Scilab Textbook Companion for Antenna and Wave Propagation by A. K. Gautam1 Created by Nizamuddin B Tech Electronics Engineering Uttarakhand Technical University Dehradun College Teacher None Cross-Checked by Chaya Ravindra July 31, 2019 1Funded by a grant from the National Mission on Education through ICT, http://spoken-tutorial.org/NMEICT-Intro. ThisTextbookCompanionandScilab codes written in it can be downloaded from the ”Textbook Companion Project” section at the website http://scilab.in 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 Scilab numbering policy used in this document and the relation to the above book. Exa Example (Solved example) Eqn Equation (Particular equation of the above book) AP Appendix to Example(Scilab Code that is an Appednix to a particular Example of the above book) Forexample, Exa3.51meanssolvedexample3.51ofthisbook. Sec2.3means a scilab code whose theory is explained in Section 2.3 of the book. 2 Contents ListofScilabCodes 4 1 Eletromagnetic Field Radiation 5 2 Antenna Terminology 37 3 Antenna Arrays 67 4 Practical Antennas 98 5 Propagation 133 3 List of Scilab Codes Exa 1.1 What is the strength of a magnetic field H in free space . . . . . . . . . . . . . . . . . . . 5 Exa 1.2 Find out the field strength . . . . . . . . . . 5 Exa 1.3 Calculate the radiation resistance . . . . . . 6 Exa 1.4 What is the power radiated and also what is the efficiency of the antenna . . . . . . . . . 6 Exa 1.5 How much power will an antenna having a radiation rasistance of fifty ohms . . . . . . 7 Exa 1.6 What is the radiation resistance of an antenna 8 Exa 1.7 How much current flows into the antenna . . 8 Exa 1.8 Calculate the strength of electric field . . . 9 Exa 1.9 Estimate the effective height of the antenna 9 Exa 1.10 Find the field strength and the power radiated 10 Exa 1.11 Calculate the power radiated . . . . . . . . 11 Exa 1.12 Calculate the radiation resistance of current elements . . . . . . . . . . . . . . . . . . . . 11 Exa 1.13 Calculate the power radiated and what is its radiation resistance . . . . . . . . . . . . . . 12 Exa 1.14 what is the electric field . . . . . . . . . . . 12 Exa 1.15 Calculate the antenna current at a distance of five eight wavelength away from the feed point . . . . . . . . . . . . . . . . . . . . . . 13 Exa 1.16 Determine the field strength of the radiated field produced . . . . . . . . . . . . . . . . 14 Exa 1.17 Calculate the effective height of the antenna in meters . . . . . . . . . . . . . . . . . . . 14 Exa 1.18 Calculate the radiation resistance . . . . . . 15 4 Exa 1.19 Find the radiation resistance and power radi- ated and also antenna efficiency . . . . . . . 15 Exa 1.20 What is the power radiated . . . . . . . . . 16 Exa 1.21 Find out the field strength . . . . . . . . . . 17 Exa 1.22 At what distance from a sixty cycle circuit is the radiation field approximately . . . . . . 17 Exa 1.23 Find out the field strength . . . . . . . . . . 18 Exa 1.24 Find the velocity of a plane wave in a loss less medium . . . . . . . . . . . . . . . . . . . . 18 Exa 1.25 What is the strength of a magnetic field H in free space . . . . . . . . . . . . . . . . . . . 19 Exa 1.26 Calculate the field strength at a distance of twenty five km . . . . . . . . . . . . . . . . 19 Exa 1.27 Calculate the radiation resistance . . . . . . 20 Exa 1.28 Derive an expression for the gain of a half wave antenna . . . . . . . . . . . . . . . . . 20 Exa 1.29 Calculate the antenna current at a distance of seventh eighth wavelength away from the feed point . . . . . . . . . . . . . . . . . . . 21 Exa 1.30 Find the average energy density . . . . . . . 22 Exa 1.31 Determine the radiation resistance . . . . . 22 Exa 1.32 What is the value of electric field strength at a point twenty five away in the same direction 23 Exa 1.33 Findthevelocityofpropogationandthewave- length and the impedence of the medium and also the rms electric field E . . . . . . . . . 23 Exa 1.34 At what distance in wavelength is the radia- tion component of magnetic field three times the induction components . . . . . . . . . . 24 Exa 1.35 Find out the field strength . . . . . . . . . . 