Electrical and Electronics Engineering Materials_J. B. Gupta

7/13/2019 Electrical and Electronics Engineering Materials_J. B. Gupta

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Scilab Textbook Companion for

Electrical And Electronics Engineering

Materials

by J. B. Gupta1

Created byLalit kumar saini

B.TechElectronics Engineering

Uttarakhand Tech. university

College TeacherArshad Khan

Cross-Checked byLavitha Pereira

March 19, 2014

1Funded by a grant from the National Mission on Education through ICT,http://spoken-tutorial.org/NMEICT-Intro. This Textbook Companion and Scilabcodes written in it can be downloaded from the Textbook Companion Projectsection at the website http://scilab.in


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Book Description

Title: Electrical And Electronics Engineering Materials

Author: J. B. Gupta

Publisher: S.k. Katariya & Sons, New Delhi

Edition: 3

Year: 2010

ISBN: 81-89757-13-x

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Scilab numbering policy used in this document and the relation to theabove 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 particularExample of the above book)

For example, Exa 3.51 means solved example 3.51 of this book. Sec 2.3 meansa scilab code whose theory is explained in Section 2.3 of the book.

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Contents

List of Scilab Codes 4

1 Crystal Stucture Of Materials 7

2 Conductivity of metals 11

3 Semiconductor 37

4 Bipolar Junction And Field Effect Transistors 56

5 Magnetic Properties Of Materials 63

6 Dielectric Properties Of Materials 67

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List of Scilab Codes

Exa 1.3 Density Of Copper Crystal . . . . . . . . . . . . . . . 7Exa 1.4 Interplanar Distance in a crystal . . . . . . . . . . . . 8Exa 1.5 Wavelength of X rays . . . . . . . . . . . . . . . . . . 8Exa 1.6 Wavelength of X rays . . . . . . . . . . . . . . . . . . 9Exa 1.7 Angle of incidence . . . . . . . . . . . . . . . . . . . . 9Exa 2.1 Drift Velocity of Electrons. . . . . . . . . . . . . . . . 11Exa 2.2 Magnitude of current . . . . . . . . . . . . . . . . . . 11Exa 2.3 Relaxation time and resistivity . . . . . . . . . . . . . 12Exa 2.4 Valance electron and mobility of electron . . . . . . . 13Exa 2.5 Mobility and relaxation time . . . . . . . . . . . . . . 13Exa 2.6 Relaxation time . . . . . . . . . . . . . . . . . . . . . 14Exa 2.7 Relaxation time of conducting electrons . . . . . . . . 14Exa 2.8 Charge density current density and drift velocity . . . 15

Exa 2.9 Drift velocity . . . . . . . . . . . . . . . . . . . . . . . 16Exa 2.10 Resistivity of silicon . . . . . . . . . . . . . . . . . . . 17Exa 2.11 Carrier density . . . . . . . . . . . . . . . . . . . . . . 17Exa 2.13 Temperature of coil . . . . . . . . . . . . . . . . . . . 18Exa 2.15 Resistance of the coil . . . . . . . . . . . . . . . . . . 18Exa 2.16 Temperature coefficient of resistance . . . . . . . . . . 19Exa 2.17 Temperature coefficient of resistance . . . . . . . . . . 19Exa 2.18 Resistance and temperature coefficient . . . . . . . . . 20Exa 2.19 Mean temperature rise. . . . . . . . . . . . . . . . . . 21Exa 2.20 Specific resistance and resistance temperature coefficient 22Exa 2.21 Resistivity of the wire material . . . . . . . . . . . . . 22

Exa 2.22 Resistance of the wire . . . . . . . . . . . . . . . . . . 23Exa 2.23 Current flowing. . . . . . . . . . . . . . . . . . . . . . 23Exa 2.24 Resistance and temperature coefficient of combination 24Exa 2.25 Impurity percent . . . . . . . . . . . . . . . . . . . . . 25

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Exa 2.26 Electronic contribution of thermal conductivity of alu-

minium . . . . . . . . . . . . . . . . . . . . . . . . . . 25Exa 2.27 EMP developed per degree centigrade . . . . . . . . . 26Exa 2.28 EMF developed in couple . . . . . . . . . . . . . . . . 26Exa 2.29 Thermo electric emf generated . . . . . . . . . . . . . 27Exa 2.30 Thermo emf neutral temperature temperature of inver-

sion and max possible thermo electric emf . . . . . . . 28Exa 2.31 Potential difference. . . . . . . . . . . . . . . . . . . . 29Exa 2.32 EMF for a copper iron thermo couple . . . . . . . . . 29Exa 2.34 Critical magnetic field . . . . . . . . . . . . . . . . . . 30Exa 2.35 Critical current . . . . . . . . . . . . . . . . . . . . . . 31Exa 2.36 Critical current density . . . . . . . . . . . . . . . . . 31

Exa 2.37 Diameter of copper wire . . . . . . . . . . . . . . . . . 32Exa 2.38 Resistance of liquid resistor . . . . . . . . . . . . . . . 33Exa 2.39 Resistivity of dielectric in a cable . . . . . . . . . . . . 33Exa 2.40 Insulation resistance . . . . . . . . . . . . . . . . . . . 34Exa 2.41 Insulation resistance and resistance of copper conductor 35Exa 3.1 Velocity of electron. . . . . . . . . . . . . . . . . . . . 37Exa 3.2 Relaxation time resistivity of conductor and velocity of

electron . . . . . . . . . . . . . . . . . . . . . . . . . . 37Exa 3.3 Electron and hole density . . . . . . . . . . . . . . . . 38Exa 3.4 Donar atom concentration mobile electron concentra-

tion hole concentration and conductivity of doped sili-con sample . . . . . . . . . . . . . . . . . . . . . . . . 39Exa 3.5 Concentration of hole in si. . . . . . . . . . . . . . . . 40Exa 3.6 Conductivity and resitivity of an intrinsic semiconductor 41Exa 3.7 Density of electron and drift velocity of holes and elec-

trons . . . . . . . . . . . . . . . . . . . . . . . . . . . 41Exa 3.8 Conductivity of Si . . . . . . . . . . . . . . . . . . . . 42Exa 3.9 Find conductivity of intrinsic Ge . . . . . . . . . . . . 43Exa 3.10 Electron and hole drift velocity conductivity of intrinsic

Ge and total current . . . . . . . . . . . . . . . . . . . 43Exa 3.11 Diffusion coefficient of electron and hole . . . . . . . . 44

Exa 3.12 Hall effect in semiconductor . . . . . . . . . . . . . . . 45Exa 3.13 Current density. . . . . . . . . . . . . . . . . . . . . . 46Exa 3.14 Value of hall coefficient . . . . . . . . . . . . . . . . . 46Exa 3.15 Magnitude of Hall voltage . . . . . . . . . . . . . . . . 47Exa 3.16 Mobility of holes . . . . . . . . . . . . . . . . . . . . . 47

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Exa 3.17 Hall voltage. . . . . . . . . . . . . . . . . . . . . . . . 48

Exa 3.18 Hall voltage. . . . . . . . . . . . . . . . . . . . . . . . 49Exa 3.19 Density and mobility of carrier . . . . . . . . . . . . . 49Exa 3.20 Hll angle . . . . . . . . . . . . . . . . . . . . . . . . . 50Exa 3.21 New position of fermi level . . . . . . . . . . . . . . . 50Exa 3.22 Potential barrier . . . . . . . . . . . . . . . . . . . . . 51Exa 3.23 Resistance level. . . . . . . . . . . . . . . . . . . . . . 51Exa 3.24 Fraction of the total number of electron . . . . . . . . 52Exa 3.25 Current flowing. . . . . . . . . . . . . . . . . . . . . . 52Exa 3.26 Forward voltage . . . . . . . . . . . . . . . . . . . . . 53Exa 3.27 Reverse saturation current density . . . . . . . . . . . 54Exa 3.28 Junction width . . . . . . . . . . . . . . . . . . . . . . 54

Exa 4.1 Resistance between gate and source . . . . . . . . . . 56Exa 4.2 AC drain resistance of the JFET . . . . . . . . . . . . 56Exa 4.3 Transconductance . . . . . . . . . . . . . . . . . . . . 57Exa 4.4 AC drain resistance transconductance and amplification

factor . . . . . . . . . . . . . . . . . . . . . . . . . . . 57Exa 4.5 Transconductance . . . . . . . . . . . . . . . . . . . . 58Exa 4.6 Calculate VGS . . . . . . . . . . . . . . . . . . . . . . 59Exa 4.7 Minimum value of VDS . . . . . . . . . . . . . . . . . 59Exa 4.8 ID gmo and gm. . . . . . . . . . . . . . . . . . . . . . 60Exa 4.9 Id and gm. . . . . . . . . . . . . . . . . . . . . . . . . 60

Exa 4.10 gm at IDS . . . . . . . . . . . . . . . . . . . . . . . . 61Exa 4.11 Drain current . . . . . . . . . . . . . . . . . . . . . . . 62Exa 5.1 Hysteresis loss . . . . . . . . . . . . . . . . . . . . . . 63Exa 5.2 Hysteresis loss . . . . . . . . . . . . . . . . . . . . . . 64Exa 5.3 Loss of energy . . . . . . . . . . . . . . . . . . . . . . 64Exa 5.4 Loss per kg in a specimen . . . . . . . . . . . . . . . . 65Exa 5.5 Eddy current loss . . . . . . . . . . . . . . . . . . . . 66Exa 6.1 Element of parallel RC circuit. . . . . . . . . . . . . . 67Exa 6.2 Charge sensitivity . . . . . . . . . . . . . . . . . . . . 68Exa 6.3 Force required to develop a voltage . . . . . . . . . . . 68Exa 6.4 Charge and its capacitance . . . . . . . . . . . . . . . 69

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Chapter 1

Crystal Stucture Of Materials

Scilab code Exa 1.3 Density Of Copper Crystal

1 //Exa32 clc ;

3 clear ;

4 close ;

5 / / g i v e n d a ta6 // a t o mi c r a d i u s

7 r = 1 . 2 7 8 ; // in Angstrum8 / / a t o m ic w e i g ht9 a w = 6 3 . 5 ;

10 // Avogadro s number11 a n = 6 . 0 2 3 * 1 0 ^ 2 3 ;

12 / / c o pp e r h as FCC s t r u c t u r e f o r w hi ch13 a = ( 4 * r ) / sqrt ( 2 ) ; / / i n A ng st ru m14 a = a * 1 0 ^ - 1 0 ; / / i n m15 / / Mass o f o ne atom16 m = a w / a n ; // in gm

17 m = m * 1 0 ^ - 3 ; / / i n k g18 // v olume o f on e u n i t c e l l o f c op pe r c r y s t a l ,19 V = a ^ 3 ; / / i n m et er c ub e20 / /Number o f a to ms p r e s e n t i n o ne u n i t c e l l o f Cu (FCC

S t r u c t u r e ) ,

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21 n = 4 ;

22 // D en s it y o f c r y s t a l23 r h o = ( m * n ) / V ; // in kg/m324 disp ( D e n s i t y o f c r y s t a l i s : + string ( r h o ) + kg/m3

) ;

Scilab code Exa 1.4 Interplanar Distance in a crystal

1 //Exa4

2 clc ;3 clear ;

4 close ;

5 / / g i v e n d at a :6 // w av e l e ng t h7 l a m d a = 1 . 5 3 9 ; // i n A ngst rum8 / / a n g l e9 t h e t a = 2 2 . 5 ; // i n d e g r ee

10 n = 1 ; // ( f i r s t or de r )11

12 / / F or mu la n lamda=2ds i n ( t h e t a ) , s o

13 / / i n t e r p l a n e r d i st a nc e ,14 d = l a m d a / ( 2 * sin ( t h e t a * % p i / 1 8 0 ) ) ;

15 disp ( I n t e r p l a n e r d i s t a n ce i s : + string ( d ) + Angstrum )

Scilab code Exa 1.5 Wavelength of X rays

1 //Exa5

2 clc ;3 clear ;

4 close ;

5 / / g i v e n d at a :6 n = 2 ;

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7 d = 0 . 4 ; / / i n n en om et er

8 d = d * 1 0 ^ - 9 ; // i n m et er9 t h e t a = 1 6 . 8 / 2 ; // i n d e g re e10 / / u s i n g Br ag g s e q u a t i o n we h av e n lamda=2ds i n (

t h e t a ) , s o11 l a m d a = ( 2 * d * sin ( 8 . 4 * % p i / 1 8 0 ) ) / n ;

12 disp ( W a ve le ng th o f Xr a y s u s e d i s : + string ( l a m d a* 1 0 ^ 1 0 ) + A ngstr um ) ;

Scilab code Exa 1.6 Wavelength of X rays

1 //Exa62 clc ;

3 clear ;

4 close ;

5 / / g i v e n d at a :6 a = 3 . 1 5 ; // in Angstrum7 a = a * 1 0 ^ - 1 0 ; / / i n m e te r8 / / a n g l e9 t h e t a = 2 0 . 2 ; / / i n d e g r e e

10 n = 1 ; // ( f i r s t or de r )11 / / f o r BCC c r y s t a l12 d 1 1 0 = a / sqrt ( 2 ) ; / / i n m e te r13 / / F o rm u la n lamda=2ds i n ( t h e t a )14 l a m d a = ( 2 * d 1 1 0 * sin ( t h e t a * % p i / 1 8 0 ) ) / n ; / / i n m e te r15 disp ( Wa velen gth i s : + string ( l a m d a * 1 0 ^ 1 0 ) +

