //CALCULATION 17 v0 =(0.593*10^6* sqrt ( V0 ) ) /10^8; // The dc e l e c t r o n

v e l o c i t y i n 1 0 ˆ 8 m/ s e c 64

18 19 20 21 22 23 24 25 26 27 28

29 30

w =2*( %pi ) * f ; // a n g u l a r f r e q u e n c y i n r a d / s e c v = v0 *10^8; c =( w / v ) ; // The dc Phase C o n s t a n t wp =( sqrt (1.759*10^11*( p0 / e0 ) ) ) /10^8; // The Plasma Frequency i n 10ˆ8 rad / s e c wp1 = wp *10^8; wq =( R * wp1 ) /10^8; // The Reduced Plasma F r e q u e n c y i n 10ˆ8 rad / s e c J0 = p0 * v ; // The dc beam c u r r e n t d e n s i t y i n A/sqm J =( p * v ) +( p0 * V ) ; // The i n s t a n t a n e o u s beam c u r r e n t d e n s i t y i n A/sqm //OUTPUT mprintf ( ’ \ nThe dc e l e c t r o n v e l o c i t y i s v0=%2 . 3 f ∗ 1 0 ˆ 8 m/ s e c \ nThe dc Phase C o n s t a n t i s c=%1 . 2 f r a d / s e c \ nThe Plasma F r e q u e n c y i s wp=%1 . 2 f ∗ 1 0 ˆ 8 r a d / s e c \ nThe Reduced Plasma F r e q u e n c y i s wq=%1 . 3 f ∗ 1 0 ˆ 8 r a d / s e c \ nThe dc beam c u r r e n t d e n s i t y i s J0=%2 . 1 f A/sqm \ nThe i n s t a n t a n e o u s beam c u r r e n t d e n s i t y i s J=%1 . 3 f A/sqm ’ ,v0 ,c , wp , wq , J0 , J ) ; //=========================END OF PROGRAM ===============================

Scilab code Exa 8.2 power and etc 1 2


3 clc ; 4 clear ; 5 6 // For a 2 c a v i t y k l y s t r o n a m p l i f i e r 7 Av =15; // V o l t a g e g a i n i n dB

65

8 9 10 11 12

Pin =0.005; // I /P power i n W Rin =30000; // Rsh o f i / p c a v i t y i n ohms R0 =40000; // Rsh o f o / p c a v i t y i n ohms Rl =40000; // l o a d i m p e d a n c e i n ohms R =20000; // P a r a l l e l r e s i s t a n c e o f R0 and Rl ( R0// Rl ) i n ohms

13 14 //CALCULATION 15 Vin = sqrt ( Pin * Rin ) ; // The i n p u t rms v o l t a g e

in V [ From Pin=Vin ˆ2/ Rin ] 16 V0 = Vin *10^( Av /20) ; // The o u t p u t rms v o l t a g e i n V [ From Av=20 l o g ( V0/ Vin ) ] 17 P0 =( V0 ^2) / R ; // The Power d e l i v e r e d t o t h e l o a d i n W 18 19 20

21 22

//OUTPUT mprintf ( ’ \ nThe i n p u t rms v o l t a g e i s Vin=%2 . 2 f V \ nThe o u t p u t rms v o l t a g e i s V0=%2 . 2 f V \ nThe Power d e l i v e r e d t o t h e l o a d i s P0=%1 . 4 f W’ ,Vin , V0 , P0 ) ; //=========================END OF PROGRAM ===============================

Scilab code Exa 8.3 efficiency and etc 1 2


3 4 5 6 7 8 9

clc ; clear ; // For a r e f l e x k l y s t r o n n =2; // peak mode v a l u e V0 =300; // beam v o l t a g e i n V I0 =0.02; // beam c u r r e n t i n A 66

10 11 12 13 14 15

Vs =40; // s i g n a l v o l t a g e i n V J1 =1.25; // b e s s e l c o e f f i c i e n t f o r n=2

//CALCULATION Pdc = V0 * I0 ; // The i n p u t power i n w a t t s Pac =((2* Pdc * J1 ) /((2* n *( %pi ) ) -(( %pi ) /2) ) ) ; // The o u t p u t power i n w a t t s 16 n =( Pac / Pdc ) *100; // E f f i c i e n c y i n p e r c e n t a g e 17 18 19

20 21

//OUTPUT mprintf ( ’ \ nThe i n p u t power i s Pdc=%1 . 0 f w a t t s \ nThe o u t p u t power i s Pac=%1 . 2 f w a t t s \ n E f f i c i e n c y i s n =%2 . 1 f p e r c e n t a g e ’ ,Pdc , Pac , n ) ; //=========================END OF PROGRAM ===============================


3 4 5 6 7 8 9 10 11 12 13 14

// c h a p t e r −8 p a g e 338 e x a m p l e 8 . 4 // ================================================================== clc ; clear ; // For a 2 c a v i t y k l y s t r o n a m p l i f i e r V0 =900; //Beam v o l t a g e i n V I0 =0.03; //Beam c u r r e n t i n A f =8*10^9; // f r e q u e n c y i n Hz d =0.001; // gap s p a c i n g i n e i t h e r c a v i t y i n m L =0.04; // s p a c i n g b e t w e e n c e n t e r s o f c a v i t i e s i n m Rsh =49000; // E f f e c t i v e s h u n t i m p e d a n c e i n ohms J1 =0.582; // v a l u e o f J1 (X) X =1.841; // b u n c h i n g p a r a m e t e r 67

15 16 //CALCULATION 17 v0 =(0.593*10^6* sqrt ( V0 ) ) /10^6; // v e l o c i t y

of electron

i n 1 0 ˆ 6 m/ s e c 18 w =2*( %pi ) * f ; // a n g u l a r f r e q u e n c y i n r a d 19 v = v0 *10^6; 20 T0 =( L / v ) /10^( -8) ; // dc t r a n s i t t i m e o f e l e c t r o n s 21 22 23 24 25 26 27 28 29 30 31 32

33 34

in 10ˆ( −8) s e c a = w * T0 *10^( -8) ; // t r a n s i t a n g l e i n r a d tg = w * d / v ; // a v e r a g e gap t r a n s i t a n g l e i n r a d Tg = tg *(180/( %pi ) ) ; Bi =( sind ( Tg /2) ) /( tg /2) ; // beam c o u p l i n g c o e f f i c i e n t Bo = Bi ; // o u t p u t c a v i t y c o u p l i n g c o e f f i c i e n t V1max =((3.68* V0 ) /( Bi * a ) ) ; // I n p u t v o l t a g e f o r Maximum output v o l t a g e in V R0 = V0 / I0 ; // i m p e d a n c e i n ohms Av =( Bo ^2* a * Rsh * J1 ) /( R0 * X ) ; // V o l t a g e g a i n AvdB =20* log10 ( Av ) ; // V o l t a g e g a i n i n dB //OUTPUT mprintf ( ’ \ n V e l o c i t y o f e l e c t r o n i s v0=%2 . 2 f ∗ 1 0 ˆ 6 m/ s e c \ nThe dc t r a n s i t t i m e o f e l e c t r o n s i s T0=%1 . 3 f ∗10ˆ( −8) s e c \ n I n p u t v o l t a g e f o r Maximum o u t p u t v o l t a g e i s V1max=%2 . 3 f V \ n V o l t a g e g a i n i s Av=%2 . 2 f \ nThe V o l t a g e g a i n i n dB i s AvdB=%2 . 2 f dB ’ ,v0 , T0 , V1max , Av , AvdB ) ; //=========================END OF PROGRAM ===============================

35 36

// Note : Check t h e c a l c u l a t i o n g i v e n i n t e x t book f o r v o l t a g e g a i n Rsh=49 kohms 37 // but , t a k e n a s 40 kohms 38 // c o r r e c t a n s w e r s a r e V o l t a g e g a i n i s Av= 2 8 . 5 2 39 // The V o l t a g e g a i n i n dB i s AvdB= 2 9 . 1 0 dB

68


3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

// c h a p t e r −8 p a g e 339 e x a m p l e 8 . 5 // ================================================================== clc ; clear ; // For a 2 c a v i t y k l y s t r o n a m p l i f i e r V0 =1200; //Beam v o l t a g e i n V I0 =0.028; //Beam c u r r e n t i n A f =8*10^9; // f r e q u e n c y i n Hz d =0.001; // gap s p a c i n g i n e i t h e r c a v i t y i n m L =0.04; // s p a c i n g b e t w e e n c e n t e r s o f c a v i t i e s i n m Rsh =40000; // E f f e c t i v e s h u n t i m p e d a n c e i n ohms J1 =0.582; // v a l u e o f J1 (X) X =1.841; // b u n c h i n g p a r a m e t e r //CALCULATION w =2*( %pi ) * f ; // a n g u l a r f r e q u e n c y i n r a d v0 =0.593*10^6* sqrt ( V0 ) ; // v e l o c i t y o f e l e c t r o n i n m/ sec Vomax =((3.68* V0 * v0 ) /( w * L ) ) ; //max o u t p u t power i n V tg =( w * d ) / v0 ; // avg gap t r a n s i t a n g l e i n r a d Tg = tg *(180/( %pi ) ) ; Bi =( sind ( Tg /2) ) /( tg /2) ; // beam c o u p l i n g c o e f f i c i e n t Bo = Bi ; // o u t p u t c a v i t y c o u p l i n g c o e f f i c i e n t Vimax = Vomax / Bi ; // The i n p u t m i c r o w a v e v o l t a g e i n o r d e r t o g e n e r a t e maximum o u t p u t v o l t a g e i n V t0 = w * L / v0 ; // t r a n s i t a n g l e i n r a d R0 = V0 / I0 ; // i m p e d a n c e i n ohms Av =(( Bo ^2* J1 * t0 * Rsh ) /( R0 * X ) ) ; // V o l t a g e g a i n I2 =2* I0 * J1 ; 69

