Scilab Textbook Companion for Antenna and Wave Propagation

7/21/2019 Scilab Textbook Companion for Antenna and Wave Propagation

1/176

Scilab Textbook Companion for

Antenna and Wave Propagation

by A. K. Gautam1

Created byNizamuddin

B TechElectronics Engineering

Uttarakhand Technical University DehradunCollege Teacher

NoneCross-Checked byChaya Ravindra

October 22, 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


2/176

Book Description

Title: Antenna and Wave Propagation

Author: A. K. Gautam

Publisher: S. K. Kataria & Sons, New Delhi

Edition: 3

Year: 2007

ISBN: 81-88458-04-X

1


3/176

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.

2


4/176

Contents

List of Scilab Codes 4

1 Eletromagnetic Field Radiation 14

2 Antenna Terminology 46

3 Antenna Arrays 77

4 Practical Antennas 108

5 Propagation 143

3


5/176

List of Scilab Codes

Exa 1.1 What is the strength of a magnetic field H in free space 14Exa 1.2 Find out the field strength . . . . . . . . . . . . . . . 14Exa 1.3 Calculate the radiation resistance . . . . . . . . . . . 15Exa 1.4 What is the power radiated and also what is the effi-

ciency of the antenna . . . . . . . . . . . . . . . . . . 15Exa 1.5 How much power will an antenna having a radiation

rasistance of fifty ohms . . . . . . . . . . . . . . . . . 16Exa 1.6 What is the radiation resistance of an antenna . . . . 17Exa 1.7 How much current flows into the antenna . . . . . . . 17Exa 1.8 Calculate the strength of electric field . . . . . . . . . 18Exa 1.9 Estimate the effective height of the antenna . . . . . . 18Exa 1.10 Find the field strength and the power radiated . . . . 19Exa 1.11 Calculate the power radiated . . . . . . . . . . . . . . 20

Exa 1.12 Calculate the radiation resistance of current elements. 20Exa 1.13 Calculate the power radiated and what is its radiation

resistance . . . . . . . . . . . . . . . . . . . . . . . . . 21Exa 1.14 what is the electric field . . . . . . . . . . . . . . . . . 21Exa 1.15 Calculate the antenna current at a distance of five eight

wavelength away from the feed point . . . . . . . . . . 22Exa 1.16 Determine the field strength of the radiated field pro-

duced . . . . . . . . . . . . . . . . . . . . . . . . . . . 23Exa 1.17 Calculate the effective height of the antenna in meters 23Exa 1.18 Calculate the radiation resistance. . . . . . . . . . . . 24Exa 1.19 Find the radiation resistance and power radiated and

also antenna efficiency . . . . . . . . . . . . . . . . . . 24Exa 1.20 What is the power radiated . . . . . . . . . . . . . . . 25Exa 1.21 Find out the field strength . . . . . . . . . . . . . . . 26

4


6/176

Exa 1.22 At what distance from a sixty cycle circuit is the radia-

tion field approximately . . . . . . . . . . . . . . . . . 26Exa 1.23 Find out the field strength . . . . . . . . . . . . . . . 27Exa 1.24 Find the velocity of a plane wave in a loss less medium 27Exa 1.25 What is the strength of a magnetic field H in free space 28Exa 1.26 Calculate the field strength at a distance of twenty five

km. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28Exa 1.27 Calculate the radiation resistance. . . . . . . . . . . . 29Exa 1.28 Derive an expression for the gain of a half wave antenna 29Exa 1.29 Calculate the antenna current at a distance of seventh

eighth wavelength away from the feed point . . . . . . 30Exa 1.30 Find the average energy density. . . . . . . . . . . . . 31

Exa 1.31 Determine the radiation resistance . . . . . . . . . . . 31Exa 1.32 What is the value of electric field strength at a point

twenty five away in the same direction . . . . . . . . . 32Exa 1.33 Find the velocity of propogation and the wavelength and

the impedence of the medium and also the rms electricfield E. . . . . . . . . . . . . . . . . . . . . . . . . . . 33

Exa 1.34 At what distance in wavelength is the radiation compo-nent of magnetic field three times the induction compo-nents . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

Exa 1.35 Find out the field strength . . . . . . . . . . . . . . . 34

Exa 1.36 Find the velocity of a plane wave in a loss less medium 35Exa 1.37 Calculate the antenna current at a distance of seventheighth wavelength away from the feed point . . . . . . 35

Exa 1.38 Determine the radiation resistance . . . . . . . . . . . 36Exa 1.39 What is the radiation resistance of an antenna . . . . 36Exa 1.40 What is the bandwidth . . . . . . . . . . . . . . . . . 37Exa 1.41 Define radiation resistance and also Calculate the radi-

ation resistance and efficiency . . . . . . . . . . . . . . 37Exa 1.42 What is the significance of electrostatic field and induc-

tion field and also radiation field of the antenna and atwhat distance in wavelength the radiation component

of magnetic field is hundred times of the induction com-ponent . . . . . . . . . . . . . . . . . . . . . . . . . . 38

Exa 1.43 Define retarded vector potential. . . . . . . . . . . . . 39Exa 1.44 What is the power radiated and what is the efficiency

of the antenna . . . . . . . . . . . . . . . . . . . . . . 40

5


7/176

Exa 1.45 Calculate the radiation resistance power radiated and

the efficiecy of an antenna . . . . . . . . . . . . . . . . 40Exa 1.46 Find the radiation resistance and efficiency . . . . . . 41Exa 1.47 What is the power radiated . . . . . . . . . . . . . . . 42Exa 1.48 What is the strength of magnetic field H in free space 42Exa 1.49 Calculate the radiated field strength and the total power

radiated and also the radiation resistance . . . . . . . 43Exa 1.50 Show the total far field electric field amplitude and also

Calculate the power that could be fed into a dipole an-tenna . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

Exa 1.51 Calculate the loss resistance and also Calculate the powerradiated and the ohmic loss and loss resistance . . . . 45

Exa 2.1 What is the wavelength . . . . . . . . . . . . . . . . . 46Exa 2.2 What is the actual velocity of EM energy . . . . . . . 46Exa 2.3 What is the wavelength in vaccum and in air . . . . . 47Exa 2.4 What is the directicity . . . . . . . . . . . . . . . . . . 47Exa 2.5 Calculate the radiation resistance. . . . . . . . . . . . 48Exa 2.6 Find the max directivity and compare it with its exact

value . . . . . . . . . . . . . . . . . . . . . . . . . . . 48Exa 2.7 What is the bandwidth and also bandwidth ratio . . . 49Exa 2.8 Calculate the max effective aperture of an antenna . . 50Exa 2.9 Find out the radiation resistance . . . . . . . . . . . . 50

Exa 2.10 How much power does a fifty ohms antenna radiate whenfed a current five amp . . . . . . . . . . . . . . . . . . 51Exa 2.11 Calculate the radiation resistance. . . . . . . . . . . . 51Exa 2.12 Calculate the front to back ratio of an antenna in dB. 52Exa 2.13 Find the received power . . . . . . . . . . . . . . . . . 52Exa 2.14 How much is the new signal picked up by the receiving

station . . . . . . . . . . . . . . . . . . . . . . . . . . 53Exa 2.15 Calculate the power gain . . . . . . . . . . . . . . . . 54Exa 2.16 Calculate the approximate gain and beamwidth of a

paraboloidal reflector antenna. . . . . . . . . . . . . . 54Exa 2.17 Find out the quality factor Q of an antenna . . . . . . 55

Exa 2.18 Calculate the bandwidth of an antennas . . . . . . . . 55Exa 2.19 Calculate the directivity of isotropic antenna . . . . . 56Exa 2.20 Calculate the max effective aperture of a microwave an-

tenna . . . . . . . . . . . . . . . . . . . . . . . . . . . 56Exa 2.21 Find the equivalent temperature . . . . . . . . . . . . 57

6


8/176

Exa 2.22 Find the noise factor . . . . . . . . . . . . . . . . . . . 57

Exa 2.23 what is the effective noise temperature . . . . . . . . . 58Exa 2.24 Calculate the available noise power per unit bandwidthand also Calculate the available noise power for a noisebandwidth . . . . . . . . . . . . . . . . . . . . . . . . 58

Exa 2.25 How much is the new signal picked up by the receivingstation . . . . . . . . . . . . . . . . . . . . . . . . . . 59

Exa 2.26 Calculate the max effective aperture of an antenna . . 59Exa 2.27 Find the equivalent temperature . . . . . . . . . . . . 60Exa 2.28 Find the noise factor . . . . . . . . . . . . . . . . . . . 60Exa 2.29 What is the effective noise temperature . . . . . . . . 61Exa 2.30 Calculate the available noise power per unit bandwidth

and also Calculate the available noise power for a noisebandwidth . . . . . . . . . . . . . . . . . . . . . . . . 61

Exa 2.31 Calculate the gain and beam width of the antenna . . 62Exa 2.32 How much is the new signal picked up by the receiving

station . . . . . . . . . . . . . . . . . . . . . . . . . . 63Exa 2.33 Calculate the radiation resistance. . . . . . . . . . . . 63Exa 2.34 Determine the total radited power . . . . . . . . . . . 64Exa 2.35 Find the max directivity of the antenna and write an

expression for the directivity . . . . . . . . . . . . . . 64Exa 2.36 Find the max directivity of the antenna and write an

expression for the directivity . . . . . . . . . . . . . . 65Exa 2.37 Show the max effective aperture of a short dipole antenna 66Exa 2.38 Show the field strength at adistance r meters from an

antenna of gain G and radiating power P . . . . . . . 67Exa 2.39 Define effective aperture and scattering aperture . . . 68Exa 2.40 Calculate the power density and magnetic and electric

field strength . . . . . . . . . . . . . . . . . . . . . . . 68Exa 2.41 Calculate the antenna gain . . . . . . . . . . . . . . . 69Exa 2.42 Calculate the effective aperture and what will the power

received . . . . . . . . . . . . . . . . . . . . . . . . . . 70Exa 2.43 Find the directivity and gain and effective aperture and

beam solid angle and radiation resistance and also ter-minal resistance . . . . . . . . . . . . . . . . . . . . . 70

Exa 2.44 Find the beam width . . . . . . . . . . . . . . . . . . 71Exa 2.45 what is the size of spot illuminated by the antenna . . 72Exa 2.46 Find the power density . . . . . . . . . . . . . . . . . 72

7


9/176

Exa 2.47 Find the max radiated electric field and what is the max

power density. . . . . . . . . . . . . . . . . . . . . . . 73Exa 2.48 Find the peak poynting vector and the average poyntingvector and also the peak value of magnetic field H . . 74

Exa 2.49 Find the magnitude of magnetic and electric fields . . 74Exa 2.50 Find the rms electric and magnetic field and the average

value of poynting vector and the average energy densityand also the time it takes a signal to reach earth . . . 75

Exa 3.1 Calculate the half power beam width of the major lobesof the array in horizontal plane . . . . . . . . . . . . . 77

Exa 3.2 Calculate the progressive phase shifts and also Calculatethe angle at which the main beam is placed for this

phase distribution . . . . . . . . . . . . . . . . . . . . 78Exa 3.3 Discuss the radiation pattern of a linear array . . . . . 79Exa 3.4 Design a eight element broad side array . . . . . . . . 81Exa 3.5 Design a five element broad side array which has the

optimum pattern . . . . . . . . . . . . . . . . . . . . . 83Exa 3.6 Design a four element broad side array . . . . . . . . . 85Exa 3.7 Determine Dolph Tchebyscheff current distribution and

also determine the half power beam width . . . . . . . 86Exa 3.8 Design an array to yield an optimum pattern . . . . . 88Exa 3.9 Calculate the directivity of a given linear broad side . 90