Angstrum )

Scilab code Exa 1.7 Angle of incidence

1 //Exa72 clc ;

3 clear ;

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4 close ;

5 / / g i v e n d at a :6 l a m b d a = 0 . 8 4 2 ; // in Angstrum7 l a m b d a = l a m b d a * 1 0 ^ - 1 0 ; // i n m et er8 / / t h e t a =8 d e g r e e 3 5 m i n u t e s9 t h e t a = 8 + 3 5 / 6 0 ; / / i n d e g r e e

10 n = 1 ; // ( f i r s t or de r )11 / / F o rm u la n lamda=2ds i n ( t h e t a )12 d = n * l a m b d a / ( 2 * s i n d ( t h e t a ) )

13 // For t h i r d Order r e f l e c t i o n :14 / / F o rm u la n lamda=2ds i n ( t h e t a )15 n = 3 ; / / o r d e r

16 t h e t a = a s i n d ( n * l a m b d a / ( 2 * d ) ) ;17 disp ( round ( t h e t a ) , Angl e o f i n c i d e n c e f o r t h i r d

o rd e r r e f l e c t i o n i n d e g r e e : ) ;

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Chapter 2

Conductivity of metals

Scilab code Exa 2.1 Drift Velocity of Electrons

1 // Exa2 . 12 clc ;

3 clear ;

4 close ;

5 / / g i v e n d at a :6 J = 2 . 4 ; // i n A/mm2

7 J = 2 . 4 * 1 0 ^ 6 ; // i n A/m28 n = 5 * 1 0 ^ 2 8 ; // u n i t l e s s9 e = 1 . 6 * 1 0 ^ - 1 9 ; // i n c ou lo mb

10 / / F o r mu l a : J=e nv11 v = J / ( e * n ) ; // i n m/ s12 disp ( D r i f t v e l o c i t y i s : + string ( v ) + m/ s o r +

string ( v * 1 0 ^ 3 ) + mm/s )

Scilab code Exa 2.2 Magnitude of current

1 //Exa22 clc ;

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3 clear ;

4 close ;5 / / g i v e n d at a :6 / / E l e c t r o n d e n s i t y7 n = 1 * 1 0 ^ 2 4 ; // u n it l e s s8 / / E l e c t r o n c h a r g e9 e = 1 . 6 * 1 0 ^ - 1 9 ; // i n c ou lo mb

10 // D r i f t v e l o c i t y11 v = 1 . 5 * 1 0 ^ - 2 ; // i n m et er p er s ec on d12 / / c r o s s s e c t i o n a l a re a13 A = 1 ; // i n c e nt i me t er s q u ar e14 A = 1 * 1 0 ^ - 4 ; // i n m et er s q ua r e

15 I = e * n * v * A ; / / i n a mpere16 disp ( Mag ni tud e o f c u r r e nt i s : + string ( I ) + A )

Scilab code Exa 2.3 Relaxation time and resistivity

1 // Exa2 . 32 clc ;

3 clear ;

4 close ;5 / / g i v e n d at a :6 m i u _ e = 7 . 0 4 * 1 0 ^ - 3 ; // in m2/Vs7 n = 5 .8 * 10 ^ 28 ; // i n /m 38 e = 1 . 6 * 1 0 ^ - 1 9 ; // i n c ou lo mb9 m = 9 . 1 * 1 0 ^ - 3 1 ; / / i n k g

10 / / ( i ) R e l a x a t i o n t im e ,11 t a u = m i u _ e / e * m ;

12 disp ( R el ax at io n t i m e i s : + string ( t a u ) + s ec on d ) ;13 s i g m a = ( n * e * m i u _ e ) ;

14 // ( i i ) R e s i s t i v i t y o f c on du ct or ,15 r h o = 1 / s i g m a ;16 disp ( R e s i s t i v i t y o f c o nd u ct o r i s : + string ( r h o ) +

ohmm e t e r ) ;

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Scilab code Exa 2.4 Valance electron and mobility of electron

1 //Exa42 clc ;

3 clear ;

4 close ;

5 / / g i v e n d at a :6 r h o = 1 . 7 3 * 1 0 ^ - 8 ; // in ohmme t e r7 t o h = 2 . 4 2* 1 0^ - 1 4 ; / / i n s e c on d8 e = 1 . 6 * 1 0 ^ - 1 9 ; / / i n C9 m = 9 . 1 * 1 0 ^ - 3 1 ; / / i n k g

10 s i g m a = 1 / r h o ;

11 // ( i ) Number o f f r e e e l e c t r o n s p er m312 n = ( m * s i g m a ) / ( e ^ 2 * t o h ) ;

13 disp ( Number o f f r e e e l e c t r o n s p er cube me t e r i s : + string ( n ) ) ;

14 // ( i i ) M o b il i t y o f e l e c t r o n s ,15 m i u _ e = ( e * t o h ) / m ;

16 disp ( M o bi li ty o f e l e c t r o n s i s : + string ( m i u _ e ) + m

2/Vs ) ;17 / / No te : Answer i n t h e bo ok i s wrong

Scilab code Exa 2.5 Mobility and relaxation time

1 //Exa52 clc ;

3 clear ;

4 close ;5 / / g i v e n d at a :6 r h o = 1 . 5 4 * 1 0 ^ - 8 ; // in ohmme t e r7 / / s i n c e s i g ma =1/ r o h8 s i g m a = 1 / r h o ;

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9 n = 5 .8 * 10 ^ 28 ; // u n it l e s s

10 e = 1 . 6 * 1 0 ^ - 1 9 ; // i n C ( e l e c t r o n c h a rg e )11 m = 9 . 1 * 1 0 ^ - 3 1 ; // i n kg ( m ass o f e l e c t r o n )12 / / ( i ) R e l a x a t i on t im e13 t o h = ( s i g m a * m ) / ( n * e ^ 2 ) ;

14 disp ( ( i ) R el ax at io n t i m e o f e l e c t r o n s i s : + string( t o h ) + s ec on ds ) ;

15 // ( i i ) M o b il i t y o f e l e c t r o n s ,16 m i u _ e = ( e * t o h ) / m ;

17 disp ( ( i i ) M o bi li ty o f e l e c t r o n s i s : + string ( m i u _ e) + m2/Vs ) ;

Scilab code Exa 2.6 Relaxation time

1 // Exa2 . 62 clc ;

3 clear ;

4 close ;

5 / / g i v e n d at a :6 r h o = 1 . 7 * 1 0 ^ - 8 ; // in ohmme t e r

7 / / s i n c e s i g ma =1/ r o h8 s i g m a = 1 / r h o ;

9 n = 8 .5 * 10 ^ 28 ; // u n it l e s s10 e = 1 . 6 * 1 0 ^ - 1 9 ; // i n C ( e l e c t r o n c h a rg e )11 m = 9 . 1 * 1 0 ^ - 3 1 ; / / i n k g12 / / R e l ax a t io n t im e13 t o h = ( s i g m a * m ) / ( n * e ^ 2 ) ;

14 disp ( R e l a xa ti o n t i m e o f e l e c t r o n s i s : + string (t o h ) + s e c on ds ) ;

Scilab code Exa 2.7 Relaxation time of conducting electrons

1 // Exa2 . 7

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2 clc ;

3 clear ;4 close ;

5 format ( v ,11);6 / / g i v e n d at a :7 E = 1 0 0 ; // in V/m8 r h o = 1 . 5 * 1 0 ^ - 8 ; // in ohmme t e r9 / / s i n c e s i g ma =1/ r o h

10 s i g m a = 1 / r h o ;

11 n = 6 *1 0 ^2 8 ; // u n it l e s s12 e = 1 . 6 0 1 * 1 0 ^ - 1 9 ; / / i n C13 m = 9 . 1 0 7 * 1 0 ^ - 3 1 ; / / i n k g

14 / / R e l ax a t io n t im e15 t o h = ( s i g m a * m ) / ( n * e ^ 2 ) ;

16 disp ( ( i ) R el ax at io n t i m e o f e l e c t r o n s i s : + string( t o h ) + s ec on ds ) ;

17 // D r i f t v e l o c i t y18 v = ( e * E * t o h ) / m ;

19 disp ( ( i i ) D r i f t v e l o c i t y i s : + string ( v ) + m / s ) ;

Scilab code Exa 2.8 Charge density current density and drift velocity

1 // Exa2 . 82 clc ;

3 clear ;

4 close ;

5 / / g i v e n d at a :6 / / D ia me te r o f c o pp e r w i r e7 d = 2 ; // i n m i l i m e t e r8 d = . 0 0 2 ; / / i n m e te r

9 // c o n d u c t i v i t y o f c op pe r10 n i t a = 5 . 8 * 1 0 ^ 7 ; // i n s e co n d p e r m et er11 / / E l e c t r o n m o b i l i t y12 m i u _ e = . 0 0 3 2 ; // i n m et er s q ua r e p er v o lt s e c o n d13 // Ap pl ie d e l e c t r i c f i e l d

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14 E = 2 0 ; // i n mV/m

15 E = . 0 2 ; // i n V/m16 e = 1 . 6 * 1 0 ^ - 1 9 ;17 / / ( i ) From e q . ( 2 . 1 3 )18 / / c h a rg e d e n s i t y19 n = n i t a / ( e * m i u _ e ) ; // i n p e r m et er c ub e20 disp ( ( i ) Charge d e ns i t y i s : + string ( n ) + / m e t e r

c u b e ) ;21 / / ( i i ) f ro m eq . ( 2 . 9 )22 / / c u r r e n t d e n s i t y23 J = n i t a * E ; // i n A/m224 disp ( ( i i ) C u r r e n t d e n s i t y i s : + string ( J ) + A/m2

) ;25 // ( i i i ) C ur re nt f l o w i n g i n t he w i re I=J Area o f x

s e c t i o n o f w i re26 / / A rea o f xs e c t i o n o f w ir e= ( %pid 2) /427 I = ( J * % p i * d ^ 2 ) / 4 ;

28 disp ( ( i i i ) C u rr e n t f l ow i ng i n t h e w ir e i s : +string ( I ) + A ) ;

29 / / ( i v ) f or m e q . 2 . 1 430 // E l e c t r o n d r i f t v e l o c i t y31 v = m i u _ e * E ;

32 disp ( ( i v ) E l e ct ro n d r i f t v e l o c i t y i s :

+ string ( v ) +m / s ) ;

Scilab code Exa 2.9 Drift velocity

1 // Exa2 . 92 clc ;

3 clear ;

4 close ;5 / / g i v e n d a ta6 r h o = 0 . 5 ; / / i n ohmme t e r7 J = 1 0 0 ; // i n A/m28 m i u _ e = 0 . 4 ; // in m2/Vs

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9 E = J * r h o ; // s i n c e E=J / s i g m a

10 / / F o rm u la v=m i u e

E11 v = m i u _ e * E ;12 disp ( E l e c t r o n d r i f t v e l o c i t y i s : + string ( v ) + m/

s ) ;13 disp ( Time t ak en by t he e l e c t r o n t o t r a v e l 10106

m i n c r y s t a l )14 / / l e t Time t a ke n by t h e e l e c t r o n t o t r a v e l 10106

m i n c r y s t a l = t15 t = ( 1 0 * 1 0 ^ - 6 ) / v ;

16 disp ( string ( t ) + s ec on d ) ;

Scilab code Exa 2.10 Resistivity of silicon

1 //Exa102 clc ;

3 clear ;

4 close ;

5 / / g i v e n d a ta6 m i u _ e = 0 . 1 7 ; // in m2/Vs

7 m i u _ h = 0 . 0 3 5 ; // in m2/Vs8 n i t a _ i = 1 . 1 * 1 0 ^ 1 6 ; // in /m39 e = 1 . 6 * 1 0 ^ - 1 9 ; // i n C ( e l e c t r o n c ha rg e )

10 // I n t r i n s i c c on d u c t i v i t y ,11 s i g m a _ i = ( n i t a _ i * e ) * ( m i u _ e + m i u _ h ) ;

12 I n t r i n s i c R e s i s t i v i t y = 1 / s i g m a _ i ;

13 disp ( I n t r i n s i c r e s i s t i v i t y i s : + string (I n t r i n s i c R e s i s t i v i t y ) + ohmm e t e r ) ;

Scilab code Exa 2.11 Carrier density

1 //Exa112 clc ;

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3 clear ;

4 close ;5 / / g i v e n d a ta6 r h o _ i = 2 * 1 0 ^ - 3 ; // in ohmm ( t he re i s m i s s p ri nt ed i n

t h i s l i n e i n t h e b ook )7 s i g m a _ i = 1 / r h o _ i ;

8 m i u _ e = 0 . 3 ; / / i n m 2 /Vs9 m i u _ h = 0 . 1 ; // i n m2/Vs

10 e = 1 . 6 * 1 0 ^ - 1 9 ; // i n C11 // Formula s i g m a i= n i t a i e ( miu e+miu h )12 n i t a _ i = s i g m a _ i / ( e * ( m i u _ e + m i u _ h ) ) ;

13 disp ( C a r r i e r d e n s i t y i s : + string ( n i t a _ i ) + /m3 )

;

Scilab code Exa 2.13 Temperature of coil

1 //Exa2 .1 32 clc ;

3 clear ;

4 close ;

5 / / g i v e n d a ta6 R _ 1 5 = 2 5 0 ; / / i n ohm7 R _ t2 = 3 00 ; / / i n ohm8 a l p h a = 0 . 0 0 3 9 ; // i n d e g re e C9 t 1 = 1 5 ;