29 30 31 32 33 34 35 36 37

38 39 40

41 42

V2 = Bo * I2 * Rsh ; disp ( ’ n e g l e c t i n g beam l o a d i n g ’ ) ; Eff =0.58*( V2 / V0 ) *100; // E f f i c i e n c y i n % G0 =1/ R0 ; GB =( G0 /2) *( Bo *( Bo - cos ( Tg /2) ) ) ; //Beam l o a d i n g c o n d u c t a n c e i n mhos RB =(1/ GB ) /1000; //Beam l o a d i n g r e s i s t a n c e i n Kohms disp ( ’ Beam l o a d i n g r e s i s t a n c e i n Kohms i s ’ ) ; disp ( RB ) ; disp ( ’ The v a l u e 73 kohms i s v e r y much c o m p a r a b l e t o Rsh and c a n n o t be n e g l e c t e d b e c a u s e Tg i s q u i t e high ’ ); //OUTPUT mprintf ( ’ \ nThe i n p u t m i c r o w a v e v o l t a g e i n o r d e r t o g e n e r a t e maximum o u t p u t v o l t a g e i s Vimax=%2 . 2 f V \ nThe v o l t a g e g a i n i s Av=%2 . 2 f p e r c e n t a g e \nBeam l o a d i n g c o n d u c t a n c e i s GB=%1 . 1 0 f mhos ’ , Vimax , Av , GB ) ; //=========================END OF PROGRAM ===============================

Scilab code Exa 8.6 electronic efficiency and etc 1 2


3 clc ; 4 clear ; 5 6 // For a r e f l e x k l y s t r o n 7 n =2; // peak mode v a l u e 8 V0 =500; // beam v o l t a g e i n V

70

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

32 33 34 35 36

Rsh =20000; // Shunt r e s i s t a n c e i n ohms L =0.001; // d i s t a n c e i n m f =8*10^(9) ; // // O p e r a t i o n f r e q u e n c y i n Hz V1 =200; // m i c r o w a v e gap v o l t a g e i n V x =1.759*10^11; // e /m v a l u e i n C/ kg J1 =0.582; //CALCULATION disp ( ’ Assume t h e gap t r a n s i t t i m e and beam l o a d i n g a r e n e g l e c t e d ’ ); w =2*( %pi ) * f ; // a n g u l a r f r e q u e n c y i n r a d VR =( V0 +(( sqrt (8* V0 / x ) * w * L ) /((2*( %pi ) * n ) -(( %pi ) /2) ) ) ) ; // R e p e l l e r v o l t a g e i n V disp ( ’ Assuming o u t p u t c o u p l i n g c o e f f i c i e n t Bo=1 ’ ) ; I0 =( V1 /(2* J1 * Rsh ) ) /10^( -3) ; //Beam c u r r e n t n e c e s s a r y t o o b t a i n an m i c r o w a v e gap v o l t a f e o f 200V i n mA v0 =0.593*10^6* sqrt ( V0 ) ; // v e l o c i t y o f e l e c t r o n i n m/ sec t0 =(( w *2* L * v0 ) /( x *( VR + V0 ) ) ) ; // t r a n s i t a n g l e i n r a d Bi =1; // beam c o u p l i n g c o e f f i c i e n t [ assume ] X =(( Bi * V1 * t0 ) /(2* V0 ) ) ; disp ( ’ S i n c e X= 1 . 5 1 , from graph , J1 (X) =0.84 ’ ) ; XJ1 =0.84; Eff =((2*( XJ1 ) ) /((2* n *( %pi ) ) -(( %pi ) /2) ) ) *100 // Efficiency in % //OUTPUT mprintf ( ’ \ n R e p e l l e r v o l t a g e i s VR=%3 . 2 f V \ nThe dc n e c e s s a r y t o g i v e an m i c r o w a v e gap v o l t a f e o f 200 V i s I 0=%1 . 2 f mA \ n E l e c t r o n i c E f f i c i e n c y i s E f f= %2 . 2 f p e r c e n t a g e ’ ,VR , I0 , Eff ) ; //=========================END OF PROGRAM =============================== // Note : Check t h e a n s w e r f o r VR o n c e // C o r r e c t a n s w e r i s R e p e l l e r v o l t a g e i s VR= 1 1 8 9 . 3 6 V

71


3 4 5 6 7 8 9 10 11 12 13 14

// c h a p t e r −8 p a g e 342 e x a m p l e 8 . 7 // ================================================================== clc ; clear ; // For a r e f l e x k l y s t r o n n =1; // mode v a l u e Pi =0.04; // t h e dc i n p u t power i n W x =0.278; // r a t i o o f V1 o v e r V0

//CALCULATION X = x *3*( %pi ) /4; J1 =0.3205; // b e s s e l c o e f f i c i e n t v a l u e [ J I (X ’ ) ] ef =((2* X * J1 ) /((2*( %pi ) * n ) -(( %pi ) /2) ) ) *100; // E f f i c i e n c y of the r e f l e x k l y s t r o n in % 15 Pout =(( ef /100) * Pi ) /10^( -3) ; // T o t a l power o u t p u t i n mW 16 p =20; // p e r c e n t a g e o f t h e power d e l i v e r e d by t h e e l e c t r o n beam d i s s i p a t e d i n t h e c a v i t y w a l l s 17 Pd = Pout *(100 - p ) /100; // Power d e l i v e r e d t o l o a d i n mW 18 19 20

21 22

//OUTPUT mprintf ( ’ \ n E f f i c i e n c y o f t h e r e f l e x k l y s t r o n i s e f= %1 . 2 f p e r c e n t a g e \ n T o t a l power o u t p u t i s Pout=%1 . 3 f mW \ n I f t h e 20 p e r c e n t a g e o f t h e power d e l i v e r e d by t h e e l e c t r o n beam i s d i s s i p a t e d i n t h e c a v i t y w a l l s t h e n t h e Power d e l i v e r e d t o l o a d i s Pd=%1 . 2 f mW’ ,ef , Pout , Pd ) ; //=========================END OF PROGRAM 72

===============================

Scilab code Exa 8.8 cyclotron frequency and etc 1 2

3 4 5 6 7 8 9 10 11 12 13 14

// c h a p t e r −8 p a g e 342 e x a m p l e 8 . 8 // ================================================================== clc ; clear ; // For a c i r c u l a r magnetron a =0.15; // i n n e r r a d i u s i n m b =0.45; // o u t e r r a d i u s i n m B =1.2*10^( -3) ; // m a g n e t i c f l u x d e n s i t y i n Wb/sqm x =1.759*10^11; // V a l u e o f e /m i n C/ kg V =6000; // beam v o l t a g e i n V

//CALCULATION V0 =(( x /8) *( B ^2) *( b ^2) *(1 -( a / b ) ^2) ^2) /1000; // H u l l cut − o f f v o l t a g e i n kV 15 Bc =(( sqrt (8*( V / x ) ) ) /( b *(1 -( a / b ) ^2) ) ) *1000; // Cut− o f f m a g n e t i c f l u x d e n s i t y i n mWb/sqm 16 fc =(( x * B ) /(2*( %pi ) ) ) /10^9; // C y c l o t r o n f r e q u e n c y i n GHz 17 18 19

20 21

//OUTPUT mprintf ( ’ \ n H u l l cut − o f f v o l t a g e i s V0=%2 . 3 f kV\ nCut− o f f m a g n e t i c f l u x d e n s i t y i s Bc=%1 . 6 f mWb/sqm \ n C y c l o t r o n f r e q u e n c y i s f c=%1 . 4 f GHz ’ ,V0 , Bc , fc ) ; //=========================END OF PROGRAM ===============================

22 23

73

// Check t h e a n s w e r s o n c e // C o r r e c t a n s w e r s a r e // H u l l cut − o f f v o l t a g e i s V0 = 5 . 0 6 6 kV // Cut− o f f m a g n e t i c f l u x d e n s i t y i s Bc = 1 . 3 0 5 9 5 3 mWb/ sqm 28 // C y c l o t r o n f r e q u e n c y i s f c = 0 . 0 3 3 6 GHz