25 Exa 1.36 Find the velocity of a plane wave in a loss less medium . . . . . . . . . . . . . . . . . . . . 25 Exa 1.37 Calculate the antenna current at a distance of seventh eighth wavelength away from the feed point . . . . . . . . . . . . . . . . . . . 26 Exa 1.38 Determine the radiation resistance . . . . . 27 Exa 1.39 What is the radiation resistance of an antenna 27 Exa 1.40 What is the bandwidth . . . . . . . . . . . . 28 5 Exa 1.41 Define radiation resistance and also Calculate the radiation resistance and efficiency . . . . 28 Exa 1.42 What is the significance of electrostatic field and induction field and also radiation field of the antenna and at what distance in wave- length the radiation component of magnetic field is hundred times of the induction com- ponent . . . . . . . . . . . . . . . . . . . . . 29 Exa 1.43 Define retarded vector potential . . . . . . . 29 Exa 1.44 What is the power radiated and what is the efficiency of the antenna . . . . . . . . . . . 30 Exa 1.45 Calculate the radiation resistance power ra- diated and the efficiecy of an antenna . . . . 31 Exa 1.46 Find the radiation resistance and efficiency . 32 Exa 1.47 What is the power radiated . . . . . . . . . 32 Exa 1.48 What is the strength of magnetic field H in free space . . . . . . . . . . . . . . . . . . . 33 Exa 1.49 Calculate the radiated field strength and the total power radiated and also the radiation resistance . . . . . . . . . . . . . . . . . . . 33 Exa 1.50 Show the total far field electric field ampli- tude and also Calculate the power that could be fed into a dipole antenna . . . . . . . . . 34 Exa 1.51 Calculate the loss resistance and also Calcu- late the power radiated and the ohmic loss and loss resistance . . . . . . . . . . . . . . 35 Exa 2.1 What is the wavelength . . . . . . . . . . . 37 Exa 2.2 What is the actual velocity of EM energy . . 37 Exa 2.3 What is the wavelength in vaccum and in air 38 Exa 2.4 What is the directicity . . . . . . . . . . . . 38 Exa 2.5 Calculate the radiation resistance . . . . . . 39 Exa 2.6 Find the max directivity and compare it with its exact value . . . . . . . . . . . . . . . . . 39 Exa 2.7 What is the bandwidth and also bandwidth ratio . . . . . . . . . . . . . . . . . . . . . . 40 Exa 2.8 Calculate the max effective aperture of an an- tenna . . . . . . . . . . . . . . . . . . . . . 41 Exa 2.9 Find out the radiation resistance . . . . . . 41 6 Exa 2.10 How much power does a fifty ohms antenna radiate when fed a current five amp . . . . . 42 Exa 2.11 Calculate the radiation resistance . . . . . . 42 Exa 2.12 Calculate the front to back ratio of an an- tenna in dB . . . . . . . . . . . . . . . . . . 43 Exa 2.13 Find the received power . . . . . . . . . . . 43 Exa 2.14 How much is the new signal picked up by the receiving station . . . . . . . . . . . . . . . 44 Exa 2.15 Calculate the power gain . . . . . . . . . . . 45 Exa 2.16 Calculatetheapproximategainandbeamwidth of a paraboloidal reflector antenna . . . . . 45 Exa 2.17 Find out the quality factor Q of an antenna 46 Exa 2.18 Calculate the bandwidth of an antennas . . 46 Exa 2.19 Calculate the directivity of isotropic antenna 47 Exa 2.20 Calculate the max effective aperture of a mi- crowave antenna . . . . . . . . . . . . . . . 47 Exa 2.21 Find the equivalent temperature . . . . . . . 48 Exa 2.22 Find the noise factor . . . . . . . . . . . . . 48 Exa 2.23 what is the effective noise temperature . . . 49 Exa 2.24 Calculate the available noise power per unit bandwidth and also Calculate the available noise power for a noise bandwidth . . . . . . 49 Exa 2.25 How much is the new signal picked up by the receiving station . . . . . . . . . . . . . . . 50 Exa 2.26 Calculate the max effective aperture of an an- tenna . . . . . . . . . . . . . . . . . . . . . 50 Exa 2.27 Find the equivalent temperature . . . . . . . 51 Exa 2.28 Find the noise factor . . . . . . . . . . . . . 51 Exa 2.29 What is the effective noise temperature . . . 52 Exa 2.30 Calculate the available noise power per unit bandwidth and also Calculate the available noise power for a noise bandwidth . . . . . . 