10 / / Fo rm ul a R t 2 = R 15 [ 1 + a l p h a 1 ( t 2 t1 ) ]11 t 2 = ( ( R _ t 2 / R _ 1 5 ) - 1 ) / a l p h a + t 1 ;

12 disp ( T em per at ur e when i t s r e s i s t a n c e i s 3 00 ohms i s: + string ( t 2 ) + d e gr e e C ) ;

Scilab code Exa 2.15 Resistance of the coil

1 //Exa2 .1 5

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2 clc ;

3 clear ;4 close ;

5 / / g i v e n d a ta6 a l p h a 0 = 0 . 0 0 3 8 ; / / i n ohm/ ohm / d e g r e e C7 t 1 = 2 0 ; // i n d e g r e e C8 a l p h a 2 0 = 1 / ( 1 / a l p h a 0 + t 1 ) ;

9 R 1 = 4 0 0 ; // in ohm10 / / Formu la R2=R1 [ 1+ al p ha2 0 ( t2t1 ) ]11 R 2 = R 1 * [ 1 + a l p h a 2 0 * ( 8 0 - 2 0 ) ] ;

12 disp ( R e s i s t a n c e o f w ir e a t 80 d eg re e C s i : +string ( R 2 ) + ohm )

Scilab code Exa 2.16 Temperature coefficient of resistance

1 //Exa2 .1 62 clc ;

3 clear ;

4 close ;

5 disp ( L e t t h e t e m p e ra t u r e c o e f f i c i e n t o f r e s i s t a n c e

o f m a t e r i a l a t 0 d eg re e C be a lp ha 0 ) ;6 disp ( R e s i s t a n ce a t 25 d e g re e C , R1 = R0 (1+25

a l p h a 0 ) ( i ) ) ;7 disp ( R e s i s t a n ce a t 70 d e g re e C , R2 = R0 (1+70

a l p h a 0 ) ( i i ) ) ;8 disp ( D i v i d i n g Eq . ( i i ) by Eq . ( i ) , we g e t ) ;9 disp ( R2/R1= (1+70al ph a0 ) /(1+25a l p h a 0 ) ) ;

10 disp ( o r 5 7. 2 /5 0 = (1+70al ph a0 ) /(1+25a l p h a 0 ) ) ;11 disp ( o r a l p h a 0 = 0 . 0 0 3 4 8 ohm/ohm/ d e g r e e C ) ;

Scilab code Exa 2.17 Temperature coefficient of resistance

1 //Exa2 .1 7

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2 clc ;

3 clear ;4 close ;

5 disp ( L e t t h e t e m p e ra t u r e c o e f f i c i e n t o f r e s i s t a n c eo f m a t e r i a l c o i l a t 0 d e gr e e C be al pha 0 , t h en ) ;

6 disp ( R e s i s t a n ce a t 25 d e g re e C , R1 = R0 (1+25a l p h a 0 ) ( i ) ) ;

7 disp ( R e s i s t a n ce a t 75 d e g re e C , R2 = R0 (1+75a l p h a 0 ) ( i i ) ) ;

8 disp ( D i v i d i n g Eq . ( i i ) by Eq . ( i ) , we g e t ) ;9 disp ( R2/R1= (1+75al ph a0 ) /(1+25a l p h a 0 ) ) ;

10 disp ( o r 4 9/ 45 = (1+75al ph a0 ) /(1+25a l p h a 0 ) ) ;

11 disp ( o r a l p h a 0 = 0 . 0 0 7 3 6 ohm/ohm/ d e g r e e C ) ;

Scilab code Exa 2.18 Resistance and temperature coefficient

1 //Exa2 .1 82 clc ;

3 clear ;

4 close ;

5 disp ( L e t t h e t e m p e ra t u r e c o e f f i c i e n t o f r e s i s t a n c eo f p la ti nu m a t 0 d e gr e e C b e a lp ha 0 andr e s i s t a n c e o f p la ti nu m c o i l a t 0 d eg re e C be R0 ,t h e n ) ;

6 disp ( R e s i s t a n ce a t 40 d e g re e C , R1 = R0 (1+40a l p h a 0 ) ( i ) ) ;

7 disp ( R e s i s t a n ce a t 10 0 d e gr e e C , R2 = R0 (1+100a l p h a 0 ) ( i i ) ) ;

8 disp ( D i v i d i n g Eq . ( i i ) by Eq . ( i ) , we h a ve ) ;9 disp ( R2/R1= (1+1 00al ph a0 ) /(1+40a l p h a 0 ) ) ;

10 disp ( o r 3 . 7 67 / 3 . 14 6 = (1+100

al ph a0 ) /(1+40

a l p h a 0 ) ) ;11 disp ( o r a l p h a 0 = 0 . 0 0 3 7 9 ohm/ohm/ d e g r e e C ) ;12 a l p h a 0 = 0 . 0 0 3 7 9 ; / / i n ohm /ohm/ d e g r e e C13 disp ( T e m p er a tu r e c o e f f i c i e n t o f r e s i s t a n c e a t 4 0

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d e g r e e C , )

14 a l p h a 4 0 = 1 / ( 1 / a l p h a 0 + 4 0 ) ;15 disp ( a l p h a 4 0 ) ;

16 disp ( S u b s t i t u t i n g R1 =3 .1 46 and a l p h a 0 = 0. 0 03 7 9 i n Eq. ( i ) we h av e )

17 R 1 = 3 . 1 4 6 ; // in ohm18 //F or mul a R1 = R0 (1+40a l p h a 0 )19 R 0 = R 1 / ( 1 + 4 0 * a l p h a 0 ) ;

20 disp ( R e s i st a nc e o f p la ti n um c o i l a t 0 d eg re e C i s : + string ( R 0 ) + o h m ) ;

Scilab code Exa 2.19 Mean temperature rise

1 //Exa2 .1 92 clc ;

3 clear ;

4 close ;

5 disp ( Le t R0 be t h e r e s i s t a n c e o f t h e c o i l a t 0d e gr e e C and a l ph a0 be i t s t em pe ra t ur ec o e f f i c i e n t o f r e s i s t a n c e a t 0 d e g r e e C ) ;

6 disp ( R e s i s t a n ce a t 20 d e g re e C , 18 = R0 (1+20a l p h a 0 ) ( i ) ) ;

7 disp ( R e s i s t a n ce a t 50 d e g re e C , 20 = R0 (1+50a l p h a 0 ) ( i i ) ) ;

8 disp ( D i v i d i n g Eq . ( i i ) by Eq . ( i ) , we h a ve ) ;9 disp ( 20/18= ( 1+50al ph a0 ) /(1+20a l p h a 0 ) ) ;

10 disp ( o r a l p h a 0 = 1 / 2 5 0 =0 . 0 0 4 ohm/ ohm / d e g r e e C ) ;11 disp ( I f t d eg r e e C i s t h e t em pe ra tu re o f c o i l when

i t s r e s i s t a n c e i s 21 ohm , t h e n ) ;12 disp ( 21=R0 ( 1 + 0 . 0 0 4t ) ) ;

13 disp ( D i v i d i n g Eq . ( i i i ) by Eq . ( i i ) , we h a ve ) ;14 disp ( 2 1 / 2 0 = ( 1 + 0 . 0 0 4t ) /( 1+ 50 0 . 0 0 4 ) ) ;15 disp ( o r t =65 d e g r e e C ) ;16 disp ( T em pe ra tu re r i s e = ts u r r o un d i n g t e mp e ra t u re =

65 15 = 50 d e g re e C ) ;

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Scilab code Exa 2.20 Specific resistance and resistance temperature coef-ficient

1 //Exa2 .2 02 clc ;

3 clear ;

4 close ;

5 / / g i v e n d a ta

6 a l p h a 2 0 = 1 / 2 5 4 . 5 ; / / i n ohm/ ohm / d e g r e e C7 t 2 = 6 0 ; / / d e g r e e C8 t 1 = 2 0 ; / / d e g r e e C9 r h o 0 = 1 . 6 * 1 0 ^ - 6 ;

10 a l p h a 6 0 = 1 / ( 1 / a l p h a 2 0 + ( t 2 - t 1 ) ) ;

11 disp ( T e m p er a tu r e c o e f f i c i e n t o f r e s i s t a n c e a t 6 0d e g r e e C i s : + string ( a l p h a 6 0 ) + ohm/ohm/ de gr eeC ) ;

12 / / f r o m a l p h a 2 0 = 1/ ( 1/ a l p h a 0 + 20 )13 alpha0 =1/(1/ alpha20 -20);

14 / / F o r mu l a r h o 6 0=r h o 0 ( 1 + a l p h a 0 t )15 r h o 6 0 = r h o 0 * ( 1 + a l p h a 0 * t 2 ) ;

16 disp ( S p e c i f i c r e s i s t a n c e a t 60 d e g r e e C i s : +string ( r h o 6 0 ) + ohmcm )

Scilab code Exa 2.21 Resistivity of the wire material

1 //Exa2 .2 12 clc ;

3 clear ;

4 close ;

5 / / g i v e n d a ta6 R = 9 5 . 5 ; // in ohm

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7 l = 1 ; / / i n m e te r

8 d = 0 . 0 8 ; // i n mm9 d = d * 1 0 ^ - 3 ; / / i n m e te r10 a = ( % p i * d ^ 2 ) / 4 ;

11 // Formula R=rho l / a12 r h o = R * a / l ;

13 disp ( R e s i s t a n c e o f t h e w i re m a t e r i a l i s : + string (r h o ) + ohmm e t e r )

Scilab code Exa 2.22 Resistance of the wire

1 //Exa2 .2 22 clc ;

3 clear ;

4 close ;

5 / / g i v e n d a ta6 R = 4 ; // in ohm7 d = 0 . 0 2 7 4 ; // i n cm8 d = 0 . 0 0 0 2 7 4 ; / / i n m e te r9 r h o = 1 0 . 3 ; // i n miu ohmcm

10 r h o = 1 0 . 3 * 1 0 ^ - 8 ; // in ohmm11 a = ( % p i * d ^ 2 ) / 4 ;

12

13 // Formula R=rho l / a14 l = R * a / r h o ;

15 disp ( Le nght o f w i re i s : + string ( l ) + m et er s )

Scilab code Exa 2.23 Current flowing

1 //Exa2 .2 32 clc ;

3 clear ;

4 close ;

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5 / / g i v e n d a ta

6 V = 2 2 0 ; // i n V7 W = 1 0 0 ; / / i n w a tt8 R 1 0 0 = V ^ 2 / W ; // in ohm9 a l p h a 2 0 = 0 . 0 0 5 ;

10 t 1 = 2 0 ;

11 t 2 = 2 0 0 0 ;

12 / / s i n c e R1 00=R20 [ 1+ al p ha2 0 ( t2t 1 ) ]13 R 2 0 = R 1 00 / ( 1 + a l p h a 20 * ( t2 - t 1 ) ) ;

14 I 2 0 = V / R 2 0 ;

15 disp ( C u r r en t f l ow i n g a t t he i n s t a n t o f s w i t ch i ng ona 100 W m e t a l f i l a m e n t lamp i s : + string ( I 2 0 ) +

A )

Scilab code Exa 2.24 Resistance and temperature coefficient of combina-tion

1 //Exa2 .2 42 clc ;

3 clear ;

4 close ;5 / / g i v e n d a ta6 t 2 = 5 0 ; // i n d eg re e C7 t 1 = 2 0 ; // i n d eg r e e C8 R 1 = 6 0 0 ; / / i n ohm9 R 2 = 3 0 0 ; / / i n ohm

10

11 / / Le t r e s i s t a n c e o f 600 ohm r e s i s t a n c e a t 5 0 d eg r e eC = R 6 00

12 R _ 6 0 0 = R 1 * ( 1 + ( t 2 - t 1 ) * . 0 0 1 ) ; / / i n ohm

13 / / Le t r e s i s t a n c e o f 300 ohm r e s i s t a n c e a t 5 0 d eg r e eC = R 3 0014 R _ 3 0 0 = R 2 * ( 1 + ( t 2 - t 1 ) * . 0 0 4 ) ; / / i n ohm15 R _ 5 0 = R _ 6 0 0 + R _ 3 0 0 ; / / i n ohm16 disp ( R e s is t a nc e o f c om bi na ti on a t 50 d e g r e e C i s :

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+ string ( R _ 5 0 ) + ohm )

17 R _ 2 0 = R 1 + R 2 ; / / i n ohm18 a l p h a _ 2 0 = ( R _ 5 0 / R _ 2 0 - 1 ) / ( t 2 - t 1 ) ;19 a l p h a _ 5 0 = 1 / ( 1 / ( a l p h a _ 2 0 ) + ( t 2 - t 1 ) ) ;

20 disp ( E f f e c t i v e t e m p e r a t u r e c o e f f i c i e n t o f c om bi na ti on a t 50 d eg re e C i s : + string ( a l p h a _ 5 0) + o r 1 /53 0 p e r d e gr ee C )

Scilab code Exa 2.25 Impurity percent

1 //Exa2 .2 52 clc ;

3 clear ;

4 close ;

5 / / g i v e n d a ta6 t o h = 1 . 7 3 / / i n m i cr oohmcm7 t o h D e s h = 1 . 7 4 ; / / i n m i cr oohmcm8 s i g m a = 1 / t o h ; // c o n d u c t i v i t i e s o f p ur e m e t a l9 s i g m a D e s h = 1 / t o h D e s h ; // c o n d u c t i v i t i e s m et al w it h

i m p u r i t y

10 P e r c e n t I m p u r i t y = ( ( s i g m a - s i g m a D e s h ) / s i g m a ) * 1 0 0 ;11 disp ( P e r c e n t i mp ur i ty i n t h e r o d i s : + string (