24 25 26 27

Scilab code Exa 8.9 phase velocity and anode voltage 1 2

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

// c h a p t e r −8 p a g e 343 e x a m p l e 8 . 9 // ================================================================== clc ; clear ; // For a h e l i c a l TWT c =3*10^8; // V e l o c i t y o f l i g h t i n m/ s e c d =0.002; // d i a m e t e r i n m x =5000; // no . o f t u r n s p e r m m =9.1*10^( -31) ; // mass o f an e l e c t r o n i n kg e =1.6*10^( -19) ; // c h a r g e o f an e l e c t r o n i n C //CALCULATION y =( %pi ) * d ; // c i r c u m f e r e n c e i n m p =1/ x ; // p i t c h i n m Vp =( c * p ) / y ; // A x i a l p h a s e v e l o c i t y i n m/ s e c V0 =(( m * Vp ^2) /(2* e ) ) ; // The Anode v o l t a g e a t which t h e TWT can be o p e r a t e d f o r u s e f u l g a i n i n V //OUTPUT mprintf ( ’ \ n A x i a l p h a s e v e l o c i t y i s Vp=%6 . 2 f m/ s e c \ nThe Anode v o l t a g e a t which t h e TWT can be o p e r a t e d f o r u s e f u l g a i n i s V0=%2 . 2 f V ’ ,Vp , V0 ) ;

21

74

22

//=========================END OF PROGRAM ===============================


3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

// c h a p t e r −8 p a g e 344 e x a m p l e 8 . 1 0 // ================================================================== clc ; clear ; // For a 2 c a v i t y k l y s t r o n a m p l i f i e r V0 =900; //Beam v o l t a g e i n V I0 =0.03; //Beam c u r r e n t i n A f =8*10^9; // f r e q u e n c y i n Hz d =0.001; // gap s p a c i n g i n e i t h e r c a v i t y i n m L =0.04; // s p a c i n g b e t w e e n c e n t e r s o f c a v i t i e s i n m Rsh =40000; // E f f e c t i v e s h u n t i m p e d a n c e i n ohms y =0.582; // v a l u e o f J1 (X) X =1.841; //CALCULATION v0 =(0.593* sqrt ( V0 ) *10^6) /10^7; // The e l e c t r o n v e l o c i t y i n 1 0 ˆ 7 m/ s e c v = v0 *10^7; t0 =( d / v ) /10^( -10) ; // T r a n s i t t i m e i n 10ˆ( −10) s e c t = t0 *10^( -10) ; a =2*( %pi ) * f * t ; //Gap t r a n s i t a n g l e i n r a d Bi =( sin ( a /2) ) /( a /2) ; //Beam c o u p l i n g c o e f f i c i e n t Bo = Bi ; to =(2*( %pi ) * f * L ) / v ; // dc t r a n s i t a n g l e i n r a d disp ( ’ For maximum o u t o u t v o l t a g e , V2 J1 (X) = 0 . 5 8 2 ,X =1.841 ’ ); V1 =((2* V0 * X ) /( Bo * to ) ) // The i n p u t v o l t a g e f o r maximum 75

output v o l t a g e in V 27 Ro =( V0 / I0 ) ; 28 Av =(( Bo ^2* to * y * Rsh ) /( Ro * X ) ) ; // V o l t a g e g a i n 29 AvdB =10* log10 ( Av ) ; // V o l t a g e g a i n i n dB 30 31 32

33 34

//OUTPUT mprintf ( ’ \ nThe e l e c t r o n v e l o c i t y i s v0=%1 . 1 f ∗ 1 0 ˆ 7 m / s e c \ nThe dc e l e c t r o n T r a n s i t t i m e i s t 0=%1 . 2 f ∗10ˆ( −10) s e c \ nThe i n p u t v o l t a g e f o r maximum o u t p u t v o l t a g e i s V1=%2 . 2 f V \ n V o l t a g e g a i n i s Av =%2 . 2 f \ n V o l t a g e g a i n i n dB i s AvdB=%2 . 2 f dB ’ ,v0 , t0 , V1 , Av , AvdB ) ; //=========================END OF PROGRAM ===============================

Scilab code Exa 8.11 dc electron velocity and etc 1 2

3 4 5 6 7 8 9 10 11 12 13

// c h a p t e r −8 p a g e 345 e x a m p l e 8 . 1 1 // ================================================================== clc ; clear ;

// For a f o u r c a v i t y K l y s t r o n V0 =20000; //Beam v o l t a g e i n V I =2; //Beam c u r r e n t i n A f =9*10^9; // O p e r a t i o n f r e q u e n c y i n Hz p0 =10^( -6) ; // dc e l e c t r o n c h a r g e d e n s i t y i n C/mˆ3 p =10^( -8) ; //RF c h a r g e d e n s i t y i n C/mˆ3 V =10^5; // V e l o c i t y p e r t u r b a t i o n s i n m/ s e c e0 =8.854*10^( -12) ; // P e r m i t t i v i t y o f f r e e s p a c e i n F/ m 14 R =0.5; 76

15 16 //CALCULATION 17 v0 =(0.593*10^6* sqrt ( V0 ) ) /1000; // The dc e l e c t r o n 18 19 20 21 22 23 24 25 26 27 28

29 30

v e l o c i t y i n Km/ s e c w =2*( %pi ) * f ; // a n g u l a r f r e q u e n c y i n r a d / s e c v = v0 *1000; c =( w / v ) ; // The dc Phase C o n s t a n t wp =( sqrt (1.759*10^11*( p0 / e0 ) ) ) /10^8; // The Plasma Frequency i n 10ˆ8 rad / s e c wp1 = wp *10^8; wq =( R * wp1 ) /10^8; // The Reduced Plasma F r e q u e n c y i n 10ˆ8 rad / s e c J0 = p0 * v ; // The dc beam c u r r e n t d e n s i t y i n A/sqm J =( p * v ) -( p0 * V ) ; // The i n s t a n t a n e o u s beam c u r r e n t d e n s i t y i n A/sqm //OUTPUT mprintf ( ’ \ nThe dc e l e c t r o n v e l o c i t y i s v0=%4 . 2 f Km/ s e c \ nThe dc Phase C o n s t a n t i s c=%3 . 2 f r a d / s e c \ nThe Plasma F r e q u e n c y i s wp=%1 . 2 f ∗ 1 0 ˆ 8 r a d / s e c \ nThe Reduced Plasma F r e q u e n c y i s wq=%1 . 3 f ∗ 1 0 ˆ 8 r a d / s e c \ nThe dc beam c u r r e n t d e n s i t y i s J0=%2 . 2 f A/sqm \ nThe i n s t a n t a n e o u s beam c u r r e n t d e n s i t y i s J=%1 . 4 f A/sqm ’ ,v0 ,c , wp , wq , J0 , J ) ; //=========================END OF PROGRAM ===============================

Scilab code Exa 8.12 gap transit angle 1 2


3 clc ;

77

4 5 6 7 8 9 10 11 12 13 14 15

clear ; // For a r e f l e x k l y s t r o n f =5*10^9; // F r e q u e n c y o f o p e r a t i o n i n hz V0 =1000; // anode v o l t a g e i n V d =0.002; // c a v i t y gap i n m Vr = -500; // r e p e l l e r v o l t a g e i n V

//CALCULATION N =7/4; // mode v a l u e VR = abs ( Vr ) ; L =((( VR + V0 ) * N ) /(6.74*10^( -6) * f * sqrt ( V0 ) ) ) /10^( -3) ; // Optimum l e n g t h o f t h e d r i f t r e g i o n i n mm 16 u =5.93*10^5* sqrt ( V0 ) ; // i n m/ s e c 17 w =2*( %pi ) * f ; // a n g u l a r f r e q u e n c y i n r a d 18 Tg =( w * d ) / u ; //Gap t r a n s i t a n g l e i n r a d 19 20 21

22 23

//OUTPUT mprintf ( ’ \nOptimum l e n g t h o f t h e d r i f t r e g i o n i s L= %1 . 3 f mm \nGap t r a n s i t a n g l e i s Tg=%1 . 3 f r a d ’ ,L , Tg ) ; //=========================END OF PROGRAM ===============================



3 clc ; 4 clear ; 5 6 // For a 2 c a v i t y

klystron amplifier 78

7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

31 32

V0 =1200; //Beam v o l t a g e i n V I0 =0.03; //Beam c u r r e n t i n A f =10*10^9; // f r e q u e n c y i n Hz d =0.001; // gap s p a c i n g i n e i t h e r c a v i t y i n m L =0.04; // s p a c i n g b e t w e e n c e n t e r s o f c a v i t i e s i n m Rsh =40000; // E f f e c t i v e s h u n t i m p e d a n c e i n ohms J1 =0.582; // v a l u e o f J1 (X) X =1.841; // b u n c h i n g p a r a m e t e r //CALCULATION v0 =0.593*10^6* sqrt ( V0 ) ; // v e l o c i t y o f r e f e r e n c e e l e c t r o n i n m/ s e c w =2*( %pi ) * f ; // a n g u l a r f r e q u e n c y i n r a d a = w * L / v0 ; // t r a n s i t a n g l e w i t h o u t RF v o l t a g e i n r a d tg = a * d / L ; // a v e r a g e gap t r a n s i t a n g l e i n r a d Bi =( sin ( tg /2) ) /( tg /2) ; // beam c o u p l i n g c o e f f i c i e n t V1max =((2* X * V0 ) /( Bi * a ) ) ; // I n p u t RF v o l t a g e f o r Maximum o u t p u t v o l t a g e i n V B0 = Bi ; // o u t p u t c a v i t y c o u p l i n g c o e f f i c i e n t V2 =2* B0 * I0 * J1 * Rsh ; // i n V Av = V2 / V1max ; // V o l t a g e g a i n AvdB =20* log10 ( Av ) ; // V o l t a g e g a i n i n dB n =0.58*( V2 / V0 ) *100; //Maximum e f f i c i e n c y i n % //OUTPUT mprintf ( ’ \ n I n p u t RF v o l t a g e f o r Maximum o u t p u t v o l t a g e i s V1max=%2 . 2 f V \ nThe V o l t a g e g a i n i s AvdB=%2 . 2 f dB \nMaximum e f f i c i e n c y i s I 0=%2 . 2 f p e r c e n t a g e ’ , V1max , AvdB , n ) ; //=========================END OF PROGRAM ===============================

