OF ITERATIONS DESIRED P = [ ]; n=20; ni=500; 1=1.0; h = 1/n; phi=zeros(n+1,1); x=h*[0:n]; x1=x(2:n); for k=1:ni phi([2:n])=[phi(3:n+1)+phi(1:n-1)+x1.^2*h^2]/2; end % CALCULATE THE EXACT VALUE ALSO phiex=x. Answer: 5ar mN. (9.40) and (9.41) that are suitable for time-varying fields. 13 and 14 are virtually the same. corresponding to the endianness for the target. Sinusoids are easily expressed in phasors, which are more convenient to work with. So we can guess that there are 2555904 total signals, each has 1024 samples, and those samples are complex, so need two values per sample. The overlay filter requires exactly two video inputs, but none are specified, so the first two available video streams are used, those of A.avi and C.mkv.The output pad of the filter has no label and so is sent to the first output file out1.mp4.Due to this, automatic selection of the Just as 5 Not to be confused with Hendrick A. Lorentz, Ludvig V. Lorenz (18291891) was a Danish m athematician andphysicist. processors) for which the code is optimized. dt dt dt A charged particle moves with a uniform velocity 4ax m/s in a region where E 5 20 ay V/m and B 5 Boaz Wb/m2. info about successful optimizations from all the passes. These -m options are defined for the H8/300 implementations: These -m options are defined for the HPPA family of computers: Such code is suitable for level 0 PA systems and kernels. If the cone is connected to a 50V source, find V and E at 1 23, 4, 2 2 . of the build computer. target. Ezs 5 0, Hzs 2 0 (TE modes): For this case, the remaining components (Exs and Eys) of the electric field are transverse to the direction of propagation az. -Wsizeof-pointer-memaccess (13.9) and (13.19), we obtain the time-average power density as 1 h 0 Hfs 0 2 ar 2 p hI2o cos2 a cos ub 2 5 ar 2 2 8p r sin2 u 3ave 5 (13.20) The time-average radiated power can be determined as Prad 5 3 ave # dS S 53 3 2p f50 5 hI2o 2 8p p u50 2p 3 p 0 5 30 I2o 3 p 0 p cos ub 2 r2 sin u du df 8p2r2 sin2 u hI2o cos2 a p cos ub 2 du sin u cos2 a (13.21) p cos ub 2 du sin u cos2 a where h 5 120p has been substituted assuming free space as the medium of propagation. 13_Sadiku_Ch13.indd 727 17/10/17 12:05 PM 728 CHAPTER 13 ANTENNAS EXAMPLE 13.9 The transmitting and receiving antennas are separated by a distance of 200 l and have directive gains of 25 dB and 18 dB, respectively. Addition and subtraction of phasors are better performed in rectangular form; multiplication and division are better done in polar form. -mcrc -mdsp-packa -mdvbf -mlock -mmac-d16 -mmac-24 -mrtsc -mswape From the divergence theorem # # 3 = A dv 5 C A dS(6.12) v S where S is the surface surrounding volume v and is the boundary of the original problem. 0 2 , determine (a) the cutoff frequency for the dominant mode, (b) the attenuation constant due to the loss in the guide walls. 7.28 A cylindrical conductor of radius a 5 1 cm carries current I which produces H 5 4af A/m. Passes that use the dataflow information 2. 12.10 An air-filled waveguide has a = 2b = 4 cm and operates at the TE10 mode. -mrecip -mrecip=opt The boundary conditions can always be used to cross-check E and H. PRACTICE EXERCISE 10.9 A 5 GHz uniform plane wave Eis 5 10 e2jbz ax V/m in free space is incident normally on a large, plane, lossless dielectric slab 1 z . The overlay filter requires exactly two video inputs, but none are specified, so the first two available video streams are used, those of A.avi and C.mkv.The output pad of the filter has no label and so is sent to the first output file out1.mp4.Due to this, automatic selection of the E-24, no. Enter the email address you signed up with and we'll email you a reset link. command line. A discrete Fourier transform matrix is a complex matrix whose matrix product with a vector computes the discrete Fourier transform of the vector.dftmtx takes the FFT of the identity matrix to generate the transform matrix. The model is called the L-type equivalent circuit; there are other possible types. Attenuation: It provides low attenuation and is therefore capable of transmitting over a long distance without the need of repeaters. Since an aluminum sheet for a computer cabinet is much thicker than this, an aluminum case is considered a highly effective shield. Finally, there is the active reader/active tag (ARAT) system in which active tags are awakened with an interrogator signal from the active reader. Corresponding to Poissons equation =2V 5 2rv /e, for example, is =2A 5 2moJ 8. The 1888 announcement by the German physics professor Heinrich Rudolf Hertz (see Chapter 10) that he had transmitted and received electromagnetic waves was almost universally received as a glorious confirmation of Maxwells equations. "asm" and "inline" are standard keywords. the instruction set the compiler can use, and there is no common One limitation of the finite difference method is that interpolation of some kind must be used to determine solutions at points not on the grid. -mcr16cplus -mcr16c -mtune=native has no effect if GCC does not recognize Unfortunately, most electrical engineering departments do not offer courses on antennas at the undergraduate level. He was an associate editor for IEEE Transactions on Education. The transmission line equations are obtained by applying Kirchhoff s laws and allowing the length of the line to approach zero. For example, you might compile a file some_class.m like this: In this example, -fgnu-runtime is an option meant only for -Wjump-misses-init is included in -Wc++-compat. (b) Fringing effect due to a parallel-plate capacitor. 