Exa 3.10 Calculate the Dolph Tchebysceff distribution which yieldthe optimum pattern. . . . . . . . . . . . . . . . . . . 90Exa 3.11 Design an array that will produce approximately a pat-

tern of the given figure. . . . . . . . . . . . . . . . . . 92Exa 3.12 Prove that the directivity of an end fire array . . . . . 93Exa 3.13 Prove that directivity for a broadside array of two iden-

tical isotropic . . . . . . . . . . . . . . . . . . . . . . 94Exa 3.14 Calculate the Dolph Tchebyscheff distribution which yield

the optimum pattern. . . . . . . . . . . . . . . . . . . 95Exa 3.15 Determine Dolph Tchebyscheff current distribution for

the minimum beamwidth of a linear in phase broad side

array of eight isotropic source . . . . . . . . . . . . . . 97Exa 3.16 Find the directivity of linear broad side . . . . . . . . 99Exa 3.17 Find the directivity of linear end fire . . . . . . . . . . 100Exa 3.18 Find the directivity of a linear end fire . . . . . . . . . 100Exa 3.19 Define antenna gain and directivity. . . . . . . . . . . 101

8


10/176

Exa 3.20 Find the array length and width and what will be these

value for a broad side array . . . . . . . . . . . . . . . 102Exa 3.21 Derive the expression for beam width . . . . . . . . . 103Exa 3.22 Find the FNBW and HPBW for a broad side linear array 104Exa 3.23 Find the location of the first nulls on a either side of

beam center . . . . . . . . . . . . . . . . . . . . . . . 105Exa 3.24 Calculate the radiated power and also FNBW of the

array . . . . . . . . . . . . . . . . . . . . . . . . . . . 106Exa 3.25 Find the array length and width of the major lobe and

what will be these values for broadside array . . . . . 106Exa 4.1 Design a log periodic antenna for a broadcast band . . 108Exa 4.2 Find the dimenssions of a three element . . . . . . . . 109

Exa 4.3 What is the gain in dB and the beam width of a helicalantenna . . . . . . . . . . . . . . . . . . . . . . . . . . 109

Exa 4.4 How large is the dish diameter . . . . . . . . . . . . . 110Exa 4.5 What is the change in gain and beam width . . . . . 111Exa 4.6 what is the change in gain. . . . . . . . . . . . . . . . 111Exa 4.7 Calculate the beamwidth and gain as a power ratio and

in dB . . . . . . . . . . . . . . . . . . . . . . . . . . . 112Exa 4.8 What are the dimensions of the elements. . . . . . . . 112Exa 4.9 Calculate the power gain of an optimum horn antenna 113Exa 4.10 Calculate the peak value of the magnetic field intensity

H of the RF wave . . . . . . . . . . . . . . . . . . . . 114Exa 4.11 Calculate the radiation resistance. . . . . . . . . . . . 114Exa 4.12 Estimate the diameter of the mouth and the half power

beam width of the antenna . . . . . . . . . . . . . . . 115Exa 4.13 Find the terminal resistance of complementary slot . . 116Exa 4.14 Estimate the diameter and the effective aperture of a

paraboloidal reflector antenna. . . . . . . . . . . . . . 116Exa 4.15 Calculate the antenna gain in dB . . . . . . . . . . . . 117Exa 4.16 Determine the gain beamwidth and capture area for a

parabolic antenna . . . . . . . . . . . . . . . . . . . . 117Exa 4.17 Calculate the gain of the horn antenna . . . . . . . . . 118

Exa 4.18 Estimate the diameter of the paraboloidal reflector . . 119Exa 4.19 Estimate the diameter and effective aperture . . . . . 119Exa 4.20 Estimate the diameter of the mouth and the half power

beamwidth . . . . . . . . . . . . . . . . . . . . . . . . 120Exa 4.21 What is the directivities of these two antennas . . . . 120

9


11/176

Exa 4.22 Calculate the directivity in dB . . . . . . . . . . . . . 121

Exa 4.23 Find out the length and width and half flare angles . . 122Exa 4.24 Calculate the angular aperture for paraboloidal reflectorantenna . . . . . . . . . . . . . . . . . . . . . . . . . . 123

Exa 4.25 Calculate the peak value of the magnetic field intensityH of the radio wave . . . . . . . . . . . . . . . . . . . 124

Exa 4.26 Calculate the input voltage to the receiver . . . . . . . 125Exa 4.27 Estimate the voltage across the capacitor . . . . . . . 125Exa 4.28 Calculate the max emf in the loop . . . . . . . . . . . 126Exa 4.29 Calculate the beamwidth between first null and what

will be its gain in dB. . . . . . . . . . . . . . . . . . . 127Exa 4.30 What should be minimum distance between primary

and secondary antenna . . . . . . . . . . . . . . . . . 127Exa 4.31 Calculate the directivity in dB . . . . . . . . . . . . . 128Exa 4.32 Find the received power . . . . . . . . . . . . . . . . 128Exa 4.33 Find the dimensions of three element. . . . . . . . . . 129Exa 4.34 How large is the dish diameter . . . . . . . . . . . . . 130Exa 4.35 What is the change in gain and beamwidth . . . . . . 130Exa 4.36 Calculate the beamwidth and gain as a power ratio in

dB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131Exa 4.37 Calculate the gain of the horn antenna . . . . . . . . . 131Exa 4.38 Define folde dipole antenna and drive its input impedance 132

Exa 4.39 Calculate the capture area of antenna . . . . . . . . . 133Exa 4.40 What is the antenna gain in decibels . . . . . . . . . . 134Exa 4.41 What is the corresponding value of illumination efficiency 134Exa 4.42 What is its gain . . . . . . . . . . . . . . . . . . . . . 135Exa 4.43 Calculate the power gain and half power point beam

width . . . . . . . . . . . . . . . . . . . . . . . . . . . 135Exa 4.44 Calculate the diameter of antenna and half power point

beam width . . . . . . . . . . . . . . . . . . . . . . . . 136Exa 4.45 Calculate the directivity and power gain as a ratio and

in dB . . . . . . . . . . . . . . . . . . . . . . . . . . . 137Exa 4.46 Calculate the aperture height . . . . . . . . . . . . . . 138

Exa 4.47 Determine the dimensions of the horn mouth and thedirective gain . . . . . . . . . . . . . . . . . . . . . . . 138

Exa 4.48 Calculate the gain of the transmitting antenna . . . . 139Exa 4.49 Calculate the gain and half power beam widths . . . . 140Exa 4.50 Calculate the HPBW and directivity . . . . . . . . . . 141

10


12/176

Exa 4.51 Calculate the number of turns and directivity in dB and

the half power point beam width in degree and axialratio of the helix . . . . . . . . . . . . . . . . . . . . . 141Exa 5.1 Calculate max line of sight range and the field strength

and also calculate the distance . . . . . . . . . . . . . 143Exa 5.2 Calculate the field strength . . . . . . . . . . . . . . . 144Exa 5.3 What will be the range for which the MUF is ten MHz 144Exa 5.4 Calculate the max electron concentrations of the layers 145Exa 5.5 What is the critical frequency for the reflection at ver-

tical incidence . . . . . . . . . . . . . . . . . . . . . . 145Exa 5.6 What is the max distance and what is the radio horizon

in this case . . . . . . . . . . . . . . . . . . . . . . . . 146

Exa 5.7 Find the basic path loss . . . . . . . . . . . . . . . . . 146Exa 5.8 Find the max range of a tropospheric transmission . . 147Exa 5.9 Find the range of LOS system . . . . . . . . . . . . . 147Exa 5.10 At what frequency a wave must propagate for the D

region . . . . . . . . . . . . . . . . . . . . . . . . . . . 148Exa 5.11 What will be the range for which the MUF is twelve MHz 148Exa 5.12 What is the max distance and the radio horizon in this

case . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149Exa 5.13 What is the critical frequency for the reflection at ver-

tical incidence . . . . . . . . . . . . . . . . . . . . . . 149

Exa 5.14 Find the basic path loss . . . . . . . . . . . . . . . . . 150Exa 5.15 Find the field strength at a distance of twenty km . . 150Exa 5.16 Determine the ground range for which this frequency is

the MUF . . . . . . . . . . . . . . . . . . . . . . . . . 151Exa 5.17 Determine the transmitter power required . . . . . . . 152Exa 5.18 Determine the strength of its ground wave . . . . . . . 153Exa 5.19 Calculate the transmission path distance for an iono-

spheric transmission . . . . . . . . . . . . . . . . . . . 154Exa 5.20 Find the effective area . . . . . . . . . . . . . . . . . . 154Exa 5.21 Calculate the open circuit voltage . . . . . . . . . . . 155Exa 5.22 Calculate the field strength at a receiving antenna . . 155

Exa 5.23 Calculate the the attenuation . . . . . . . . . . . . . . 156Exa 5.24 Explain what is meant by the gyro frequency and Cal-

culate the max range obtain able in a single hop trans-mission utilizing . . . . . . . . . . . . . . . . . . . . . 157

11


13/176

Exa 5.25 Calculate the max range obtainable in single hop trans-

mission utilizing E layer . . . . . . . . . . . . . . . . . 157Exa 5.26 Calculate the max range obtainable in single hop trans-mission utilizing D layer . . . . . . . . . . . . . . . . . 158

Exa 5.27 Find the virtual heightof the reflected layer . . . . . . 158Exa 5.28 Calculate the max line of sight range and the field strength

and also distance . . . . . . . . . . . . . . . . . . . . . 159Exa 5.29 Calculate the power density reating the moon surface. 160Exa 5.30 What is the max disance along the surface of the earth 160Exa 5.31 What will be the range for which the MUF is twenty

MHz. . . . . . . . . . . . . . . . . . . . . . . . . . . . 161Exa 5.32 Calculate the power received by an antenna . . . . . . 161

Exa 5.33 What is the max power received by the receiver . . . . 162Exa 5.34 Calculate the MUF for the given path . . . . . . . . . 163Exa 5.35 Calculate the value of frequency at which an electro-

magnetic wave must be propagate . . . . . . . . . . . 163Exa 5.36 Determine the ground range for which this frequency is

MUF . . . . . . . . . . . . . . . . . . . . . . . . . . . 164Exa 5.37 At what frequency a wave must propogate for the D

regions . . . . . . . . . . . . . . . . . . . . . . . . . . 165Exa 5.38 Find the received power . . . . . . . . . . . . . . . . 165Exa 5.39 Explain the Directivity polarization and virtual height 166

Exa 5.40 Calculate the LOS range and field strength . . . . . . 167Exa 5.41 Find the field strenght . . . . . . . . . . . . . . . . . . 167Exa 5.42 What is standing wave ratio and explain how it is mea-

sured experimentally . . . . . . . . . . . . . . . . . . . 168Exa 5.43 Calculate the value of the frequency . . . . . . . . . . 168Exa 5.44 What will be the effects of earth magnetic field on re-

fractive index of th eionosphere . . . . . . . . . . . . . 169Exa 5.45 At what frequency a wave must propogate for D region

and what is the critical frequency. . . . . . . . . . . . 170Exa 5.46 Find the skip distance . . . . . . . . . . . . . . . . . . 171Exa 5.47 What is the max power thet can be received. . . . . . 172

Exa 5.48 Find the max range of the radar and also the max rangewhen frequency is doubled. . . . . . . . . . . . . . . . 172

Exa 5.49 Find the max allowable distance between the two an-tennas . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

Exa 5.50 What is the voltage available at the terminals . . . . . 174

12


14/176

Exa 5.51 What transmitter power is required for a received signal 175

13


15/176

Chapter 1

Eletromagnetic Field Radiation

Scilab code Exa 1.1 What is the strength of a magnetic field H in freespace

1 / / Ex : 1 . 12 clc ;

3 clear ;

4 close ;