33 34 35 36

// Note : Check t h e a n s w e r s o n c e // There a r e s l i g h t c h a n g e s i n v a l u e s // I n p u t RF v o l t a g e f o r Maximum o u t p u t v o l t a g e i s V1max = 5 5 . 2 8 V 37 // The V o l t a g e g a i n i s AvdB= 2 4 . 3 5 dB 79

38

//Maximum e f f i c i e n c y

i s I0 =44.11 p e r c e n t a g e

Scilab code Exa 8.14 cyclotron angular frequency and etc 1 2

3 4 5 6 7 8 9 10 11 12 13 14

// c h a p t e r −8 p a g e 347 e x a m p l e 8 . 1 4 // ================================================================== clc ; clear ; // For aa X−band c y l i n d r i c a l magnetron a =0.04; // i n n e r r a d i u s i n m b =0.08; // o u t e r r a d i u s i n m B =0.01; // m a g n e t i c f l u x d e n s i t y i n Wb/sqm x =1.759*10^11; // V a l u e o f e /m i n C/ kg V =30000; // beam v o l t a g e i n V

//CALCULATION w =( x * B ) /10^9; // C y c l o t r o n a n g u l a r f r e q u e n c y i n 1 0 ˆ 9 rad / s e c 15 VHC =(( x /8) *( B ^2) *( b ^2) *(1 -( a / b ) ^2) ^2) /1000; // H u l l cut − o f f v o l t a g e i n kV 16 Bc =(( sqrt (8*( V / x ) ) ) /( b *(1 -( a / b ) ^2) ) ) *1000; // Cut− o f f m a g n e t i c f l u x d e n s i t y i n mWb/sqm 17 18 19

20 21

//OUTPUT mprintf ( ’ \ n C y c l o t r o n a n g u l a r f r e q u e n c y i s w=%1 . 3 f ∗ 1 0 ˆ 9 r a d / s e c \ n H u l l cut − o f f v o l t a g e i s VHC=%1 . 4 f kV \ nCut− o f f m a g n e t i c f l u x d e n s i t y i s Bc=%2 . 3 f mWb/sqm ’ ,w , VHC , Bc ) ; //=========================END OF PROGRAM ===============================

80


3 4 5 6 7 8 9 10 11 12 13 14 15

// c h a p t e r −8 p a g e 348 e x a m p l e 8 . 1 5 // ================================================================== clc ; clear ; // For a r e f l e x k l y s t r o n n =2; // peak mode v a l u e V0 =280; // beam v o l t a g e i n V I0 =0.022; // beam c u r r e n t i n A Vs =30; // s i g n a l v o l t a g e i n V J1 =1.25; // b e s s e l c o e f f i c i e n t f o r n=2

//CALCULATION Pdc = V0 * I0 ; // The i n p u t power i n w a t t s Pac =((2* Pdc * J1 ) /((2* n *( %pi ) ) -(( %pi ) /2) ) ) ; // The o u t p u t power i n w a t t s 16 n =( Pac / Pdc ) *100; // E f f i c i e n c y i n p e r c e n t a g e 17 18 19

20 21

//OUTPUT mprintf ( ’ \ nThe i n p u t power i s Pdc=%1 . 2 f w a t t s \ nThe o u t p u t power i s Pac=%1 . 1 f w a t t s \ n E f f i c i e n c y i s n =%2 . 2 f p e r c e n t a g e ’ ,Pdc , Pac , n ) ; //=========================END OF PROGRAM ===============================

Scilab code Exa 8.16 repeller voltage and etc

81

1 2

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

25 26

// c h a p t e r −8 p a g e 348 e x a m p l e 8 . 1 6 // ================================================================== clc ; clear ; // For a r e f l e x k l y s t r o n n =2; // peak mode v a l u e V0 =300; // beam v o l t a g e i n V Rsh =20000; // Shunt r e s i s t a n c e i n ohms L =0.001; // d i s t a n c e i n m J1 =0.582; // b e s s e l c o e f f i c i e n t v a l u e [ J I (X ’ ) ] f =8*10^(9) ; // // O p e r a t i o n f r e q u e n c y i n Hz V1 =200; //RF gap v o l t a g e i n V x =1.759*10^11; // e /m v a l u e i n C/ kg //CALCULATION disp ( ’ Assume t h e gap t r a n s i t t i m e and beam l o a d i n g a r e n e g l e c t e d ’ ); w =2*( %pi ) * f ; // a n g u l a r f r e q u e n c y i n r a d VR =( V0 +(( sqrt (8* V0 / x ) * w * L ) /((2*( %pi ) * n ) -(( %pi ) /2) ) ) ) ; // R e p e l l e r v o l t a g e i n V disp ( ’ Assuming o u t p u t c o u p l i n g c o e f f i c i e n t Bo=1 ’ ) ; I0 =( V1 /(2* J1 * Rsh ) ) /10^( -3) ; //Beam c u r r e n t n e c e s s a r y t o o b t a i n an RF gap v o l t a f e o f 200V i n mA //OUTPUT mprintf ( ’ \ nThe R e p e l l e r v o l t a g e i s VR=%3 . 2 f V \nBeam c u r r e n t n e c e s s a r y t o o b t a i n an RF gap v o l t a f e o f 200V i s I 0=%1 . 2 f mA ’ ,VR , I0 ) ; //=========================END OF PROGRAM ===============================

82

Chapter 9 Solid State Microwave Devices

Scilab code Exa 9.1 frequency 1 2

3 4 5 6 7 8 9 10 11 12 13 14 15

// c h a p t e r −9 p a g e 411 e x a m p l e 9 . 1 // ================================================================== clc ; clear ; L =2*10^( -6) ; // D r i f t Length o f a IMPATT d i o d e i n m Vd =(10^7) *(10^( -2) ) ; // D r i f t V e l o c i t y f o r S i i n m/ s e c //CALCULATION f =( Vd /(2* L ) ) /10^9; // O p e r a t i n g F r e q u e n c y i n GHz //OUTPUT mprintf ( ’ \ n O p e r a t i n g F r e q u e n c y o f t h e IMPATT d i o d e i s f=%2 . 0 f GHz ’ ,f ) ; //=========================END OF PROGRAM ===============================

83

Scilab code Exa 9.2 threshold electric field 1 2

3 4 5 6 7 8 9 10 11 12 13 14 15 16

// c h a p t e r −9 p a g e 411 e x a m p l e 9 . 2 // ================================================================== clc ; clear ; L =75*10^( -6) ; // D e v i c e Length i n m V =25; // V o l t a g e P u l s e A m p l i f i e d i n V f =10*10^9; // O p e r a t i n g F r e q u e n c y i n Hz //CALCULATION Eth =( V / L ) /10^5; // T h r e s h o l d E l e c t r i c F i e l d i n kV/cm //OUTPUT mprintf ( ’ \ n T h r e s h o l d E l e c t r i c F i e l d i s Eth=%1 . 2 f kV/ cm ’ , Eth ) ; //=========================END OF PROGRAM ===============================

Scilab code Exa 9.3 power gain 1 2


3 clc ; 4 clear ; 5

84

6 7 8 9

fs =2*10^9; // S i g n a l F r e q u e n c y i n Hz fp =12*10^9 //Pump F r e q u e n c y i n Hz Ri =16; //O/P r e s i s t a n c e o f s i g n a l g e n e r a t o r i n ohms Rs =1000; //On t y p e s r e s i s t a n c e o f s i g n a l g e n e r a t o r i n ohms

10 11 //CALCULATION 12 P =10* log10 (( fp - fs ) / fs ) ; // Power g a i n i n dB 13 Pusb =10* log10 (( fp + fs ) / fs ) ; // Power g a i n a s USB

c o n v e r t e r i n dB 14 15 16 17 18

//OUTPUT mprintf ( ’ \ nPower g a i n i s P=%1 . 2 f dB \ nPower g a i n a s USB c o n v e r t e r i s Pusb=%1 . 2 f dB ’ ,P , Pusb ) ; //=========================END OF PROGRAM ===============================

19 20 21

// Note : Answer g i v e n i n t e x t b o o k i s wrong Check i t once . . 22 // C o r r e c t a n s w e r s a r e Power g a i n i s P=6.99 dB 23 // Power g a i n a s USB c o n v e r t e r i s Pusb =8.45 dB

Scilab code Exa 9.4 breakdown voltage and etc 1 2


3 clc ; 4 clear ; 5 6 es =12.5; // R e l a t i v e

D i e l e c t r i c constant 85

7 e0 =8.854*10^( -12) ; // P e r m i t t i v i t y 8 9 10 11 12 13

i n F r e e S p a c e i n F/

m N =3.2*10^22; // Donor C o n c e n t r a t i o n p e r mˆ3 L =8*10^( -6) ; // Length o f S i BARITT d i o d e i n m q =1.6*10^( -19) ; // Charge o f an E l e c t r o n i n C