P e r c e n t I m p u r i t y ) + %)

Scilab code Exa 2.26 Electronic contribution of thermal conductivity ofaluminium

1 //Exa2 .2 6

2 clc ;3 clear ;

4 close ;

5 / / g i v e n d a ta6 E l e c t r i c a l R e s i s t i v i t y = 2 . 8 6 * 1 0 ^ - 6 ; // in ohmcm

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7 s i g m a = 1 / E l e c t r i c a l R e s i s t i v i t y ;

8 T = 2 7 3 + 2 0 ; / / i n K e l v i n ( T e mp e ra t ur e )9 //F or mul a K/( s i gma T ) = 2. 4410810 disp ( Thermal c o n d u c t i v i t y o f Al )11 K = ( 2 . 4 4 * 1 0 ^ - 8 * T * s i g m a ) ;

12 disp ( K ) ;

Scilab code Exa 2.27 EMP developed per degree centigrade

1 //Exa2 .2 72 clc ;

3 clear ;

4 close ;

5 / / g i v e n d a ta6 E _ A C = 1 6 * 1 0 ^ - 6 ; // i n V p er d e gr e e C7 E _ B C = - 3 4 * 1 0 ^ - 6 ; // i n V p er d e g re e C8 //By l aw o f s u c c e s s i v e c o nt a ct ( o r i n t e r m e di a t e

m e t a l s )9 E _ A B = E _ A C - E _ B C ; / / i n V/ d e g r e e C

10 E _ A B = E _ A B * 1 0 ^ 6 ; // i n miu V/ d e g r ee C

11 disp ( EMF of i r o n w i th r e s p e c t t o c on st an ta n i s : +string ( E _ A B ) + m i cr o V/ d e g r e e C )

Scilab code Exa 2.28 EMF developed in couple

1 //Exa2 .2 82 clc ;

3 clear ;

4 close ;5 / / g i v e n d a ta6 E _ A C = 7 . 4 ; // i n miu V p e r d e g r e e C7 E _ B C = - 3 4 . 4 ; / / i n miu V p e r d e g r e e C

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8 //By l aw o f s u c c e s s i v e c o nt a ct ( o r i n t e r m e di a t e

m e t a l s )9 E _ A B = E _ A C - E _ B C ; / / i n miu V/ d e g r e e C10 E _ A B = E _ A B * 1 0 ^ - 6 ; // i n V/ d eg re e C11 // Le t Ther moemf f o r a t em pe ra tu re d i f f e r e n c e o f

2 5 0 d e g r e e C = EMF 25012 E M F _ 2 5 0 = E _ A B * 2 5 0 ; // i n V13 E M F _ 2 5 0 = E M F _ 2 5 0 * 1 0 ^ 3 ; // i n mV14 disp ( Termoemf f o r a t em pe r at ur e d i f f e r e n c e o f 250

d eg re e C i s + string ( E M F _ 2 5 0 ) + mV) ;

Scilab code Exa 2.29 Thermo electric emf generated

1 //Exa2 .2 92 clc ;

3 clear ;

4 close ;

5 / / g i v e n d a ta6 // Take i r o n a s m et al A and c op pe r a s m et al B w it h

r e s pe c t t o l e a d

7 / / F or m e ta l A :8 p _ A = 1 6 . 2 ;

9 q _ A = - 0 . 0 2 ;

10 / / F or m e ta l B :11 p _ B = 2 . 7 8 ;

12 q _ B = + 0 . 0 0 9 ;

13 p _ A B = p _ A - p _ B ;

14 q _ A B = q _ A - q _ B ;

15 T 2 = 2 1 0 ; // i n d e g r e e C16 T 1 = 1 0 ; // i n d eg re e C

17 E = p _ A B * ( T 2 - T 1 ) + q _ A B / 2 * ( T 2 ^ 2 - T 1 ^ 2 ) ;18 disp ( Thermoe l e c t r i c e mf i s : + string ( E ) + m ic r o V ) ;

19 T n = - p _ A B / q _ A B ;

20 disp ( N e u tr al t em pe ra tu re i s : + string ( T n ) + d e g r ee

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C ) ;

Scilab code Exa 2.30 Thermo emf neutral temperature temperature of in-version and max possible thermo electric emf

1 //Exa2 .3 02 clc ;

3 clear ;

4 close ;

5 / / g i v e n d a ta6 p _ A = 1 7 . 3 4 ;

7 q _ A = - 0 . 0 4 8 7 ;

8 p _ B = 1 . 3 6 ;

9 q _ B = + 0 . 0 0 9 5 ;

10 p _ A B = p _ A - p _ B ;

11 q _ A B = q _ A - q _ B ;

12 T 2 = 2 1 0 ; // i n d e g r e e C13 T 1 = 1 0 ; // i n d eg re e C14 E = p _ A B * ( T 2 - T 1 ) + q _ A B / 2 * ( T 2 ^ 2 - T 1 ^ 2 ) ; / / i n miu V15 E = E * 1 0 ^ - 3 ; / / i n m V

16 disp ( Thermoe l e c t r i c e mf i s : + string ( ceil ( E ) ) + mV ) ;

17 T n = - p _ A B / q _ A B ;

18 disp ( N e u tr al t em pe ra tu re i s : + string ( ceil ( T n ) ) + d e g r e e C ) ;

19 T c = 1 0 ; // i n d eg re e C20 T i = T n + ( T n - T c ) ;

21 disp ( Te mper at ur e o f i n v e r s i o n i s : + string ( ceil ( Ti) ) + d e gr e e C ) ;

22 E _ m a x = 1 5 . 9 8 * ( 2 7 5 - 1 0 ) - 1 / 2 * 0 . 0 5 82 * [ 2 7 5 ^ 2 - 1 0 ^ 2 ] ; // in

mi u V23 E _ m a x = E _ m a x * 1 0 ^ - 3 ; / / i n mV24 disp ( Maximum p o s s i b l e t he rm oe l e c t r i c emf at

n e u t r al t em pe ra tu re t ha t i s a t 2 75 d eg re e C i s : + string ( E _ m a x ) + mV) ;

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Scilab code Exa 2.31 Potential difference

1 //Exa2 .3 12 clc ;

3 clear ;

4 close ;

5 / / g i v e n d a ta6 r h o = 1 4 6 * 1 0 ^ - 6 / / i n ohmcm

7 a = 1 ; // in cm28 l = 1 ; // i n cm9 / / l e t c ur r e nt = i

10 i = 0 . 0 6 ; // in amp11 R = r h o * l / a ; // in ohm12 // Le t p o t e n t i a l d i f f e r e n c e p e r d eg re e c e nt i g ra d e =

P13 P = i * R ; // By Ohm s law14 disp ( P o t en t i al d i f f e r e n c e p er d eg r e e c e nt i g r a d e i s

: + string ( P ) + v o l t ) ;

Scilab code Exa 2.32 EMF for a copper iron thermo couple

1 //Exa2 .3 22 clc ;

3 clear ;

4 close ;

5 / / g i v e n d a ta6 T _ l o w e r = 1 0 ;

// i n d eg re e C7 T _ u p p e r = 1 5 0 ; // i n d eg r e e C8

9 // Thermoe l e c t r i c p ow er f o r i r o n a t a ny t e m p e r a tu r eT d e gr e e C w. r . t . l e a d i s g i v en by ( 17 . 34 0 . 0 4 8 7

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T) 10 6 a nd t ha t f o r c op pe r b y ( 1. 36 . 0 0 9 5 T )

10

61011 // Thermoe l e c t r i c pow er , P=dE/dT12 // or dE=PdT13 // Thermoemf f o r c o pp e r b et we en t e m pe r a tu r e 1 0

d e gr e e C a nd 1 50 d e gr e e C ,14 E _ c = i n t e g r a t e ( ( 1. 36 0 . 0 0 9 5T) 10 6 , T ,T_low er ,

T _ u p p e r ) ;

15

16 // Thermoemf f o r i r o n b et we en t em p er a tu re 10 d e g re eC and 15 0 d e g re e C ,

17 E _ i = i n t e g r a t e ( ( 1 7 . 3 4 0 . 0 4 8 7T) 10 6 , T ,T_lowe r ,T _ u p p e r ) ;

18

19 // Thermoemp f o r c o pp eri r o n t her moc o u p l e20 E = E _ i - E _ c ;

21

22 disp ( Thermoemf f o r i r o n b et we en t em pe ra t ur e 10d eg re e C and 150 d eg re e C i s : + string ( E * 1 0 ^ 6 ) +

m i c r o V ) ;

Scilab code Exa 2.34 Critical magnetic field

1 //Exa2 .3 42 clc ;

3 clear ;

4 close ;

5 / / g i v e n d a ta6 H c _ 0 = 8 * 1 0 ^ 5 ; // i n A/m

7 T c = 7 . 2 6 ; / / i n K8 T = 4 ; / / i n K9 H c _ T = H c _ 0 * [ 1 - ( T / T c ) ^ 2 ] ;

10 disp ( The c r i t i c a l v a l u e o f m a g n e t i c f i e l d a t T=4 Ki s : + string ( H c _ T ) + A/m ) ;

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Scilab code Exa 2.35 Critical current

1 //Exa2 .3 52 clc ;

3 clear ;

4 close ;

5 / / g i v e n d a ta6 H c = 7 9 0 0 ; // in A/m

7 d = 1 ; // i n mm8 r = d / 2 ; // i n mm9 r = r * 1 0 ^ - 3 ; / / i n m

10 I c = 2 * % p i * r * H c ;

11 disp ( C r i t i c a l c ur re nt i s : + string ( I c ) + A ) ;

Scilab code Exa 2.36 Critical current density

1 //Exa2 .3 62 clc ;

3 clear ;

4 close ;

5 / / g i v e n d a ta6 H c _ 0 = 8 * 1 0 ^ 4 ; // i n A/m7 T c = 7 . 2 ; / / i n K8 T = 4 . 5 ; / / i n K9 d = 1 ; // i n mm

10 r = d / 2 ; // i n mm11 r = r * 1 0 ^ - 3 ; / / i n m

12 H c = H c _ 0 * [ 1 - ( T / T c ) ^ 2 ] ;13 disp ( The c r i t i c a l f i e l d a t T= 4. 5 K i s : + string ( Hc

) + A/m ) ;14 I c = 2 * % p i * r * H c ;

15 disp ( C r i t i c a l c ur re nt i s : + string ( I c ) + A ) ;

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Scilab code Exa 2.37 Diameter of copper wire

1 //Exa2 .3 72 clc ;

3 clear ;

4 close ;

5 format ( v ,5)6 // Formula R=rho l / a

7 / / p u t ti n g v a lu e f o r c op pe r w i re8 R = 2 ; / / i n ohm9 l = 1 0 0 ; / / i n m e te r

10 r h o = 1 . 7 * 1 0 ^ - 8 ; // ( f o r c o pp e r )11 a = r h o * l / R ; / / i n m e te r12 a = a * 1 0 ^ 6 ; / / i n mm13 // F or mul a a=%pi /4d 214 d _ c o p p e r = sqrt ( a * 4 / % p i ) ; // ( d co pp er i s d ia me te r

f o r c o pp e r )15

16 // Formula R=rho l / a17 / / p u t t i n g v a l u e f o r Aluminium w i r e18 R = 2 ; / / i n ohm19 l = 1 0 0 ; / / i n m e te r20 r h o = 2 . 8 * 1 0 ^ - 8 ; / / ( f o r a l um i ni u m )21 a = r h o * l / R ; / / i n m e te r22 a = a * 1 0 ^ 6 ; / / i n mm23 // F or mul a a=%pi /4d 224 d _ a l u m i n i u m = sqrt ( a * 4 / % p i ) ; // ( d al umi ni u m i s

d i a m e t e r f o r a lu mi ni um )25 D i a R a t i o = d _ a l u m i n i u m / d _ c o p p e r ; // ( D ia Ra ti o i s

r a t i o o f d i am e te r o f a lu mi ni um and c op pe r )26 disp ( The d i am et er o f t he al umi niu m w i re i s + string

( D i a R a t i o ) + t im es t ha t o f c op pe r w ir e ) ;

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Scilab code Exa 2.38 Resistance of liquid resistor

1 //Exa2 .3 82 clc ;

3 clear ;

4 close ;

5 format ( v ,7)6 / / g i v e n d a ta7 l = 6 0 ; // i n cm8 l = l * 1 0 ^ - 2 ; / / i n m e te r9 d = 2 0 ; // i n cm

10 d = d * 1 0 ^ - 2 ; / / i n m e te r11 D = 3 5 ; // i n cm ;12 D = D * 1 0 ^ - 2 ; / / i n m e te r13 r 1 = d / 2 ;

14 r 2 = D / 2 ;

15 r h o = 8 0 0 0 ; / / i n ohmcm16 r h o = 8 0 ; / / i n ohmm17 // L et I n s u l a t i o n r e s i s t a n c e o f t h e l i q u i d r e s i s t o r

= I r18 I r = [ r h o / ( 2 * % p i * l ) ] * log ( r 2 / r 1 ) ;

19 disp ( I n s u l a t i o n r e s i s t a n c e o f t he l i q u i d r e s i s t o ri s : + string ( I r ) + ohm)