5 E = 2 ; // e l e c t r i v f i e l d s t r e n g t h i n V/m

6 n = 1 2 0 * % p i ;7 H = E / n ; // s t r e n g t h o f a m ag ne ti c f i e l d H8 printf ( The s t r e n g t h o f a m a g n et i c f i e l d H = %f mA/

m e t e r , H * 1 0^ 3) ;

Scilab code Exa 1.2 Find out the field strength

1 / / Ex : 1 . 22 clc ;

14


16/176

3 clear ;

4 close ;5 W = 6 2 5 * 1 0 ^ 3 ; / / p ow er i n W6 r = 3 0 * 1 0 ^ 3 ; // i n m7 Erms=( sqrt ( 9 0 * W ) ) / r ; / / t h e f i e l d s t r e n g t h i n V/m8 printf ( The f i e l d s t r e n g t h = %d mV/ m e t e r , E rm s

* 1 0 ^ 3 ) ;

Scilab code Exa 1.3 Calculate the radiation resistance

1 / / Ex : 1 . 32 clc ;

3 clear ;

4 close ;

5 f = 1 0 ; / / f r e q u e n c y i n MHz6 l e = 6 0 ; // h e i g h t o f a nt e n na i n m

7 y = 3 0 0 / f ; // w av el en gt h i n m8 R r = ( 1 6 0 * % p i ^ 2 * l e ^ 2 ) / y ^ 2 ; // r a d i a t i o n r e s i s t a n c e i n

ohm9 printf ( The r a d i a t i o n r e s i s t a n c e = %f Kohm , Rr

/ 1 0 0 0 ) ;

Scilab code Exa 1.4 What is the power radiated and also what is the ef-ficiency of the antenna

15


17/176

1 / / Ex : 1 . 4

2 clc ;3 clear ;

4 close ;

5 f = 4 0 0 0 0 ; // f r e q ue n cy i n Hz6 f 1 = 0 . 0 4 0 ; // f r e q u e n c y i n MHz7 l e = 1 0 0 ; // h e i g h t o f a n t e n na i n m8 I r m s = 4 5 0 ; // c u r r e n t i n Amp9 R t = 1 . 1 2 ; // t o t a l r e s i s t a n c e i n ohm

10 y = 3 0 0 / f 1 ; // w av el en gt h i n m11 R r = ( 1 6 0 * % p i ^ 2 * l e ^ 2 ) / y ^ 2 ; // r a d i a t i o n r e s i s t a n c e i n

ohm

12 W = I r m s ^ 2 * R r ; // power r a d i a t e d i n Watts13 n = R r / R t ; // e f f i c i e n c y o f t h e a n t e n n a14 printf ( The p o we r r a d i a t e d = % f KW , W / 1 00 0) ;15 printf ( \n The e f f i c i e n c y o f t he a nt en na = %f %% , n

* 1 0 0 ) ;

Scilab code Exa 1.5 How much power will an antenna having a radiationrasistance of fifty ohms

1 / / Ex : 1 . 52 clc ;

3 clear ;

4 close ;

5 I = 2 0 ; // c u r r e nt i n amp6 R r = 5 0 ;

// r a d i a t i o n r e s i s t a n c e i n ohm7 W r = I ^ 2 * R r ; // r a d i at e d power i n W8 printf ( The r a d i a t e d p o we r = %d W , Wr ) ;

16


18/176

Scilab code Exa 1.6 What is the radiation resistance of an antenna

1 / / Ex : 1 . 62 clc ;

3 clear ;

4 close ;

5 I = 1 5 ; // c u r r e nt i n amp6 W = 5 0 0 0 ; // r a d i at e d power i n W7 R r = W / I ^ 2 ; // r a d i a t i o n r e s i s t a n c e i n ohm8 printf ( The r a d i a t i o n r e s i s t a n c e = %f ohm , Rr );

Scilab code Exa 1.7 How much current flows into the antenna

1 / / Ex : 1 . 72 clc ;

3 clear ;

4 close ;

5 W = 1 0 * 1 0 0 0 ; // r a d i at e d power i n W6 R r = 7 5 ; // r a d i a t i o n r e s i s t a n c e i n ohm

7 I = sqrt ( W / R r ) ;// c u r r e n t i n amp8 printf ( The c u r r e n t = % f Amp , I ) ;

17


19/176

Scilab code Exa 1.8 Calculate the strength of electric field

1 / / Ex : 1 . 82 clc ;

3 clear ;

4 close ;

5 W = 1 0 0 * 1 0 0 0 ; // r a d i a t e d power i n W6 r = 1 0 0 * 1 0 0 0 ; // d i st a n c e i n m7 Erms=( sqrt ( 9 0 * W ) ) / r ; / / s t r e n g t h o f e l e c t r i c f i e l d i n

V/m8 printf ( The st r e ng t h of e l e c t r i c f i e l d = %f V/m ,

E r m s ) ;

Scilab code Exa 1.9 Estimate the effective height of the antenna

1 / / Ex : 1 . 92 clc ;

3 clear ;

4 close ;

5 I r m s = 2 5 ; / / c u r r e n t i n Amp6 f = 0 . 1 5 0 ; / / f r e q u e n cy i n MHz7 y = 2 0 0 0 ;

8 E r m s = 1 . 5 * 1 0 ^ - 3 ; / / s t r e n g t h o f e l e c t r i c f i e l d i n V/m9 r = 2 5 * 1 0 0 0 ; // d i s t a n ce i n m

18


20/176

10 l e = ( E r m s * y * r ) / ( 6 0 * % p i * I r m s ) ; // e f f e c t i v e h ei gh t o f

a nt en na i n m11 printf ( The e f f e c t i v e h e i g h t o f a nt e nn a = %f m , le );

Scilab code Exa 1.10 Find the field strength and the power radiated

1 / / E x : 1 . 1 02 clc ;

3 clear ;

4 close ;

5 l e = 1 0 0 ; // e f f e c t i v e h ei gh t o f a n t e n na i n m6 I r m s = 1 0 0 ; // c u r r e n t i n Amp7 f = 0 . 3 0 0 ; / / f r e q u e n cy i n MHz8 r = 1 0 * 1 0 0 0 ; // d i s t a n ce i n m9 y = 3 0 0 / f ; // i n m

10 E r m s = ( 1 2 0 * % p i * I r m s * l e ) / ( y * r ) ; / / s t r e n g t h o f e l e c t r i cf i e l d i n V/m

11 R r = 1 6 0 * ( % p i ^ 2 ) * ( l e / y ) ^ 2 ; // r a d i a t i o n r e s i s t a n c e i nohm

12 W = I r m s ^ 2 * R r ; // r a d i a t e d p ower i n Watt13 printf ( The st r e ng t h of e l e c t r i c f i e l d = %f mV/m ,

E r m s * 1 0 0 0 ) ;

14 printf ( \n The r a d i a t e d p ow er = % f KW , W / 1 00 0) ;

19


21/176

Scilab code Exa 1.11 Calculate the power radiated

1 / / E x : 1 . 1 12 clc ;

3 clear ;

4 close ;

5 l e = 1 0 ; // e f f e c t i v e h e i gh t o f a n t e n n a i n m6 I r m s = 5 0 ; / / c u r r e n t i n Amp7 f = 0 . 6 0 0 ; / / f r e q u e n cy i n MHz8 y = 3 0 0 / f ; // i n m9 R r = 1 6 0 * ( % p i ^ 2 ) * ( l e / y ) ^ 2 ; // r a d i a t i o n r e s i s t a n c e i n

ohm

10 W = I r m s ^ 2 * R r ; // r a d i a t e d p ower i n Watt11 printf ( The r a d i a t e d p o we r = %f KW , W / 1 00 0) ;

Scilab code Exa 1.12 Calculate the radiation resistance of current ele-

ments

1 / / E x : 1 . 1 22 clc ;

3 clear ;

4 close ;

5 / / d l =y / 5 06 / / t h en d l / y =( (y / 5 0 ) / y = 1/ 50 )7 d l _ y = 1 / 5 0 ; // t h e v al ue o f d l /y8 R r = 8 0 * % p i ^ 2 * ( d l _ y ^ 2 ) ; // R ad ia t i on r e s i s t a n c e i n ohm9 printf (

The r a d i a t i o n r e s i s t a n c e = %f ohm, Rr );

20


22/176

Scilab code Exa 1.13 Calculate the power radiated and what is its radia-tion resistance

1 / / E x : 1 . 1 32 clc ;

3 clear ;

4 close ;

5 // Prad=n( pi /3 ) ( I o d l / y ) 2 , w he re n =120 p i & y i sw a v e l e n g t h

6 // P r ad= 120 p i ( pi /3) ( 1 0 0 y / 1 6y )7 P r a d = 1 2 0 * 3 . 1 4 * ( 3 . 1 4 / 3 ) * ( 1 0 0 / 1 6 ) ^ 2 ; // p ower r a d i a t e d

i n W at ts8 // Rr=80 p i ( y / 1 6 y ) 29 R r = 8 0 * 3 . 1 4 ^ 2 * ( 1 / 1 6 ) ^ 2 ; // t h e r a d i a t i o n r e s i s t a n c e i n

ohm

10 printf ( The p ower r a d i a t e d = %f w a tt s , P ra d ) ;11 printf ( \n The r a d i a t i o n r e s i s t a n c e = %f ohm , Rr );

Scilab code Exa 1.14 what is the electric field

1 / / E x : 1 . 1 42 clc ;

3 clear ;

4 close ;

21


23/176

5 r = 5 * 1 0 0 0 ; // d i s t a n c e i n m

6 r 1 = 1 0 * 1 0 0 0 ; // d i st a n c e i n m7 W = 1 ;8 Erms=( sqrt ( 9 0 * W ) ) / r ; / / e l e c t r i c f i e l d s t r e n g t h a t a

d i s t a n v e 5 km9 E r m s 1 = ( sqrt ( 9 0 * W ) ) / r 1 ; / / e l e c t r i c f i e l d s t r e n g t h a t

a d i s t a n v e 10 km10 E _ E 1 = E r m s / E r m s 1 ; / / t h e r a t i o o f e l e c t r i c f i e l d

s t r e n g t h s11 E r m s = 1 0 ; // e l e c t r i c f i e l d st r e ng t h i n mV/m12 E r m s 2 = E r m s / E _ E 1 ; // e l e c t r i c f i e l d st r e ng t h i n mV/m

a t a d i s t a n c e o f 10 km

13 printf ( The e l e c t r i c f i e l d s t r e n g t h i n mV/m a t ad i s t a n c e o f 1 0 km = %d mV/m , E rm s2 ) ;

Scilab code Exa 1.15 Calculate the antenna current at a distance of five

eight wavelength away from the feed point

1 / / E x : 1 . 1 52 clc ;

3 clear ;

4 close ;

5 I r m s = 1 0 ; // rms v al ue o f c u r r e nt i n amp6 // Erms=(120p i Ir ms l e ) / y r , w he r e y= w a v e l e n g t h7 // Erms=(120p i1 0 ( 3 y / 2 ) ) / y r=1200p i3/2r =1800p i

/ r V/m8 // now , Erms1=120 p i I r m s 1 5 y / ( 8 y r )=75 p i I r m s 1 / r9 / / now e q u a t e t h e s e two Erms , we h av e

10 / / 1 8 00p i / r =75 p i I r m s1 / r i . e . , I r m s 1 = 18 00 /7 511 I r m s 1 = 1 8 0 0 / 7 5 ; // a nt en na c u r r e n t i n amp12 printf ( The a n t en n a c u r r e n t = %d amp , I rm s1 ) ;

22


24/176

Scilab code Exa 1.16 Determine the field strength of the radiated fieldproduced

1 / / E x : 1 . 1 62 clc ;

3 clear ;

4 close ;

