Microwave Engineering_M. Kulkarni

Scilab Textbook Companion for Microwave Engineering by M. Kulkarni1 Created by Karan Bhargava B.Tech Electronics Engineering Uttarakhand Technical University College Teacher Vatsalya Sharma Cross-Checked by Madhu N. Belur August 10, 2013

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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 Engineering Author:  M. Kulkarni Publisher:   Umesh Publications, New Delhi Edition: 1 Year:   2011 ISBN:   81-88114-26-X

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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.

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Contents Listt of Scilab Codes Lis

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3 Tran ransmi smissi ssion on Line Liness

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4 Micro Microwa waves ves Transmi Transmission ssion Lines Lines

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5 Ca Cavit vity y Reso Resonat nators ors

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6 Micro Microwa wave ve Compone Components nts

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7 Micro Microwa wave ve Measure Measuremen ments ts

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8 Mic Micro rowa wave ve Tubes Tubes and Circui Circuits ts

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9 Sol Solid id State State Microw Microwav ave e Devices Devices

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List of Scilab Codes Exa 3.1 Exa 3.2

Exa 3.3 Exa 3.4 Exa 3.5 Exa 3.6 Exa 3.7 Exa 3.8 Exa 3.9 Exa 3.10 Exa 4.1

Exa 4.2 Exa 4.3 Exa 4.4 Exa 4.5

Program to find value of terminating impedance of lossless transmission line . . . . . . . . . . . . . . . . . . . Calculate the charcteristic impedance and attenuation constant and phase constant of transmission line and Calculate power delivered to load if line length is 500 km Calculate phase velocity of the wave that propogates on line . . . . . . . . . . . . . . . . . . . . . . . . . . . . Calculate Current drawn from generator and Magnitune and phase of load current and Power delivered to load Calculate VSWR and reflection coefficient   . . . . . . . Determine point of attachment and length of stub   . . Calculate terminating impedance   . . . . . . . . . . . . Determine the VSWR and Position of 1st Vmin to Vmax and Vmin and Vmax and Impedance at Vmin and Vmax Determine in dB the reflection loss and transmission line and return loss   . . . . . . . . . . . . . . . . . . . . . . Calculate the charcterstic impedance and phase velocity Calculate the inductance per unit length and capacitance per unit length and charcteristic impedance and velocity of propagation . . . . . . . . . . . . . . . . . . Calculate the attenuation and phase constants and phase velocity and relative permittivity and power loss   . . . Calculate the breakdown power of air filled coaxial cable Calculate charcteristic impedance and velocity of propagation . . . . . . . . . . . . . . . . . . . . . . . . . . Calculate charcteristic impedance and effective dielectric constant and velocity of propagation . . . . . . . .

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9

9 11 11 12 13 14 14 15 16

18 19 20 20 21

Exa 4.6 Exa 4.7 Exa 4.8 Exa 4.9 Exa 4.10 Exa 4.11 Exa 4.12 Exa 4.13 Exa 4.14 Exa 4.15 Exa 4.16 Exa 4.17 Exa 4.18 Exa 4.19 Exa 4.20 Exa 4.21 Exa 4.22 Exa 4.23 Exa 4.24 Exa 5.1 Exa 5.2 Exa 5.3 Exa 5.4

Calculate ratio of circular waveguide crosssectional area to rectangular waveguide crosssection . . . . . . . . . Calculate breadth of rectangular waveguide   . . . . . . Calculate the cutoff wavelength and guide wavelength and group and phase velocities . . . . . . . . . . . . . Calculate the possible modes and cutoff frequencies and guide wavelength   . . . . . . . . . . . . . . . . . . . . . Calculate the required size of guide and frequencies that can be used for this mode of propagation . . . . . . . Find all modes that can propagate at 5000MHz . . . . Calculate the cutoff wavelength and cutoff frequency and wavelength in guide   . . . . . . . . . . . . . . . . . Calculate the frequency of the wave . . . . . . . . . . Calculate the guide wavelength and phase constant and phase velocity for dominant mode . . . . . . . . . . . Calculate what modes propagate at free space wavelength of 10 cm and 5 cm   . . . . . . . . . . . . . . . . Determine the charcteristic wave impedance . . . . . . Determine the diameter of waveguide and guide wavelength   . . . . . . . . . . . . . . . . . . . . . . . . . . . Show TE01 mode propagates under given conditions . Calculate the amount of attenuation if signal of frequency is 6GHz . . . . . . . . . . . . . . . . . . . . . . Calculate the maximum power handling capacity . . . Calculate the maximum power . . . . . . . . . . . . . Calculate the peak value of electric feild occuring in the waveguide . . . . . . . . . . . . . . . . . . . . . . . . . Calculate the breakdown power of air filled rectangular waveguide for dominant mode . . . . . . . . . . . . . . Calculate the breakdown power of circular waveguide . Determine the minimum distance between two end plates Calculate the lowest frequency of a rectangular cavity resonator . . . . . . . . . . . . . . . . . . . . . . . . . Calculate the resonant frequency of a circular cavity resonator . . . . . . . . . . . . . . . . . . . . . . . . . . . Calculate the resonant frequency of a circular cavity resonator . . . . . . . . . . . . . . . . . . . . . . . . . . .

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22 23 24 25 25 26 27 28 29 30 31 32 33 34 35 35 36 37 37 39 40 40 41

Exa 6.2 Exa 6.3 Exa 6.4 Exa 6.5 Exa 6.6 Exa 6.7 Exa 6.9 Exa 6.10 Exa 6.11 Exa 6.12 Exa 6.13 Exa 7.1 Exa 7.2 Exa 7.3 Exa 7.4 Exa 8.1

Exa 8.2 Exa 8.3 Exa 8.4

Exa 8.5 Exa 8.6

Exa 8.7

Find the distance that the position of port 1 should be shifted . . . . . . . . . . . . . . . . . . . . . . . . . . . Determine the scattering parameters for 10 dB direction coupler . . . . . . . . . . . . . . . . . . . . . . . . . . Determine the powers in the remaining ports   . . . . . Determine the powers in the remaining ports   . . . . . Determine the powers reflected at port 3 and power divisions at other ports . . . . . . . . . . . . . . . . . . Calculate the scattering matrix   . . . . . . . . . . . . . Calculate the scattering matrix   . . . . . . . . . . . . . Calculate the scattering matrix   . . . . . . . . . . . . . Calculate the directivity and coupling and isolation . . Calculate the value of VSWR   . . . . . . . . . . . . . . Calculate the phase shift of the component . . . . . . Calculate the SWR of the transmission line   . . . . . . Calculate the SWR of the main waveguide . . . . . . . Calculate the SWR of the waveguide   . . . . . . . . . . Calculate the value of reflected power . . . . . . . . . Calculate the dc electron velocity and dc phase constant and plasma frequency and reduced plasma frequency and dc beam current beam density and instantaneous beam current density . . . . . . . . . . . . . . . . . . Calculate the input rms voltage and output rms voltage and power delivered to load   . . . . . . . . . . . . . . . Calculate the input power in watts and output power in watts and efficiency . . . . . . . . . . . . . . . . . . . Calculate the electron velocity and dc transit time and input voltage for maximum output voltage and voltage gain in dB . . . . . . . . . . . . . . . . . . . . . . . . Calculate the input microwave voltage and voltage gain and efficiency of amplifier and beam loading conductance Calculate the value of repeller voltage and beam current necessary to give gap voltage of 200V and electronic efficiency . . . . . . . . . . . . . . . . . . . . . . . . . Calculate the efficiency of reflex klystron and total output power in mW and power delivered to load . . . . .

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43 44 45 45 46 47 48 48 49 50 50 52 53 53 54

55 56 57

58 58

60 61

Exa 8.8

Exa 8.9 Exa 8.10

Exa 8.11

Exa 8.12 Exa 8.13 Exa 8.14 Exa 8.15 Exa 8.16 Exa 9.1 Exa 9.2 Exa 9.3 Exa 9.4 Exa 9.5 Exa 9.6 Exa 9.7 Exa 9.8 Exa 9.9 Exa 9.10

Calculate the Hull cutoff voltage and cutoff magnetic flux density if beam voltage is 6000V and cyclotron frequency in GHz   . . . . . . . . . . . . . . . . . . . . . . Calculate the Axial phase velocity and Anode voltage at which TWT can be operated for useful gain   . . . . Calculate the electron velocity and dc transit time and input voltage for maximum output voltage and voltage gain in dB . . . . . . . . . . . . . . . . . . . . . . . . Calculate the dc electron velocity and dc phase constant and plasma frequency and reduced plasma frequency and dc beam current beam density and instantaneous beam current density . . . . . . . . . . . . . . . . . . Calculate the gap transit angle   . . . . . . . . . . . . . Calculate the input rf voltage and voltage gain and efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . Calculate the cyclotron angular frequency and cutoff  voltage and cutoff magnetic flux . . . . . . . . . . . . Calculate the input power and output power in watts and efficiency   . . . . . . . . . . . . . . . . . . . . . . . Calculate the repeller voltage and beam current necessary to give gap voltage of 200V . . . . . . . . . . . . Calculate i repeller voltage Vr ii beam current necessary to give gap voltage of 200V   . . . . . . . . . . . . . . . Determine threshold electric field   . . . . . . . . . . . . Calculate the power gain in dB and power gain if it is USB converter . . . . . . . . . . . . . . . . . . . . . . Calculate the critical voltage and breakdown voltage and breakdown electric field . . . . . . . . . . . . . . . Calculate the power gain in dB and power gain if it is USB converter . . . . . . . . . . . . . . . . . . . . . . Calculate the power gain in dB   . . . . . . . . . . . . . Calculate the minimum voltage needed to GUNN effect Calculate the rational frequency and critical velocity of  diode . . . . . . . . . . . . . . . . . . . . . . . . . . . Calculate the resonant frequency and efficiency   . . . . Calculate the drift time of carrier and operating frequency of diode . . . . . . . . . . . . . . . . . . . . . .

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62 63

63

64 65 66 67 68 69 71 71 72 73 73 74 74 75 76 76

Exa 9.11 Exa 9.12 Exa 9.13

Calculate the breakdown voltage and breakdown electric field   . . . . . . . . . . . . . . . . . . . . . . . . . . . . Calculate the maximum power gain and noise figure and bandwidth . . . . . . . . . . . . . . . . . . . . . . . . Calculate the equivalent noise resistance and gain and noise figure and bandwidth . . . . . . . . . . . . . . .

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77 78 79

Chapter 3 Transmission Lines

Scilab code Exa 3.1   Program to find value of terminating impedance of 

lossless transmission line 1 / / C ap ti on : Program t o f i n d

value of terminating i m pe da n ce o f l o s s l e s s t r a n s m i s s i o n l i n e . 2 / / Exa : 3 . 1 3 4 5 6 7 8 9 10

clc ;   clear ;   close ;

// Given :        

Z_ch=100; // in ohms S=5; //VSWR ( u n i t l e s s ) Z=Z_ch*S; printf ( ” \ n \ n \ t The t e r m i n a t i n g i m pe d en c e = %d o hms ” ,Z);

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Scilab code Exa 3.2  Calculate the charcteristic impedance and attenua-

tion constant and phase constant of transmission line and Calculate power delivered to load if line length is 500 km 1 / / C ap ti on : C a l c u l a t e t h e c h a r c t e r i s t i c i mp ed an ce ,

a t t e n u a ti o n c o ns ta n t , p ha se c o n st a n t o f   t r a n s m i s s i o n l i n e C a l c ul a te power d e l i v e r e d t o l o a d , i f l i n e l e n g t h =500 km . 2 / / Exa : 3 . 2 3 4 5 6 7 8 9 10 11 12 13 14 15

clc ;   clear ;   close ;   e=2.718;

17 18 19 20 21 22 23 24

  y={(R+%i*w*L)*(G+%i*w*C)}^0.5; a= real ( y ) ; / / a t t e n e u a t i o n c o n s t a n t b= imag ( y ) ; / / p ha s e c o n s t a n t   disp (a , ” A t t e n e u a t i o n c o n s t a n t ( i n NP/km ) =” ) ;   disp (b , ” P ha se c o n s t a n t ( i n r a d i a n /km ) =” );   V_in=2; // i n v o l t s   l=500; // i n k i l o m e t e r s   Z_in=Z_ch; // S i nc e l i n e t er mi n a te d a t i t s c ha r . imped