Scilab code Exa 2.39 Resistivity of dielectric in a cable

1 //Exa2 .3 9

2 clc ;3 clear ;

4 close ;

5 format ( v ,11)6 / / g i v e n d a ta

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7 R _ d e s h = 1 8 2 0 ; / / i n M ohm

8 R _ d e s h = R _ d e s h * 1 0 ^ 6 ; / / i n ohm9 d 1 = 1 . 5 ; // i n cm10 d 1 = d 1 * 1 0 ^ - 2 ; // i n m et er11 d 2 = 5 ; // i n cm12 d 2 = d 2 * 1 0 ^ - 2 ; // i n m et er13 l = 3 0 0 0 ; // i n m et er14 r 1 = d 1 / 2 ;

15 r 2 = d 2 / 2 ;

16

17 r h o = ( 2* % p i * l * R _ d es h ) / log ( r 2 / r 1 ) ;

18 disp ( R e s i s t i v i t y o f d i e l e c t r i c i s : + string ( r h o ) +

ohm me t e r )

Scilab code Exa 2.40 Insulation resistance

1 //Exa2 .4 02 clc ;

3 clear ;

4 close ;

5 format ( v ,9)6 / / g i ve n d at a7 // F i r s t Case :8 r 1 = 1 . 5 / 2 ; // i n cm9 / / l e t r ad i u s t h i c k n e s s o f i n s u l a t i o n = r 1 t

10 r 1 _ t = 1 . 5 ; // i n cm11 r 2 = r 1 + r 1 _ t ;

12 R _ d e s h = 5 0 0 ; / / i n M ohm13 R _ d e s h = R _ d e s h * 1 0 ^ 6 ; / / i n ohm14 / / S ec on d c a s e :

15 r 1 _ d e s h = r 1 ; // i n cm ( a s b e f o r e )16 / / l e t r ad i u s t h i c k n e s s o f i n s u l a t i o n = r 2 t17 r 2 _ t = 2 . 5 ; // i n cm18 r 2 _ d e s h = r 1 + r 2 _ t ;

19 / / s i n c e I n s u l a t i o n r e s i s t a n c e , R desh= si gm a / (2

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%p il ) l o g ( r 2 / r 1 ) a nd

20 // R 1 de sh= si g ma / ( 2

%p il ) l o g ( r 2 d e s h / r 1 d e s h )21 / / D i v i d i n g R 1 d es h by R1 , We g e t22 / / R 1 d e sh / R d e sh = l o g ( r 2 d e s h / r 1 d e s h ) / l o g ( r 2 / r 1 )23 / / L e t R = R 1 d e sh / R de sh , Now24 R = log ( r 2 _ d e s h / r 1 _ d e s h ) / log ( r 2 / r 1 ) ;

25 R 1 _ d e s h = R * R _ d e s h ;

26 disp ( New i n s u l a t i o n r e s i s t a n c e i s : + string (R 1 _ d e s h * 1 0 ^ - 6 ) + M ohm ) ;

Scilab code Exa 2.41 Insulation resistance and resistance of copper con-ductor

1 //Exa2 .4 12 clc ;

3 clear ;

4 close ;

5 / / g i ve n d at a6 t 1 = 2 0 ; // i n d eg re e C

7 t 2 = 3 6 ; // i n d eg re e C8 a l p h a _ 2 0 = 0 . 0 0 4 3 ; // i n p er d e g re e C ( T em pe ra tu re

C o e f f i c i e n t )9 I n s u l a t i o n R e s i s t a n c e = 4 8 0 * 1 0 ^ 6 ; / / i n ohm

10 c o p p e r _ c o n d _ r e s = 0 . 7 ; // i n ohm ( c op pe r c on d uc to rr e s i s t a n c e )

11 l = 5 0 0 * 1 0 ^ - 3 ; // i n k i l o me t e r ( l e ng t h )12 R 1 _ d e sh = I n s u l at i o n R es i s t a nc e * l ; / / i n ohm13

14 // From F or mul a l o g ( R 2 de sh )= l o g ( R 1 de shK ( t2t 1 ) )

15 // K= 1/ ( t2

t 1 )

l o g ( R 1 d e s h / R 2 d e s h )16 / / s i n c e when t2t 1 =10 d e g r e e C a nd R 1 d es h / R 2 d e sh=2

17

18 K = 1 / 1 0 * log ( 2 ) ;

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19

20 // ( i ) I n s u l a t i o n r e s i s t a n c e a t any t em pe ra tu re t2 ,R2 d es h i s g i v e n by21 l o g R 2 _ d e s h = log ( R 1 _ d e s h ) - ( t 2 - t 1 ) / 1 0 * log ( 2 ) ;

22 R 2 _ de s h = % e ^ l o g R 2_ d e s h

23

24 disp ( ( i ) I n s u l a t i o n r e s i s t a n c e a t any t em pe ra tu re: + string ( R 2 _ d e s h * 1 0 ^ - 6 ) + Mega ohm ) ;

25

26 / / ( i i )27 R _ 20 = c o p p er _ c o nd _ r e s / l ; / / i n ohm28 R _ 3 6 = R _ 2 0 * [ 1 + a l p h a _ 2 0 * ( t 2 - t 1 ) ] ;

2930 disp ( R e s i st a n c e a t 36 d eg re e C i s : + string (

R _ 3 6 ) + ohm )

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Chapter 3

Semiconductor

Scilab code Exa 3.1 Velocity of electron

1 // Exa3 . 12 clc ;

3 clear ;

4 close ;

5 / / g i ve n d at a6 E = 2 . 1 ; / / i n eV

7 E = E * 1 . 6 0 2 * 1 0 ^ - 1 9 ; // i n J8 m = 9 . 1 0 7 * 1 0 ^ - 3 1 ; // i n kg ( mass o f e l e c t r o n )9 // F or mul a E =1/2mv 2

10 v = sqrt ( 2 * E / m ) ;

11 disp ( V e lo c i t y o f e l e c t r o n a t F ermi l e v e l i s : +string ( v ) + m/ s )

Scilab code Exa 3.2 Relaxation time resistivity of conductor and velocity

of electron

1 // Exa3 . 22 clc ;

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3 clear ;

4 close ;5 / / g i ve n d at a6 E = 5 . 5 ; / / i n eV ; ( F erm i e n er g y )7 E = E * 1 . 6 * 1 0 ^ - 1 9 ; // i n J8 m i u _ e = 7 . 0 4 * 1 0 ^ - 3 ; // in m2/Vs ( M ob il it y o f

e l e c t r o n s )9 n = 5 .8 * 10 ^ 28 ; // i n /m3 ( Number o f c o nd u ct i on

e l e c t r o n s /m 3 )10 e = 1 . 6 * 1 0 ^ - 1 9 ; // i n c ou lo mb11 m = 9 . 1 * 1 0 ^ - 3 1 ; / / i n k g12 / / ( i ) R e l a x a t i o n t im e ,

13 t a u = m i u _ e / e * m ;14 disp ( ( i ) R el ax at io n t i m e i s : + string ( t a u ) +

s e c o n d ) ;15 s i g m a = ( n * e * m i u _ e ) ;

16 // ( i i ) R e s i s t i v i t y o f c on du ct or ,17 r h o = 1 / s i g m a ;

18 disp ( ( i i ) R e s i s t i v i t y o f c o nd u ct o r i s : + string (r h o ) + ohmm e t e r ) ;

19 // ( i i i ) L et V e l o ci t y o f e l e c t r o n s w i th f e rm i e ne rg y= v

20 v = sqrt ( 2 * E / m ) ;

21 disp ( ( i i i ) V e l o c i t y o f e l e c t r o n w it h Fermi l e v e l i s: + string ( v ) + m/ s ) ;

Scilab code Exa 3.3 Electron and hole density

1 // Exa3 . 32 clc ;

3 clear ;4 close ;

5 / / g i ve n d at a6 n _ i = 2 . 5 * 1 0 ^ 1 3 ; / / i n /cm 37 r h o = 0 . 0 3 9 ; / / i n ohmcm

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8 s i g m a _ n = 1 / r h o ;

9 e = 1 . 6 0 2 * 1 0 ^ - 1 9 ; // i n C10 m i u _ e = 3 6 0 0 ; / / i n cm 2 /Vs11 // s i n c e s ig ma n = n e m iu e = N D e m i u e12 N _ D = s i g m a _ n / ( e * m i u _ e ) ;

13 n = N _ D ; // ( appr ox )14 disp ( C on ce nt ra ti on o f e l e c t r o n s i s : + string ( n ) +

/cm3 ) ;15 p = n _ i ^ 2 / n ;

16 disp ( C on ce nt ra ti on o f h o l e s i s : + string ( p ) + / cm3 ) ;

Scilab code Exa 3.4 Donar atom concentration mobile electron concentra-tion hole concentration and conductivity of doped silicon sample

1 // Exa3 . 42 clc ;

3 clear ;

4 close ;

5 / / g i ve n d at a

6 S i l i c o n A t o m = 5 * 1 0 ^ 2 2 ; // u n it l e s s ( Number o f s i l i c o natom)

7 D o n o r I m p u r i t y = 1 / 1 0 ^ 6 ;

8 n _ i = 1 . 4 5 * 1 0 ^ 1 0 ; / / i n cm39 e = 1 . 6 0 2 * 1 0 ^ - 1 9 ; // i n C

10 m i u _ e = 1 3 0 0 ; // t a ki n g mi u e f o r S i a s 13 00 cm2/Vs11 / / ( i ) Don or atom c o n c e n t r a i o n12 / / F o rm u la N D= N umber o f s i l i c o n a t om s / cm 3 donor

i m p u r i t y13 N _ D = S i l i c o n A t o m * D o n o r I m p u r i t y ;

14 disp ( ( i ) Donor atom c o n c e n t r a t i o n i s : + string ( N _ D) + p e r cm 3 ) ;15

16 // ( i i ) M ob il e e l e c t r o n c o n c e n t r a t i o n17 n = N _ D ; / / ( a p p r o x . )

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18 disp ( ( i i ) M o b i l e e l e c t r o n c o nc e nt r at i o n i s : +

string ( n ) + p e r cm 3 ) ;1920 / / ( i i i ) H ol e c o n c e n t r a t i o n21 p = n _ i ^ 2 / N _ D ;

22 disp ( ( i i i ) H o le c o n c e n t r a t i o n i s : + string ( p ) + /cm3 ) ;

23

24 / / ( i v ) c o n d u c t i v i t y o f d op ed s i l i c o n s am pl e25 s i g m a = n * e * m i u _ e ;

26 disp ( ( i v ) c o n d u ct i v i t y o f doped s i l i c o n sa mp le i s : + string ( s i g m a ) + S/cm) ;

2728 r h o = 1 / s i g m a ;

29 // ( v ) r e s i s t a n c e o f g i v en s em ic on du ct or30 l = 0 . 5 ; // i n cm31 a = ( 5 0 * 1 0 ^ - 4 ) ^ 2

32 R = r h o * l / a ;

33 disp ( R e s i st a nc e o f g i ve s em ic on du ct or i s : + string( R ) + ohm ) ;

Scilab code Exa 3.5 Concentration of hole in si

1 // Exa3 . 52 clc ;

3 clear ;

4 close ;

5 / / g i ve n d at a6 n _ i = 1 . 4 * 1 0 ^ 1 8 ; / / i n m 37 N _ D = 1 . 4 * 1 0 ^ 2 4 ; / / i n m 3

8 n = N _ D ; // ( appr ox )9 p = n _ i ^ 2 / n ;10 / / l e t R a t i o o f e l e c t r o n t o h ol e c o n c e n t r a t i o n = r11 r = n / p ;

12 disp ( R a t i o o f e l e c t r o n t o h ol e c o n c e n t r a t i o n i s :

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+ string ( r ) ) ;

Scilab code Exa 3.6 Conductivity and resitivity of an intrinsic semicon-ductor

1 // Exa3 . 62 clc ;

3 clear ;

4 close ;

5 / / g i ve n d at a6 n _ i = 2 . 5 * 1 0 ^ 1 3 ; / / i n cm 37 e = 1 . 6 * 1 0 ^ - 1 9 ; / / i n c ou lo mb8 m i u _ h = 1 8 0 0 ; / / i n cm 2 /Vs9 m i u _ e = 3 8 0 0 ; / / i n cm 2 /Vs

10 s i g m a _ i = n _ i * e * ( m i u _ e + m i u _ h ) ;

11 disp ( I n t r i n s i c c o n d u c t i v i t y i s : + string ( s i g m a _ i ) + /ohmcm ) ;

12 r h o _ i = 1 / s i g m a _ i ;

13 disp ( I n t r i n s i c r e s i s t i v i r y i s : + string ( r h o _ i ) + ohmcm )

Scilab code Exa 3.7 Density of electron and drift velocity of holes andelectrons

1 // Exa3 . 72 clc ;

3 clear ;

4 close ;

5 / / g i ve n d at a6 r h o _ i = 0 . 4 7 ; / / i n ohmme t e r7 s i g m a _ i = 1 / r h o _ i ;

8 m i u _ e = 0 . 3 9 ; / / i n m 2 /Vs9 m i u _ h = 0 . 1 9 ; / / i n m 2 /Vs

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10 e = 1 . 6 * 1 0 ^ - 1 9 ; // i n C

1112 / / s i n c e s i gm a i=n i e ( miu e+miu h ) ;13 n _ i = s i g m a _ i / ( e * ( m i u _ e + m i u _ h ) ) ;