//CALCULATION Vc =(( q * N * L ^2) /(2* es * e0 ) ) /10^3; // C r i t i c a l V o l t a g e i n kV 14 Vbd =2* Vc ; // Breakdown V o l t a g e i n kV 15 Ebd =( Vbd / L ) /100; // Breakdown E l e c t r i c F i e l d i n kV/cm 16 17 18

19 20

//OUTPUT mprintf ( ’ \ n C r i t i c a l V o l t a g e i s Vc=%1 . 2 f kV \ nBreakdown V o l t a g e i s Vbd=%1 . 2 f kV \ nBreakdown E l e c t r i c F i e l d i s Ebd=%6 . 2 f kV/cm ’ ,Vc , Vbd , Ebd ) ; //=========================END OF PROGRAM ===============================

Scilab code Exa 9.5 Avalanche zone velocity 1 2


3 clc ; 4 clear ; 5 6 J =33000; // C u r r e n t d e n s i t y i n A/ sqcm 7 Na =2.5*10^16; // Doping C o n c e n t a t i o n i n TRAPATT d i o d e

p e r c u b i c cm 8 q =1.6*10^( -19) ; // Charge o f an E l e c t r o n i n C 9 10

//CALCULATION 86

11 Vz =( J /( q * Na ) ) /10^5; // A v a l a n c h e Zone V e l o c i t y

i n Km/

sec 12 13 14 15 16

//OUTPUT mprintf ( ’ \ n A v a l a n c h e Zone V e l o c i t y i s Vz=%2 . 1 f Km/ s e c ’ , Vz ) ; //=========================END OF PROGRAM ===============================


3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

// c h a p t e r −9 p a g e 412 e x a m p l e 9 . 6 // ================================================================== clc ; clear ; // For an IMPATT d i o d e power a m p l i f i e r Rd =25; // N e g a t i v e R e s i s t a n c e i n ohms Rl =50; // Load R e s i s t a n c e i n ohms //CALCULATION x = abs ( Rd ) ; G =(( - x - Rl ) /( - x + Rl ) ) ^2; // Power g a i n o f an IMPATT diode //OUTPUT mprintf ( ’ \ nPower g a i n o f an IMPATT d i o d e i s G=%1 . 0 f ’ ,G ) ; //=========================END OF PROGRAM ===============================

87

Scilab code Exa 9.7 minimum voltage 1 2


3 clc ; 4 clear ; 5 6 // For a Gunn Diode 7 L =5*10^( -4) ; // D r i f t Length i n cm 8 Vg =3300; // V o l t a g e g r a d i e n t i n V/cm [ Vg>3.3 kV/cm ] 9 10 //CALCULATION 11 Vmin = Vg * L ; // Minimum V o l t a g e n e e d e d t o i n i t i a t e Gunn

e f f e c t in volts 12 13 14 15 16

//OUTPUT mprintf ( ’ \nMinimum V o l t a g e n e e d e d t o i n i t i a t e Gunn e f f e c t i s Vmin=%1 . 2 f v o l t s ’ , Vmin ) ; //=========================END OF PROGRAM ===============================

Scilab code Exa 9.8 rational frequency 1 2


3 clc ; 4 clear ;

88

5 6 7 8 9 10 11 12 13 14 15 16

17 18

// For a Gunn Diode L =20*10^( -4) ; // A c t i v e Length i n cm Vd =2*10^7; // D r i f t V e l o c i t y o f E l e c t r o n s i n cm/ s e c Ec =3.3*10^3; // C r i t i c l F i e l d f o r GaAs i n V/cm //CALCULATION fn =( Vd / L ) /10^9; // N a t u r a l ( R a t i o n a l ) F r e q u e n c y i n GHz Vc = L * Ec ; // C r i t i c a l V o l t a g e o f t h e d i o d e i n v o l t s //OUTPUT mprintf ( ’ \ n N a t u r a l ( R a t i o n a l ) F r e q u e n c y i s f n=%2 . 0 f GHz \ n C r i t i c a l V o l t a g e o f t h e d i o d e i s Vc=%1 . 1 f v o l t s ’ ,fn , Vc ) ; //=========================END OF PROGRAM ===============================


3 4 5 6 7 8 9 10 11 12 13

// c h a p t e r −9 p a g e 412 e x a m p l e 9 . 9 // ================================================================== clc ; clear ; // For an IMPATT d i o d e Lp =0.5*10^( -9) ; // I n d u c t a n c e i n Henry Cj =0.5*10^( -12) ; // C a p a c i t a n c e i n Farad Ip =0.8; //RF peak c u r r e n t i n A Rl =2; // Load R e s i s t a n c e i n ohms Vbd =100; // Breakdown V o l t a g e i n V Ib =0.1; // dc B i a s c u r r e n t i n A

89

14 //CALCULATION 15 f =(1/(2*( %pi ) * sqrt ( Lp * Cj ) ) ) /10^9; // R e s o n a n t

F r e q u e n c y i n GHz 16 n =(( Rl * Ip ^2) /(2* Vbd * Ib ) ) *100; // E f f i c i e n c y i n Percentage 17 18 19 20 21

//OUTPUT mprintf ( ’ \ n R e s o n a n t F r e q u e n c y i s f=%2 . 0 f GHz \ n E f f i c i e n c y i s n=%1 . 1 f p e r c e n t a g e ’ ,f , n ) ; //=========================END OF PROGRAM ===============================

Scilab code Exa 9.10 drift time 1 2


3 clc ; 4 clear ; 5 6 // For an IMPATT d i o d e 7 L =2*10^( -6) ; // D r i f t Length i n m 8 Vd =10^5; // C a r r i e r D r i f t V e l o c i t y ( Assume / C o n s i d e r )

i n m/ s e c 9 10 //CALCULATION 11 t =( L / Vd ) /10^( -9) ; // D r i f t Time o f t h e C a r r i e r

i n nano s e c [ From f =(1/2 t ) =(Vd/2L ) ] 12 t1 = t *10^( -9) ; 13 f =(1/(2* t1 ) ) /10^9; // O p e r a t i n g F r e q u e n c y o f t h e d i o d e i n GHz 14 15

//OUTPUT 90

16

17 18

mprintf ( ’ \ n D r i f t Time o f t h e C a r r i e r i s t=%1 . 2 f nano s e c \ n O p e r a t i n g F r e q u e n c y o f t h e d i o d e i s f=%2 . 0 f GHz ’ ,t , f ) ; //=========================END OF PROGRAM ===============================

Scilab code Exa 9.11 breakdown voltage and etc 1 2

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

19 20

// c h a p t e r −9 p a g e 413 e x a m p l e 9 . 1 1 // ================================================================== clc ; clear ; // For an M−S i −M B a s i t t d i o d e er =11.8; // R e l a t i v e d i e l e c t r i c c o n s t a n t o f S i e0 =8.854*10^( -12) ; // P e r m i t t i v i t y o f f r e e s p a c e i n F/m N =3*10^(21) ; // Donor C o n c e n t r a t i o n p e r mˆ3 L =6.2*10^( -6) ; // S i Length i n m q =1.6*10^( -19) ; // Charge o f an E l e c t r o n i n C //CALCULATION Vbd =(( q * N * L ^2) /( er * e0 ) ) ; // Breakdown V o l t a g e i n V Ebd =( Vbd / L ) /10^3; // Breakdown E l e c t r i c F i e l d i n kV/m //OUTPUT mprintf ( ’ \ nBreakdown V o l t a g e i s Vbd=%3 . 1 f V \ nBreakdown E l e c t r i c F i e l d i s Ebd=%5 . 0 f kV/m ’ ,Vbd , Ebd ) ; //=========================END OF PROGRAM ===============================

91

Scilab code Exa 9.12 max power gain and etc 1 2


3 clc ; 4 clear ; 5 6 // For an u p c o n v e r t e r p a r a m e t r i c a m p l i f i e r 7 rQ =8; // f i g u r e o f m e r i t f o r a d i o d e n o n l i n e a r

capacitor 8 r =0.2; 9 y =8; // r a t i o

of output frequency over s i g n a l frequency ( f0 / fs ) 10 Td =300; // Diode T e m p e r a t u r e i n K 11 T0 =300; // Ambient T e m p e r a t u r e i n K 12 13 14 15 16 17 18 19 20 21 22

23 24

//CALCULATION X =(( rQ ) ^2) / y ; G =(( y * X ) /(1+ sqrt (1+ X ) ) ^2) ; //Max power g a i n GdB =10* log10 ( G ) ; //Maximum Power Gain i n dB F =(1+((2* Td / T0 ) *((1/ rQ ) +(1/ rQ ) ^2) ) ) ; // N o i s e F i g u r e FdB =10* log10 ( F ) ; // N o i s e F i g u r e i n dB BW =2* r * sqrt ( y ) ; // Bandwidth //OUTPUT mprintf ( ’ \nMaximum Power Gain i s GdB=%1 . 2 f dB\ n N o i s e F i g u r e i s FdB=%1 . 2 f dB \ nBandWidth i s BW=%1 . 2 f ’ , GdB , FdB , BW ) ; //=========================END OF PROGRAM ===============================