// Given :   R=8; / / i n ohm / k i l o m e t e r   L=2*10^-3; / / i n h e nr y / k i l o m e t e r   C=0.002*10^-6; / / i n f a r a d / k i l o m e t e r   G=0.07*10^-6; / / s e c o n d / k i l o m e t e r   f=2000; // i n h e r t z / / S i n c e [ w=2 ∗ ( p i ) ∗ f ] & [ Z ch = { (R+jwL ) / (G+jwC )  } ˆ 0 . 5 ]   w=2*%pi*f; / / i n r a d i a n s   Z_ch={(R+%i*w*L)/(G+%i*w*C)}^0.5; / / c o m p u t i n g c h a r a c t e r i s t i c i mp ed a nce 16   disp (Z_ch, ” C h a r a c t e r i s t i c i mp ed an ce ( i n ohms ) =” ) ;

. s o , Z i n =Z c h=Z ( l o a d ) 25   I_s=V_in/Z_in; 26   Imag=[[{{ real (I_s)}^2}+{{ imag (I_s)}^2}]^0.5]*10^3; //

i n m i l l i am p e r e 27   Iang= atan ( imag (I_s)/ real (I_s))*(180/%pi); // in

degrees 10

28 29 30 31

  I=Imag*e^-1.99; // I=I s ∗ eˆ− y l

/ /P ( p ow er d e l i v e r e d )=I ∗ I ∗REAL( Z c h )   P=I*I* real (Z_ch);   disp (P , ” Power d e l i v e r e d t o l o ad ( i n m ic ro wa tt =)” );

Scilab code Exa 3.3  Calculate phase velocity of the wave that propogates

on line 1 // C ap ti on : C a l c u l a te p ha se v e l o c i t y

o f t he wave t h at p r o p og a te s on l i n e a s g i ve n i n ex a mp l e 3 . 2 2 / / Exa : 3 . 3 3 4 5 6 7 8 9

           

clc ; clear ; close ; w=4*%pi*10^3; / / i n r a d / s e c b=0.02543; / / i n r a d /km V_p=w/b; // p ha se v e l o c i t y disp (V_p, ” P ha se v e l o c i t y ( i n km/ s e c ) =” );

Scilab code Exa 3.4  Calculate Current drawn from generator and Magni-

tune and phase of load current and Power delivered to load 1 / / C a pt i on : C a l c u l a t e

( a )− C u rr e nt dra wn f ro m g e n e r a t o r . ( b )− M ag ni tu ne & p ha se o f l o a d c u r r e n t . ( c ) − Power d e l i v e r e d t o l o ad . 11

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

/ / Exa : 3 . 4                

clc ; clear ; close ; f=37.5*10^6; / / f r e q u e n c y ( i n h e r t z ) wl=(3*10^8)/f; / / w a v e l e n g t h ( i n m e t e r s ) Z_l=100; / / i n o hm s Z_o=200; / / i n o hm s l=5*wl/4; // l e n g th o f l i n e ( i n m et er s ) b=2*%pi/wl;

/ / At g e n e r a t o r end ,        

Z_i=Z_o*(Z_l+%i*Z_o* tan (b*l))/(Z_o+%i*Z_l* tan (b*l)); V_s=200*Z_i/(200+Z_i); I_s=200/(200+Z_i); disp ( real ( I _ s ) , ” C u r r en t drawn f ro m g e n e r a t o r ( i n amps ) =” ) ;

17 / / f o r a l o s s l e s s l i n e , P ( a vg ) ∗ I i n p u t =P ( a v g ) ∗ I l o a d 18   P_avg=V_s*I_s; / / i n w a t ts 19   disp ( real ( P _ a v g ) , ” Power d e l i v e r e d t o l o ad ( i n w at ts ) =) ” ) ; 20 / / R e a l ( V s ∗ I s )=Rea l ( Vs ∗ I l o a d ) 21   I_load=(P_avg/Z_l)^0.5; / / i n a mp s 22   disp ( real ( I _ l o a d ) , ” C u rr en t f l o w i n g i n l o ad ( i n amps ) =) ” ) ;

Scilab code Exa 3.5   Calculate VSWR and reflection coefficient

1 2 3 4

/ / C a p t i o n : C a l c u l a t e VSWR & r e f l e c t i o n / / Exa : 3 . 5 clc ;   clear ;

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coefficient .

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

                         

close ; Z_o=50; / / i n o hm s f=300*10^6; / / i n Hz Z_l=50+%i*50; / / i n o hm s wl=(3*10^8)/f; / / w a v e l e n g t h ( i n m e t e r s ) P=[(Z_l-Z_o)/(Z_l+Z_o)]; P_mag={( real (P)^2)+( imag (P)^2)}^0.5; P_ang= atan ( imag (P)/ real (P))*180/%pi; / / i n d e g r e e s S={1+P_mag}/{1-P_mag}; disp (P , ” R e f l e c t i o n c o e f f i c i e n t =” ) ; disp (P_mag, ” Ma gn itu de o f r e f l e c t i o n c o e f f c i e n t =” ); disp (P_ang, ” A n gl e ( i n d e g r e e ) =” ); disp (S , ”VSWR =” );

Scilab code Exa 3.6  Determine point of attachment and length of stub

1 / / C ap ti on : D et er mi ne p o i n t o f a t ta ch m en t & l e n g t h o f  

stub . 2   / / Exa 3 . 6 3 4 5 6 7 8 9 10 11 12 13 14

           

clc ; clear ; close ; Z_l=100; / / i n o hm s Z_o=600; / / i n o hm s f=100*10^6; / / i n Hz wl=(3*10^8)/f;

// P o s i t i o n o f s t u b i s :        

m=((Z_l*Z_o)/(Z_l-Z_o))^0.5; pos={wl/(2*%pi)}* atan ((Z_l/Z_o)^0.5); / / i n m e t er s l={wl/(2*%pi)}*{ atan (m)}; / / i n m e t er s disp (pos, ” P o s i t i o n o f s tu b ( i n m et er s ) =” ) ;

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15   disp ( abs ( l ) , ” L en gt h o f s t ub ( i n m e te r s ) =” );

Scilab code Exa 3.7   Calculate terminating impedance

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

/ / C a pt i on : C a l c u l a t e t e r m i n a t i n g i m pe da n ce . / / Exa : 3 . 7          

clc ; clear ; close ; Z_o=50; S=3.2; X_min=0.23; / / i n t e rm s o f w a v el e n g th ( w l ) )

  / /So :   Z_l=Z_o*[[1-%i*S* tan (2*%pi*X_min)]/[S-%i* tan (2*%pi* X_min)]]; / / i n o hm s   Z_lmag=[( real (Z_l)^2)+( imag (Z_l)^2)]^0.5;   Z_lang= atan ( imag (Z_l)/ real ( Z _ l ) ) ;   disp ( ” The l o a d i m pe d an c e ” );   disp (Z_lmag, ” m a g n i tu d e ( i n ohms ) =” );   disp (Z_lang*180/%pi, ” a n g l e ( i n d e g r e es ) =” );

Scilab code Exa 3.8  Determine the VSWR and Position of 1st Vmin to

Vmax and Vmin and Vmax and Impedance at Vmin and Vmax

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1 / / C a p t i o n : D e t e r m i n e : ( a )VSWR ; ( b ) P o s i t i o n

o f 1 s t Vmin & Vmax ; ( c ) V min & Vmax ; ( d ) I m p e d a n ce a t Vmin & Vmax. 2 / / Exa : 3 . 8 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

                   

clc ; clear ; close ; Z_o=50; / / i n o hm s Z_l=100; / / i n o hm s f=300*10^3; / / i n Hz P_l=50*10^-3; / / i n w a t ts wl=(3*10^8)/f; p=(Z_l-Z_o)/(Z_l+Z_o); S=(1+ abs (p))/(1- abs (p)); disp (S , ”VSWR =” );

// S i nc e r e a l Z l

>

Zo ,

  pos=wl/4;   disp ( ” F i r s t Vmax i s l o c a t e d   disp ( ” F i r s t Vmin i s l o c a t e d );   disp (pos, ” ( i n m e t er s ) ” );   V_max=(P_l*Z_l)^0.5;   V_min=V_max/S;   disp (V_max, ” Vmax ( i n v o l t s )   disp (V_min, ” Vmin ( i n v o l t s )   disp (Z_o/S, ” Z i n a t Vmin ( i n   disp (Z_o*S, ” Z i n a t Vmax ( i n

−−−> a t t h e l oa d ” ); a t −−−>( w a v e l e n g t h / 4 ) = ”

=” ); =” ); ohms ) =: ” ); ohms ) =” ) ;

Scilab code Exa 3.9  Determine in dB the reflection loss and transmission

line and return loss

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1 / / C a pt i on : D e te r mi n e i n dB :

( a )− r e f l e c t i o n l o s s , ( b ) − t r a n s m i s s i o n l i n e ( c )− r e tu r n l o s s . 2 / / Exa : 3 . 9 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

                 

clc ; clear ; close ; Z_o=600; // in ohm Z_s=50; // in ohm l=200; / / i n m e te r Z_l=500; // in ohm p=(Z_l-Z_o)/(Z_l+Z_o); ref_los=10*( log (1/(1-( abs (p))^2)))/( log (10)); / / i n dB disp (ref _los , ” R e f l e c t i o n l o s s ( i n dB ) =” );

// a t t e n u a ti o n l o s s = 0 dB // T r an sm is so n l o s s = ( a t t e n u a ti o n l o s s ) +( r e f l e c t i o n loss ) = ( refle ctio n loss )        

tran_los=ref_los; disp (tr an_los , ” T r an s mi ss o n l o s s ( i n dB ) =” ); ret_los=10*(( log ( abs (p)))/( log (10))); disp (ret _los , ” R e tu rn l o s s ( i n dB ) =” );

Scilab code Exa 3.10  Calculate the charcterstic impedance and phase ve-

locity 1 // C ap ti on : C a l c u l a te t he

c h a r c t e r s t i c i mp ed an ce &

p ha se v e l o c i t y 2 / / Exa : 3 . 1 0 3 4 5 6

clc ;   clear ;   close ;   e=2.718;

16

7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

                   

f=1000; / / i n Hz l=10000; / / i n m e t e r s Z_sc=(2631+%i*1289); // in ohms Z_oc=(221-%i*137); / / i n o hm s Z_o=[Z_sc*Z_oc]^0.5; Z_mag=[ real (Z_o)^2+ imag (Z_o)^2]^0.5; Z_ang=[ atan (( imag (Z_o))/ real (Z_o))]*180/%pi; disp (Z_mag, ” C h a r a c t e r i s t i c i mp ed an ce ( i n ohms ) =” ); disp (Z_ang, ” A n gl e ( i n d e g r e e s ) =” ) ; x=[(Z_oc/Z_sc)^0.5];

// x=tanh ( v ∗ l ) / / As , t a n h ( t ) = [ e ˆ t −eˆ− t ] / [ e ˆ t +e ˆ− t ]   v=(261+%i*2988)/l; a= real ( v ) ; b= imag ( v ) ;   disp (2*%pi*f/b, ” Pha se v e l o c i t y ”);

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( i n m e t e r p er s e c . ) =

Chapter 4 Microwaves Transmission Lines

Scilab code Exa 4.1  Calculate the inductance per unit length and capaci-

tance per unit length and charcteristic impedance and velocity of propagation 1 //Caption : Cal cul ate

( i )− i n d uc t an c e p er u n i t l en g th , ( i i )− c a p a c i t a n c e p er u n i t l e ng t h , ( i i i ) − c h a r c t e r i s t i c i mp ed an ce , ( i v ) − v e l o c i t y o f   propagation 2 / / Exa : 4 . 1 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

clc ;   clear ;   close ;

// Given :   d=0.49; / / i n cm   D=1.1; / / i n cm                  

e_r=2.3; c=3*10^8; / / i n m e te r / s e c o n d L=2*(10^-7)* log (D/d); / / i n H en ry / m e t e r C=55.56*(10^-12)*(e_r)/ log (D/d); / / i n f a r a d / m e t e r R_o=(60/ sqrt ( e _r ) ) * log (D/d); / / i n o hm s v=c/ sqrt (e_r); / / i n m e te r / s e c o n d disp (L , ’ I n d u c t a n c e p e r u n i t l e n g t h ( i n H/m) = ’ ); disp (C , ’ C a p a c i t a nc e p e r u n i t l e n g t h ( i n F/m) = ’ ) ; disp (R_o, ’ C h a r a c t e r i s t i c I mp ed an ce ( i n ohms ) = ’ );

18

18   disp (v , ’ V e l o c i t y

o f p r o p a g a ti o n ( i n m/ s )= ’ );

Scilab code Exa 4.2   Calculate the attenuation and phase constants and

phase velocity and relative permittivity and power loss 1 / / C ap ti on : C a l c u l a t e t h e a t t e n u at i o n , p ha s e c o n s t an t s