14 / / s o D en si ty o f e l e c t r o n s = I n t r i n s i c C on ce n tr a ti on, n i

15 disp ( D en si ty o f e l e c t o n s i s : + string ( n _ i ) + /m3 );

16 E = 1 0 ^ 4 ; / / i n V/m17 v _ n = m i u _ e * E ;

18 disp ( 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 s : + string ( v _ n )+ m / s ) ;

19 v _ h = m i u _ h * E ;20 disp ( D r i f t v e l o c i t y o f h ol e s i s : + string ( v _ h ) + m

/ s ) ;

Scilab code Exa 3.8 Conductivity of Si

1 // Exa3 . 82 clc ;

3 clear ;4 close ;

5 / / g i ve n d at a6 n _ i = 1 . 5 * 1 0 ^ 1 0 ; / / i n /cm 37 m i u _ e = 1 3 0 0 ; / / i n cm 2 /Vs8 m i u _ h = 4 5 0 ; / / i n cm 2/Vs9 e = 1 . 6 * 1 0 ^ - 1 9 ; // i n C ( c h ar g e o f e l e c t r o n s )


11 disp ( C o n d u c t i v i t y o f s i l i c o n ( i n t r i n s i c ) i s : +string ( s i g m a _ i ) + /ohmcm ) ;

12 N _ A = 1 0 ^ 1 8 ; / / i n /cm 313 disp ( c o n d u c t i v i t y o f t he r e s u l t i n g Pt yp e s i l i c o ns e m i c o n d u c t o r )

14 s i g m a _ p = e * N _ A * m i u _ h ;

15 disp ( string ( s i g m a _ p ) + /ohmcm ) ;

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Scilab code Exa 3.9 Find conductivity of intrinsic Ge

1 // Exa3 . 92 clc ;

3 clear ;

4 close ;

5 / / g i ve n d at a6 n _ i = 2 . 5 * 1 0 ^ 1 3 ; / / i n /m 3

7 m i u _ e = 3 8 0 0 ; / / i n cm 2 /Vs8 m i u _ h = 1 8 0 0 ; / / i n cm 2 /Vs9 e = 1 . 6 * 1 0 ^ - 1 9 ; // i n C ( c h ar g e o f e l e c t r o n s )


11 disp ( I n t r i n s i c c o n d u c t i v i t y i s : + string ( s i g m a _ i ) + /ohmcm ) ;

12 / / L e t Number o f g er ma ni um a to ms / cm 3 = n o g13 n o _ g = 4 . 4 1 * 1 0 ^ 2 2 ;

14 // s i n c e Donor i m pu r it y = 1 d on or atom / 1 0 7ge rmani um at oms , so

15 D o n o r I m p u r i t y = 1 0 ^ - 7 ;

16 N _ D = n o _ g * D o n o r I m p u r i t y ;

17 n = N _ D ; // ( appr ox )18 p = n _ i ^ 2 / N _ D ;

19 / / s o20 s i g m a _ n = e * N _ D * m i u _ e ;

21 disp ( c o n d u ct i v i t y i n Nt y p e g er ma ni um s e m i c o n d u c t o ri s : + string ( s i g m a _ n ) + /ohmcm ) ;

Scilab code Exa 3.10 Electron and hole drift velocity conductivity of in-trinsic Ge and total current

1 //Exa3 .1 0

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2 clc ;

3 clear ;4 close ;

5 / / g i ve n d at a6 e = 1 . 6 * 1 0 ^ - 1 9 ; / / i n C7 m i u _ e = . 3 8 ; / / i n m 2 /Vs8 m i u _ h = . 1 8 ; / / i n m 2 /Vs9 l = 2 5 ; / / i n mm ( l e n g t h )

10 l = l * 1 0 ^ - 3 ; // i n m11 w = 4 ; // i n mm ( w i dt h )12 w = w * 1 0 ^ - 3 ; // i n m13 t = 1 . 5 ; / / i n mm ( t h i c k n e s s )

14 t = t * 1 0 ^ - 3 ; // i n m15 V = 1 0 ; // i n V16 l = 2 5 ; / / i n mm17 l = l * 1 0 ^ - 3 ; / / i n m18 E = V / l ;

19 // ( i )20 v _ e = m i u _ e * E ;

21 v _ h = m i u _ h * E ;

22 disp ( E le c tr on d r i f t v e l o c i t y i s : + string ( v _ e ) + m/ s ) ;

23 disp ( Hol e d r i f t v e l o c i t y i s :

+ string ( v _ h ) + m / s

)

;

24 n _ i = 2 . 5 * 1 0 ^ 1 9 ; // in /m325 // ( i i )26 s i g m a _ i = n _ i * e * ( m i u _ e + m i u _ h ) ;

27 disp ( I n t r i n s i c c o n d u c t i v i r y o f Ge i s : + string (s i g m a _ i ) + /ohmcm ) ;

28 // ( i i i )29 a = w * t ;

30 I = s i g m a _ i * E * a ; / / i n amp31 I = I * 1 0 ^ 3 ; // i n m A

32 disp ( T o t a l c u r r en t i s : + string ( I ) + mA) ;

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Scilab code Exa 3.11 Diffusion coefficient of electron and hole

1 //Exa3 .1 12 clc ;

3 clear ;

4 close ;

5 / / g i ve n d at a6 k _ d e s h = 1 . 3 8 * 1 0 ^ - 2 3 ; // i n J d eg re e 17 e = 1 . 6 0 2 * 1 0 ^ - 1 9 ; // i n C8 m i u _ e = 3 6 0 0 ; / / i n cm 2 /Vs9 m i u _ h = 1 7 0 0 ; / / i n cm 2 /Vs

10 T = 3 0 0 ; // i n K

11 D _ e = m i u _ e * k _ d e s h * T / e ;12 disp ( D i f f u s i o n c on st an t o f e l e c t r o n s i s : + string (

D _ e ) + cm2/ s ) ;13 D _ h = m i u _ h * k _ d e s h * T / e ;

14 disp ( D i f f u s i o n c on st an t o f h o l e s i s : + string ( D _ h )+ cm2/ s ) ;

Scilab code Exa 3.12 Hall effect in semiconductor

1 //Exa3 .1 22 clc ;

3 clear ;

4 close ;

5 / / g i ve n d at a6 e = 1 . 6 * 1 0 ^ - 1 9 ; / / i n c ou lo mb7 R e s i s t i v i t y = 9 * 1 0 ^ - 3 ; / / i n ohmm8 R _ H = 3 . 6 * 1 0 ^ - 4 ; / / i n m 3 c ou lo mb 1 ( H a l l

C o e f f i c i e n t )

9 s i g m a = 1 / R e s i s t i v i t y ;10 r h o = 1 / R _ H ;

11 n = r h o / e ;

12 disp ( D e n s i t y o f c h a r g e c a r r i e r s i s : + string ( n ) + /m3 ) ;

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13 m i u = s i g m a * R _ H ;

14 disp ( M o bi li ty i s : + string ( m i u ) + m2/V

s ) ;

Scilab code Exa 3.13 Current density

1 //Exa3 .1 32 clc ;

3 clear ;

4 close ;

5 / / g i ve n d at a6 E _ x = 1 0 0 ; / / i n V/m7 e = 1 . 6 * 1 0 ^ - 1 9 ; // i n C8 R _ H = 0 . 0 1 4 5 ; / / i n m 3 / c o ul om b9 m i u _ n = 0 . 3 6 ; / / i n m 2 / v o l t s e c o n d

10 // F or mul a R H =1/( n e )11 n = 1 / ( R _ H * e ) ;

12 s i g m a = n * e * m i u _ n ;

13 J = s i g m a * E _ x ;

14 disp ( C u r r e n t d e n s i t y i s : + string ( J ) + A p e r m 2 );

Scilab code Exa 3.14 Value of hall coefficient

1 //Exa3 .1 42 clc ;

3 clear ;

4 close ;


6 R e s i s t i v i t y = 9 ; // i n m i l l i ohmm7 R e s i s t i v i t y = 9 * 1 0 ^ - 3 ; / / i n ohmm8 m i u = 0 . 0 3 ; / / i n m 2 /Vs9 s i g m a = 1 / R e s i s t i v i t y ;

10 R _ H = m i u / s i g m a ;

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11 disp ( H a l f c o e f f i c i e n t i s : + string ( R _ H ) + m3/C ) ;

Scilab code Exa 3.15 Magnitude of Hall voltage

1 //Exa3 .1 52 clc ;

3 clear ;

4 close ;


6 E _ x = 5 ; / / i n V/ cm7 m i u _ e = 3 8 0 0 ; / / i n cm 2 /Vs8 B _ z = 0 . 1 ; // i n Wb/m29 d = 4 ; / / i n mm

10 d = d * 1 0 ^ - 3 ; // i n m11 v = m i u _ e * E _ x ; / / i n cm / s e c o n d12 v = v * 1 0 ^ - 2 ; / / i n m/ s e c o n d13 V _ H = B _ z * v * d ; // i n V14 V _ H = V _ H * 1 0 ^ 3 ; // i n m V15 disp ( H a l l v o lt ag e i s : + string ( V _ H ) + mV) ;

Scilab code Exa 3.16 Mobility of holes

1 //Exa3 .1 62 clc ;

3 clear ;

4 close ;

5 / / g i ve n d at a6 r h o = 2 0 0 ; // i n K i lo ohmcm

7 r h o = r h o * 1 0 ^ - 2 ; // i n k i l o ohm m8 r h o = r h o * 1 0 ^ 3 ; / / i n ohm m et er9 s i g m a = 1 / r h o ;

10 V _ H = 5 0 ; / / i n mV11 V _ H = V _ H * 1 0 ^ - 3 ; / / i n V

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12 I = 1 0 ; // i n miu A

13 I = I * 1 0 ^ - 6 ; / / i n A14 B _ z = 0 . 1 ; // i n Wb/m215 w = 3 ; // i n mm16 w = w * 1 0 ^ - 3 ; / / i n m e te r17 R _ H = V _ H * w / ( B _ z * I ) ;

18 disp ( M ob i l i t y o f h o l e s i n pt y p e s i l i c o n b ar i s : )

19 m i u _ h = s i g m a * R _ H ;

20 disp ( string ( m i u _ h ) + m2/Vs ) ;

Scilab code Exa 3.17 Hall voltage

1 //Exa3 .1 72 clc ;

3 clear ;

4 close ;

5 / / g i ve n d at a6 N _ D = 1 * 1 0 ^ 2 1 ; / / i n /m 37 B _ Z = 0 . 2 ; // i n T

8 J = 6 0 0 ; // i n A/m29 n = N _ D ;

10 d = 4 ; // i n mm11 d = d * 1 0 ^ - 3 ; // i n m et er r12 e = 1 . 6 * 1 0 ^ - 1 9 ; // i n C ( e l e c t r o n c ha rg e )13 / / Formula V Hw / ( B Z I ) = 1 / ( n e ) , h e n c e V H=B Z

I /( n e w)14 / / w h er e I=Jwd15 / / p u t t i n g I=Jwd i n V H=B Z I /( n ew) , we g e t16 V _ H = B _ Z * J * d / ( n * e ) ; // i n V

17 V _ H = V _ H * 1 0 ^ 3 ; / / i n mV18 disp ( H a ll V o l t a g e i s : + string ( V _ H ) + mV) ;

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Scilab code Exa 3.18 Hall voltage

1 //Exa3 .1 82 clc ;

3 clear ;

4 close ;

5 / / g i ve n d at a6 w = 0 . 1 ; / / i n mm7 B _ Z = 0 . 6 ; // i n T8 R _ H = 3 . 8 * 1 0 ^ - 4 ; / / i n m 3 /C9 I = 1 0 ; / / i n mA

10 I = I * 1 0 ^ - 3 ; / / i n A

11 V _ H = R _ H * B _ Z * I / w ; // i n V12 V _ H = V _ H * 1 0 ^ 6 ; // i n V13 disp ( H a l l v o lt ag e i s : + string ( V _ H ) + m ic ro v o l t )

;

Scilab code Exa 3.19 Density and mobility of carrier

1 //Exa3 .1 9

2 clc ;3 clear ;

4 close ;

5 / / g i ve n d at a6 R e s i s t i v i t y = 9 . 2 3 * 1 0 ^ - 3 ; / / i n ohmm7 R _ H = 3 . 8 4 * 1 0 ^ - 4 ; // i n m3/C ( H a ll C o e f f i c i e n t )8 s i g m a = 1 / R e s i s t i v i t y ;

9 r h o = 1 / R _ H ;

10 e = 1 . 6 * 1 0 ^ - 1 9 ; // i n C ( e l e c t r o n c ha rg e )11 n = r h o / e ;

12 disp ( D e n s i t y o f c h a r g e c a r r i e r s i s : + string ( n ) + /m2 ) ;13 m i u = s i g m a * R _ H ;

14 disp ( M o bi li ty i s : + string ( m i u ) + m2/Vs )

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Scilab code Exa 3.20 Hll angle

1 //Exa3 .2 02 clc ;

3 clear ;

4 close ;

5 / / g i ve n d at a6 B = 0 . 4 8 ; // i n Wb/m27 R _ H = 3 . 5 5 * 1 0 ^ - 4 ; / / i n m 3 /C8 R e s i s t i v i t y = . 0 0 9 1 2 ; / / i n ohm9 s i g m a = 1 / R e s i s t i v i t y ;

10 t h e t a _ H = a t a n d ( s i g m a * B * R _ H ) ;