5 r = 1 0 0 0 ; // d i s t a n ce i n m6 l = 1 ; // l e n gt h i n m7 I r m s = 5 ; // c u r r e n t i n Amp8 f = 1 ; // f r e q u e n c y i n MHz9 y = 3 0 0 / f ; / / W av el en gt h i n m

10 l e = ( 2 / % p i ) * l ; // e f f e c t i v e l en gt h i n m11 E r m s = ( 1 2 0 * % p i * l e * I r m s ) / ( y * r ) ; // f i e l d s t r e n g t h i n V/

m

12 printf ( The f i e l d s tr en g th = %d mV/m , E rm s * 1 00 0) ;

Scilab code Exa 1.17 Calculate the effective height of the antenna in me-ters

1 / / E x : 1 . 1 72 clc ;

3 clear ;

4 close ;

23


25/176

5 r = 1 0 0 ; // d i st a n c e i n m

6 I r m s = 3 2 ; / / c u r r e n t i n Amp7 y = 3 0 0 * 1 0 0 0 ; / / W av el en gt h i n m8 E r m s = 9 * 1 0 ^ - 3 ; / / f i e l d s t r e n g t h i n V/m9 l e = ( E r m s * y * r ) / ( 1 2 0 * 3 . 1 4 * I r m s ) ; // e f f e c t i v e h ei gh t o f

a nt en na i n m10 printf ( The e f f e c t i v e h e i g h t o f a nt e nn a = %f m , le )

;


1 / / E x : 1 . 1 82 clc ;

3 clear ;

4 close ;

5 I = 1 0 ; / / c u r r e n t i n Amp

6 W t = ( 1 0 * I ) ^ 2 / 3 0 ; / / p ow er i n Watt7 R t = W t / I ^ 2 ; // R ad i a ti on r e s i s t a n c e i n ohm8 printf ( The R a d i a ti o n r e s i s t a n c e = %f ohm , Rt );

Scilab code Exa 1.19 Find the radiation resistance and power radiatedand also antenna efficiency

1 / / E x : 1 . 1 92 clc ;

24


26/176

3 clear ;

4 close ;5 l e = 6 1 . 4 ; // e f f e c t i v e h ei gh t i n m6 I r m s = 5 0 ; // c u r r e n t i n amp7 y = 6 2 5 ; // w av el en gt h i n m8 R r = 1 6 0 * ( % p i * l e ) ^ 2 / ( y ^ 2 ) ; // R ad ia ti on r e s i s t a n c e o f

an a n te n na i n ohm9 W = ( I r m s ^ 2 ) * R r ; // p ower r a d i a t e d i n Watt

10 R t = 5 0 ; // t o t a l a n t e n na r e s i s t a n c e i n ohm11 n = R r / R t ; // e f f i c i e n c y12 printf ( The R a di a ti o n r e s i s t a n c e o f an a nt en na = %f

ohm , Rr );

13 printf ( \n The p ow er r a d i a t e d = % f KW , W / 1 00 0) ;14 printf ( \n The e f f i c i e n c y = %f %% , n * 1 00 ) ;

Scilab code Exa 1.20 What is the power radiated

1 / / E x : 1 . 2 02 clc ;

3 clear ;

4 close ;

5 l e = 4 9 . 1 2 ; // e f f e c t i v e h ei gh t i n m6 I r m s = 2 2 0 ; // c u r r e nt i n amp7 f = 3 7 . 5 ; // f r e q u e n c y i n KHz8 f 1 = f / 1 0 0 0 ; / / f r e q u e n c y i n MHz9 y = 3 0 0 / f 1 ; // w av el en gt h i n m

10 R r = 1 6 0 * ( % p i ^ 2 ) * ( l e / y ) ^ 2 ;// R ad ia ti on r e s i s t a n c e i nohm

11 W = I r m s ^ 2 * R r ; // power r a di a t e d i n w a tt s12 printf ( The p ow er r a d i a t e d = %f kW , W / 1 00 0) ;

25


27/176


1 / / E x : 1 . 2 12 clc ;

3 clear ;

4 close ;

5 W = 3 5 * 1 0 ^ 3 ; / / p ow er i n Wa tts6 r = 6 0 * 1 0 ^ 3 ; // i n m7 Erms=( sqrt ( 9 0 * W ) ) / r ; / / f i e l d s t r e n g t h i n mV/m8 printf ( The f i e l d st r e ng t h = %f mV/m , E rm s * 1 00 0) ;

Scilab code Exa 1.22 At what distance from a sixty cycle circuit is theradiation field approximately

1 / / E x : 1 . 2 22 clc ;

3 clear ;

4 close ;

5 f = 6 0 * 1 0 ^ - 6 ; / / f r e q u e n cy i n MHz

6 y = 3 0 0 / f ; // w av el en gt h i n m7 r = y / ( 2 * 3 . 1 4 ) ; // d i s t a n c e i n m8 printf ( The d i s t a n c e = %f 106 m , r / 1 0^ 6) ;

26


28/176


1 / / E x : 1 . 2 32 clc ;

3 clear ;

4 close ;

5 W = 1 * 1 0 ^ 3 ; / / p ow er i n W atts6 r = 1 0 ^ 3 ; // i n m7 Erms=( sqrt ( 3 0 * W ) ) / r ; / / f i e l d s t r e n g t h i n mV/m8 printf ( The f i e l d st r e ng t h = %f mV/m , E rm s * 1 00 0) ;

Scilab code Exa 1.24 Find the velocity of a plane wave in a loss lessmedium

1 / / E x : 1 . 2 42 clc ;

3 clear ;

4 close ;

5 E r = 1 5 ; // r e l a t i v e p e r m i t t i v i t y

6 u r = 5 ; // r e l a t i v e m o b i l i t y7 B = 1 / sqrt ( E r * u r ) ;

8 A = 3 * 1 0 ^ 8 ; // t he v a lu e o f 1/ s q r t ( Eouo )9 V = A * B ; // v e l o c i t y o f p ro pa ga ti on i n v o l t

10 printf ( The f i e l d s t r e n g t h = %f 1 0 7 m / s , V / 1 0^ 7) ;

27


29/176

Scilab code Exa 1.25 What is the strength of a magnetic field H in freespace

1 / / E x : 1 . 2 5

2 clc ;3 clear ;

4 close ;

5 E = 6 ; / / e l e c t r i c f i e l d s t r e n g t h i n V/m6 n = 1 2 0 * % p i ; // e f f i c i e n c y7 H = E / n ; / / m a g n e t i c f i e l d s t r e n g t h i n Amp/m8 printf ( The m a g n e t i c f i e l d s t r e n g t h = %f mA/m , H

* 1 0 0 0 ) ;

Scilab code Exa 1.26 Calculate the field strength at a distance of twentyfive km

1 / / E x : 1 . 2 62 clc ;

3 clear ;

4 close ;

5 l = 7 0 ; // a nt en na h e ig h t i n m6 l e = 2 * l / % p i ; // e f f e c t i v e l en gt h i n m7 I r m s = 2 5 ; // c u r r e n t i n amp

28


30/176

8 f = 1 0 ; / / f r e q u e n c y i n MHz

9 y = 3 0 0 / f ; // w av el en gt h i n m10 r = 2 5 * 1 0 ^ 3 ; // d i s t a n ce i n m11 E r m s = ( 1 2 0 * % p i * l e * I r m s ) / ( y * r ) ; / / f i e l d s t r e n g t h i n mV

/m12 printf ( The f i e l d s tr en g th = %d mV/m , E rm s * 1 0^ 3) ;


1 / / E x : 1 . 2 72 clc ;

3 clear ;

4 close ;

5 l e = 5 0 ; // e f f e c t i v e h e i gh t o f a n t e n n a i n m6 f = 1 0 ; / / f r e q u e n c y i n MHz7 y = 3 0 0 / f ; // w av el en gt h i n m

8 R r = 1 6 0 * ( % p i ^ 2 ) * ( l e / y ) ^ 2 ; // R ad ia ti on r e s i s t a n c e i nohm

9 printf ( The R a di a ti o n r e s i s t a n c e = %f kohm , Rr/ 1 0 0 0 ) ;

Scilab code Exa 1.28 Derive an expression for the gain of a half waveantenna

1 / / E x : 1 . 2 8

29


31/176

2 clc ;

3 clear ;4 close ;

5 // G=Pr/ pi6 // G=Pr /( Wi/4%pi r 2 )7 // G=4%p i r 2Pr/Wi8 / / P r =( 30 I r m s 2 / % p i r 2 ) ( ( c os ( %pi /2 ( cos ( x ) ) ) ) 2 /(

s i n ( x ) 2 )9 / / t h i s i s max when x =90 d e g r e e

10 / / t h e n Pr = (3 0 Ir ms 2/( %pi r 2 ) )11 // Wi = 73. 14I r m s 212 / / t h e n G= (4%pi r 230I r m s 2 ) / ( 7 3 . 1 4I r m s 2%pi r

2 )13 / / G = 1 2 0 / 7 3 . 1 414 G = 1 2 0 / 7 3 . 1 4 ; / / G ai n15 g = 1 0 * log ( G ) / log ( 1 0 ) ; / / Gain i n dB16 printf ( The Gain = %f dB , g ) ;

Scilab code Exa 1.29 Calculate the antenna current at a distance of sev-enth eighth wavelength away from the feed point

1 / / E x : 1 . 2 92 clc ;

3 clear ;

4 close ;

5 I r m s = 1 5 ; / / c u r r e n t i n Amp6

// Erms=(120%pi Ir ms l e ) /( y r )7 / / h e r e I r m s =15 amp a nd l e =3y / 28 / / t he n9 // Erms=(120%pi 153 y / 2 ) / ( y r )

10 // Erms=2700%pi /r

30


32/176

11 / / Now , l e =7y , t h e n

12 // Erms1=(120%pi I r m s 1 7 y ) / ( y r )13 // Erms1=105%pi /r14 // and Erms=Erms115 / / 2 7 00%pi/r=105%pi I r m s 1 / r16 / / I r m s 1 = 2 70 0 /1 0 517 I r m s 1 = 2 7 0 0 / 1 0 5 ; / / c u r r e n t i n Amp18 printf ( The c u r r e n t = % f Amp , I rm s1 ) ;

Scilab code Exa 1.30 Find the average energy density

1 / / E x : 1 . 3 02 clc ;

3 clear ;

4 close ;

5 P r = 1 5 ; / / p o y n t i n g v e c t o r i n W/m 2

6 v = 3 * 1 0 ^ 8 ; // a ve ra ge v e l o c i t y ( t h e s pe e d o f l i g h t )7 d a v = P r / v ; // a v e r ag e e n er g y d e n s i t y i n W S /m 3 o r J /m

38 d a v 1 = d a v * 1 0 ^ 9 ; // a v e r ag e e n er g y d e n s i t y i n nJ /m 39 printf ( The a v e r a g e e n e r g y d e n s i t y = %d n J /m 3 ,

d a v 1 ) ;

Scilab code Exa 1.31 Determine the radiation resistance

31


33/176

1 / / E x : 1 . 3 1

2 clc ;3 clear ;

4 close ;

5 l e _ y = 1 / 1 0 ; // t he r a t i o o f l e t o y6 R r = 1 6 0 * ( % p i ^ 2 ) * ( l e _ y ) ^ 2 ; // r a d i a t i o n r e s i s t a n c e i n

ohm7 printf ( The r a d i a t i o n r e s i s t a n c e = %f ohm , Rr );

Scilab code Exa 1.32 What is the value of electric field strength at a pointtwenty five away in the same direction

1 / / E x : 1 . 3 22 clc ;

3 clear ;

4 close ;