, p ha se v e l o c i t y , r e l a t i v e p e r m i t t i v i t y , power l o s s . 2 / / Exa : 4 . 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

                                           

clc ; clear ; close ; R=0.05; / / i n o hm s G=0; l=50; / / i n m e te r e=2.3; // d i e l e c t r i c co n s ta nt c=3*10^8; / / i n m/ s L=2*(10^-7); / / f r om Exa : 4 . 1 C=1.58*(10^-10); / / f r om Exa : 4 . 1 P_in=480; / / i n w a t ts f=3*10^9; // i n h e r t z Z_o= sqrt (L/C); a=R/Z_o; // i n Np/m b=2*%pi*f* sqrt (L*C); / / i n r a d /m V_p=1/ sqrt (L*C); e_r=(c/V_p)^2; P_loss=P_in*2*l; disp (a , ’ A t t e n e u a t i o n ( i n Np/m) = ’ ) ; disp (b , ’ P ha se c o n s t a n t ( i n r a d /m) = ’ ) ; disp (V_p, ’ P ha se v e l o c i t y ( i n m/ s ) = ’ ) ; disp (e_r, ’ R e l a ti v e p e r m i t t i v i t y = ’ ); disp (P_loss, ’ P ower l o s s ( i n w a tt s ) = ’ );

19

Scilab code Exa 4.3   Calculate the breakdown power of air filled coaxial

cable 1 / / C ap ti on : C a l c u l a t e t h e b rea kdo wn p ower o f

ai r

f i l l e d c o a x i a l c a b l e a t 9 . 3 7 5 GHz . 2 / / Exa : 4 . 3 3 4 5 6 7 8 9 10 11 12

clc ;   clear ;   close ;

// Given :   a=2.42; / / i n cm   x=2.3; / / x = ( b / a )   P_bd=3600*a^2* log (x); // i n k i l o w a t t s   disp (P_bd, ’ B re a kd o wn P ow er ( i n kW) = ’ );

  / / a ns we r i n book i s w ro ng ly w r i t t en a s 39 8 kW.

Scilab code Exa 4.4 Calculate charcteristic impedance and velocity of prop-

agation 1 // C ap ti on : C a l c u l a te

c h a r c t e r i s t i c i mp ed an ce & v e l o c i t y o f p r op a ga t io n . 2 / / Exa : 4 . 4 3 clc ;

20

4 5 6 7 8 9 10 11 12 13

                   

clear ; close ; b=0.3175; / / i n cm d=0.0539; / / i n cm c=3*10^8; / / i n m/ s e_r=2.32; Z_o=60* log (4*b/(%pi*d))/ sqrt (e_r); / / i n o hm s V_p=c/ sqrt (e_r); / / i n m/ s disp (Z_o, ’ C h a r c t e r i s t i c i mp ed an ce ( i n ohms ) = ’ ) ; disp (V_p, ’ V e l o c i t y o f p r op a g at i on ( i n m/ s ) = ’ );

Scilab code Exa 4.5   Calculate charcteristic impedance and effective di-

electric constant and velocity of propagation 1 // C ap ti on : C a l c u l a te

c h a r c t e r i s t i c i mp ed an ce & ef fe ct iv e d i e l e c t r i c constant & vel oc ity of  propagation 2 / / Exa : 4 . 5 3 4 5 6 7 8 9 10 11

           

clc ; clear ; close ; e_r=9.7; c=3*10^8; / / i n m/ s r_1=0.5; / / w he n r a t i o : (W/ h ) = 0 . 5 r_2=5; / / wh en r a t i o : (W/ h ) =5

/ / F o r W/ h r a t i o = 0 .5

  e_eff_1=(e_r+1)/2+((e_r-1)/2)*[1/{ sqrt (1+12*(1/r_1)) +0.04*(1-r_1)}]; 12   Z_o_1=60* log (8/r_1+r_1/4)/ sqrt (e_eff_1); 13   v_1=c/ sqrt (e_eff_1); 14   disp ( ” F o r W/ h = 0 .5 , ” );

21

15 16 17 18 19 20 21 22 23 24 25

  disp (e_e ff_1 ,  ’ 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 = ’ ) ;   disp (Z_o_1, ’ C h a r c t e r i s t i c i mp ed an ce ( i n ohms ) = ’ ) ;   disp (v_1, ’ V e l o c i t y o f p r op a g at i on ( i n m/ s ) = ’ );

/ / F or W/ h r a t i o =5   e_eff_2=(e_r+1)/2+((e_r-1)/2)*[1/{ sqrt (1+12*(1/r_2)) }];   Z_o_2=120*%pi*[1/{r_2+1.393+0.667* log (1.444+r_2)}]/ sqrt (e_eff_2);   v_2=c/ sqrt (e_eff_2);   disp ( ”For W/h=5, ” );   disp (e_e ff_2 ,  ’ 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 = ’ ) ;   disp (Z_o_2, ’ C h a r c t e r i s t i c i mp ed an ce ( i n ohms ) = ’ ) ;   disp (v_2, ’ V e l o c i t y o f p r op a g at i on ( i n m/ s ) = ’ );

Scilab code Exa 4.6   Calculate ratio of circular waveguide crosssectional

area to rectangular waveguide crosssection 1 // C ap ti on : C a l c u l a te

r a t i o o f c i r c u l a r w av eg ui de c r o s s − s e c t i o n a l a re a t o r e c t a n g u l a r w a ve gu i de c r o s s − s e c t i o n 2 / / Exa : 4 . 6 3 4 5 6 7 8 9 10 11 12

clc ;   clear ;   close ;

/ / F o r TE Wave p r o p a g a t e d : // f o r R ec t an g ul a r , t a k in g ( a=2b )   r=100; / / a s s u m e / / f o r TE11 , w a v e l e n g t h =2∗ p i ∗ r / 1 . 8 4 1 / / f o r TE10 , w a v e l e n g t h =2 a   a=(2*%pi*r/1.841)/2;   ar_rec_TE=(a)*(a/2);

22

13   ar_cir_TE=%pi*r^2; 14   ratio_TE=(ar_cir_TE)/(ar_rec_TE); 15   disp (ra tio_TE , ’ R at io o f C i r c u l a r & R e ct a ng u la r c os s − s e c t i o n a r ea ( i n TE) = ’ ); 16 / / F o r TM Wave p r o p a g a t e d : 17 // f o r R ec t an g ul a r , t a k in g ( a=2b ) 18 / / f o r TE01 , w a v e l e n g t h = 2 . 6 1 5 5 ∗ r 19 / / f o r TE11 , w a v e l e n g t h =4b / s q r t ( 5 ) 20   b=(2.6155*r)/1.78885; 21   ar_rec_TM=(b)*(b); 22   ar_cir_TM=%pi*r^2; 23   ratio_TM=(ar_cir_TM)/(ar_rec_TM); 24   disp (ra tio_TM , ’ R at io o f C i r c u l a r & R e ct a ng u la r c os s − s e c t i o n a r e a ( i n TM) = ’ );

Scilab code Exa 4.7  Calculate breadth of rectangular waveguide

1 2 3 4 5 6 7 8 9 10 11 12

/ / C ap ti on : C a l c u l a t e b r ea d th o f r e c t a n g u l a r w av eg ui de / / Exa : 4 . 7                  

clc ; clear ; close ; f=9*10^9; / / i n Hz c=3*10^10; / / i n cm / s wl_g=4; / / i n m wl_o=c/f; wl_c=[ sqrt (1-((wl_o/wl_g)^2))/wl_o]^-1; b=wl_c/4; disp (b , ’ B re ad th o f r e c t a n g u l a r w av eg ui de ( i n cm ) = ’ ) ;

23

Scilab code Exa 4.8 Calculate the cutoff wavelength and guide wavelength

and group and phase velocities 1 / / C ap ti on : C a l c u l a t e t h e c u t o f f

w av el en g th , g u i d e waveleng th , group & phase v e l o c i t i e s 2 / / Exa : 4 . 8 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

                           

clc ; clear ; close ; a=10; / / i n cm c=3*10^10; / / i n cm / s wl_c=2*a; / / i n cm f=2.5*10^9; / / i n Hz wl_o=c/f; wl_g=wl_o/( sqrt (1-(wl_o/wl_c)^2)); / / i n cm V_p=c/( sqrt (1-(wl_o/wl_c)^2)); V_g=c^2/V_p; disp (wl_c,  ’ Cut− o f f w a ve l en g th ( i n cm ) = ’ ); disp (wl_g, ’ G ui de w a v el e n g th ( i n cm ) = ’ ) ; disp (V_p, ’ P ha se v e l o c i t y ( i n cm/ s ) = ’ ); disp (V_g, ’ G roup v e l o c i t y ( i n cm/ s ) = ’ );

24

Scilab code Exa 4.9  Calculate the possible modes and cutoff frequencies

and guide wavelength ( i )− p o s s i b l e modes , ( i i )− cut − o f f  f r e q u e n c i e s , ( i i i )− g u i d e w a v el e n g th 2 / / Exa : 4 . 9 1 //Caption : Cal cul ate

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

clc ;   clear ;   close ;                          

// For TE mode : a=2.5; / / i n cm b=1; / / i n cm f=8.6*10^9; / / i n Hz c=3*10^10; / / i n cm / s wl_o=c/f; wl_c_1=2*b; / / f o r TE01 wl_c_2=2*a; / / f o r TE10 disp ( ’ O nly TE10 mode i s p o s s i b l e ’ ); f_c=c/wl_c_2; wl_c_3=2*a*b/ sqrt (a^2+b^2); // f o r TE11 & TM11 wl_g_TE10=wl_o/( sqrt (1-(wl_o/wl_c_2)^2)); / / f o r TE10 disp (f_c,  ’ Cut− o f f f r e q u e n c y ( i n Hz ) = ’ ); disp (wl_g_TE10 , ’ G ui de w a v el e n g th f o r TE10 ( i n cm ) = ’ );

// For TM mode :   disp ( ’ TM11 a l s o p r o p a g a t e s ’ );   wl_c_TM11=wl_c_3;   wl_g_TM11=wl_o/( sqrt (1-(wl_o/wl_c_2)^2)); // f o r TM11   disp (wl_g_TM11 , ’ G ui de w a v el e n g th f o r TM11 ( i n cm ) = ’ );

Scilab code Exa 4.10  Calculate the required size of guide and frequencies

that can be used for this mode of propagation 25

1 //Caption : Cal cul ate

( i )− r e q u i r e d s i z e o f g ui de , ( i i ) − f r e q u e n c i e s t ha t ca n be u s e d f o r t h i s mode o f   propagation 2 / / Exa : 4 . 1 0 3 4 5 6 7 8 9 10 11 12

                 

13   14   15  

clc ; clear ; close ; wl_c=10; / / i n cm c=3*10^10; / / i n cm / s r=wl_c/(2*%pi/1.841); / / i n cm area=%pi*r^2; / / i n s q . cm f_c=c/wl_c; disp (r , ’ R ad iu s o f c i r c u l a r w av eg ui de ( i n cm ) = ’ ) ; disp (area, ’ A rea o f c r o s s − s e c t i o n o f c i r c u l a r w a v e g u i d e ( i n cm ) = ’ ) ; disp (  ’ F r e q u e n cy a b o v e ’ ); disp (f_c); disp ( ’ c a n b e p r o p a g a t e d ’ );

Scilab code Exa 4.11  Find all modes that can propagate at 5000MHz

1 / / C ap ti on : Fi nd a l l modes t h a t c an p r o pa g a te a t 5 00 0

MHz. 2   / / Exa : 4 1 1 3 4 5 6 7 8 9

           

clc ; clear ; close ; a=4; / / i n cm b=3; / / i n cm f=5*10^9; / / i n Hz c=3*10^10; / / i n cm / s

26

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

  wl_o=c/f;

/ / F o r TE w a v e s :   wl_c_TE01=2*b; / / f o r TE01   wl_c_TE10=2*a; / / f o r TE10   wl_c_TE11=2*a*b/ sqrt (a^2+b^2); / / f o r TE11 if (wl_c_TE01 >wl_o )   disp ( ’ TE01 c an p r o p a g a t e ’ );   else   disp ( ’ TE01 c a n n o t p r o p a g a t e ’ ); end if (wl_c_TE10 >wl_o )   disp ( ’ TE10 c an p r o p a g a t e ’ );   else   disp ( ’ TE10 c a n n o t p r o p a g a t e ’ ); end if (wl_c_TE11 >wl_o )   disp ( ’ TE11 c an p r o p a g a t e ’ );   else   disp ( ’ TE11 c a n n o t p r o p a g a t e ’ ); end