92

Scilab code Exa 9.13 gain and etc 1 2

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

// c h a p t e r −9 p a g e 414 e x a m p l e 9 . 1 3 // ================================================================== clc ; clear ; // For a n e g a t i v e r e s i s t a n c e p a r a m e t r i c a m p l i f i e r fs =2*10^9; // S i g n a l F r e q u e n c y i n Hz fp =12*10^9; //pump F r e q u e n c y i n Hz fi =10*10^9; // i d l e r F r e q u e n c y i n Hz fd =5*10^9; // F r e q u e n c y i n Hz Ri =1000; // o / p r e s i s t a n c e o f i d l e r g e n e r a t o r i n ohms Rg =1000; // o / p r e s i s t a n c e o f s i g n a l g e n e r a t o r i n ohms RTs =1000; // t o t a l s e r i e s r e s i s t a n c e a t f s i n ohms RTi =1000; // t o t a l s e r i e s r e s i s t a n c e a t f i i n ohms r =0.35; rQ =10; // f i g u r e o f m e r i t Td =300; // Avg Diode T e m p e r a t u r e i n K T0 =300; // Ambient T e m p e r a t u r e i n K C =0.01*10^( -12) ; // C a p a c i t a n c e i n F //CALCULATION ws =2*( %pi ) * fs ; wi =2*( %pi ) * fi ; R =(( r ^2) /( ws * wi * RTi * C ^2) ) ; // E q u i v a l e n t n o i s e r e s i s t a n c e i n ohms a =( R / RTs ) ; G =((4* fi * a * Rg * Ri ) /( fs * RTs * RTi *(1 - a ) ^2) ) ; // Gain GdB =10* log10 ( G ) ; // Gain i n dB F =(1+((2* Td / T0 ) *((1/ rQ ) +(1/ rQ ) ^2) ) ) ; // N o i s e F i g u r e FdB =10* log10 ( F ) ; // N o i s e F i g u r e i n dB 93

30 BW =(( r /2) *( sqrt ( fd /( fs * G ) ) ) ) ; 31 32 //OUTPUT 33 mprintf ( ’ \ n E q u i v a l e n t n o i s e r e s i s t a n c e

i s R=%4 . 1 f ohms \ nGain i s GdB=%2 . 1 f dB\ n N o i s e F i g u r e i s FdB= %1 . 2 f dB \ nBandWidth i s BW=%1 . 3 f ’ ,R , GdB , FdB , BW ) ;

34 35 36 37

//=========================END OF PROGRAM =============================== // Note : Check t h e Bandwidth a n s w e r i s o n c e I t s h o u l d be 0 . 0 2 7

94

Chapter 10 Microwave Communication Systems

Scilab code Exa 10.1 radio horizon 1 2

// c h a p t e r −10 p a g e 486 e x a m p l e 1 0 . 1 // ==================================================================

3 clc ; 4 clear ; 5 6 ht =144; //TV t r a n s m i t t e r a n t e n n a h e i g h t i n m 7 hr =25; //TV r e c e i v e r a n t e n n a h e i g h t i n m 8 // Radio h o r i z o n i s a b o u t 4/3 a s f a r a s t h e o p t i c a l

horizon 9 10 //CALCULATION 11 dr =4* sqrt ( hr ) ; // d i s t a n c e i n km 12 dt =4* sqrt ( ht ) ; // Radio H o r i z o n i n km 13 d = dt + dr ; // The Maximum d i s t a n c e o f P r o p a g a t i o n o f t h e

TV s i g n a l i n km 14 15

//OUTPUT 95

16

17 18

mprintf ( ’ \ nThe Maximum d i s t a n c e o f P r o p a g a t i o n o f t h e TV s i g n a l i s d=%2 . 0 f km \ nRadio H o r i z o n i s d t =%2 . 0 f km ’ ,d , dt ) ; //=========================END OF PROGRAM ===============================

Scilab code Exa 10.2 value of factor 1 2


3 clc ; 4 clear ; 5 6 r =6370*10^3; // r a d i u s o f t h e e a r t h i n m 7 x = -0.05*10^( -6) ; // t h e g r a d i e n t o f r e f r a c t i v e

index

o f a i r n e a r t h e g r o u n d p e r m [ du / dh ] 8 9 //CALCULATION 10 k =1/(1+( r * x ) ) ; // The v a l u e o f t h e

f a c t o r by which t h e h o r i z o n d i s t a n c e o f a t r a n s m i t t e r w i l l be modified

11 12 13

14 15

//OUTPUT mprintf ( ’ \ nThe v a l u e o f t h e f a c t o r by which t h e h o r i z o n d i s t a n c e o f a t r a n s m i t t e r w i l l be m o d i f i e d i s k=%1 . 4 f ’ ,k ) ; //=========================END OF PROGRAM ===================================

96


3 4 5 6 7 8 9 10

// c h a p t e r −10 p a g e 487 e x a m p l e 1 0 . 3 // ================================================================== clc ; clear ;

// For a m i c r o w a v e LOS l i n k f =2*10^9; // f r e q u e n c y o f o p e r a t i o n i n Hz c =3*10^8; // V e l o c i t y o f l i g h t i n m/ s e c r =50000; // r e p e a t e r s p a c i n g i n m PrdBm = -20; // r e q u i r e d c a r r i e r power a t t h e r e c e i v e r i / p t o a v o i d d e t e r i o r a t i o n due t o f a d i n g and n o i s e i n dBm 11 GtdB =34; // a n t e n n a g a i n o f t r a n s m i t t e r i n dB 12 GrdB =34; // a n t e n n a g a i n o f r e c e i v e r i n dB 13 LdB =10; // c o u p l i n g and w a v e g u i d e l o s s i n t r a n s m i t t e r i n dB 14 15 //CALULATION 16 w = c / f ; // w a v e l e n g t h i n m 17 x =( w ^2) /(4*( %pi ) ) ; 18 y =(4*( %pi ) * r ^2) ; 19 PtdBm = PrdBm +(10* log10 ( y ) ) - GtdB -(10* log10 ( x ) ) + LdB -

GrdB ; // The r e q u i r e d C a r r i e r T r a n s m i t t e r power i n dBm 20 21 22 23 24

//OUTPUT mprintf ( ’ \ nThe r e q u i r e d C a r r i e r T r a n s m i t t e r power i s PtdBm=%2 . 1 f dBm ’ , PtdBm ) ; //=========================END OF PROGRAM ===================================

97



3 4 5 6 7 8 9

clc ; clear ;

10 11 12 13 14 15 16 17 18 19 20

// For a g e o s t a t i o n a r y c o m m u n i c a t i o n s a t e l l i t e f =6*10^(9) ; // u p l i n k f r e q u e n c y i n Hz Pt =1000; // T r a n s m i t t e r power i n W x =36000*10^3; // v e r t i c a l d i s t a n c e b e t w e e n s u r f a c e o f e a r t h and s a t e l l i t e i n m a =5; // a n t e n n a e l e v a t i o n a n g l e i n deg GtdB =60; // a n t e n n a g a i n o f t r a n s m i t t e r i n dB GrdB =0; // a n t e n n a g a i n o f r e c e i v e r i n dB c =3*10^8; // V e l o c i t y o f l i g h t i n m/ s e c

//CALCULATION Gt =10^( GtdB /10) ; // a n t e n n a g a i n o f t r a n s m i t t e r Gr =10^( GrdB /10) ; // a n t e n n a g a i n o f r e c e i v e r w = c / f ; // w a v e l e n g t h i n m Ar =( w ^2) *( Gr /(4*( %pi ) ) ) ; // a r e a i n sqm r = x /( sind ( a ) ) ; // d i s t a n c e b e t w e e n t r a n s m i t t e r and r e c e i v e r i n m [ From S i n e f o r m u l a and d i a g r a m ] 21 Pr =(( Pt * Gt * Ar ) /(4*( %pi ) * r ^2) ) /10^( -12) ; // The r e c e i v e d power a t t h e i n p u t o f t h e s a t e l l i t e r e c e i v e r in pico watts 22 23 24

//OUTPUT mprintf ( ’ \ nThe r e c e i v e d power a t t h e i n p u t o f t h e s a t e l l i t e r e c e i v e r i s Pr=%1 . 2 f p i c o w a t t s (pW) ’ , Pr ); 98

25 26

//=========================END OF PROGRAM ===============================

Scilab code Exa 10.5 antenna beam angle 1 2


3 clc ; 4 clear ; 5 6 x1 =35855; // D i s t a n c e b e t w e e n g e o s t a t i o n a r y

o r b i t to

s u r f a c e o f e a r t h i n km 7 x2 =6371; // D i s t a n c e b e t w e e n c e n t e r o f e a r t h t o s u r f a c e o f e a r t h i n km 8 9 //CALCULATION 10 x = x1 + x2 ; // d i s t a n c e

o f s a t e l l i t e from c e n t e r o f e a r t h

i n km 11 y = x2 *( %pi ) ; // C i r c u m f e r e n c e o f h a l f c i r c l e a r c i n km 12 b = y / x ; //Beam a n g l e i n r a d 13 Bdeg =( b *180) /( %pi ) ; //Beam a n g l e i n deg 14 15 //OUTPUT 16 mprintf ( ’ \ nAntenna Beam a n g l e r e q u i r e d by a

s a t e l l i t e antenna to provide f u l l g l o b a l coverage from a g e o s t a t i o n a r y o r b i t i s Bdeg=%2 . 2 f deg ’ , Bdeg ) ; 17 18