5 r = 1 5 * 1 0 ^ 3 ; // d i s t a n ce i n m6 r 1 = 2 5 * 1 0 ^ 3 ; // d i st a n c e i n m7 E r m s _ E r m s 1 = r 1 / r ; // t he r a t i o o f Erms t o Erms18 E r m s = 2 5 ; // mV/m;/ / e l e c t r i c f i e l d s tr en gt h in mV/m9 E r m s 1 = E r m s / E r m s _ E r m s 1 ; / / e l e c t r i c f i e l d s t r e n g t h i n

mV/m a t a p o i nt 25 away i n t he same d i r e c t i o n10 printf ( The e l e c t r i c f i e l d s tr en g th = %d mV/ meter ,

E r m s 1 ) ;

32


34/176

Scilab code Exa 1.33 Find the velocity of propogation and the wavelength

and the impedence of the medium and also the rms electric field E

1 / / E x : 1 . 3 32 clc ;

3 clear ;

4 close ;

5 f = 2 0 * 1 0 ^ 6 ; // f r eq u en c y i n Hz6 P = 1 0 ; / / p o y n t i ng v e c t o r i n W/m 27 u = 4 ; // r e l a t i v e m o b i l i t y8 E r = 5 ; // r e l a t i v e p e r m e ab i l i t y9 c = 3 * 1 0 ^ 8 ; // t he s pe ed o f l i g h t = 1/ s q r t ( uoEo )

10 V = c / sqrt ( u * E r ) ;// t he v e l o c i t y o f p r o pa ga t i on i n m/ s11 y = V / f ; // w av el en gt h i n m12 E = sqrt ( P * 1 2 0 * % p i * sqrt ( 4 / 5 ) ) ; // e l e c t r i c f i e l d i n V/m13 E r m s = sqrt ( E ^ 2 / sqrt ( 2 ) ) ; // rms e l e c t r i c f i e l d14 E = sqrt ( 2 ) * E r m s ; // e l e c t r i c f i e l d15 n = E ^ 2 / P ; / / i mp ed an ce o f t h e medium i n ohm16 printf ( The v e l o c i t y o f p r op a ga t io n = %f 1 0 8 m / s ,

V / 1 0 ^ 8 ) ;

17 printf ( \n The w a v e l e n g t h = %f m , y ) ;18 printf ( \n The i m pe d an c e o f t h e medium = % f ohm , n )

;

19 printf ( \n The rms e l e c t r i c f i e l d = %f V/m , E rm s ) ;

Scilab code Exa 1.34 At what distance in wavelength is the radiation com-

ponent of magnetic field three times the induction components

1 / / E x : 1 . 3 42 clc ;

3 clear ;

33


35/176

4 close ;

5 // 3 ( 1 / r 2 )=w/ ( r c )6 / / 3 / r =(2%p if /c )7 / / r = ( 1 / (2%pi) ) 38 r = ( 1 / ( 2 * % p i ) ) * 3 ; // d i s t a n c e i n t er ms o f y ( w av el en gt h

)9 r 1 = ( 1 / ( 2 * % p i ) ) * 5 0 ; // d i s t a n c e i n t e r m s o f y (

w a v e l e n g t h )10 printf ( The d i s t a n c e when c om po ne nt o f M f i e l d t h r e e

t i m es t h e i n d u c t i o n f i e l d = % f y , r ) ;11 printf ( \n The d i s t a n c e when co mp on ent o f M f i e l d 50

t i m es t h e i n d u c t i o n f i e l d = %f y , r1 );


1 / / E x : 1 . 3 5

2 clc ;3 clear ;

4 close ;

5 W = 5 0 * 1 0 0 0 ; // r a d i at e d power i n W6 r = 9 0 * 1 0 0 0 ; // d i s t a n ce i n m7 Erms=( sqrt ( 9 0 * W ) ) / r ; / / s t r e n g t h o f e l e c t r i c f i e l d i n

V/m8 printf ( The st r e ng t h of e l e c t r i c f i e l d = %f mV/m ,

E r m s * 1 0 0 0 ) ;

34


36/176

Scilab code Exa 1.36 Find the velocity of a plane wave in a loss lessmedium

1 / / E x : 1 . 3 62 clc ;

3 clear ;

4 close ;

5 c = 3 * 1 0 ^ 8 ; // t h e s p e e d o f l i g h t i n m/ s6 u r = 1 ; // r e l a t i v e p e r m i t t i v i t y7 E r = 4 ; // r e l a t i v e p e r m e ab i l i t y8 v p = c / sqrt ( u r * E r ) ; // v e l o c i t y o f a p la ne wave9 printf ( The v e l o c i t y o f a p l an e wave = %f 1 0 8 m / s ,

v p / 1 0 ^ 8 ) ;

Scilab code Exa 1.37 Calculate the antenna current at a distance of sev-enth eighth wavelength away from the feed point

1 / / E x : 1 . 3 72 clc ;

3 clear ;4 close ;

5 I r m s = 1 5 ; / / c u r r e n t i n Amp6 // Erms=(120%pi Ir ms l e ) /( y r )7 / / h e r e I r m s =15 amp a nd l e =7y / 2

35


37/176

8 / / t he n

9 // Erms=(120%pi 157 y / 2 ) / ( y r )10 // Erms=6300%pi /r11 / / Now , l e =7y , t h e n12 // Erms1=(120%pi I r m s 1 7 y ) / ( y r )13 // Erms1=105%pi /r14 // and Erms=Erms115 / / 6 3 00%pi/r=105%pi I r m s 1 / r16 / / I r m s 1 = 6 30 0 /1 0 517 I r m s 1 = 6 3 0 0 / 1 0 5 ; / / c u r r e n t i n Amp18 printf ( The c u r r e n t = %d Amp , I rm s1 ) ;

Scilab code Exa 1.38 Determine the radiation resistance

1 / / E x : 1 . 3 82 clc ;

3 clear ;4 close ;

5 l e _ y = 1 / 1 5 0 ; // t h e r a t i o o f l e t o y6 R r = 1 6 * ( % p i ^ 2 ) * ( l e _ y ) ^ 2 ; // r a d i a t i o n r e s i s t a n c e i n

ohm7 printf ( The r a d i a t i o n r e s i s t a n c e = %f 10 3 ohm , Rr

* 1 0 0 0 ) ;

Scilab code Exa 1.39 What is the radiation resistance of an antenna

36


38/176

1 / / E x : 1 . 3 9

2 clc ;3 clear ;

4 close ;

5 P r = 1 0 * 1 0 ^ 3 ; / / p ow er i n Wa tts6 I = 1 8 ; / / c u r r e n t i n Amp7 R = P r / I ^ 2 ; // r a d i a t i o n r e s i s t a n c e o f a n a n t e n n a i n

ohm8 printf ( The r a d i a t i o n r e s i s t a n c e o f an a nt e n na = %f

ohm , R ) ;

Scilab code Exa 1.40 What is the bandwidth

1 / / E x : 1 . 4 02 clc ;

3 clear ;

4 close ;5 f o = 2 5 * 1 0 ^ 6 ; // f r e q ue n cy i n Hz6 Q = 4 0 ;

7 B _ W = f o / Q ; / / b an dw id th i n Hz8 printf ( The bandwidth = %d KHz, B _W / 1 0 00 ) ;

Scilab code Exa 1.41 Define radiation resistance and also Calculate theradiation resistance and efficiency

37


39/176

1 / / E x : 1 . 4 1

2 clc ;3 clear ;

4 close ;

5 R l = 1 . 5 ; // l o s s r e s i s t a n c e i n ohm6 l e _ y = 1 / 5 0 ; // t he r a t i o o f l e t o y7 R r = 8 0 * ( % p i ^ 2 ) * ( l e _ y ) ^ 2 ; // r a d i a t i o n r e s i s t a n c e i n

ohm8 R t = R l + R r ; // t o t a l r e s i s t a n c e i n ohm9 n = R r / R t ; // e f f e c i e n c y

10 printf ( The e f f e c i e n c y = %f %% , n * 1 00 ) ;

Scilab code Exa 1.42 What is the significance of electrostatic field andinduction field and also radiation field of the antenna and at what distancein wavelength the radiation component of magnetic field is hundred times ofthe induction component

1 / / E x : 1 . 4 22 clc ;

3 clear ;

4 close ;

5 / / 1 00 (1 / r 2 )=w/ ( r c )6 / / 1 0 0 / r = (2%p if / c )7 / / r = ( 1 / (2%pi) )1008 r = ( 1 / ( 2 * % p i ) ) * 1 0 0 ; // d i s t a n c e i n t e r m s o f y (

w a v e l e n g t h )9 printf (

The d i s t a n c e when c om po ne nt o f M f i e l d t h r e et i m es t h e i n d u c t i o n f i e l d = % f y , r ) ;

38


40/176

Scilab code Exa 1.43 Define retarded vector potential

1 / / E x : 1 . 4 32 clc ;

3 clear ;

4 close ;

5 printf ( R et ar de d v e c t o r p o t e n t i a l The v e c t o rp o t e n t i a l e x pr e s s i o n r e p r e s e n t s t h e s up erp o s i t i o n s o f v a ri o u s c u r r e n t e le me nt s I . dl , a t ad i s t a n t p oi nt P a t a d i s t a n c e o f r . I f t he se a res i mp l y a dded up , i t means an a s su m pt i on i s madet h a t t h e s e f i e l d e f f e c t s w hi ch a r e s u p er i mp os eda t t i m e t , a l l s t a r t e d from t he c u r r e n t e le me nt so f t he same v a lu e o f c u r r e n t and e ve n t ho ug h t he y

have t r a v e l l e d d i f f e r e n t . V a r y i n g d i s t a n c e s i n

o t h e r w or ds f i n i t e t im e o f p r o p a g a t io n h as b ee ni g n o re d whi ch i s n ot c o r r e c t . T hi s would h avebe en c o r r e c t p r o vi de d t he v e l o c i t y o f p r o p ag a ti o n

w ou ld h av e b ee n i n f i n i t e w hi ch i s a c t u a l l y n o t . ) ;

6 printf ( \n I f t h e e x p r e ss i o n f o r v ec to r p o t e n t i a l i nI n t e g r a t e d i t f o l l o w s t he t p o t e n t i a l due t o

v a r i o u s c u r r e nt e le me nt a r e added up l e t uss up po se t ha t c u r r e nt ( I ) i s i s t a nt a n e ou s c u r r e n t( I ) i n t he e le me nt be S i n u s o i d a l f u n c t i o n o f t im e

a s ) ;

7 printf ( \n I =Im . s i n ( w t ) , w h er e Im= max c u r r e n t ) ;8 printf ( \n I=I n s t a n t a n e o u s c u r r e n t ) ;9 printf ( \n w=2 hf , a n g u l a r f r e q u e n c y ) ;

39


41/176

Scilab code Exa 1.44 What is the power radiated and what is the effi-ciency of the antenna

1 / / E x : 1 . 4 42 clc ;

3 clear ;

4 close ;

5 c = 3 * 1 0 ^ 8 ; // t h e s p e e d o f l i g h t i n m/ s6 I r m s = 4 5 0 ; // c u r r e n t i n Amp7 d l = 1 0 0 ; // e f f e c t i v e l en gt h i n m8 f = 4 0 * 1 0 ^ 3 ; // f r eq u en c y i n Hz9 y = c / f ; // w av el en gt h i n m

10 w = 8 0 * % p i ^ 2 * I r m s ^ 2 * ( d l / y ) ^ 2 ; // power r a d i a t e d i nWatts

11 R r = 0 . 1 4 ; // r a d i a t i o n r e s i s t a n c e i n ohm

12 R t = 1 . 1 2 ; // t o t a l r e s i s t a n c e i n ohm13 n = R r / R t ; // e f f e c i e n c y14 printf ( The p ow er r a d i a t e d = %f kW , w / 1 00 0) ;15 printf ( \n The e f f e c i e n c y = %f %% , n * 1 00 ) ;