Scilab code Exa 4.12 Calculate the cutoff wavelength and cutoff frequency

and wavelength in guide 1 / / C ap ti on : Fi nd a l l modes t h a t c an p r o pa g a te a t 5 00 0

MHz. 2   / / Exa : 4 1 1 3 4 5 6

clc ;   clear ;   close ;   a=4; / / i n cm

27

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

       

b=3; / / i n cm f=5*10^9; / / i n Hz c=3*10^10; / / i n cm / s wl_o=c/f;

/ / F o r TE w a v e s :   wl_c_TE01=2*b; / / f o r TE01   wl_c_TE10=2*a; / / f o r TE10   wl_c_TE11=2*a*b/ sqrt (a^2+b^2); / / f o r TE11 if (wl_c_TE01 >wl_o )   disp ( ’ TE01 c an p r o p a g a t e ’ );   else   disp ( ’ TE01 c a n n o t p r o p a g a t e ’ ); end if (wl_c_TE10 >wl_o )   disp ( ’ TE10 c an p r o p a g a t e ’ );   else   disp ( ’ TE10 c a n n o t p r o p a g a t e ’ ); end if (wl_c_TE11 >wl_o )   disp ( ’ TE11 c an p r o p a g a t e ’ );   else   disp ( ’ TE11 c a n n o t p r o p a g a t e ’ ); end

Scilab code Exa 4.13  Calculate the frequency of the wave

1 //Caption : Cal cul ate

( i )− c u t o f f w a ve l en g th , ( i i ) − c u t o f f f r eq u en c y , ( i i i ) − w av el en gt h i n g u id e 2 / / Exa : 4 . 1 2 3 clc ; 4   clear ;

28

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

                       

close ; c=3*10^10; / / i n cm / s d=4; / / i n cm r=d/2; / / i n cm wl_c=2*%pi*r/1.841; / / i n cm f_c=c/wl_c; f_signal=5*10^9; / / i n Hz wl_o=c/f_signal; wl_g=wl_o/ sqrt (1-(wl_o/wl_c)^2); disp (wl_c,  ’ Cut− o f f w a ve l en g th ( i n cm ) = ’ ); disp (f_c,  ’ Cut− o f f f r eq u en c y ( i n Hz ) = ’ ) ; disp (wl_g, ’ G ui de w a v el e n g th ( i n cm ) = ’ ) ;

Scilab code Exa 4.14  Calculate the guide wavelength and phase constant

and phase velocity for dominant mode 1 //Caption : Cal cul ate

( i )− g u i d e w a v el e n g th , ( i i )− p h a s e c o n s t a n t , ( i i i )− p ha se v e l o c i t y f o r d om ina nt mode 2 / / Exa : 4 . 1 4 3 4 5 6 7 8 9 10 11 12 13 14

           

clc ; clear ; close ; c=3*10^10; / / i n cm / s a=5; / / i n cm b=2.5; / / i n cm wl_o=4.5; / / i n cm

// For TE10 mode :        

wl_c=2*a; wl_g=wl_o/ sqrt (1-(wl_o/wl_c)^2); V_p=c/ sqrt (1-(wl_o/wl_c)^2); w=2*%pi*c/wl_o;

29

15 16 17 18 19 20 21

  w_c=2*%pi*c/wl_c; b= sqrt (w^2-w_c^2)/c;   disp (wl_g, ’ G ui de w a v el e n g th ( i n cm ) = ’ ) ;   disp (b , ’ P ha se c o n s t a n t = ’ );   disp (V_p, ’ P ha se v e l o c i t y ( i n cm/ s ) = ’ );

  / / an s we r i n book i s w r on gl y w r i t t e n a s g u i de w a v e l e n g t h = 7 .8 0 3 cm 22   / / an sw er i n book i s w ro ng ly w r i t t en a s Ph ase v e l o c i t y = 5 . 2 2 ∗ 1 0 ˆ 1 0 cm / s

Scilab code Exa 4.15  Calculate what modes propagate at free space wave-

length of 10 cm and 5 cm 1 / / C ap ti on : C a l c u l a t e what modes p r o pa g a t e a t f r e e

s p a c e w a v el e n g th o f ( i ) 1 0 cm , ( i i ) 5 cm 2 / / Exa : 4 . 1 5 3 4 5 6 7 8 9 10 11 12 13 14 15 16

           

clc ; clear ; close ; c=3*10^10; / / i n cm / s wl_c_TE10=16; / / C r i t i c a l w a ve l en g th o f TE10 wl_c_TM11=7.16; / / C r i t i c a l w a ve l en g th o f TM11 wl_c_TM21=5.6; // C r i t i c a l w a ve l en g th o f TM21

/ / F or ( i ) : 1 0 cm   wl_o=10; / / i n cm   disp (wl_o, ’ F or f r e e s p ac e w av el en gt h ( i n cm ) = ’ ); if (wl_c_TE10 >wl_o )   disp ( ’ TE10 ca n p ro pa ga te ’ ) ;   else   disp ( ’ TE10 c an n o t p r op ag at e ’ ) ;

30

17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45

end if (wl_c_TM11 >wl_o )   disp ( ’ TM11   else   disp ( ’ TM11 end if (wl_c_TM21 >wl_o )   disp ( ’ TM21   else   disp ( ’ TM21 end

ca n p ro pa g a te ’ ) ; ca nn ot p ro pa g a te ’ ) ;

ca n p ro pa g a te ’ ) ; ca nn ot p ro pa g a te ’ ) ;

/ / F or ( i i ) : 5 cm   wl_o=5; / / i n cm   disp (wl_o, ’ F or f r e e s p ac e w av el en gt h ( i n cm ) = ’ ); if (wl_c_TE10 >wl_o )   disp ( ’ TE10   else   disp ( ’ TE10 end if (wl_c_TM11 >wl_o )   disp ( ’ TM11   else   disp ( ’ TM11 end if (wl_c_TM21 >wl_o )   disp ( ’ TM21   else   disp ( ’ TM21 end

ca n p ro pa ga te ’ ) ; c an n o t p r op ag at e ’ ) ;

ca n p ro pa g a te ’ ) ; ca nn ot p ro pa g a te ’ ) ;

ca n p ro pa g a te ’ ) ; ca nn ot p ro pa g a te ’ ) ;

Scilab code Exa 4.16  Determine the charcteristic wave impedance

31

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

/ / C ap ti on : D et er mi ne t h e c h a r c t e r i s t i c wave i mp ed an ce / / Exa : 4 . 1 6                      

clc ; clear ; close ; c=3*10^10; / / i n cm / s f=10*10^9; / / i n Hz a=3; / / i n cm b=2; / / i n cm n=120*%pi; wl_o=c/f; wl_c=2*a*b/ sqrt (a^2+b^2); Z_TM=n* sqrt (1-(wl_o/wl_c)^2); disp (Z_TM, ’ C h a r a c t e r i s t i c i mp ed an ce ( i n ohms ) = ’ ) ;

  / / an sw er i n book i s w ro ng ly w r i t t en a s 6 1 . 61 8 ohms

Scilab code Exa 4.17 Determine the diameter of waveguide and guide wave-

length 1 / / C a pt i on : D e te r mi n e t h e d i a m e t e r o f w a ve g ui d e &

g u i d e w a v el e n g th 2 / / Exa : 4 . 1 7 3 4 5 6 7 8

         

clc ; clear ; close ; c=3*10^10; / / i n cm / s f=6*10^9; / / i n Hz f_c=0.8*f;

32

9 10 11 12 13 14

           

wl_c=c/f_c; D=1.841*wl_c/%pi; wl_o=c/f; wl_g=wl_o/ sqrt (1-(wl_o/wl_c)^2); disp (D , ’ D i am e te r o f w a ve g ui d e ( i n cm ) = ’ ); disp (wl_g, ’ G ui de w a v el e n g th ( i n cm ) = ’ ) ;

Scilab code Exa 4.18   Show TE01 mode propagates under given condi-

tions 1 / / C a p t i o n : Show TE01 mode p r o p a g a t e s u n d er g i v e n

conditions 2 / / Exa : 4 . 1 8 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

                   

clc ; clear ; close ; a=1.5; / / i n cm b=1; / / i n cm e_r=4; // d i e l e c t r i c c=3*10^10; / / i n cm / s wl_c=2*b; f_c=c/wl_c; f_imp=6*10^9; / / i m p r es s e d f r e q u e n c y ( i n Hz ) wl_air=c/f_imp;

// I n s e r t i n g d i e l e c t r i c :   wl_dielec=wl_air/ sqrt (e_r); if (wl_dielec >wl_c )   disp ( ’ TE01 ca n p ro pa ga te ’ ) ;   else   disp ( ’ TE01 c an n o t p r op ag at e ’ ) ; end

33

Scilab code Exa 4.19  Calculate the amount of attenuation if signal of fre-

quency is 6GHz 1 / / C ap ti on : C a l c u l a t e t h e amount o f a t t e n u a t i o n

s i g n a l o f f r eq u en c y i s 6GHz 2 / / Exa : 4 . 1 9 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

               

clc ; clear ; close ; u=4*%pi*10^-7; e=8.85*10^-12; c=3*10^10; / / i n cm / s f=6*10^9; / / i n Hz a=1.5; / / i n cm b=1; / / i n cm

// For TE10 mode :              

m=1; n=0; wl_c=2*a; f_c=c/wl_c; t_1=(m*%pi/a)^2; t_2=(n*%pi/b)^2; t_3=(((2*%pi*f)^2)*u*e); a= sqrt (t_1+t_2-t_3); / / i n n e p e r /m   disp (a*20/ log (10), ’ A t t e n u a t i o n ( i n dB /m) = ’ ) ;

34

i f 

Scilab code Exa 4.20  Calculate the maximum power handling capacity

1 //Caption : Cal cul ate

t h e maximum p ow er h a n d l i n g

capacity 2 / / Exa : 4 . 2 1 3 4 5 6 7 8 9 10 11 12 13 14 15

                       

clc ; clear ; close ; c=3*10^10; / / i n cm / s f=9*10^9; / / i n H z a=3; / / i n cm b=1; / / i n cm E_max=3000; // in V/cm wl_o=c/f; wl_c=2*a; // in TE10 wl_g= ceil   (wl_o/ sqrt (1-(wl_o/wl_c)^2)); P_max=(6.63*10^-4)*E_max^2*a*b*(wl_o/wl_g); disp (P_max/1000, ’ Maximum p ow er f o r r e c t a n g u l a r w a ve g ui d e ( i n k i l o w a t t s )= ’ ) ;

Scilab code Exa 4.21  Calculate the maximum power

1 / / C a p t i o n : C a l c u l a t e t h e maximum p o we r 2 / / Exa : 4 . 2 1

35

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

             

clc ; clear ; close ; c=3*10^10; / / i n cm / s f=9*10^9; / / i n H z E_max=300; // in V/cm d=5; wl_o=c/f;

  // For TE11        

wl_c=d*%pi/1.841; wl_g=wl_o/ sqrt (1-(wl_o/wl_c)^2); P_max=0.498*E_max^2*d^2*(wl_o/wl_g); disp (P_max, ’ Maximum p o w er ( i n w a t t s ) = ’ );

Scilab code Exa 4.22  Calculate the peak value of electric feild occuring in

the waveguide 1 //Caption : Cal cul ate

t h e p ea k v a l u e o f e l e c t r i c o c c u ri n g i n t he w av eg ui de 2 / / Exa : 4 . 2 2 3 4 5 6 7 8 9 10 11 12 13

                   

clc ; clear ; close ; c=3*10^10; / / i n cm / s f=30*10^9; / / i n H z a=1; / / i n cm b=1; P_max=746; / / i n w a t t s wl_o=c/f; wl_c=2*a; Z=120*%pi/ sqrt (1-(wl_o/wl_c)^2);

36

feild

14   E_max= sqrt (P_max*4*Z/(a*b/10000)); 15   disp (E_max/1000, ’ P ea k v a l u e o f e l e c t r i c /m) =’ ) ;

f i e l d ( i n kV

Scilab code Exa 4.23  Calculate the breakdown power of air filled rectan-

gular waveguide for dominant mode 1 / / C ap ti on : C a l c u l a t e t h e b rea kdo wn p ower o f

ai r f i l l e d r e c t a n g u l a r w a ve g ui d e f o r d om in an t mode a t 9 . 3 7 5 GHz . 2 / / Exa : 4 . 2 3 3 4 5 6 7 8 9 10 11 12 13

clc ;   clear ;   close ;