//=========================END OF PROGRAM ===============================

99

Scilab code Exa 10.6 round trip time 1 2


3 clc ; 4 clear ; 5 6 // For a s a t e l l i t e c o m m u n i c a t i o n s y s t e m 7 h =35855; // D i s t a n c e b e t w e e n g e o s t a t i o n a r y

o r b i t to

s u r f a c e o f e a r t h i n km 8 r =6371; // D i s t a n c e b e t w e e n c e n t e r 9

of earth to s u r f a c e

o f e a r t h i n km a =5; // e a r t h s t a t i o n e l e v a t i o n a n g l e wrt t h e g e o s t a t i o n a r y s a t e l l i t e i n deg b =5; // a n g l e i n deg c =3*10^5; // V e l o c i t y o f l i g h t i n km/ s e c b1 =90; // a n g l e f o r v e r t i c a l t r a n s m i s s i o n i n deg a1 =0;

10 11 12 13 14 15 //CALCULATION 16 d =( sqrt (( r + h ) ^2 -( r * cosd ( a ) ) ^2) ) - sind ( b ) ; // d i s t a n c e

i n km 17 T =2*( d / c ) ; // The round t r i p t i m e b e t w e e n t h e e a r t h s t a t i o n and t h e s a t e l l i t e i n s e c 18 d1 =( sqrt (( r + h ) ^2 -( r * cosd ( a ) ) ^2) ) - sind ( b ) ; // d i s t a n c e i n km 19 Tv =(2/ c ) *( d1 - r ) ; // The round t r i p t i m e f o r v e r t i c a l t r a n s m i s s i o n b e t w e e n t h e e a r t h s t a t i o n and t h e s a t e l l i t e in sec 20 21 22

//OUTPUT mprintf ( ’ \ nThe round t r i p t i m e b e t w e e n t h e e a r t h 100

s t a t i o n and t h e s a t e l l i t e i s T=%1 . 3 f s e c \ nThe round t r i p t i m e f o r v e r t i c a l t r a n s m i s s i o n b e t w e e n t h e e a r t h s t a t i o n and t h e s a t e l l i t e i s Tv=%1 . 3 f s e c ’ ,T , Tv ) ; 23 24

//=========================END OF PROGRAM ===============================

Scilab code Exa 10.7 figure of merit 1 2

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

// c h a p t e r −10 p a g e 488 e x a m p l e 1 0 . 7 // ================================================================== clc ; clear ; Tant =25; // e f f e c t i v e n o i s e t e m p e r a t u r e i n K Tr =75; // r e c e i v e r n o i s e t e m p e r a t u r e i n K GdB =45; // I s o t r o p i c power g a i n o f t h e a n t e n n a i n dB //CALCULATION T = Tant + Tr ; // The t o t a l n o i s e i n K TdB =10* log10 ( T ) ; // The t o t a l n o i s e i n dB MdB = GdB - TdB ; // F i g u r e o f m e r i t o f e a r t h s t a t i o n i n dB //OUTPUT mprintf ( ’ \ n F i g u r e o f m e r i t o f e a r t h s t a t i o n i s MdB= %2 . 0 f dB ’ , MdB ) ; //=========================END OF PROGRAM ===============================

101

Scilab code Exa 10.8 CNR 1 2


3 clc ; 4 clear ; 5 6 // For a S a t e l l i t e c o m m u n i c a t i o n l i n k 7 EIRPdB =55.5; // S a t e l l i t e ESM i n dBW 8 MdB =35; //G/T r a t i o o f e a r t h s t a t i o n i n dB 9 LfsdB =245.3 // F r e e s p a c e l o s s i n dB 10 11 //CALCULATION 12 CNRdB = EIRPdB + MdB - LfsdB +228.6; // C a r r i e r t o N o i s e

R a t i o a t t h e e a r t h s t a t i o n r e c e i v e r i n dB 13 14 15 16 17

//OUTPUT mprintf ( ’ \ n C a r r i e r t o N o i s e R a t i o a t t h e e a r t h s t a t i o n r e c e i v e r i s CNRdB=%2 . 1 f dB ’ , CNRdB ) ; //=========================END OF PROGRAM ===============================

Scilab code Exa 10.9 system noise temperature 1 2


3 clc ; 4 clear ; 5 6 D =30; // D i a m e t e r o f a d i s h a n t e n n a w i t h

102

circular

aperture in m 7 f =4*10^9; // down l i n k f r e q u e n c y i n Hz 8 MdB =20; //G/T r a t i o o f e a r t h s t a t i o n i n dB 9 c =3*10^8; // V e l o c i t y o f l i g h t i n m/ s e c 10 11 12 13 14 15 16 17 18 19 20 21

//CALCULATION A =(( %pi ) /4) * D ^2; // a r e a i n sqm w = c / f ; // w a v e l e n g t h i n m G =(4*( %pi ) * A ) / w ^2; // Gain GdB =10* log10 ( G ) ; // Gain i n dB TsdB = GdB - MdB ; // The System N o i s e T e m p e r a t u r e i n dB //OUTPUT mprintf ( ’ \ nThe System N o i s e T e m p e r a t u r e i s TsdB=%2 . 2 f dB ’ , TsdB ) ; //=========================END OF PROGRAM ===============================

Scilab code Exa 10.10 HPBW 1 2

3 4 5 6 7 8 9 10 11

// c h a p t e r −10 p a g e 489 e x a m p l e 1 0 . 1 0 // ================================================================== clc ; clear ; // For a p a r a b o l i c a n t e n n a Gp =1500; // Power g a i n w =0.1; // w a v e l e n g t h i n m //CALCULATION D = sqrt ( Gp ) *( w /( %pi ) ) ; // D i a m e t e r o f t h e c i r c u l a r mouth o f a p a r a b o l i c a n t e n n a i n m 103

12 13 14 15

16 17

HPBW =58*( w / D ) ; // H a l f Power BeamWidth o f t h e a n t e n n a i n deg //OUTPUT mprintf ( ’ \ n D i a m e t e r o f t h e c i r c u l a r mouth o f a p a r a b o l i c a n t e n n a i s D=%1 . 4 f m \ n H a l f Power BeamWidth o f t h e a n t e n n a i s HPBW=%1 . 3 f deg ’ ,D , HPBW ) ; //=========================END OF PROGRAM ===============================

Scilab code Exa 10.11 gain 1 2

// c h a p t e r −10 p a g e 490 e x a m p l e 1 0 . 1 1 // ==================================================================

3 clc ; 4 clear ; 5 6 D =1; // Assume d i a m e t e r o f t h e p a r a b o l i c

r e f l e c t o r s in

the o r i g i n a l system in m 7 w =1; // Assume w a v e l e n g t h i n m 8 9 //CALCULATION 10 D1 =2* D ; // d i a m e t e r o f t h e p a r a b o l i c 11 12 13 14

r e f l e c t o r s in the

modified system in m G =6*( D / w ) ^2; // g a i n i n o r i g i n a l s y s t e m G1 =6*( D1 / w ) ^2; // g a i n i n m o d i f i e d s y s t e m GdB =10* log10 ( G1 / G ) ; // O v e r a l l g a i n t h a t can be e x p e c t e d i n dB GdBo =2* GdB ; // O v e r a l l g a i n o f t h e s y s t e m ( c o m b i n i n g t h e two a n t e n n a s one a t t h e Tx and o t h e r a t t h e Rx ) i n dB 104

15 16 17

18 19 20 21

//OUTPUT mprintf ( ’ \ n O v e r a l l g a i n t h a t can be e x p e c t e d i s GdB= %1 . 0 f dB \ n O v e r a l l g a i n o f t h e s y s t e m ( c o m b i n i n g t h e two a n t e n n a s one a t t h e Tx and o t h e r a t t h e Rx ) i s GdBo=%1 . 0 f dB ’ ,GdB , GdBo ) ; //=========================END OF PROGRAM =============================== // Note : Check t h e a n s w e r o n c e . . i t s h o u l d be GdB=10 l o g ( 4 ) =6 dB and GdBo=12dB

Scilab code Exa 10.12 gain 1 2

3 4 5 6 7 8 9 10 11 12

// c h a p t e r −10 p a g e 490 e x a m p l e 1 0 . 1 2 // ================================================================== clc ; clear ; D =3; // d i m e n s i o n o f a p a r a b o l o i d i n m f =3*10^9; // f r e q u e n c y ( S band ) i n Hz c =3*10^8; // V e l o c i t y o f l i g h t i n m/ s e c

//CALCULATION w = c / f ; // wave l e n g t h i n m BWFN =140*( w / D ) ; // BeamWidth b e t w e e n F i r s t N u l l s i n deg 13 BWHP =70*( w / D ) ; // BeamWidth b e t w e e n H a l f P o w e r p o i n t s i n deg 14 G =6*( D / w ) ^2; // Gain o f t h e a n t e n n a 15 16