Scilab code Exa 1.45 Calculate the radiation resistance power radiatedand the efficiecy of an antenna

1 / / E x : 1 . 4 5

40


42/176

2 clc ;

3 clear ;4 close ;

5 l e = 6 9 . 9 6 ; // e f f e c t i v e l en gt h i n m6 I r m s = 5 0 ; / / c u r r e n t i n Amp7 R t = 5 0 ; // t o t a l r e s i s t a n c e i n ohm8 c = 3 * 1 0 ^ 8 ; // t h e s p e e d o f l i g h t i n m/ s9 f = 0 . 4 8 0 * 1 0 ^ 6 ; // f r e q ue n cy i n Hz

10 y = c / f ; // w av el en gt h i n m11 R r = 1 6 0 * % p i ^ 2 * ( l e / y ) ^ 2 ; // r a d i a t i o n r e s i s t a n c e i n ohm12 w = I r m s ^ 2 * R r ; // power r a d i a t e d i n Watts13 n = R r / R t ; // e f f e c i e n c y

14 printf ( The r a d i a t i o n r e s i s t a n c e = %f ohm , Rr );15 printf ( \n The p ow er r a d i a t e d = %f kW , w / 1 00 0) ;16 printf ( \n The e f f e c i e n c y = %f %% , n * 1 00 ) ;

Scilab code Exa 1.46 Find the radiation resistance and efficiency

1 / / E x : 1 . 4 62 clc ;

3 clear ;

4 close ;

5 R l = 1 . 5 ; // l o s s r e s i s t a n c e i n ohm6 d l _ y = 1 / 1 5 ; // t he r a t i o o f d l t o y ( w av el en gt h )7 R r = 8 0 * ( % p i ^ 2 ) * ( d l _ y ) ^ 2 ; // r a d i a t i o n r e s i s t a n c e i n

ohm8 R t = R l + R r ;

// t o t a l r e s i s t a n c e i n ohm9 n = R r / R t ; // e f f e c i e n c y10 printf ( The r a d i a t i o n r e s i s t a n c e = %f ohm , Rr );11 printf ( \n The e f f e c i e n c y = %d %% , n * 1 00 ) ;

41


43/176

Scilab code Exa 1.47 What is the power radiated

1 / / E x : 1 . 4 72 clc ;

3 clear ;

4 close ;

5 I = 1 0 ; / / p ea k c u r r e n t i n Amp6 I r m s = I / sqrt ( 2 ) ; / / rms c u r r e n t i n Amp7 A = 8 0 * I r m s ^ 2 ;

8 printf ( The t he v a lu e o f A = %f , A ) ;9 printf ( \n p ow er r a d i a t e d = 40 00 ( p i dl ) 2/y 2 ) ;

10 printf ( \n Where , y=w a v e l e n g t h & p i = 3 . 14 ) ;

Scilab code Exa 1.48 What is the strength of magnetic field H in freespace

1 / / E x : 1 . 4 82 clc ;

3 clear ;

4 close ;5 E = 6 0 ; / / e l e c t r i c f i e l d s t r e n g t h i n V/m6 n = 1 2 0 * % p i ; // e f f i c i e n c y7 H = E / n ; / / m a g n e t i c f i e l d s t r e n g t h i n Amp/m8 printf ( The m a g n e t i c f i e l d s t r e n g t h = %f A/m , H ) ;

42


44/176

Scilab code Exa 1.49 Calculate the radiated field strength and the totalpower radiated and also the radiation resistance

1 / / E x : 1 . 4 9

2 clc ;3 clear ;

4 close ;

5 c = 3 * 1 0 ^ 8 ; // s p e e d o f t h e l i g h t i n m/ s6 f = 1 0 * 1 0 ^ 6 ; // f r eq u en c y i n Hz7 y = c / f ; // w av el en gt h i n m8 I = 1 ; // c u r r e nt i n amp9 l = 1 ; // l e n gt h i n m

10 r = 5 0 0 * 1 0 ^ 3 ; // d i st a n c e i n m11 n = 1 2 0 * % p i ;

12 E x = ( n * I * l * sin ( % p i / 2 ) ) / ( 2 * r * y ) ; / / t h e m ag ni tu de o f e l e c t r i c f i e l d i n uV/m

13 H x = ( I * l * sin ( % p i / 2 ) ) / ( 2 * r * y ) ; / / t h e m ag ni tu de o f magn e t i c f i e l d i n AT/m

14 P m = ( 8 0 * % p i ^ 2 * I ^ 2 * l ^ 2 ) / ( y ^ 2 ) ; // the maximum powerr a d i at e d i n w at ts

15 P a v = ( 1 / 2 ) * P m ; // t he a v e ra ge power r a d i a t e d i n w at ts16 R r = 8 0 * % p i ^ 2 * ( l / y ) ^ 2 ; // t h e r a d i a t i o n r e s i s t a n c e i n

ohm17 printf ( The magni tude o f e l e c t r i c f i e l d = %f uV/m ,

E x * 1 0 ^ 6 ) ;

18 printf ( \n The m a gn i tu d e o f m a g n e t i c f i e l d = % f 10 8 AT/m, H x * 10 ^8 ) ;

19 printf ( \n The maximum p ow er r a d i a t e d = %f w a t t s ,P m ) ;

20 printf ( \n The a v e r ag e po wer r a d i a t e d = %f w a tt s ,

43


45/176

P a v ) ;

21 printf ( \n The r a d i a t i o n r e s i s t a n c e = %f ohm , Rr );

Scilab code Exa 1.50 Show the total far field electric field amplitude andalso Calculate the power that could be fed into a dipole antenna

1 / / E x : 1 . 5 02 clc ;

3 clear ;

4 close ;

5 V = 5 * 1 0 ^ - 3 ; // rms v al ue i n v o l t6 r = 3 * 1 0 ^ 3 ; // i n m et er7 R r = 7 3 ; // t h e r a d i a t i o n r e s i s t a n c e i n ohm8 / / The e l e c t r i c f i e l d i n t h e f a r r e g i o n may b e g i v e n

by9 / / Ex = ( 6 0 . p i . I m . s i n ( x ) / y . r ) e (j k o . r ) i n t e g r a t e ( (

co s ( ko z ) e ( jk o . z . co s ( x ) ) ) , z , y / 4 , y / 4 )10 / / Ex = ( 6 0 . p i . I m . s i n ( x ) / y . r ) e (j k o . r ) i n t e g r a t e

( ( 2 . co s ( ko ) ( co s ( ko . z ) . co s ( x )+j . s i n (ko . z ) . co s ( x ) ) , z ,0 , y /4 )

11 / / Ex = ( 6 0 . p i . I m . s i n ( x ) / y . r ) e (j k o . r ) i n t e g r a t e( ( 2 . co s ( ko . z ) . co s ( ko . z . co s ( x ) ) ) , z ,0 , y /4 )

12 // on i n t e g r a t i n g , we g et ,13 // Ex = (60Im/r ) ( c o s ( pi /2 . c os ( x ) ) / s i n ( x ) )14 E m a x = V * sqrt ( 2 ) ; / / t h e p ea k v a l u e o f f i e l d i n V/m15 / / on p u t t i n g x=90 d e g r e e i n Ex =(60Im/r ) ( co s ( pi /2 .

c o s ( x ) ) / s i n ( x ) ) , we g e t16 / / Emax=60Im / r , t h e n17 I m = E m a x * r / 6 0 ; / / max c u r r e n t i n amp18 P a v = ( I m ^ 2 / 2 ) * ( R r ) ; // t he a v er a ge power i n w at ts19 printf ( The e x p r e s s i o n o f t o t a l e l e c t r i c f i e l d

44


46/176

ampl i dude , Ex = (60Im/r ) ( c o s ( pi /2 . c os ( x ) ) / s i n ( x ) )

)20 printf ( \n The v a l u e o f t h e a v e ra g e po we r= %f w a tt s , P av ) ;

Scilab code Exa 1.51 Calculate the loss resistance and also Calculate thepower radiated and the ohmic loss and loss resistance

1 / / E x : 1 . 5 12 clc ;

3 clear ;

4 close ;

5 I = 4 ; // p ea k c u r r e n t i n Amp6 I r m s = I / sqrt ( 2 ) ; / / rms c u r r e n t i n Amp7 R r = 1 8 ; // r a d i a t i o n r e s i s t a n c e i n ohm8 P r = I r m s ^ 2 * R r ; / / p owe r r a d i a t e d i n Watts

9 R l = ( 0 . 1 * R r ) / 0 . 9 ; // l o s s r e s i s t a n c e i n ohm10 P l = I r m s ^ 2 * R l ; // ohmic l o s s i n Watt11 printf ( The p ow er r a d i a t e d = %f Wa tts , Pr );12 printf ( \n The l o s s r e s i s t a n c e = %d ohm , Rl );13 printf ( \n The ohmic l o s s = %f w at ts , Pl );

45


47/176

Chapter 2

Antenna Terminology

Scilab code Exa 2.1 What is the wavelength

1 / / Ex : 2 . 12 clc ;

3 clear ;

4 close ;

5 c = 3 * 1 0 ^ 8 ; // t h e s p e e d o f l i g h t i n m/ s6 f = 1 0 0 0 0 0 0 ; // f r eq u en c y i n Hz

7 y = c / f ; // w av el en gt h i n m8 printf ( The w a v e l e n g t h = %d m e te r , y ) ;

Scilab code Exa 2.2 What is the actual velocity of EM energy

1 / / Ex : 2 . 22 clc ;

3 clear ;

4 close ;

46


48/176

5 c = 3 * 1 0 ^ 8 ; // t h e s p e e d o f l i g h t i n m/ s

6 f = 0 . 7 5 ; // p r o p ag a ti o n f e c t o r7 v = c * f ; // a c tu a l v e l o i t y i n m/ s8 printf ( The a c t ua l v e l o i t y = %f 1 0 8 m e t e r / s e c , v

/ 1 0 ^ 8 ) ;

Scilab code Exa 2.3 What is the wavelength in vaccum and in air

1 / / Ex : 2 . 32 clc ;

3 clear ;

4 close ;

5 c = 3 * 1 0 ^ 8 ; // t h e s p e e d o f l i g h t i n m/ s6 f = 6 0 * 1 0 0 0 0 0 0 ; // f r e q ue n cy i n Hz7 y = c / f ; / / w a ve l en g th i n vaccum i n m8 y 1 = y * 0 . 9 8 ; // w a ve l en g th i n a i r i n m

9 printf ( The w a v e l e n g t h i n va cc um = %d m e te r , y ) ;10 printf ( \n The w av el en gt h i n a i r = %f m et er , y1 ) ;

Scilab code Exa 2.4 What is the directicity

1 / / Ex : 2 . 42 clc ;

3 clear ;

4 close ;

47


49/176

5 R r = 8 0 ; // r a d i a t i o n r e s i s t a n c e i n ohm

6 R l = 1 0 ; // l o ssr e s i s t a n c e i n ohm7 n = R r / ( R r + R l ) ; // e f f e c i e n c y8 G = 2 0 ; / / P ow er G ai n9 D = G / n ; // d i r e c t i v i t y

10 printf ( The d i r e c t i v i t y = %f , D ) ;


1 / / Ex : 2 . 52 clc ;

3 clear ;

4 close ;

5 d l _ y = 1 / 2 0 ; // t he r a t i o o f d l t o y ( w av el en gt h )6 R r = 8 0 * ( % p i ^ 2 ) * ( d l _ y ) ^ 2 ; // r a d i a t i o n r e s i s t a n c e i n

ohm

7 printf ( The r a d i a t i o n r e s i s t a n c e = %f ohm , Rr );

Scilab code Exa 2.6 Find the max directivity and compare it with its ex-act value

1 / / Ex : 2 . 62 clc ;

3 clear ;

4 close ;