// Given :              

c=3*10^10; / / i n cm / s a=2.3; / / i n cm b=1; / / i n cm f=9.375*10^9; / / i n Hz wl_o=c/f; P_bd_TE11=597*2.3*1*{1-{wl_o/(2*a)}^2}^0.5; disp (P_bd_TE11 , ’ B re ak do wn p ow er f o r d o mi na n t mode ( i n kW) = ’ ) ;

37

Scilab code Exa 4.24  Calculate the breakdown power of circular waveg-

uide 1 / / C ap ti on : C a l c u l a t e t h e b rea kdo wn p ower o f

ci rc ul ar

waveguide 2 / / Exa : 4 . 2 4 3 4 5 6 7 8 9 10 11 12 13 14 15

clc ;   clear ;   close ;

// Given :   d=5; / / i n cm   c=3*10^10; / / i n cm / s   f=9*10^9; / / i n H z   / / D om in an t mode i s TE11 :          

wl_o=c/f; wl_c=%pi*d/1.841; f_c=c/wl_c; P_bd_TE11=1790*(d/2)^2*[1-{f_c/f}^2]^0.5; disp (P_bd_TE11/1000, ’ B re ak do wn p o we r ( i n kW) = ’ );

38

Chapter 5 Cavity Resonators

Scilab code Exa 5.1   Determine the minimum distance between two end

plates 1 / / C a p t i o n : D e t er m i ne t h e minimum d i s t a n c e b e tw e en t wo

end p l a t e s 2 / / Exa : 5 . 1 3 4 5 6 7 8 9 10 11 12

clc ;   clear ;   close ;

// Given :   a=3; / / i n cm   c=3*10^10; / / i n cm / s   f=10*10^9; / / i n Hz   P_01=2.405;   d=%pi/ sqrt (f^2*4*%pi^2/c^2-(P_01/a)^2);   disp (d , ’ Minimum d i s t a n c e ( i n cm ) = ’ );

39

Scilab code Exa 5.2 Calculate the lowest frequency of a rectangular cavity

resonator 1 // C ap ti on : C a l c u l a te t he l o w e st f r eq u e nc 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 na t o r 2 / / Exa : 5 . 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

clc ;   clear ;   close ;

// Given :                    

c=3*10^10; / / i n cm / s a=2; / / i n cm b=1; / / i n cm d=3; / / i n cm disp ( ’ D o mi n an t mode i s TE 10 1 ’ ); m=1; n=0; p=1; f=(c/2)*[(m/a)^2+(n/b)^2+(p/d)^2]^0.5; disp (f/10^9, ’ L o we s t r e s o n a n t f r e q u e n c y ( i n GHz ) = ’ );

Scilab code Exa 5.3  Calculate the resonant frequency of a circular cavity

resonator 1 // C ap ti on : C a l c u l a te t he r e so n a n t f r e qu e n cy o f a

circular 2 / / Exa : 5 . 3 3 4 5 6

c a vi t y r e s o n a t o r

clc ;   clear ;   close ;

// Given : 40

7 8 9 10 11 12 13 14 15 16 17 18 19

       

d=12.5; / / d i a m e t e r ( i n cm ) c=3*10^10; / / i n cm / s l=5; / / l e n g t h ( i n cm ) a=d/2;

// For TM012 mode :            

n=0; m=1; p=2; P=2.405; f=(c/(2*%pi))*[(P/a)^2+(p*%pi/d)^2]^0.5; disp (f/10^9, ’ R e so n a nt f r e q u e n c y ( i n GHz ) = ’ ) ;

  / / Answer i n bo ok i n w ro ng l y g i v e n a s 6 . 2 7 GHz

Scilab code Exa 5.4  Calculate the resonant frequency of a circular cavity

resonator 1 // C ap ti on : C a l c u l a te t he r e so n a n t f r e qu e n cy o f a

circular 2 / / Exa : 5 . 4 3 4 5 6 7 8 9 10 11 12 13

c a vi t y r e s o n a t o r

clc ;   clear ;   close ;

// Given :        

c=3*10^10; / / i n cm / s a=3; / / i n cm b=2; / / i n cm d=4; / / i n cm

// For TE101 :   m=1;   n=0;

41

14   p=1; 15   f=(c/2)*[(m/a)^2+(n/b)^2+(p/d)^2]^0.5; 16   disp (f/10^9, ’ R e s o n a nt f r e q u e n c y ( i n GHz ) = ’ );

42

Chapter 6 Microwave Components

Scilab code Exa 6.2  Find the distance that the position of port 1 should

be shifted 1   / / C ap ti on : Fi nd t he d i s t a n c e

t h at t he p o s i t i o n o f   p or t 1 s h ou l d b e s h i f t e d . 2 / / Exa : 6 . 2 3 4 5 6 7 8 9 10 11 12 13

clc ;   clear ;   close ;   Beeta=34.3; / / i n r a d /m

/ / S = [ 0 , 0 . 5 ∗ %eˆ(%i ∗ 5 3 . 1 3 ) ; 0 . 5 ∗ %eˆ(%i ∗ 5 3 . 13 ) , 0 ] ; / / S ’ = [ 0 , 0 . 5 ∗ %eˆ(%i ∗ 53.13 − x ) ; 0 . 5 ∗ %eˆ(%i ∗ 53.13 − x ) , 0 ] ;   / / For S12& S21 t o be r e a l ,   x=53.5; // i n d e g r e e s   x_rad=53.5*%pi/180;   l=x_rad/Beeta;   disp (l*100, ’ D i s t a n c e ( i n cm )= ’ );

43

Scilab code Exa 6.3  Determine the scattering parameters for 10 dB direc-

tion coupler 1   / / C a pt io n : D et er mi ne t h e s c a t t e r i n g

dB d i r e c t i o n c o up l er 2 / / Exa : 6 . 3 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

         

clc ; clear ; close ; D=30; / / i n dB VSWR=1; C=10;

  //p1 p4 = p1/p4                                

p1_p4=10^(C/-10); S_41= sqrt (p1_p4); S_14=S_41; //As matched & l o s s l e s s S_31=S_41^2/10^(D/10); S_11=(VSWR -1)/(VSWR+1); S_22=S_11; S_44=S_11; S_33=S_11; S_21= sqrt (1-0.1-10^-4); S_12=S_21; S_34= sqrt (1-0.1-10^-4); S_43=S_34; S_24= sqrt (1-0.1-S_34^2); S_42=S_24; S_23=S_41; S_32=S_23; S_13=S_31;

44

p a r am e te r s f o r 1 0

27   S=[S_11,S_12,S_13,S_14;S_21,S_22,S_23,S_24;S_31,S_32 ,S_33,S_34;S_41,S_42,S_43,S_44]; 28   disp (S , ’ R e qu i re d S c a t t e r i n g P a ra m et er s a r e ’ ) ;

Scilab code Exa 6.4  Determine the powers in the remaining ports

1 / / C a pt i on : D e te r mi n e t h e p o we rs i n t h e r e m a i n i n g

ports 2 / / Exa : 6 . 4 3 4 5 6 7 8 9 10 11 12 13 14

                     

clc ; clear ; close ; a_2=0; a_3=0; a_1=32; // i n mW b_1=(a_1/2^2)+(a_2/-2)+(a_3/ sqrt (2)); b_2=(a_1/(-2)^2)+(a_2/-2)+(a_3/ sqrt (2)); b_3=(a_1/2)+(a_2/ sqrt (2))+(a_3/- sqrt (2)); disp (b_1, ’ P ow er a t p o r t 1 ( i n mW) = ’ ) ; disp (b_2, ’ P ow er a t p o r t 2 ( i n mW) = ’ ); disp (b_3, ’ P ow er a t p o r t 3 ( i n mW) = ’ );

Scilab code Exa 6.5  Determine the powers in the remaining ports

45

1 / / C a pt i on : D e te r mi n e t h e p o we rs i n t h e r e m a i n i n g

ports 2 / / Exa : 6 . 5 3 4 5 6 7 8 9 10 11 12 13

                   

clc ; clear ; close ; b_1=20; b_2=20; p_1= abs ((60-50)/(60+50)); p_2= abs ((75-50)/(75+50)); P_1=b_1*(1-p_1^2)/2; P_2=b_2*(1-p_2^2)/2; disp (P_1, ’ P o wer i n p o r t 1 ( i n mW) = ’ ); disp (P_2, ’ P o wer i n p o r t 2 ( i n mW) = ’ );

Scilab code Exa 6.6  Determine the powers reflected at port 3 and power

divisions at other ports 1 // C ap ti on : D et er mi ne t he p ow er s r e f l e c t e d

power d i v i s i o n s a t o t he r p o r ts . 2 / / Exa : 6 . 6 3 4 5 6 7 8 9 10 11 12

                 

clc ; clear ; close ; p_1=0.5; p_2=0.6; p_4=0.8; b_1=0.6566; b_2=0.7576; b_3=0.6536; b_4=0.00797;

46

a t p o rt 3 &

13 14 15 16 17 18 19 20

               

a_1=p_1*b_1; a_2=p_2*b_2; a_3=1; / / i n W a tt s a_4=p_4*b_4; disp (b_1^2, ’ P ower disp (b_2^2, ’ P ower disp (b_3^2, ’ P ower disp (b_4^2, ’ P ower

at at at at

port port port port

1( in 2( in 3( in 4( in

W)= ’ ); W)= ’ ); W)= ’ ); W)= ’ );

Scilab code Exa 6.7   Calculate the scattering matrix

1 2 3 4 5 6 7 8 9 10 11 12 13

/ / C ap ti on : C a l c u l a t e t h e s c a t t e r i n g m a tr i x . / / Exa : 6 . 7                    

clc ; clear ; close ; In_loss=0.5; / / i n dB S_21=10^(-In_loss/20); Isolation=30; / / i n dB S_12=10^(-Isolation/20); S_11=0; S_22=0; S=[S_11,S_12;S_21,S_22]; disp (S , ’ S c a t t e r i n g m at ri x = ’ ) ;

47

Scilab code Exa 6.9   Calculate the scattering matrix

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

/ / C ap ti on : C a l c u l a t e t h e s c a t t e r i n g m a tr i x . / / Exa : 6 . 9                                

clc ; clear ; close ; VSWR=1; In_loss=0.5; / / i n dB S_21=10^(-In_loss/20); Isolation=20; / / i n dB S_12=10^(-Isolation/20); S_23=S_12; S_31=S_12; S_32=S_21; S_13=S_21; p=( VSWR -1)/( VSWR+1) ; S_11=p; S_22=p; S_33=p; S=[S_11,S_12,S_13;S_21,S_22,S_23;S_31,S_32,S_33]; disp (S , ’ S c a t t e r i n g m at ri x = ’ ) ;

Scilab code Exa 6.10   Calculate the scattering matrix

1 2 3 4 5 6

/ / C ap ti on : C a l c u l a t e t h e s c a t t e r i n g m a tr i x . / / Exa : 6 . 1 0 clc ;   clear ;   close ;   In_loss=0.5; // i n s e r t i o n

l o s s ( i n dB ) 48

7 8 9 10 11 12 13 14 15 16

                 

C=20; / / i n dB D=35; / / i n dB Pi_Pf=10^(C/10); Pi=90; / / i n W a tt s 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 Wa tts ) 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 p ower

r e c e i v e d ( i n dB ) 17   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 )= ’ ) ;

Scilab code Exa 6.11  Calculate the directivity and coupling and isolation

/ / C a p t i o n : C a l c u l a t e ( i )− d i r e c t i v i t y ( i i i )− i s o l a t i o n 2 / / Exa : 6 . 1 1 1

3 4 5 6 7 8 9 10 11 12 13

                   

clc ; clear ; close ; S_13=0.1; S_14=0.05; C=-20* log (S_13)/ log (10); D=20* log (S_13/S_14)/ log (10); I=C+D; disp (C , ’ C o u pl i n g ( i n dB ) = ’ ); disp (D , ’ D i r e c t i v i t y ( i n dB ) ) = ’ ) ; disp (I , ’ I s o l a t i o n ( i n dB ) = ’ ) ;

49

, ( i i )− c o u p l i n g ,

Scilab code Exa 6.12  Calculate the value of VSWR

1 2 3 4 5 6 7 8 9 10

/ / C a p t i o n : C a l c u l a t e t h e v a l u e o f VSWR / / Exa : 6 . 1 2              

clc ; clear ; close ; D=3.5; // d i s t a n c e o f s e p e r a t i o n ( i n cm ) w_l=2*D; / / w a v e l e n g t h d2_d1=2.5; //d2−d 1 ( i n m) S=w_l/(%pi*d2_d1*10^-1); disp (S ,  ’VSWR = ’ );