11 disp ( H a l l a n g l e i s : + string ( t h e t a _ H ) + d e g r e e )

Scilab code Exa 3.21 New position of fermi level

1 //Exa3 .2 12 clc ;

3 clear ;

4 close ;

5 / / g i ve n d at a6 T = 2 7 ; // i n d eg r e e C7 T = T + 2 7 3 ; // i n K8 // L et E C E F =E CF9 E _ C F = 0 . 3 ; // i n eV

10 / / F or mu la E C E F = kTl o g ( n C / N D )11 // L et l o g ( n C /N D ) = L , s o

12 L = E _ C F / T ;13 T _ d e s h = 5 5 ; // i n d eg r e e C14 T _ d e s h = T _ d e s h + 2 7 3 ; // i n K15 / / At t e m p e r at u r e T d es h16 n e w _ fe r m i _l e v e l = T _ de s h * L ; / / w h er e L= l o g ( n C / N D )

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17 disp ( The new p o s i t i o n o f Fermi L ev el i s : + string (

n e w _ f e r m i _ l e v e l ) + V ) ;

Scilab code Exa 3.22 Potential barrier

1 //Exa3 .2 22 clc ;

3 clear ;

4 close ;

5 / / g i ve n d at a6 N _ A = 8 * 1 0 ^ 1 4 ; / / i n /cm 37 N _ D = N _ A ;

8 n _ i = 2 * 1 0 ^ 1 3 ; / / i n /cm 39 k = 8 . 6 1 * 1 0 ^ - 5 ; / / i n eV /K

10 T = 3 0 0 ; // i n K11 V _ 0 = k * T * log ( N _ D * N _ A / n _ i ^ 2 ) ;

12 disp ( P o t e n t i a l b a r r i e r i s : + string ( V _ 0 ) + V ) ;

Scilab code Exa 3.23 Resistance level

1 //Exa3 .2 32 clc ;

3 clear ;

4 close ;

5 / / g i ve n d at a6 / / ( i ) when7 I _ D = 2 ; / / i n mA8 I _ D = I _ D * 1 0 ^ - 3 ; // i n A

9 V _ D = 0 . 5 ; // i n V10 R 1 = V _ D / I _ D ;

11 disp ( R e s i st a c e i s : + string ( R 1 ) + ohm ) ;12 / / ( i i ) wh en13 I _ D = 2 0 ; / / i n mA

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14 I _ D = I _ D * 1 0 ^ - 3 ; // i n A

15 V _ D = 0 . 8 ; // i n V16 R 2 = V _ D / I _ D ;17 disp ( R e s i st a c e i s : + string ( R 2 ) + ohm ) ;18 / / ( i i ) wh en19 I _ D = - 1 ; // i n miu A20 I _ D = I _ D * 1 0 ^ - 6 ; // i n A21 V _ D = - 1 0 ; // i n V22 R 3 = V _ D / I _ D ; / / i n ohm23 R 3 = R 3 * 1 0 ^ - 6 ; / / i n M ohm24 disp ( R e s i st a c e i s : + string ( R 3 ) + M ohm ) ;

Scilab code Exa 3.24 Fraction of the total number of electron

1 //Exa3 .2 42 clc ;

3 clear ;

4 close ;

5 format ( v ,12)6 / / g i ve n d at a

7 E _ G = 0 . 7 2 ; // i n eV8 E _ F = E _ G / 2 ; // i n eV9 k = 8 . 6 1 * 1 0 ^ - 5 ; / / i n eV /K

10 T = 3 0 0 ; // i n K11 / / F o rm u la n C / n = 1 /1+%e ( E GE F ) / kT12 // L et n C /n = N13 N = 1 / ( 1 + % e ^ ( ( E _ G - E _ F ) / ( k * T ) ) ) ;

14

15 disp ( F ra c t i o n o f t he t o t a l number o f e l e c t r o n s (c on du c t io n band a s w e l l a s v a l e n ce band ) : +string ( N ) ) ;

Scilab code Exa 3.25 Current flowing

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1 //Exa3 .2 5

2 clc ;3 clear ;

4 close ;

5 format ( v ,3)6 / / g i ve n d at a7 I _ 0 = . 1 5 ; / / i n m ic ro amp8 I _ 0 = I _ 0 * 1 0 ^ - 6 ; // i n A9 V = 0 . 1 2 ; // i n V

10 V _ T = 2 6 ; / / i n mV11 V _ T = V _ T * 1 0 ^ - 3 ; // i n V12 I = I _ 0 * ( % e ^ ( V / V _ T ) - 1 ) ; / / i n amp

13 I = I * 1 0 ^ 6 ; // i n m ic ro amp14 disp ( La r g e r e v e r s e b i a s c ur r e nt i s : + string ( I ) +

mi c r o amp) ;

Scilab code Exa 3.26 Forward voltage

1 //Exa3 .2 62 clc ;

3 clear ;4 close ;

5 format ( v ,5)6 / / g i ve n d at a7 I = . 0 1 ; // i n A8 I _ 0 = 2 . 5 * 1 0 ^ - 6 ; // i n amp9 n i t a = 2 ; // f o r s i l i c o n

10 V _ T = 2 6 ; / / i n mV11 V _ T = V _ T * 1 0 ^ - 3 ; // i n V12 / / F or mu la I= I 0 ( %e ( V/( n i t a V T ) ) 1) ;

13 V = n i t a * V _ T * log ( I / I _ 0 + 1 ) ;14 disp ( Forward v o l t a ge i s : + string ( V ) + V ) ;

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Scilab code Exa 3.27 Reverse saturation current density

1 //Exa3 .2 72 clc ;

3 clear ;

4 close ;

5 / / g i ve n d at a6 N _ D = 1 0 ^ 2 1 ; / / i n m37 N _ A = 1 0 ^ 2 2 ; / / i n m38 D _ e = 3 . 4 * 1 0 ^ - 3 ; / / i n m 2 / s9 D _ h = 1 . 2 * 1 0 ^ - 3 ; / / i n m 2 / s

10 L _ e = 7 . 1 * 1 0 ^ - 4 ; // i n m

11 L _ h = 3 . 5 * 1 0 ^ - 4 ; // i n m12 n _ i = 1 . 6 0 2 * 1 0 ^ 1 6 ; / / i n /m 313 e = 1 . 6 * 1 0 ^ - 1 9 ; // i n C ( e l e c t r o n c ha rg e )14 // F ormula I 0=a e [ D h / ( L hN D ) + D e / ( L e N A ) ]

n i 215 //and16 // R ev er se s a t u r a t i o n c u r r e nt d e n si t y = I 0 / a = [ D h

/( L hN D ) + D e / ( L e N A ) ] e n i 2 , So17 C u r r e n t De n s i ty = [ D _ h / ( L _h * N _ D ) + D _e / ( L _ e * N _A ) ] * e *

n _ i ^ 2 ; // i n A18 C u r r e n t D e n s i t y = C u r r e n t D e n s i t y * 1 0 ^ 6 ;

// i n m ic ro A19 disp ( R e v e r s e s a t u r at i o n c ur r e nt d e n s i t y i s : +string ( C u r r e n t D e n s i t y ) + m ic ro amp ) ;

Scilab code Exa 3.28 Junction width

1 //Exa3 .2 82 clc ;

3 clear ;4 close ;

5 / / g i v e n d at a 6 format ( v ,13)7 N _ D = 1 0 ^ 1 7 * 1 0 ^ 6 ; / / i n m3

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8 N _ A = 0 . 5 * 1 0 ^ 1 6 * 1 0 ^ 6 ; / / i n a t om s /m 3

9 e p s i l o n _ r = 1 0 ; / / i n F/m10 e p s i l o n _ o = 8 . 8 5 * 1 0 ^ - 1 2 ; / / i n F/m11 e p s i l o n = e p s i l o n _ r * e p s i l o n _ o ;

12 e = 1 . 6 0 2 * 1 0 ^ - 1 9 ; // i n C ( e l e c t r o n c ha rg e )13 // ( i ) when no e x t e r n al v o l t a g e i s a p p l i e d i . e .14 V = 0 ;

15 V _ B = 0 . 7 ; // i n V16 W = sqrt ( 2 * e p s i l o n * V _ B / e * ( 1 / N _ A + 1 / N _ D ) ) ;

17 disp ( J un ct io n w i dt h i s : + string ( W ) + m) ;18 // ( i i ) when e x t e r n a l v o l t a g e o f 10 V i s a p pl i ed i .

e .

19 V = - 1 0 ; // i n V20 V _ o = 0 . 7 ; // i n V21 V _ B = V _ o - V ;

22 W = sqrt ( 2 * e p s i l o n * V _ B / e * ( 1 / N _ A + 1 / N _ D ) ) ;

23 disp ( J un ct io n w i dt h i s : + string ( W ) + m) ;24

25 / / No te : Answer i n t h e b oo k i s wrong

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Chapter 4

Bipolar Junction And Field

Effect Transistors

Scilab code Exa 4.1 Resistance between gate and source

1 / / Exa 4 . 12 clc ;

3 clear ;

4 close ;

5 / / g i v e n d at a :6 format ( v ,11)7 V G S = 1 0 ; / / i n V o l t8 I G = 0 . 0 0 1 ; // in uAmpere9 I G = I G * 1 0 ^ - 6 ; // in Ampere

10 R G S = V G S / I G ; // i n Ohm11 disp ( R G S * 1 0 ^ - 6 , R e s i s t a n c e b et we en g a t e and s o u r c e

i n Mohm : ) ;

Scilab code Exa 4.2 AC drain resistance of the JFET

1 / / Exa 4 . 2

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2 clc ;

3 clear ;4 close ;

5 / / g i v e n d at a :6 d e l V D S = 1 . 5 ; / / i n V o l t7 d e l I D = 1 2 0 ; // in uAmpere8 d e l I D = d e l I D * 1 0 ^ - 6 ; // in Ampere9 r d = d e l V D S / d e l I D ; // i n Ohm

10 disp ( r d * 1 0 ^ - 3 , AC d r a i n R e s i s t a n c e o f JFET i n Kohm : ) ;

Scilab code Exa 4.3 Transconductance

1 / / Exa 4 . 32 clc ;

3 clear ;

4 close ;

5 / / g i v e n d at a :6 I D 2 = 1 . 5 ; // i n mAmpere7 I D 1 = 1 . 2 ; // i n mAmpere

8 d e l I D = I D 2 - I D 1 ; // in Ampere9 V G S 1 = - 4 . 2 5 ; / / i n V o l t

10 V G S 2 = - 4 . 1 0 ; / / i n V o l t11 d e l V G S = V G S 2 - V G S 1 ; / / i n V o l t12 g m = d e l I D / d e l V G S ; // i n Ohm13 disp ( g m , T r a n s c o nd u c ta n c e i n mA/V : ) ;14 disp ( g m * 1 0 ^ 3 , T r an sc on du ct an ce i n uS : ) ;

Scilab code Exa 4.4 AC drain resistance transconductance and amplifica-tion factor

1 / / Exa 4 . 42 clc ;

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3 clear ;

4 close ;5 / / g i v e n d at a :6 V D S 1 = 5 ; / / i n V o l t7 V D S 2 = 1 2 ; / / i n V o l t8 V D S 3 = 1 2 ; / / i n V o l t9 V G S 1 = 0 ; / / i n V o l t

10 V G S 2 = 0 ; / / i n V o l t11 V G S 3 = - 0 . 2 5 ; / / i n V o l t12 I D 1 = 8 ; // i n mAmpere13 I D 2 = 8 . 2 ; // i n mAmpere14 I D 3 = 7 . 5 ; // i n mAmpere

15 / /AC d r a i n r e s i s t a n c e16 d e l V D S = V D S 2 - V D S 1 ; / / i n V o l t17 d e l I D = I D 2 - I D 1 ; // i n mAmpere18 r d = d e l V D S / d e l I D ; // i n Kohm19 disp ( r d , AC D ra in r e s i s t a n c e i n Kohm : ) ;20 / / T r a n s c o n d u c t a n c e21 d e l I D = I D 3 - I D 2 ; // i n mAmpere22 d e l V G S = V G S 3 - V G S 2 ; / / i n V o l t23 g m = d e l I D / d e l V G S ; // in mA/V or mS24 disp ( g m , T r a n s c o nd u c ta n c e i n mA/V : ) ;25

/ / A m p l i f i c a t i o n F a ct o r26 m e u = r d * 1 0 0 0 * g m * 1 0 ^ - 3 ; // u n i t l e s s27 disp ( m e u , A m p l i f i c a ti o n F ac to r : ) ;

Scilab code Exa 4.5 Transconductance

1 / / Exa 4 . 52 clc ;

3 clear ;4 close ;

5 / / g i v e n d at a :6 V P = - 4 . 5 ; / / i n V o l t7 I D S S = 1 0 ; // i n mAmpere

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8 I D S = 2 . 5 ; // i n mAmpere

9 // F or mul a : IDS=IDSS

[1

VGS/VP]210 V G S = V P * ( 1 - sqrt ( I D S / I D S S ) ) ; / / i n V o l t11 g m = ( - 2 * I D S S * 1 0 ^ - 3 ) * ( 1 - V G S / V P ) / V P ; // in mA/V or mS12 disp ( g m * 1 0 0 0 , T r a n s c o nd u c ta n c e i n mA/V : ) ;

Scilab code Exa 4.6 Calculate VGS

1 / / Exa 4 . 6

2 clc ;3 clear ;

4 close ;