48


50/176

5 x 1 r = 2 * % p i / 3 ; // i n r ad ia n

6 x 2 r = 2 * % p i / 3 ; // i n r ad ia n7 D = 4 * % p i / ( x 1 r ) ^ 2 ; // t h e max d i r e c t i v i t y8 / / Now , l e t us f i n d t he e xa ct v al ue o f t h e max

d i r e c t i v i t y and c ompare t he r e s u l t9 // y=Bo . co s ( x )

10 // ymax=Bo11 / / Prad= i n t e g r a t i o n o f ( Bo . c o s ( x ) . s i n ( x ) ) w it h l i m i t

0 t o 2p i12 P = i n t e g r a t e ( s i n ( 2 x ) , x ,0,2*3.14);13 // Prad=%piBoi n t e g r a t i o n o f ( Bo . c o s ( x ) . s i n ( x ) )

w i t h l i m i t 0 t o 2p i

14 / / t h e n we g e t P ra d=%piBo15 // Do=(4p i ymax)/Prad=4 p i Bo/%piBo16 D o = 4 ; // e xa ct v al ue o f t h e max d i r e c t i v i t y17 printf ( The max d i r e c t i v i t y = %f ( d i m e n s i o n l e s s ) , D

) ;

18 printf ( \n The e xa ct v al ue o f t he max d i r e c t i v i t y =%d ( d i m e n s i o n l e s s ) , Do );

19 printf ( \n The e xa ct max d i r e c t i v i t y i s 4 a nd i t sappr o x . v al ue i s 2 . 8 4 . B e tt e r a pp ro x i ma ti on s canbe o b ta i ne d i f t he p a t t e r n s h ave much n ar ro we r

beamw idths . ) ;

Scilab code Exa 2.7 What is the bandwidth and also bandwidth ratio

1 / / Ex : 2 . 72 clc ;

3 clear ;

4 close ;

5 f c = 2 2 0 ; // c e n te r f r e q ue nc y i n Hz

49


51/176

6 f 3 d b = 1 9 0 ; // 3 d b f r eq u en c y i n Hz

7 f 3 d b 1 = 2 4 0 ; // 3 db f r eq u en c y i n Hz8 B l = ( f c - f 3 d b ) / f c ; / / l o w er band w id th9 B u = ( f 3 d b 1 - f c ) / f c ; / / u p pe r band w id t h

10 R = f 3 d b 1 / f 3 d b ; // max t o min r a t i o11 printf ( The l o w e r b an d w i d t h = %f %% , B l * 10 0) ;12 printf ( \n The u p p e r b an d w i d t h = %f %% , B u * 10 0) ;13 printf ( \n The max t o min r a t i o = %f t o 1 , R ) ;

Scilab code Exa 2.8 Calculate the max effective aperture of an antenna

1 / / Ex : 2 . 82 clc ;

3 clear ;

4 close ;

5 y = 2 ; // w av el en gt h i n m

6 D = 1 0 0 ; // d i r e c t i v i t y7 A e m = ( D * y ^ 2 ) / ( 4 * % p i ) ; // max e f e e c t i v e a p e r t ur e i n m28 printf ( The max e f e e c t i v e a p e r t u r e = %f m 2 , A em ) ;

Scilab code Exa 2.9 Find out the radiation resistance

1 / / Ex : 2 . 92 clc ;

3 clear ;

50


52/176

4 close ;

5 d l _ y = 1 / 8 ; // t he r a t i o o f d l t o y ( w av el en gt h )6 R r = 8 0 * ( % p i ^ 2 ) * ( d l _ y ) ^ 2 ; // r a d i a t i o n r e s i s t a n c e i nohm


Scilab code Exa 2.10 How much power does a fifty ohms antenna radiatewhen fed a current five amp

1 / / E x : 2 . 1 02 clc ;

3 clear ;

4 close ;

5 I r m s = 5 ; // c u r r e n t i n Amp6 R r = 5 0 ; // r a d i a t i o n r e s i s t a n c e i n m7 W = I r m s ^ 2 * R r ; / / p ow er i n Watt s

8 printf ( The pow er = %d Watt s , W ) ;


1 / / E x : 2 . 1 12 clc ;

3 clear ;

4 close ;

5 G = 2 0 ; / / P ow er G ai n

51


53/176

6 D = 2 2 ; // d i r e c t i v i t y

7 n = G / D ; // e f f e c i e n c y8 R l = 1 0 ; // l o ssr e s i s t a n c e i n ohm9 R r = ( n * R l ) / ( 1 - n ) ; // r a d i a t i o n r e s i s t a n c e i n ohm


Scilab code Exa 2.12 Calculate the front to back ratio of an antenna indB

1 / / E x : 2 . 1 22 clc ;

3 clear ;

4 close ;

5 P 1 = 3 0 0 0 ; / / i n Watts6 P 2 = 5 0 0 ; // i n Watts7 G d b = 1 0 * log ( P 1 / P 2 ) / log ( 1 0 ) ; // f r o n t t o back r a t i o o f

an a nt en na i n dB8 printf ( The f r o n t t o back r a t i o o f an a nt en na = %f

dB , G db ) ;

Scilab code Exa 2.13 Find the received power

1 / / E x : 2 . 1 32 clc ;

3 clear ;

52


54/176

4 close ;

5 G = 4 0 ; // power g a in i n dB6 G t = 4 0 ; // power g a in i n dB7 G r = 4 0 ; // power g a in i n dB8 G 1 = 1 0 ^ ( G / 1 0 ) ; / / po we r g a i n9 G t 1 = 1 0 ^ ( G t / 1 0 ) ; / / p ower g a i n

10 G r 1 = 1 0 ^ ( G r / 1 0 ) ; / / p ower g a i n11 f = 1 0 * 1 0 ^ 3 ; / / f r e q u e n c y i n MHz12 y = 3 0 0 / f ; // w av el en gt h i n m13 W t = 1 ; / / T r a ns m i t te r i n Watts14 r = 3 0 * 1 0 ^ 3 ; // r a n g e o f l i n k i n m15 W r = ( W t * G 1 ^ 2 * y ^ 2 ) / ( 4 * % p i * r ) ^ 2 ; // r e c e i v e power i n

Watts16 printf ( The r e c e i v e p ower = %f 10 6 W at ts , Wr

* 1 0 ^ 6 ) ;

Scilab code Exa 2.14 How much is the new signal picked up by the re-ceiving station

1 / / E x : 2 . 1 42 clc ;

3 clear ;

4 close ;

5 V 2 = 5 0 ; // i n m ic r o v o l t6 G = 5 ; // v o l t a ge g ai n i n dB7 G 1 = 1 0 ^ ( G / 2 0 ) ; // v o l t a g e g ai n8 V 1 = V 2 * G 1 ;

// s i g n a l a t r e c e i v i n g s t a t i o n i n v o l t9 printf ( The s i g n a l a t r e c e i v i n g s t a t i o n = %f m i c r ov o l t s , V1 );

53


55/176

Scilab code Exa 2.15 Calculate the power gain

1 / / E x : 2 . 1 52 clc ;

3 clear ;

4 close ;

5 P i = 4 0 0 * 1 0 ^ - 3 ; // i n pu t power t o r e f e r e n c e Antenna6 P t = 1 0 0 * 1 0 ^ - 3 ; // i n pu t power t o t e s t a nt en na7 G d b = 1 0 * log ( P i / P t ) / log ( 1 0 ) ; // power g a in i n dB8 printf ( The p ow er g a i n = %f dB , G db ) ;

Scilab code Exa 2.16 Calculate the approximate gain and beamwidth ofa paraboloidal reflector antenna

1 / / E x : 2 . 1 62 clc ;

3 clear ;

4 close ;

5 D = 2 0 ; // d i r e c t i v i t y

6 A = % p i * ( D / 2 ) ^ 2 ;7 f = 4 * 1 0 ^ 3 ; // f r e q u e n c y i n MHz8 y = 3 0 0 / f ; / / w a ve l en g th i n m et er9 n = 0 . 5 5 ; // e f f e c i e n c y

10 G = ( 4 * % p i * n * A ) / y ^ 2 ; // g a in

54


56/176

11 G d b = 1 0 * log ( G ) / log ( 1 0 ) ; // g ai n i n dB

12 B _ W = ( 7 0 * y / D ) ; // beamwidth o f a p a r a b o l o i d a lr e f l e c t o r a nt e nn a13 printf ( The g a i n = %f dB , G db ) ;14 printf ( \n The b eamwidth o f a p a r a b o l o i da l r e f l e c t o r

a nt en na = %f d e g r e e , B _W ) ;

Scilab code Exa 2.17 Find out the quality factor Q of an antenna

1 / / E x : 2 . 1 72 clc ;

3 clear ;

4 close ;

5 d f = 0 . 6 0 0 ; / / b a n d wi d t h i n MHz6 f r = 3 0 ; / / f r e q u e n cy i n MHz7 Q = f r / d f ; // q u a l i t y f a c t o r

8 printf ( The q u a l i t y f a c t o r = %d , Q ) ;

Scilab code Exa 2.18 Calculate the bandwidth of an antennas

1 / / E x : 2 . 1 82 clc ;

3 clear ;

4 close ;

5 f r = 1 1 0 * 1 0 ^ 6 ; // f r eq u en c y i n Hz

55


57/176

6 Q = 7 0 ; // q u a l i t y f a c t o r

7 d f = f r / Q ; / / b a n dw i d th i n MHz8 printf ( The band width= %f MHz , d f / 10 ^6 ) ;9 printf ( \n The a ns we r i s wrong i n t he t ex t bo o k ) ;

Scilab code Exa 2.19 Calculate the directivity of isotropic antenna

1 / / E x : 2 . 1 92 clc ;

3 clear ;

4 close ;

5 A = 4 * % p i ; // f o r i s o t r o p i c a n t e n na6 D = 4 * % p i / A ; // d i r e c t i v i t y7 printf ( The d i r e c t i v i t y = %d , D ) ;

Scilab code Exa 2.20 Calculate the max effective aperture of a microwaveantenna

1 / / E x : 2 . 2 02 clc ;

3 clear ;4 close ;

5 D = 9 0 0 ; // d i r e c t i v i t y6 // Aem=(D. y 2 ) /( 4 %p i ) , w h er e y= W a v el e n gt h7 A e m = ( D / ( 4 * % p i ) ) ; // max e f f e c t i v e a p e r t ur e

56


58/176

8 printf ( The max e f f e c t i v e a p e r t ur e= %f y 2 , w he re y=

w a v e l e n g t h , A em ) ;

Scilab code Exa 2.21 Find the equivalent temperature

1 / / E x : 2 . 2 12 clc ;3 clear ;

4 close ;

5 F d B = 0 . 2 ; // n o i s e f i g u r e i n dB6 F = 1 0 ^ ( F d B / 1 0 ) ; // n o i s e f i g u r e7 T o = 2 9 0 ; // t em p er at u re i n k8 T e = ( F - 1 ) * T o ; // e q u i v a l e n t t em pe ra tu re i n k9 printf ( The e q u i v a l e n t t e m pe r a tu r e= %f k , Te );

10 printf ( \n The a ns we r i s wrong i n t he t ex t bo o k ) ;

Scilab code Exa 2.22 Find the noise factor

1 / / E x : 2 . 2 22 clc ;

3 clear ;4 close ;

5 T e = 2 0 ; // e q u i v a l e n t t em pe ra tu re i n k6 T o = 2 9 0 ; // t em p er at u re i n k7 F = 1 + T e / T o ; // n o i s e f i g u r e

57


59/176

8 printf ( The n o i s e f i g u r e = %f , F ) ;

Scilab code Exa 2.23 what is the effective noise temperature

1 / / E x : 2 . 2 3

2 clc ;3 clear ;

4 close ;