Scilab code Exa 6.13  Calculate the phase shift of the component

1 2 3 4 5 6 7 8

  / / C a pt io n : C a l c u l a t e t h e p ha s e s h i f t o f t h e c om po nen t / / Exa : 6 . 1 3          

clc ; clear ; close ; w_l=7.2; / / w a v e l e n g t h ( i n cm ) x=10.5-9.3; Phase_shift=(2*%pi*x)/(w_l);

50

9   disp (Phase_shift*180/%pi, ’ P ha se S h i f t ( i n d e g r e e ) = ’ );

51

Chapter 7 Microwave Measurements

Scilab code Exa 7.1  Calculate the SWR of the transmission line

1 2 3 4 5 6 7 8 9 10 11

/ / C ap ti on : C a l c u l a t e t h e SWR o f t h e t r a n s m i s s i o n l i n e / / Exa : 7 . 1 clc ;   clear ;   close ;

// Given :          

c=3*10^10; / / i n cm / s a=4; / / i n cm b=2.5; / / i n cm f=10*10^9; / / i n Hz d=0.1; / / d i s t a n c e b e tw e en 2 minimum p ow er p o i n t s ( i n

cm ) 12 // For TE10 mode : 13 14 15 16 17

         

wl_c=2*a; wl_o=c/f; wl_g=wl_o/ sqrt (1-(wl_o/wl_c)^2); S=wl_g/(%pi*d); disp (S , ’ V o lt ag e s t a nd i n g wave r a t i o = ’ ) ;

52

Scilab code Exa 7.2  Calculate the SWR of the main waveguide

1 2 3 4 5 6 7 8 9 10 11

/ / C a p t i o n : C a l c u l a t e t h e SWR o f t h e m ai n w a v eg u i d e / / Exa : 7 . 2 clc ;   clear ;   close ;

// Given :   P_i=300; // i n mW   P_r=10; // i n mW p= sqrt (P_r/P_i);   S=(1+p)/(1-p);   disp (S , ’ V o lt ag e s t a nd i n g wave r a t i o = ’ ) ;

Scilab code Exa 7.3  Calculate the SWR of the waveguide

1 2 3 4 5 6 7 8

/ / C a pt i on : C a l c u l a t e t h e SWR o f t h e w a ve g ui d e / / Exa : 7 . 3 clc ;   clear ;   close ;

// Given :   P_i=2.5; // i n mW   P_r=0.15; // i n mW

53

9 p= sqrt (P_r/P_i); 10   S=(1+p)/(1-p); 11   disp (S , ’ V o lt ag e s t a nd i n g wave r a t i o = ’ ) ;

Scilab code Exa 7.4  Calculate the value of reflected power

1 2 3 4 5 6 7 8 9 10 11 12 13

// C ap ti on : C a l c u l a te t he v a lu e o f r e f l e c t e d power / / Exa : 7 . 4 clc ;   clear ;   close ;

// Given :              

P_i=4.5; // i n mW S=2; //VSWR C=30; / / i n dB p=(S-1)/(S+1); P_f=P_i/(10^(C/10)); P_r=p^2*P_i; disp (P_r, ’ R e f l e c t e d p ower ( i n w a tt s ) = ’ );

54

Chapter 8 Microwave Tubes and Circuits

Scilab code Exa 8.1  Calculate the dc electron velocity and dc phase con-

stant and plasma frequency and reduced plasma frequency and dc beam current beam density and instantaneous beam current density ( i )− dc e l e c t r o n v e l o c i t y , ( i i ) −dc p h as e c o n s t a n t , ( i i i )− p la sm a f r e q u e nc y , ( i v ) − r e du c ed p la sm a f r e q u e n c y f o r R= 0. 4 , ( v ) −dc beam c u r r e n t beam d e n s i t y , ( v i ) − i n s t a n t a n e o u s beam c u rr e nt d e n si t y 2 / / Exa : 8 . 1 1 //Caption : Cal cul ate

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

                       

clc ; clear ; close ; V_o=14.5*10^3; // i n v o l t s I_o=1.4; / / i n A f=10*10^9; / / i n Hz p_o=10^-6; // in c/mˆ3 p=10^-8; // in c/mˆ3 v=10^5; / / i n m/ s R=0.4; v_o=0.593*10^6* sqrt (V_o); k=2*%pi*f/v_o; w_p=[1.759*10^11*(10^-6/(8.854*10^-12))]^0.5;

55

16 17 18 19 20 21 22 23 24

                 

w_q=R*w_p; J_o=p_o*v_o; J=p*v_o+p_o*v; disp (v_o, ’ Dc e l e c t r o n v e l o c i t y ( i n m/ s ) = ’ ); disp (k , ’ Dc p ha se c o n s t a n t ( i n r ad / s ) = ’ ); disp (w_p, ’ P la sma f r e q u e n c y ( i n r ad / s ) = ’ ); disp (w_q, ’ R edu ced p la sm a f r e q u e n c y ( i n r ad / s ) = ’ ) ; disp (J_o, ’ Dc beam c u r r e n t d e n s i t y ( i n A/ s q . m) = ’ ); disp (J , ’ 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/ s q . m ) = ’ );

25 26   / / Answer i n bo ok a r e w ro n gl y w r i t t e n a s : ( Dc p ha se

c o n s t a n t = 1. 41 ∗ 1 0 ˆ8 r a d / s e c )

Scilab code Exa 8.2  Calculate the input rms voltage and output rms volt-

age and power delivered to load 1 //Caption : Cal cul ate

( i )− i n p u t rms v o l t a g e , ( i i )− o u tp u t rms v o l t a g e , ( i i i )− power d e l i v e r e d t o l o a d 2 / / Exa : 8 . 2 3 4 5 6 7 8 9 10 11 12 13

                   

clc ; clear ; close ; A_v=15; / / i n dB P_i=5*10^-3; / / i n W R_sh_i=30000; / / i n o hm s R_sh_o=40000; / / i n o hm s R_l=20000; // in ohms V_i= sqrt (P_i*R_sh_i); V_o=10^((A_v/20))*12.25; P_out=V_o^2/R_l;

56

14   disp (V_i, ’ I np ut rms v o l t a g e ( i n v o l t s ) = ’ ) ; 15   disp (V_o, ’ O utput rms v o l t a g e ( i n v o l t s ) = ’ ); 16   disp (P_out, ’ Power d e l i v e r e d t o l o ad ( i n w at ts ) = ’ );

Scilab code Exa 8.3  Calculate the input power in watts and output power

in watts and efficiency 1 //Caption : Cal cul ate

( i )− i n p u t p ow er i n w a tt s , ( i i ) − o u tp u t p ow er i n w at ts , ( i i i )− e f f i c i e n c y 2 / / Exa : 8 . 3 3 4 5 6 7 8 9 10 11 12 13 14 15 16

                         

clc ; clear ; close ; n=2; V_o=300; // i n v o l t s I_o=20*10^-3; / / i n A V_i=40; // i n v o l t s J=1.25; / / J ( X ’ ) P_dc=V_o*I_o; P_ac=2*V_o*I_o*J/(2*n*%pi-%pi/2); eff=(P_ac/P_dc)*100; disp (P_dc, ’ I n p u t p ow er ( i n w a t ts ) = ’ ) ; disp (P_ac, ’ O utp ut p ow er ( i n w a t ts ) = ’ ); disp (eff, ’ E f f i c i e n c y ( i n p e r ce n t ) = ’ ) ;

57

Scilab code Exa 8.4   Calculate the electron velocity and dc transit time

and input voltage for maximum output voltage and voltage gain in dB ( i )− e l e c t r o n v e l o c i t y , ( i i ) −dc t r a n s i t t im e , ( i i i )− i n p u t v o l t a g e f o r maximum o u tp u t v o l t a g e , ( i v )− v o l t a g e g ai n i n dB 2 / / Exa : 8 . 4 1 //Caption : Cal cul ate

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

                     

clc ; clear ; close ; V_o=900; // i n v o l t s I_o=30*10^-3; / / i n A f=8*10^9; / / i n Hz d=0.001; / / i n m l=0.04; / / i n m R_sh=40*10^3; // in ohm v_o=0.593*10^6* sqrt (V_o); T_o=l/v_o; Theeta_o=(2*%pi*f)*T_o; / / T r a n s i t a n g l e s b et we en

c a v i t i e s ( i n r a d ia n ) 15   Theeta_g=(2*%pi*f)*d/v_o; // A ve ra ge gap t r a n s i t

a n g le

( in radian ) 16 17 18 19 20 21 22 23

b= sin (Theeta_g/2)/(Theeta_g/2);   V_in_max=V_o*3.68/(b*Theeta_o);

// As , { J(X)/X=0.582 }          

A_r=b^2*Theeta_o*0.582*R_sh/(30*10^3*1.841); disp (v_o, ’ E l e ct r o n v e l o c i t y ( i n m/ s ) = ’ ); disp (T_o, ’ Dc T r a n s i t Time ( i n s e c )= ’ ) ; disp (V_ in_max , ’ Maximum i n p u t v o l t a g e ( i n v o l t s ) = ’ ); disp (A_r, ’ V o l ta g e g a i n ( i n dB ) = ’ ) ;

58

Scilab code Exa 8.5   Calculate the input microwave voltage and voltage

gain and efficiency of amplifier and beam loading conductance ( i )− i / p m i cr o wa v e v o l t a g e , ( i i )− v o l t a g e g ai n , ( i i i )− e f f i c i e n c y o f a m p l i f i e r , ( i v ) − beam l o a d i n g c o n d u ct a n c e 2 / / Exa : 8 . 5 1 //Caption : Cal cul ate

3 4 5 6 7 8 9 10 11 12 13

                   

clc ; clear ; close ; V_o=1200; // i n v o l t s I_o=28*10^-3; / / i n A f=8*10^9; / / i n H z d=0.001; / / i n m l=0.04; / / i n m R_sh=40*10^3; / / i n o hm s V_p_max=1200*3.68*0.593*10^6* sqrt (V_o)/(2*%pi*f*l); Theeta_g=(2*%pi*f)*d/(0.593*10^6* sqrt (V_o)); //

t r a n s i t a n gl e ( i n r a d ) beeta= sin (Theeta_g/2)/(Theeta_g/2); V_i_max=V_p_max/beeta; Beeta_o=0.768; J=0.582; / / J ( X ) A_v=(Beeta_o)^2*97.88*J*R_sh/(1200/(28*10^-3*1.841)) ; // c a l c u l a t i n g v o l t a g e g a i n 19   eff=[0.58*[2*28*10^-3*J*Beeta_o*R_sh]/V_o]*100; // 14 15 16 17 18

         

c a lc u la t in g e f f i c i e n c y 20   G_o=23.3*10^-6; 21   G_b=(G_o/2)*{Beeta_o^2-Beeta_o* cos (Theeta_g)}; //beam 22   23   24   25  

l o a d i n g c o nd u ct a nc e R_b=1/(G_b*1000); // beam l o a d i n g r e s i s t a n c e ( i n k i l o ohms) disp (V_i _max , ’ I n p ut m ic ro wa ve v o l t a g e ( i n v o l t s ) = ’ ); disp (A_v, ’ V o l ta g e g a i n = ’ ); disp (eff, ’ E f f e c i e n c y o f a m p l i f i e r ( i n p e rc e n t a g e ) = ’

); 26   disp (R_b, ’ Beam l o a d i n g r e s i s t a n c e ( i n k i l o ohms ) = ’ ); 27

59

28   / / Answer i n book i s

w ro ng ly g i ve n a s : V o lt ag e g a in

=17.034

Scilab code Exa 8.6  Calculate the value of repeller voltage and beam cur-

rent necessary to give gap voltage of 200V and electronic efficiency 1 //Caption : Cal cul ate

( i )− v al ue o f r e p e l l e r v o l t a g e V r , ( i i )−beam c u r r e n t n e c es s a r y t o g i v e gap v o l t a g e o f 2 00V , ( i i i )− e l e c t r o n i c e f f i c i e n c y 2 / / Exa : 8 . 6 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

                                 

21   22  

clc ; clear ; close ; e_m_ratio=1.759*10^11; // ( e /m) V_o=500; // i n v o l t s R_sh=20*10^3; / / i n o hm s f=8*10^9; / / i n H z w=2*%pi*f; n=2; //mode L=0.001; // s p a c in g b etw een r e p e l l e r & c a v i t y ( i n m) x=0.023; volt_diff= sqrt (V_o*(x)); V_r=volt_diff+V_o; // r e p e l l e r v o l a tg e Beeta_o=1; //Assuming J=0.582; V_1=200; / / g i v e n ( i n v o l t s ) I_o=V_1/(R_sh*2*J); Theeta_o=2*%pi*f*J*10^6*2*10^-3* sqrt ( V _ o ) /(1.579*10^11*(V_r+V_o)); X=V_1*Theeta_o/(2*V_o); //X’ j=0.84; / / J ( X ’ )