5 / / g i v e n d at a :6 g m = 1 0 ; // in mS7 g m = g m * 1 0 ^ - 3 ; / / i n S8 I D S S = 1 0 ; // in uAmpere9 I D S S = I D S S * 1 0 ^ - 6 ; // in Ampere

10 //VGS( OFF) : VGS=VP11 // Formula : gm=gmo=2IDSS/VP=2IDSS /VG( Of f )12 V G S _ O F F = - 2 * I D S S / g m ; / / i n V o l t

13 disp ( V G S _ O F F * 1 0 0 0 , VGS(OFF) in mV : ) ;

Scilab code Exa 4.7 Minimum value of VDS

1 / / Exa 4 . 72 clc ;

3 clear ;

4 close ;

5 / / g i v e n d at a :6 V P = - 4 ; / / i n V o l t7 V G S = - 2 ; / / i n V o l t8 I D S S = 1 0 ; // i n mAmpere9 I D S S = I D S S * 1 0 ^ - 3 ; // in Ampere

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10 // F or mul a : ID=IDSS[1VGS/VP]2

11 I D = I D S S * [ 1 - V G S / V P ] ^ 2 ; // in Ampere12 disp ( I D * 1 0 0 0 , D ra in C ur re nt i n mA : ) ;13 disp ( The minimum v a l u e o f VDS f o r p i n cho f f r e g i o n

i s e q u a l t o VP . Thus t h e minimum v a l u e o f VDS :VDS(min) = + string ( V P ) + V o l t ) ;

Scilab code Exa 4.8 ID gmo and gm

1 / / Exa 4 . 82 clc ;3 clear ;

4 close ;

5 / / g i v e n d at a :6 I D S S = 8 . 7 ; // i n mAmpere7 I D S S = I D S S * 1 0 ^ - 3 ; // in Ampere8 V P = - 3 ; / / i n V o l t9 V G S = - 1 ; / / i n V o l t

10 //ID11 I D = I D S S * [ 1 - V G S / V P ] ^ 2

12 disp ( I D * 1 0 0 0 , D ra in c u r r e nt ID i n mA : ) ;13 //gmo14 g m o = - 2 * I D S S / V P ; / / i n S15 disp ( g m o * 1 0 0 0 , T r an sc on duc t anc e f o r VGS=0V i n mA/V

o r mS : ) ;16 //gm17 g m = g m o * ( 1 - V G S / V P ) ; / / i n S18 disp ( g m * 1 0 0 0 , T r a n s c o nd u c ta n c e i n mA/V o r mS : ) ;

Scilab code Exa 4.9 Id and gm

1 / / Exa 4 . 92 clc ;

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3 clear ;

4 close ;5 / / g i v e n d at a :6 I D S S = 8 . 4 ; // i n mAmpere7 I D S S = I D S S * 1 0 ^ - 3 ; // in Ampere8 V P = - 3 ; / / i n V o l t9 V G S = - 1 . 5 ; / / i n V o l t

10 //ID11 I D = I D S S * [ 1 - V G S / V P ] ^ 2

12 disp ( I D * 1 0 0 0 , D ra in c u r r e nt ID i n mA : ) ;13 //gmo14 g m o = - 2 * I D S S / V P ; / / i n S

15 disp ( g m o * 1 0 0 0 , T r an sc on duc t anc e f o r VGS=0V i n mA/Vo r mS : ) ;

16 g m = g m o * ( 1 - V G S / V P ) ; / / i n S17 disp ( g m * 1 0 0 0 , T r a n s c o nd u c ta n c e i n mA/V o r mS : ) ;

Scilab code Exa 4.10 gm at IDS

1 / / Exa 4 . 1 0

2 clc ;3 clear ;

4 close ;

5 / / g i v e n d at a :6 V P = - 4 . 5 ; / / i n V o l t7 I D S S = 9 ; // i n mAmpere8 I D S S = I D S S * 1 0 ^ - 3 ; // in Ampere9 I D S = 3 ; // i n mAmpere

10 I D S = I D S * 1 0 ^ - 3 ; // in Ampere11 // F or mul a : IDS=IDSS[1VGS/VP]2

12 V G S = V P * ( 1 - sqrt ( I D S / I D S S ) ) ; / / i n V o l t13 disp ( V G S , ID=3mA at VGS i n V ol t : ) ;14 g m = ( - 2 * I D S S ) * ( 1 - V G S / V P ) / V P ; // i n mA/V or mS15 disp ( g m * 1 0 0 0 , T r a n s c o n d u c t a n ce i n mA/V o r mS : ) ;

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Scilab code Exa 4.11 Drain current

1 / / Exa 4 . 1 12 clc ;

3 clear ;

4 close ;

5 / / g i v e n d at a :6 I D _ o n = 5 ; // i n mAmpere7 V G S _ o n = 8 ; / / i n V o l t8 V G S = 6 ; / / i n V o l t9 V G S T = 4 ; / / i n V o l t

10 k = I D _ o n / ( V G S _ o n - V G S T ) ^ 2 ; // i n mA/V211 I D = k * ( V G S - V G S T ) ^ 2 ; // i n mA12 disp ( I D , D ra in c u r r e nt i n mA : ) ;

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Chapter 5

Magnetic Properties Of

Materials

Scilab code Exa 5.1 Hysteresis loss

1 / / Exa 5 . 12 clc ;

3 clear ;

4 close ;

5 / / g i ve n d at a6 A r e a _ h y s t e r e s i s _ c u r v e = 9 . 3 ; // i n cm27 C o r d i n a t e 1 _ 1 c m = 1 0 0 0 ; // i n AT/m8 C o r d i n a t e 2 _ 1 c m = 0 . 2 ; / / i n T9 / / P a r t ( i )

10 h y s t e r e s i s _ l o s s = A r e a _ h y s t e r e s i s _ c u r v e * C o r d i n a t e 1 _ 1 c m

* C o r d i n a t e 2 _ 1 c m ; // i n J /m3/ c y c l e11 disp (hyst eresis_loss , H y s t e r e s i s l o s s /m 3/ c y c l e i n J

/m 3 / c y c l e : ) ;12 / / P a r t ( i i )

13 f = 5 0 ; / / i n Hz14 H _ L o s s P e r C u b i c M e t e r = h y s t e r e s i s _ l o s s * f ; // i n Watt s15 disp ( H _ L o s s P e r C u b i c M e t e r * 1 0 ^ - 3 , H y s t e r e s i s l o s s Per

C ub i c M et er i n KWatts : ) ;

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Scilab code Exa 5.2 Hysteresis loss

1 / / Exa 5 . 22 clc ;

3 clear ;

4 close ;

5 format ( v ,11)6 / / g i ve n d at a7 A r e a _ h y s t e r e s i s _ l o o p = 9 3 ; // in cm28 s c a l e 1 _ 1 c m = 0 . 1 ; // i n Wb/m29 s c a l e 2 _ 1 c m = 5 0 ; // i n AT/m

10

11 h y s t e r e s i s _ l o s s = A r e a _ h y s t e r e s i s _ l o o p * s c a l e 1 _ 1 c m *

s c a l e 2 _ 1 c m ; // i n J /m3/ c y c l e12 disp (hyst eresis_loss , H y s t e r e s i s l o s s /m 3/ c y c l e i n J

/m 3 / c y c l e : ) ;13

14 f = 6 5 ; // u n it l e s s15 V = 1 5 0 0 * 1 0 ^ - 6 ; / / i n m 3

16 P _ h = h y s t e r e s i s _ l o s s * f * V ;17 disp ( H y s t e r e s i s l o s s i s : + string ( P _ h ) + W ) ;

Scilab code Exa 5.3 Loss of energy

1 / / Exa 5 . 32 clc ;

3 clear ;

4 close ;5 format ( v , 11)6 / / g i ve n d at a7 n i t a = 6 2 8 ; / / i n J /m 38 B _ m a x = 1 . 3 ; // i n Wb/m2

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9 f = 2 5 ; // i n Hz

10 i r o n M a s s = 5 0 ; // i n kg11 d e n s i t y O f I r o n = 7 . 8 * 1 0 ^ 3 ; / / i n k g /m 312 V = i r o n M a s s / d e n s i t y O f I r o n ;

13 x = 1 2 . 5 ; // in AT/m14 y = 0 . 1 ; // i n T15 // f or mu la H y s t e r e s i s l o s s / s ec on d = n i t a B max 1 . 6 f

V16 H _ L o s s _ pe r _ s e co n d = n i ta * B _ m a x ^ 1 . 6* f * V ; / / i n J / s17 H _ L o s s _ p e r _ s e c o n d = floor ( H _ L o s s _ p e r _ s e c o n d ) ;

18 H _ L o ss _ p e r_ h o u r = H _ L o ss _ p e r _s e c o nd * 6 0 *6 0 ; // i n J19 disp ( H y s t e r e s i s L o ss p er hour i s : + string (

H _ L o s s _ p e r _ h o u r ) + J ) ;20 / / Le t H y s t e r e s i s L os s p er m3 p er c y c l e = H121 H 1 = n i t a * B _ m a x ^ 1 . 6 ;

22 // f or mu la h y s t e r e s i s l o s s /m3/ c y c l e = xy a re a o f BH l o o p

23 A r e a _ o f _ B _ H _ l o o p = H 1 / ( x * y ) ;

24 A r e a _ o f _ B _ H _ l o o p = floor ( A r e a _ o f _ B _ H _ l o o p ) ;

25 disp ( Area o f BH l o o p i s : + string (A r e a _ o f _ B _ H _ l o o p ) + c m 2 ) ;

Scilab code Exa 5.4 Loss per kg in a specimen

1 / / Exa 5 . 42 clc ;

3 clear ;

4 close ;

5 / / g i ve n d at a6 H _ L _ p e r _ M _ C u b e _ p e r _ C = 3 8 0 ; // i n WS

7 f = 5 0 ; // u n it l e s s8 d e n s i t y = 7 8 0 0 ; / / i n k g /m 39 V = 1 / d e n s i t y ; / / i n m 3

10 // f or mu la H y s t e r e s i s l o s s = H y s t e r e s i s l o s s /m3/c y c l e f V

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11 P _ h = H _ L _p e r_ M _C u be _ pe r _C * f * V ;

12 disp ( H y s t e r e s i s l o s s i s : + string ( P _ h ) + W ) ;

Scilab code Exa 5.5 Eddy current loss

1 / / Exa 5 . 52 clc ;

3 clear ;

4 close ;

5 / / g i ve n d at a6 P _ e 1 = 1 6 0 0 ; // i n w at ts7 B _ m a x 1 = 1 . 2 ; // i n T8 f 1 = 5 0 ; // i n Hz9 B _ m a x 2 = 1 . 5 ; // i n T

10 f 2 = 6 0 ; // i n Hz11 // P e p r o p ot i o n a l t o B max 2f 2 , s o12 P _ e 2 = P _ e 1 * ( B _ m a x 2 / B _ m a x 1 ) ^ 2 * ( f 2 / f 1 ) ^ 2

13 disp ( Eddy c u r r e n t l o s s i s : + string ( P _ e 2 ) + w at ts ) ;

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Chapter 6

Dielectric Properties Of

Materials

Scilab code Exa 6.1 Element of parallel RC circuit

1 / / Exa 6 . 12 clc ;

3 clear ;

4 close ;

5 / / g i ve n d at a6 e p s i l o n _ r = 2 . 5 ;

7 e p s i l o n _ o = 8 . 8 5 4 * 1 0 ^ - 1 2 ;

8 d = . 2 * 1 0 ^ - 3 ; // i n m9 A = 2 0 * 1 0 ^ - 4 ; / / i n m 2

10 o m e g a = 2 * % p i * 1 0 ^ 6 ; // i n r a d ia n s / s11 f = 1 0 ^ 6 ;

12 t a n _ d e l t a = 4 * 1 0 ^ - 4 ;

13 C = e p s i l o n _ o * e p s i l o n _ r * A / d ; // i n F14 disp ( C a p i c i t a n c e i s : + string ( C * 1 0 ^ 1 2 ) + m i u m i u F

) ;15 // F or mul a P=V2/R , so16 // R=V2/P and P= V22%pi f C t a n d e l t a ,

p u t t i ng t he v al ue o f P , we g et17 R = 1 / ( 2 * % p i * f * C * t a n _ d e l t a ) ; / / i n ohm

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18 disp ( The e le m en t o f p a r a l l e l RC c i r c u i t i s : +

string ( R * 1 0 ^ - 6 ) + M ohm ) ;

Scilab code Exa 6.2 Charge sensitivity

1 / / Exa 6 . 22 clc ;

3 clear ;

4 close ;

5 / / g i ve n d at a6 g = 0 . 0 5 5 ; // i n Vm/N7 t = 2 * 1 0 ^ - 3 ; // i n m8 P = 1 . 2 5 * 1 0 ^ 6 ; // i n N/m29 e p s i l o n = 4 0 . 6 * 1 0 ^ - 1 2 ; / / i n F/m

10 V _ o u t = g * t * P ;

11 disp ( Output v o l t a ge i s : + string ( V _ o u t ) + V ) ;12 / / Fo rm ul a C ha rg e S e n s i v i t y =e p s i l o n o e p s i l o n r g=

e p s i l o n g13 C h a r g e S e n s i v i t y = e p s i l o n * g ;

14 disp ( Charge S e ns i v i t y i s : + string ( C h a r g e S e n s i v i t y

) + C/N) ;

Scilab code Exa 6.3 Force required to d

Electrical and Electronics Engineering Materials_J. B. Gupta

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