5 F d B = 1 . 1 ; // n o i s e f i g u r e i n dB6 F = 1 0 ^ ( F d B / 1 0 ) ; // n o i s e f i g u r e7 T o = 2 9 0 ; // t em p er at u re i n k8 T e = ( F - 1 ) * T o ; // e q u i v a l e n t t em pe ra tu re i n k9 printf ( The e q u i v a l e n t t e m pe r a tu r e= %f k , Te );

Scilab code Exa 2.24 Calculate the available noise power per unit band-width and also Calculate the available noise power for a noise bandwidth

1 / / E x : 2 . 2 42 clc ;

3 clear ;

4 close ;5 T a = 1 5 ; // e f f e c t i v e t em pe ra tu re i n k6 T n = 2 0 ; // e f f e c t i v e n o i s e t e m p er a t ur e i n k7 B = 4 * 1 0 ^ 6 ; // n o i s e b and wi dt h i n Hz8 k = 1 . 3 8 * 1 0 ^ - 2 3 ; / / b ol t zm a nn s c o n s t a n t

58


60/176

9 P s _ B n = k * ( T a + T n ) ; // n o i s e power p er u n i t b and wi dt h i n

Watts/Hz10 P s = P s _ B n * B ; // t h e t o t a l a v a i l a b l e n o i s e power i nWatts

11 printf ( The n o i s e p ow er p e r u n i t b an dw id th= %f 1023 Watts/Hz, P s _B n * 1 0 ^ 2 3) ;

12 printf ( \n The t o t a l a v a i l a b l e n o i s e power= %f 101 7 W at ts , P s * 10 ^ 17 ) ;


1 / / E x : 2 . 2 52 clc ;

3 clear ;

4 close ;

5 V 2 = 5 0 ; // i n u v o l t6 G = 5 ; // v o l t a ge g ai n i n dB7 G 1 = 1 0 ^ ( G / 2 0 ) ; // v o l t a g e g ai n8 V 1 = V 2 * G 1 ; // s i g n a l a t r e c e i v i n g s t a t i o n i n v o l t9 printf ( The s i g n a l a t r e c e i v i n g s t a t i o n = %f uv o l t s

, V1 );

Scilab code Exa 2.26 Calculate the max effective aperture of an antenna

59


61/176

1 / / E x : 2 . 2 6

2 clc ;3 clear ;

4 close ;

5 y = 5 ; // w av el en gt h i n m6 D = 7 5 ; // d i r e c t i v i t y7 A e m = ( D * y ^ 2 ) / ( 4 * % p i ) ; // max e f e e c t i v e a p e r t ur e i n m28 printf ( The max e f e e c t i v e a p e r t u r e = %f m 2 , A em ) ;

Scilab code Exa 2.27 Find the equivalent temperature

1 / / E x : 2 . 2 72 clc ;

3 clear ;

4 close ;

5 F d B = 0 . 5 ; // n o i s e f i g u r e i n dB

6 F = 1 0 ^ ( F d B / 1 0 ) ; // n o i s e f i g u r e7 T o = 2 9 0 ; // t em p er at u re i n k8 T e = ( F - 1 ) * T o ; // e q u i v a l e n t t em pe ra tu re i n k9 printf ( The e q u i v a l e n t t e m pe r a tu r e= %f k , Te );

Scilab code Exa 2.28 Find the noise factor

1 / / E x : 2 . 2 82 clc ;

60


62/176

3 clear ;

4 close ;5 T e = 4 0 ; // e q u i v a l e n t t em pe ra tu re i n k6 T o = 2 9 0 ; // t em p er at u re i n k7 F = 1 + T e / T o ; // n o i s e f i g u r e8 printf ( The n o i s e f i g u r e = %f , F ) ;

Scilab code Exa 2.29 What is the effective noise temperature

1 / / E x : 2 . 2 92 clc ;

3 clear ;

4 close ;

5 F d B = 1 . 5 ; // n o i s e f i g u r e i n dB6 F = 1 0 ^ ( F d B / 1 0 ) ; // n o i s e f i g u r e7 T o = 2 9 0 ; // t em p er at u re i n k

8 T e = ( F - 1 ) * T o ; // e q u i v a l e n t t em pe ra tu re i n k9 printf ( The e q u i v a l e n t t e m pe r a tu r e= %f k , Te );

Scilab code Exa 2.30 Calculate the available noise power per unit band-

width and also Calculate the available noise power for a noise bandwidth

1 / / E x : 2 . 3 02 clc ;

3 clear ;

61


63/176

4 close ;

5 T a = 2 5 ; // e f f e c t i v e t em pe ra tu re i n k6 T n = 4 5 ; // e f f e c t i v e n o i s e t e m p er a t ur e i n k7 B = 7 * 1 0 ^ 6 ; // n o i s e b and wi dt h i n Hz8 k = 1 . 3 8 * 1 0 ^ - 2 3 ; / / b ol t zm a nn s c o n s t a n t9 P s _ B n = k * ( T a + T n ) ; // n o i s e power p er u n i t b and wi dt h i n

Watts/Hz10 P s = P s _ B n * B ; // t h e t o t a l a v a i l a b l e n o i s e power i n

Watts11 printf ( The n o i s e p ow er p e r u n i t b an dw id th= %f

1023 Watts/Hz, P s _B n * 1 0 ^ 2 3) ;12 printf ( \n The t o t a l a v a i l a b l e n o i s e power= %f

101 7 W at ts , P s * 10 ^ 17 ) ;

Scilab code Exa 2.31 Calculate the gain and beam width of the antenna

1 / / E x : 2 . 3 12 clc ;

3 clear ;

4 close ;

5 f = 7 . 3 7 5 * 1 0 ^ 3 ; / / f r e q u e n cy i n MHz6 y = 3 0 0 / f ; // w av el en gt h i n m7 D = 2 . 7 ; // d i r e c t i v i t y8 A e = % p i * ( D / 2 ) ^ 2 * 0 . 6 5 ; // e f f e c t i v e a pe r t ur e9 G = ( 4 * % p i / y ^ 2 ) * A e ; // g a in

10 B W = 7 0 * y / D ; / / B ea mwi dth i n A11 printf (

The g a i n = %f , G ) ;

12 printf ( \n The Beamw idth = %f A , BW );

62


64/176


1 / / E x : 2 . 3 22 clc ;

3 clear ;

4 close ;

5 V 2 = 6 0 ; // i n u v o l t6 G = 1 5 ; // v o l t a ge g ai n i n dB7 G 1 = 1 0 ^ ( G / 2 0 ) ; // v o l t a g e g ai n8 V 1 = V 2 * G 1 ; // s i g n a l a t r e c e i v i n g s t a t i o n i n v o l t9 printf ( The s i g n a l a t r e c e i v i n g s t a t i o n = %f uv o l t s

, V1 );


1 / / E x : 2 . 3 32 clc ;

3 clear ;

4 close ;5 G = 3 0 ; / / P ow er G ai n6 D = 4 2 ; // d i r e c t i v i t y7 n = G / D ; // e f f e c i e n c y8 R l = 2 5 ; // l o ssr e s i s t a n c e i n ohm

63


65/176

9 R r = ( n * R l ) / ( 1 - n ) ; // r a d i a t i o n r e s i s t a n c e i n ohm


Scilab code Exa 2.34 Determine the total radited power

1 / / E x : 2 . 3 42 clc ;3 clear ;

4 close ;

5 / / F or a c l os e d s u r fa c e , a s ph er e o f r a d i u s r i sc ho os en . To f i n d t he t o t a l r a d i a t e d power , t her a d i a t e d component o f t he power d e n s i t y i si n t e g r a t e d o ve r i t s s u r f a c e . t h e r e f o r e ,

6 / / Wt=d o u b l e i n t e g r a t i o n o f ( a r . Ao . ( s i n ( x ) / r 2 ) ) ( a r. r 2 . s i n ( x ) ) w it h l i m i t s fro m 0 t o 2p i and fr om0 t o p i , and on i n t e g r a t i o n we g et , p i 2Ao

w a t t s7 printf ( The t o t a l r a d i a t e d p ower= p i 2Ao w a t ts ) ;

Scilab code Exa 2.35 Find the max directivity of the antenna and write

an expression for the directivity

1 / / E x : 2 . 3 52 clc ;

3 clear ;

64


66/176

4 close ;

5 / / The max r a d i a t i o n i s d i r e c t e d a l on g x=p i / 2 .Th er ef or e , Ymax=Ao6 / / r a d i a t i o n i n t e n s i t y i n ex ample 2 . 34 i s , Wt=p i 2

Ao7 / / t he n , max d i r e c t i v i t y , Do=4p i Ymax/Wt=4p i A o/pi

2Ao=4/pi8 D o = 4 / % p i ; // t h e max d i r e c t i v i t y9 // s i n c e t h e r a d i a t i o n i n t e n s i t y i s o nl y a f u n c t i o n

o f a ng le x , t h e d i r e c t i v i t y a s a f un c t i o n o f t h ed i r e c t i o n a l a n g l es i s r e p r e s e nt e d by , D=Dos i n ( x )

10 printf ( The max d i r e c t i v i t y = %f , Do );

11 printf ( \n The d i r e c t i v i t y a s a f u n c t i o n o f t h ed i r e c t i o n a l a n g l es i s r e p r e s e nt e d by , D=Dos i n ( x ), where Do i s t he max v al u e o f d i r e c t i v i t y ) ;

Scilab code Exa 2.36 Find the max directivity of the antenna and writean expression for the directivity

1 / / E x : 2 . 3 62 clc ;

3 clear ;

4 close ;

5 // The r a d i a t i o n i n t e n s i t y i s g i v en by , F=r 2Wr=Ao( s i n ( x ) ) 2

6 / / The max r a d i a t i o n i s d i r e c t e d a l on g x=p i / 2 .

t h e r ef o r e , Ymax=Ao7 // t he t o t a l r a d i a t e d power i s g i ve n by , Wt= Ao (8p i/ 3 )

8 // t h e n t h e max d i r e c t i v i t y i s e qu al t o9 // Do=4 p i Ymax/Wt=4p i Ao/(8p i Ao/3)=3/2

65


67/176

10 D o = 3 / 2 ; // t he max d i r e c t i v i t y

11 printf ( The max d i r e c t i v i t y = %f , Do );12 printf ( \n The d i r e c t i v i t y a s a f u n c t i o n o f t h ed i r e c t i o n a l a n gl e s i s r e pr e s e nt e d by , D= 1 . 5 ( s i n (x ) ) 2 ) ;

Scilab code Exa 2.37 Show the max effective aperture of a short dipoleantenna

1 / / E x : 2 . 3 72 clc ;

3 clear ;

4 close ;

5 // I t i s assume t ha t6 / / 1 . s ho rt d i p o l e i s c o i n c i d e w i t h xa x i s7 // 2 . P l a ne p o l a r i z e d wave i n t r a v e l l i n g a lo ng y

a x i s and i n c l u d i n g c u rr e n t a lo ng t he xa x i s o f a nt en na whi ch c o n st a n t t hr ou g ho ut t he l e n g th o f t he d i p o l e and i n t he same p ha se

8 // 3 . Le ngt h o f t h e s ho r t d i p o l e i s s ma ll i nc o mp a ri s on t o w a ve l en g th i . e . d l


68/176

16 / / t he r a d i a t i o n R e s i st a nc e o f s h or t d i p o l e a n t e n n a

i s g iv en by17 // Rr=80 pi 2 ( d l / y ) 2 i n ohm18 // t he n ( A e ) max=(E dl ) 2 /( 4 ( E 2 / n ) ( 8 0p i 2) ( d l / y )

2 )19 // ( Ae ) max=(ny 2 ) / ( 8 0p i 24) =(120p i

Documents

Scilab Textbook Companion for Antenna and Wave Propagation