60

23 24 25 26

       

eff=[2*j/(2*%pi*2-%pi/2)]*100; disp (V_r, ’ R e p e l l e r v o l t a g e ( i n v o l t s ) = ’ ); disp (I_o, ’ N e c e s s a r y beam c u r r e n t ( i n Amp . s ) = ’ ) ; disp (eff, ’ E f f e c i e n c y ( i n p e rc e nt a g e ) = ’ );

Scilab code Exa 8.7   Calculate the efficiency of reflex klystron and total

output power in mW and power delivered to load ( i )− e f f i c i e n c y o f r e f l e x k l y s t r o n , ( i i )− t o t a l o u t p u t p ow er i n mW, ( i i i )− power d e l i v e r e d t o l o a d 2 / / Exa : 8 . 7 1 //Caption : Cal cul ate

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

                       

clc ; clear ; close ; P_dc_in=40; // i n mW ratio=0.278; / / V 1 / V o ; n=1; X=ratio*(2*n*%pi-%pi/2); J=2.35; eff=ratio*J*100; / / i n p e r c e n t a g e P _ ou t = 8 . 91 * P _ d c _ in / 1 00 ; P_load=3.564*80/100; disp (eff, ’ E f f e c i e n c y ( i n p e rc e nt a g e ) = ’ ); disp (P_out, ’ T o t a l p o we r o u t p u t ( i n mW) = ’ ) ; disp (P_load, ’ P ower d e l i v e r e d t o l o a d ( i n mW) = ’ );

61

Scilab code Exa 8.8  Calculate the Hull cutoff voltage and cutoff magnetic

flux density if beam voltage is 6000V and cyclotron frequency in GHz ( i )− H u ll c ut − o f f v o l t a g e , ( i i )− cu t − o f f m ag ne ti c f l u x d e n s i t y i f beam v o l t a g e V o i s 6 00 0V , ( i i i )− c y c l o t r o n f r e qu e n cy i n GHz 2 / / Exa : 8 . 8 1 //Caption : Cal cul ate

3 4 5 6 7 8 9 10 11 12 13

             

clc ; clear ; close ; e_m_ratio=1.759*10^11; // ( e /m) R_a=0.15; / / i n m R_o=0.45; / / i n m B_o=1.2*10^-3; // in weber /mˆ2 V_o={(e_m_ratio)*B_o^2*R_o^2*[1-(R_a/R_o)^2]^2}/8;

// Given :   V=6000; // i n v o l t s   B_c= sqrt (8*V/e_m_ratio)/[[1-(R_a/R_o)^2]*(R_o)]; // in

weber/mˆ2 w_c=(e_m_ratio)*B_o; f_c=w_c/(2*%pi); / / i n Hz disp (V_o,  ’ Cut− o f f v o l t a g e ( i n v o l t s ) = ’ ); disp (B_c*10^5,  ’ Cut− o f f m ag ne t ic f l u x d e n s i t y ( i n m i l l i web er / s q . m) = ’ ) ; 18   disp (f_c*10^-9, ’ C y c l o t r o n f r e q u e n c y ( i n GHz ) = ’ ); 19 20 / / Answer i n bo ok i s w ro ng l y g i v e n a s : f c = 0. 33 6Hz & 14 15 16 17

       

V o = 5 0 . 6 66 kV

62

Scilab code Exa 8.9  Calculate the Axial phase velocity and Anode voltage

at which TWT can be operated for useful gain ( i )− A xi al p ha se v e l o c i t y , ( i i )− Anode v o l t a g e a t w hi ch TWT c an b e o p e r a t e d f o r u s e f u l g ai n 2 / / Exa : 8 . 9 1 //Caption : Cal cul ate

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

                     

clc ; clear ; close ; e_m_ratio=1.759*10^11; // ( e /m) c=3*10^8; / / i n m/ s d=0.002; / / d i a m e t e r ( i n m) pitch=(1/50)/100; / /As , 5 0 t u r n s p e r cm ( i n m) circum=%pi*d; v_p=c*pitch/circum; V_o=v_p^2/(2*e_m_ratio); disp (v_p, ’ A x ia l p ha se v e l o c i t y ( i n m/ s ) = ’ ); disp (V_o, ’ A node V o l t a g e ( i n kV ) = ’ );

// Answer i n book i s w ro ng ly g i ve n a s V o = 25 .9 2 V

Scilab code Exa 8.10  Calculate the electron velocity and dc transit time

and input voltage for maximum output voltage and voltage gain in dB 63

1 //Caption : Cal cul ate

( i )− e l e c t r o n v e l o c i t y , ( i i ) −dc t r a n s i t t im e , ( i i i )− i n p u t v o l t a g e f o r maximum o u tp u t v o l t a g e , ( i v )− v o l t a g e g ai n i n dB 2 / / Exa : 8 . 1 0 3 4 5 6 7 8 9 10 11 12 13 14

                     

clc ; clear ; close ; V_o=900; // i n v o l t s I_o=30*10^-3; / / i n A f=8*10^9; / / i n Hz d=0.001; / / i n m l=0.04; / / i n m R_sh=40*10^3; // in ohm v_o=0.593*10^6* sqrt (V_o); T_o=l/v_o; Theeta_o=(2*%pi*f)*T_o; / / T r a n s i t a n g l e s b et we en

c a v i t i e s ( i n r a di a n ) 15   Theeta_g=(2*%pi*f)*d/v_o; // A ve ra ge gap t r a n s i t

a n g le

( in radian ) 16 17 18 19 20 21 22 23

b= sin (Theeta_g/2)/(Theeta_g/2);   V_in_max=V_o*3.68/(b*Theeta_o);

// As , { J(X)/X=0.582 }          

A_r=b^2*Theeta_o*0.582*R_sh/(30*10^3*1.841); disp (v_o, ’ E l e ct r o n v e l o c i t y ( i n m/ s ) = ’ ); disp (T_o, ’ Dc T r a n s i t Time ( i n s e c )= ’ ) ; disp (V_ in_max , ’ Maximum i n p u t v o l t a g e ( i n v o l t s ) = ’ ) ; disp (A_r, ’ V o l ta g e g a i n ( i n dB ) = ’ ) ;

Scilab code Exa 8.11  Calculate the dc electron velocity and dc phase con-

stant and plasma frequency and reduced plasma frequency and dc beam current beam density and instantaneous beam current density 64

1 //Caption : Cal cul ate

( i )− dc e l e c t r o n v e l o c i t y , ( i i ) −dc p h as e c o n s t a n t , ( i i i )− p la sm a f r e q u e nc y , ( i v ) − r e du c ed p la sm a f r e q u e n c y f o r R= 0. 5 , ( v ) −dc beam c u r r e n t beam d e n s i t y , ( v i ) − i n s t a n t a n e o u s beam c u rr e nt d e n si t y 2 / / Exa : 8 . 1 1 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

                                         

clc ; clear ; close ; V_o=20*10^3; // i n v o l t s I_o=2; / / i n A f=10*10^9; / / i n Hz p_o=10^-6; // in c/mˆ3 p=10^-8; // in c/mˆ3 v=10^5; / / i n m/ s R=0.5; v_o=0.593*10^6* sqrt (V_o); k=2*%pi*f/v_o; w_p=[1.759*10^11*(10^-6/(8.854*10^-12))]^0.5; w_q=R*w_p; J_o=p_o*v_o; J=p*v_o-p_o*v; disp (v_o, ’ Dc e l e c t r o n v e l o c i t y ( i n m/ s ) = ’ ); disp (k , ’ Dc p ha se c o n s t a n t ( i n r ad / s ) = ’ ); disp (w_p, ’ P la sma f r e q u e n c y ( i n r ad / s ) = ’ ); disp (w_q, ’ R edu ced p la sm a f r e q u e n c y ( i n r ad / s ) = ’ ) ; disp (J_o, ’ Dc beam c u r r e n t d e n s i t y ( i n A/ s q . m) = ’ ); disp (J , ’ 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/ s q . m ) = ’ );

Scilab code Exa 8.12  Calculate the gap transit angle

65

1 2 3 4 5 6 7 8 9 10 11 12

// C ap ti on : C a l c u l a te t he gap t r a n s i t a n g l e / / Exa : 8 . 1 2                  

clc ; clear ; close ; V_o=1000; / / Anode v o l t a g e ( i n v o l t s ) gap=0.002; / / i n m f=5*10^9; / / i n Hz L=2.463*10^-3; // l e n g th o f d r i f t r e g i o n ( i n m) u_o=5.93*10^5* sqrt (V_o); / / i n m/ s Theeta_g=2*%pi*f*2*10^-3/u_o; / / r a d i a n s disp (Th eeta_g , ’ T r a n s i t a n g l e ( i n r a d i a n s ) = ’ ) ;

Scilab code Exa 8.13  Calculate the input rf voltage and voltage gain and

efficiency 1 //Caption : Cal cul ate

( i )− i / p r f v o l t a g e , ( i i ) − v o l t a g e g a i n , ( i i i )− e f f i c i e n c y 2 / / Exa : 8 . 1 3 3 4 5 6 7 8 9 10 11 12 13 14

                     

clc ; clear ; close ; V_o=1200; // i n v o l t s I_o=30*10^-3; / / i n A f=10*10^9; / / i n H z d=0.001; / / i n m l=0.04; / / i n m R_sh=40*10^3; / / i n o hm s v_o=0.593*10^6* sqrt (V_o); Theeta_o=2*%pi*f*l/(20.54*10^6); X=1.84; / / f o r maximum o u t p u t p o w er

66

15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

                         

V_max=2*X*V_o/122.347; Theeta_g=122.347*10^-3/(4*10^-2); Beeta_i= sin (Theeta_g/2)/(Theeta_g/2); V_1_max=V_max/Beeta_i; J=0.58; Beeta_o=Beeta_i; I_2=2*I_o*J; V_2=Beeta_o*I_2*R_sh; A_v=V_2/V_1_max; / / i n dB eff=0.58*(V_2/V_o)*100; / / i n p e r c e n t a g e disp (V_1 _max , ’ I np ut r f v o l t a g e ( i n v o l t s ) = ’ ) ; disp (A_v, ’ V o l ta g e g a i n ( i n dB ) = ’ ) ; disp (eff, ’ Maximum e f f i c i e n c y ( i n p e r c e n t a g e ) = ’ );

/ / Answer i n bo ok i s w ro ng l y g i v e n a s : A v = 24 .3 3 dB

Scilab code Exa 8.14   Calculate the cyclotron angular frequency and cut-

off voltage and cutoff magnetic flux ( i )− c y c l o t r o n a n g ul a r f re qu e nc y , ( i i )− cu t − o f f v o l t a g e , ( i i i )− cut − o f f m ag ne ti c flux 2 / / Exa : 8 . 1 4 1 //Caption : Cal cul ate

3 4 5 6 7 8 9 10

             

clc ; clear ; close ; e_m_ratio=1.759*10^11; // ( e /m) a=0.04; b=0.08; V_o=30*10^3; // i n v o l t s I_o=80; / / i n A

67

11 12 13 14 15 16

           

B_o=0.01; / / i n w e be r / s q . m w=(e_m_ratio)*B_o; disp (w , ’ C y c lo t r o n a n g u l a r f r e q u e n cy ( i n r ad / s ) = ’ ); V_c={(e_m_ratio)*B_o^2*b^2*[1-(a/b)^2]^2}/8; disp (V_c,  ’ Cut− o f f v o l t a g e ( i n v o l t s ) = ’ ); B_c= sqrt (8*V_o/e_m_ratio)/[[1-(a/b)^2]*(b)]; // i n

weber/mˆ2 17   disp (B_c*10^3,  ’ Cut− o f f

m ag ne t ic f l u x d e n s i t y ( i n m i l l i web er / s q . m) = ’ ) ;

Scilab code Exa 8.15 Calculate the input power and output power in watts

and efficiency 1 //Caption : Cal cul ate

( i )− i n p u t p ow er , ( i i )− o u t p u t p ow er i n w a tt s , ( i i i )− e f f i c i e n c y 2 / / Exa : 8 . 1 5 3 4 5 6 7 8 9 10 11 12 13 14 15 16