52 Exa 2.31 Calculate the gain and beam width of the an- tenna . . . . . . . . . . . . . . . . . . . . . 53 Exa 2.32 How much is the new signal picked up by the receiving station . . . . . . . . . . . . . . . 54 Exa 2.33 Calculate the radiation resistance . . . . . . 54 Exa 2.34 Determine the total radited power . . . . . . 55 7 Exa 2.35 Find the max directivity of the antenna and write an expression for the directivity . . . . 55 Exa 2.36 Find the max directivity of the antenna and write an expression for the directivity . . . . 56 Exa 2.37 Show the max effective aperture of a short dipole antenna . . . . . . . . . . . . . . . . 57 Exa 2.38 Show the field strength at adistance r me- ters from an antenna of gain G and radiating power P . . . . . . . . . . . . . . . . . . . . 58 Exa 2.39 Define effective aperture and scattering aper- ture . . . . . . . . . . . . . . . . . . . . . . 58 Exa 2.40 Calculatethepowerdensityandmagneticand electric field strength . . . . . . . . . . . . . 59 Exa 2.41 Calculate the antenna gain . . . . . . . . . . 60 Exa 2.42 Calculate the effective aperture and what will the power received . . . . . . . . . . . . . . 60 Exa 2.43 Find the directivity and gain and effective aperture and beam solid angle and radiation resistance and also terminal resistance . . . 61 Exa 2.44 Find the beam width . . . . . . . . . . . . . 62 Exa 2.45 what is the size of spot illuminated by the antenna . . . . . . . . . . . . . . . . . . . . 62 Exa 2.46 Find the power density . . . . . . . . . . . . 63 Exa 2.47 Find the max radiated electric field and what is the max power density . . . . . . . . . . . 64 Exa 2.48 Find the peak poynting vector and the aver- age poynting vector and also the peak value of magnetic field H . . . . . . . . . . . . . . 64 Exa 2.49 Find the magnitude of magnetic and electric fields . . . . . . . . . . . . . . . . . . . . . . 65 Exa 2.50 Find the rms electric and magnetic field and the average value of poynting vector and the average energy density and also the time it takes a signal to reach earth . . . . . . . . . 66 Exa 3.1 Calculate the half power beam width of the major lobes of the array in horizontal plane 67 8 Exa 3.2 Calculatetheprogressivephaseshiftsandalso Calculate the angle at which the main beam is placed for this phase distribution . . . . . 68 Exa 3.3 Discuss the radiation pattern of a linear array 69 Exa 3.4 Design a eight element broad side array . . 71 Exa 3.5 Design a five element broad side array which has the optimum pattern . . . . . . . . . . . 73 Exa 3.6 Design a four element broad side array . . . 75 Exa 3.7 Determine Dolph Tchebyscheff current dis- tribution and also determine the half power beam width . . . . . . . . . . . . . . . . . . 76 Exa 3.8 Design an array to yield an optimum pattern 78 Exa 3.9 Calculatethedirectivityofagivenlinearbroad side . . . . . . . . . . . . . . . . . . . . . . 80 Exa 3.10 Calculate the Dolph Tchebysceff distribution which yield the optimum pattern . . . . . . 80 Exa 3.11 Design an array that will produce approxi- mately a pattern of the given figure . . . . . 82 Exa 3.12 Prove that the directivity of an end fire array 83 Exa 3.13 Prove that directivity for a broadside array of two identical isotropic . . . . . . . . . . . . 84 Exa 3.14 Calculate the Dolph Tchebyscheff distribu- tion which yield the optimum pattern . . . . 85 Exa 3.15 Determine Dolph Tchebyscheff current distri- bution for the minimum beamwidth of a lin- earinphasebroadsidearrayofeightisotropic source . . . . . . . . . . . . . . . . . . . . . 87 Exa 3.16 Find the directivity of linear broad side . . 89 Exa 3.17 Find the directivity of linear end fire . . . . 89 Exa 3.18 Find the directivity of a linear end fire . . . 90 Exa 3.19 Define antenna gain and directivity . . . . . 90 Exa 3.20 Find the array length and width and what will be these value for a broad side array . . 91 Exa 3.21 Derive the expression for beam width . . . . 92 Exa 3.22 Find the FNBW and HPBW for a broad side linear array . . . . . . . . . . . . . . . . . . 93 Exa 3.23 Find the location of the first nulls on a either side of beam center . . . . . . . . . . . . . . 94 9