//OUTPUT 105

17

18 19

mprintf ( ’ \nBeamWidth b e t w e e n F i r s t N u l l s i s BWFN=%1 . 2 f deg \nBeamWidth b e t w e e n H a l f P o w e r p o i n t s i s BWHP=%1 . 2 f deg \ nGain o f t h e Antenna i s G=%4 . 0 f ’ , BWFN , BWHP , G ) ; //=========================END OF PROGRAM ===============================


// c h a p t e r −10 p a g e 490 e x a m p l e 1 0 . 1 3 // ==================================================================

3 clc ; 4 clear ; 5 6 l =1; // ( Assume )−d i m e n s i o n ( w a v e l e n g t h ) i n cm 7 8 //CALCULATION 9 x =5* l ; // g i v e n s q u a r e a p e r t u r e o f an optimum h o r n

a n t e n n a a s a s i d e d i m e n s i o n i n cm 10 A = x * x ; // Area i n s q . cm 11 Gp =4.5*( A / l ^2) ; // Power g a i n o f an optimum h o r n antenna 12 13 14 15 16

//OUTPUT mprintf ( ’ \ nPower g a i n o f an optimum h o r n a n t e n n a i s Gp=%3 . 1 f ’ , Gp ) ; //=========================END OF PROGRAM ===============================

106

Chapter 11 Radars

Scilab code Exa 11.1 max range 1 2


3 clc ; 4 clear ; 5 6 // For a r a d a r s y s t e m 7 Pt =600000; // peak p u l s e power i n W 8 Smin =10^( -13) ; // minimum d e t e c t a b l e s i g n a l i n W 9 Ae =5; // c r o s s s e c t i o n a l a r e a o f t h e r a d a r a n t e n n a i n

sq m 10 w =0.03; // w a v e l e n g t h i n m 11 s =20; // r a d a r c r o s s s e c t i o n a l a r e a i n s q m 12 13 14

//CALCULATION Rmax =((( Pt * s * Ae ^2) /(4*( %pi ) * Smin * w ^2) ) ^(1/4) ) /1000; //Maximum r a n g e o f a r a d a r s y s t e m i n km 15 RMax = Rmax /1.853; // I n n a u t i c a l m i l e s ; 1 nm= 1 . 8 5 3 km 16 17

//OUTPUT 107

mprintf ( ’ \nMaximum r a n g e o f a r a d a r s y s t e m i s Rmax= %3 . 3 f km ’ , Rmax ) ; 19 disp ( ’ I n n a u t i c a l m i l e s ; 1 nm= 1 . 8 5 3 km ’ ) ; 20 mprintf ( ’ \nMaximum r a n g e o f a r a d a r s y s t e m i n n a u t i c a l m i l e s i s RMax=%3 . 0 f nm ’ , RMax ) ; 18

21 22

//=========================END OF PROGRAM ===============================


3 4 5 6 7 8 9 10

// c h a p t e r −11 p a g e 504 e x a m p l e 1 1 . 2 // ================================================================== clc ; clear ;

// For a r a d a r s y s t e m Pt =250000; // peak t r a n s m i t t e d power i n W G =2500; // power g a i n o f t h e a n t e n n a Smin =10^( -14) ; // minimum d e t e c t a b l e s i g n a l i n W Ae =10; // c r o s s s e c t i o n a l a r e a o f t h e r a d a r a n t e n n a i n sq m 11 f =10*10^9; // f r e q u e n c y o f r a d a r i n Hz 12 s =2; // r a d a r c r o s s s e c t i o n a l a r e a i n s q m 13 c =3*10^8; // V e l o c i t y o f l i g h t i n m/ s e c 14 15 //CALCULATION 16 w = c / f ; // w a v e l e n g t h i n m 17 Rmax =((( Pt * G * Ae * s ) /( Smin *(4*( %pi ) ) ^2) ) ^(1/4) ) /1000;

//Maximum r a n g e o f a r a d a r s y s t e m i n km 18 19 20

//OUTPUT mprintf ( ’ \nMaximum r a n g e o f a r a d a r s y s t e m i s Rmax= 108

%3 . 2 f km ’ , Rmax ) ; 21 22

//=========================END OF PROGRAM ===============================

Scilab code Exa 11.3 RCS 1 2

3 4 5 6 7 8 9 10 11 12 13 14 15 16

// c h a p t e r −11 p a g e 504 e x a m p l e 1 1 . 3 // ================================================================== clc ; clear ; // For a m a r i n e r a d a r s y s t e m Pt =250000; // peak t r a n s m i t t e d power i n W G =4000; // power g a i n o f t h e a n t e n n a R =50000; //maximum r a n g e o f r a d a r i n m Pr =10^( -11) ; // minimum d e t e c t a b l e s i g n a l i n W f =10*10^9; // f r e q u e n c y o f r a d a r i n H c =3*10^8; // V e l o c i t y o f l i g h t i n m/ s e c

//CALCULATION w = c / f ; // w a v e l e n g t h i n m Ae =(( G * w ^2) /(4*( %pi ) ) ) ; // c r o s s s e c t i o n a l a r e a o f t h e radar antenna in sq m 17 s =(( Pr *(4*( %pi ) * R ^2) ^2) /( Pt * G * Ae ) ) ; // The c r o s s s e c t i o n o f t h e t a r g e t t h e r a d a r can s i g h t i n s q m 18 19 20 21 22

//OUTPUT mprintf ( ’ \ nThe c r o s s s e c t i o n o f t h e t a r g e t t h e r a d a r can s i g h t i s s=%2 . 2 f s q m ’ ,s ) ; //=========================END OF PROGRAM =============================== 109

Scilab code Exa 11.4 Duty cycle and etc 1 2


3 clc ; 4 clear ; 5 6 // For a g u i d e d m i s s i l e t r a c k i n g r a d a r 7 Pt =400000; // t r a n s m i t t e d power i n W 8 prf =1500; // p u l s e r e p i t i t i o n f r e q u e n c y i n pps ( p u l s e

per sec ) 9 tw =0.8*10^( -6) ; // p u l s e w i d t h i n s e c 10 c =3*10^8; // V e l o c i t y o f l i g h t i n m/ s e c 11 12 13 14 15 16 17 18 19 20 21 22

//CALCULATION Runamb =( c /(2* prf ) ) /1000; // Unambiguous r a n g e i n km dc = tw /(1/ prf ) ; // Duty c y c l e Pav = Pt * dc ; // A v e r a g e power i n W n1 =1; BW1 =( n1 / tw ) /10^6; // S u i t a b l e BW i n MHz f o r n=1 n2 =1.4; BW2 =( n2 / tw ) /10^6; // S u i t a b l e BW i n MHz f o r n =1.4

//OUTPUT mprintf ( ’ \ nUnambiguous r a n g e i s Runamb=%3 . 0 f km \ nDuty c y c l e i s dc=%1 . 4 f \ n A v e r a g e power i s Pav=%3 . 0 f W’ , Runamb , dc , Pav ) ; 23 disp ( ’ For e f f i c i e n c y n =1 , s u i t a b l e bandwidth i n MHz i s ’ ); 24 disp ( BW1 ) ; 25 disp ( ’ For e f f i c i e n c y n = 1 . 4 , s u i t a b l e bandwidth i n MHz i s ’ ); 110

26 27 28

disp ( BW2 ) ; //=========================END OF PROGRAM ===============================


3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

// c h a p t e r −11 p a g e 505 e x a m p l e 1 1 . 5 // ================================================================== clc ; clear ; // For a m i l i t a r y r a d a r Pt =2500000; // power o u t p u t i n W f =5*10^9; // f r e q u e n c y o f r a d a r i n H c =3*10^8; // V e l o c i t y o f l i g h t i n m/ s e c D =5; // a n t e n n a d i a m e t e r i n m B =1.6*10^6; // r e c e i v e r bandwidth i n Hz s =1; // r a d a r c r o s s s e c t i o n a l a r e a i n s q m NF =12; // n o i s e f i g u r e i n dB //CALCULATION w = c / f ; // w a v e l e n g t h i n m F =10^( NF /10) ; // n o i s e f i g u r e Rmax =(48*(( Pt * s * D ^4) /( B *( F -1) * w ^2) ) ^(1/4) ) ; //Maximum d e t e c t i o n r a n g e i n km //OUTPUT mprintf ( ’ \nMaximum d e t e c t i o n r a n g e o f a r a d a r i s Rmax=%3 . 0 f km ’ , Rmax ) ; //=========================END OF PROGRAM =============================== 111

Scilab code Exa 11.6 factor 1 2


3 clc ; 4 clear ; 5 6 // For a c i v i l i a n r a d a r 7 Rmax =30; //maximum r a n g e i n kms 8 x =50; 9 y =2; 10 disp ( ’ Maximum r a n g e w i t h an e q u i v a l e n t

echoing area

o f 50 t i m e s i n kms i s ’ ) ; 11 R = Rmax * x ^(1/4) ; 12 disp ( R ) ; 13 disp ( ’ Range would be i n c r e a s e d

i f Tx power i s

d o u b l e d by a f a c t o r o f ’ ) ; 14 f = y ^(1/4) ; 15 disp ( f ) ; 16 17

//=========================END OF PROGRAM ===============================

112

Microwave and Radar Engineering_M. Kulkarni

Recommend Documents