                         

clc ; clear ; close ; n=2; V_o=280; // i n v o l t s I_o=22*10^-3; / / i n A V_i=30; // i n v o l t s J=1.25; / / J ( X ’ ) P_dc=V_o*I_o; P_ac=2*V_o*I_o*J/(2*n*%pi-%pi/2); eff=(P_ac/P_dc)*100; disp (P_dc, ’ I n p u t p ow er ( i n w a t ts ) = ’ ) ; disp (P_ac, ’ O utp ut p ow er ( i n w a t ts ) = ’ ); disp (eff, ’ E f f i c i e n c y ( i n p e r ce n t ) = ’ ) ;

68

Scilab code Exa 8.16 Calculate the repeller voltage and beam current nec-

essary to give gap voltage of 200V ( i )− r e p e l l e r v o l t a g e V r , ( i i ) − beam c u r r e n t n e c es s a r y t o g i v e gap v o l t a g e o f 2 00 V 2 / / Exa : 8 . 1 6 1 //Caption : Cal cul ate

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

                                 

clc ; clear ; close ; e_m_ratio=1.759*10^11; // ( e /m) V_o=300; // i n v o l t s R_sh=20*10^3; / / i n o hm s f=8*10^9; / / i n H z w=2*%pi*f; n=2; //mode L=0.001; // s p a c in g b etw een r e p e l l e r & c a v i t y ( i n m) x=(e_m_ratio)*(2*%pi*n-%pi/2)^2/(8*w^2*L^2); volt_diff= sqrt (V_o/(x)); V_r=(volt_diff)+V_o; // r e p e l l e r v o l a t g e J=0.582; V_1=200; / / g i v e n ( i n v o l t s ) I_o=V_1/(R_sh*2*J); disp (V_r, ’ R e p e l l e r v o l t a g e ( i n v o l t s ) = ’ ); disp (I_o*10^3, ’ N e c e s s a r y beam c u r r e n t ( i n m il li Am p . s ) = ’ );

69

70

Chapter 9 Solid State Microwave Devices

Scilab code Exa 9.1  Calculate i repeller voltage Vr ii beam current neces-

sary to give gap voltage of 200V 1 / / C a pt p t i on on : C a l c u l a t e

o p e r a t i n g f r e q u e n c y o f IMPATT

diode 2 / / Ex Exa : 9 . 1 3 4 5 6 7 8 9

           

clc ; clear ; close ; v_d=10^7*10^-2; / / d r i f t v e l o c i t y ( i n m/ s ) L=2*10^-6; / / d r i f t l e n g t h ( i n m) f=v_d/(2*L); / / i n Hz disp (f/10^9, ’ O p e r a t i n g F r e qu q u e n cy c y ( i n GHz ) = ’ ) ;

Scilab code Exa 9.2  Determine threshold electric field

1 // Caption : Determine

th re sh ol d e l e c t r i c 71

field

2 3 4 5 6 7 8 9 10

  / / Ex Exa : 9 2              

clc ; clear ; close ; f=10*10^9; / / i n Hz L=75*10^-6; / / D e v ic i c e l e n g t h ( i n m) V=25; / / V ol o l ta ta g e p u l s e a m p l i f i e d ( i n v o l t s ) E_th=V/L; disp (E_th, ’ T h r es e s h o l d E l e c t r i c f i e l d ( i n kV / cm ) = ’ ) ;

Scilab code Exa 9.3  Calculate the power gain in dB and power gain if it

is USB converter 1 //Caption : Cal cul ate

g ai n i f 2 / / Ex Exa : 9 . 3 3 4 5 6 7 8 9 10 11 12 13

                   

it

( i )− p ow o w e r g a i n i n dB , ( i i )−power i s USB c o n v e r t e r .

clc ; clear ; close ; f_s=2*10^9; / / i n Hz f_p=12*10^9; / / i n Hz R_i=16; R_s=1000; A_p=10* l o g ((f_p-f_s)/f_s); A_p_usb=10* l o g ((f_p+f_s)/f_s); disp ( l o g (10), ’ P ow ow e r g a i n ( i n dB ) = ’ ) ; disp (A_p _usb , ’ P ow ow e r g a i n a s USB c o n v e r t e r ( i n dB ) = ’ );

72

Scilab code Exa 9.4  Calculate the critical voltage and breakdown voltage

and breakdown electric field ( i )− c r i t i c a l v o l t a g e , ( i i ) − b re r e ak a k do do w wn n v o l t a g e , ( i i i )−brea kdo wn e l e c t r i c f i e l d 2 / / Ex Exa : 9 . 4 1 //Caption : Cal cul ate

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

                           

clc ; clear ; close ; E_s=12.5; E_o=8.85*10^-12; E=E_o*E_s; N=3.2*10^22; / / p e r c u b i c m et e t er er L=8*10^-6; / / i n m q=1.6*10^-19; / / i n c o u l o m b s V_c=q*N*L^2/(2*E); V_bd=2*V_c; E_bd=V_bd/L; disp (V_c/10^3, ’ C r i t i c a l v o l t a g e ( i n kV ) = ’ ) ; disp (V_bd/10^3, ’ B re re ak ak do do wn wn V o l t a g e ( i n kV ) = ’ ) ; disp (E_bd, ’ B re re ak ak do do wn wn E l e c t r i c f i e l d ( i n V/ cm ) = ’ ) ;

Scilab code Exa 9.5  Calculate the power gain in dB and power gain if it

is USB converter 73

1 //Caption : Cal cul ate

g ai n i f 2 / / Ex Exa : 9 . 5 3 4 5 6 7 8 9 10

             

it

( i )− p ow o w e r g a i n i n dB , ( i i )−power i s USB c o n v e r t e r .

clc ; clear ; close ; N_a=2.5*10^16; / / p e r c u b i c cm J=33; // in kA/c A/cmˆ2 mˆ2 q=1.6*10^-19; V_z=J/(q*N_a); / / A v al a l an a n ch c h e z on o n e v e l o c i t y ( i n cm / s ) disp (V_z, ’ A va v a la l a nc n c he h e z on o n e v e l o c i t y ( i n cm / s ) = ’ ) ;

Scilab code Exa 9.6  Calculate the power gain in dB

1 2 3 4 5 6 7 8 9

/ / C ap a p ti t i on o n : C a l c u l a t e t h e p ow o w e r g a i n i n dB / / Ex Exa : 9 . 6            

clc ; clear ; close ; R_neg=25; // in ohm R_load=50; // in ohm G={[- a b s (R_neg)-R_load]/[- a b s (R_neg)+R_load]}^2; disp ( G , ’ P ow ow e r g a i n = ’ ) ;

74

Scilab code Exa 9.7  Calculate the minimum voltage needed to GUNN ef-

fect 1 / / C a pt i on : C a l c u l a t e

t h e minimum v o l t a g e n e ed ed t o

GUNN e f f e c t 2 / / Exa : 9 . 7 3 4 5 6 7 8 9

           

clc ; clear ; close ; volt_grad=3.3*10^3; // v o l t a g e g r a d i e n t L=5*10^-4; // i n d r i f t l e n g th V_min=volt_grad*L; // i n v o l t s disp (V_min, ’ Minimum v o l t a g e n e ed e d ( i n V o l t s ) = ’ ) ;

Scilab code Exa 9.8  Calculate the rational frequency and critical velocity

of diode 1 // C ap ti on : C a l c u l a te t he r a t i o n a l

critical 2 / / Exa : 9 . 8 3 4 5 6 7 8 9 10 11

               

f r e qu e n cy &

ve lo ci ty of diode .

clc ; clear ; close ; v_d=2*10^7; / / i n cm / s L=20*10^-4; / / i n cm f=v_d/L; disp (f*10^-9, ’ N a t u r a l f r e q u e n c y ( i n GHz ) = ’ ) ; critical_field=3.3*10^3; V=L*critical_field;

75

12   disp (V , ’ C r i t i c a l

v o lt a ge ( i n v o l t s ) = ’ );

Scilab code Exa 9.9  Calculate the resonant frequency and efficiency

1 / / C ap ti on : C a l c u l a t e t h e r e s o n a n t f r e q u e n c y &

effi cien cy . 2 / / Exa : 9 . 9 3 4 5 6 7 8 9 10 11 12 13 14 15

                       

clc ; clear ; close ; L_p=0.5*10^-9; / / i n H C_j=0.5*10^-12; / / i n F V_bd=100; // b re akd ow n v o l t a g e ( i n v o l t s ) I_bias=100*10^-3; / / b i a s c u r r e n t ( i n A) I_rf_peak=0.8; R_l=2; f=1/(2*%pi* sqrt (L_p*C_j)); eff={(0.5*I_rf_peak^2*R_l)/(V_bd*I_bias)}*100; disp (f*10^-9, ’ R e so n a nt f r e q u e n c y ( i n GHz ) = ’ ); disp (eff, ’ E f f i c i e n c y ( i n p e r ce n t ag e ) = ’ );

Scilab code Exa 9.10  Calculate the drift time of carrier and operating fre-

quency of diode 1 //Caption : Cal cul ate

( i )− d r i f t t i m e o f c a r r i e r o p e ra t i ng f r e q ue n cy o f d i o de 2 / / Exa : 9 . 1 0 76

, ( i i )−

3 4 5 6 7 8 9 10 11

               

clc ; clear ; close ; L=2*10^-6; // d r i f t l e n g th ( i n m) v_d=10^5; / / i n cm / s drift_time=L/v_d; f=1/(2*drift_time); disp (drift_time , ’ D r i f t t im e ( i n s e c ) = ’ ); disp (f*10^-9, ’ O p e r a t i n g F r e q u e n cy ( i n GHz )= ’ );

Scilab code Exa 9.11   Calculate the breakdown voltage and breakdown

electric field 1 //Caption : Cal cul ate

( i )− b re ak do wn v o l t a g e brea kdo wn e l e c t r i c f i e l d . 2 / / Exa : 9 . 1 1 3 4 5 6 7 8 9 10 11 12 13 14

                     

, ( i i )−

clc ; clear ; close ; E_r=11.8; E_o=8.85*10^-12; N=3*10^21; // i n p er c u b ic m et er L=6.2*10^-6; / / i n m e te r q=1.6*10^-19; / / i n c o u l o m b s V_bd=q*N*L^2/(E_o*E_r); E_bd=V_bd/L; disp (V_bd, ’ B reakdown v o l t a g e ( i n v o l t s ) = ’ ); disp (E_bd,  ’ Breakdown e l e c t r i c f i e l d ( in V/m) =’ );

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Scilab code Exa 9.12  Calculate the maximum power gain and noise figure

and bandwidth / / C a p t i o n : C a l c u l a t e ( i )−maximum p o we r g a i n i n d Bs , ( i i )− n o i s e f i g u r e F i n dBs , ( i i i ) − b an dw id th f o r r =0.2 2 / / Exa : 9 . 1 2 1

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

                       

16   17   18  

clc ; clear ; close ; ratio=8; r=0.2; r_Q=8; T_d=300; / / i n K e l v i n T_o=300; / / i n K e l v i n X=8; G=(ratio)*X/(1+ sqrt (1+X))^2; G_in_dB=(10* log ( G ) ) / log (10); / / g a i n disp (G_i n_dB , ’Maximum Gain ( in dB)= ’ ) ; F=[10* log (1+(2*T_d/T_o)*[(1/(r_Q))+(1/(r_Q)^2)])]/ log (10); // n o i s e f i g u r e disp (F , ’ N oi s e f i g u r e ( i n dB ) = ’ ) ; B_W=2*r* sqrt (ratio); / / b a n d w i d t h disp (B_W,  ’ b a n d w i d t h = ’ );

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Scilab code Exa 9.13   Calculate the equivalent noise resistance and gain

and noise figure and bandwidth ( i )− 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 i )− g a i n , ( i i i )− n o i s e f i g u r e , ( i v )− b a n d w i d t h 2 / / Exa : 9 . 1 3 1 //Caption : Cal cul ate

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

                                         

clc ; clear ; close ; f_s=2*10^9; / / i n Hz f_p=12*10^9; / / i n Hz f_i=10*10^9; / / i n Hz f_d=5*10^9; / / i n Hz R_i=1*10^3; // in ohm R_g=1*10^3; // in ohm R_T_s=1*10^3; // in ohm R_T_i=1*10^3; // in ohm T_d=300; / / i n K e l v i n T_o=300; / / i n K e l v i n w_s=2*%pi*f_s; w_i=2*%pi*f_i; r=0.35; r_Q=10; r_d=300; // in ohm C=0.01*10^-12; / / i n F a ra d R=r^2/(w_s*w_i*C^2*R_T_i); a=R/R_T_s; g=((4*f_i*R_g*R_i*a)/(f_s*R_T_s*R_T_i*(1-a)^2)); //

gain 25   Gain=[10* log (g)]/ log (10); / / g a i n i n dB

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