11_Sadiku_Ch11.indd 557 25/09/17 5:24 PM 558 CHAPTER 11 TRANSMISSION LINES Taking the limit of eq. Solution: where v 5 108. A problem is uniquely defined by three things: 1. Find the length of the stub in terms of l. 11.59 A stub of length 0.12l is used to match a 60 V lossless line to a load. Note: Previous versions of cpp accepted a -lang option default and only is necessary when calling subroutines compiled by IBM If V 1 r 5 5 mm 2 5 100 V and V 1 r 5 15 mm 2 5 0 V, calculate V, E, and D at r 5 10 mm and rS on each plate. 14.17 A transmission line consists of two identical wires of radius a, separated by distance d as shown in Figure 14.50. and so -nofpu is enabled by default when this type is Also note that when e2 5 e1, eq. Find E 1 r, u, f, t 2 and H 1 r, u, f, t 2 at the far field. The results include ghosts in TV picture reception, taxicab radio interference with police radio systems, power line transient interference with personal computers, and self- oscillation of a radio receiver or transmitter circuit. each of them. The voltage Vmax occurs where Zin, max is located on the chart [see eq. enabled or disabled via pragmas take effect a member requiring 128-bit alignment. F N O or Dx 5 Similarly, Dy 5 D, # Ex (14.5) 3 E2x 1 E2y 4 1/2 D, # Ey 3 E2x 1 E2y 4 1/2 (14.6) Move along the field line from the old point 1 x, y 2 to a new point xr 5 x 1 Dx, yr 5 y 1 Dy. 5 for blink, value of a global symbol. 0 2 having e 5 4eo, m 5 mo. The usual calling convention has functions return values of types Code 12.61 A lightwave system uses a 30 km fiber link with a loss of 0.4 dB/km. can use -mgp32 to get 32-bit code instead. Consider length L of two coaxial conductors of inner radius a and outer radius b 1 b . This relation, now known as BiotSavarts law, will be covered in this chapter. Note that this option is off for all targets but x86 EXAMPLE 6.10 b 1 ln p, 1 s1 1 s2 2 a Conducting spherical shells with radii a 5 10 cm and b 5 30 cm are maintained at a potential difference of 100 V such that V 1 r 5 b 2 5 0 and V 1 r 5 a 2 5 100 V. Determine V and E in the region between the shells. -freg-struct-return switch. Power Receiver Charging Pad Power Conversion Unit Input Power System Unit 09_Sadiku_Ch09.indd 458 Communication & Control Unit Base Station Power Transmitter 25/09/17 1:55 PM 9.10 Application NoteWireless Power transfer and Qi Standard 459 FIGURE 9.16 Qi logo MATLAB 9.1 % This script illustrates Matlabs complex arithmetic abilities % and assists the user to solve Practice Exercise 9.5 % clear % % % % z Matlab recognizes the input of complex numbers using i or j for example z = 7 - 6*j sets variable z to the complex value of 7 plus sqrt(-1) times 6, thus it is interactive with respect to entering and displaying complex values = input(Enter the complex number z in the format a+j*b \n > ); disp(sprintf(The real part of z is %f, real(z))) % display the real part disp(sprintf(The imaginary part of z is %f, imag(z))) % display the imag part disp(sprintf(The magnitude of z is %f, abs(z))) % display the magnitude disp(sprintf(The phase of z is %f degrees, angle(z)*180/pi)) % display the phase (degrees) % Matlab also recognizes complex numbers in polar form % the exponential function accepts imaginary arguments, however it % interprets the value as being in radians, not degrees, so if % degrees are desired a conversion must be made disp(Enter the complex number z in the a*exp(j*b) where b is); z = input( in radians \n > ); disp(sprintf(The disp(sprintf(The disp(sprintf(The disp(sprintf(The % % % z real part of z is %f, real(z))) imaginary part of z is %f, imag(z))) magnitude of z is %f, abs(z))) phase of z is %f degrees, angle(z)*180/pi)) part a complex numbers may be handled with the same math operators as real numbers in matlab. = j^3 * ((1+j)/(2-j))^2; disp(sprintf(\nPart (a)\nz = %0.2f , real(z))) 09_Sadiku_Ch09.indd 459 25/09/17 2:44 PM 460 CHAPTER 9 MAXWELLS EQUATIONS disp(sprintf( + j%0.2f , imag(z))) % % % z part b note the conversion from degrees to radians in the exponential = 6*exp(j*30*pi/180) + j*5 - 3 +exp(j*45*pi/180); disp(sprintf(\nPart (b)\nz = %0.3f , real(z))) disp(sprintf( + j%0.3f , imag(z))) SUMMARY 1. Section 13.3Half-Wave Dipole Antenna 13.7 A half-wave dipole antenna is driven by a 24 V, 200 MHz source having an internal impedance of 40 . Ocean 10_Sadiku_Ch10.indd 547 11/11/17 2:48 PM 548 CHAPTER 10 ELECTROMAGNETIC WAVE PROPAGATION F F Air FIGURE 10.25 For Problem 10.65. (b) This is the case of motional emf: Vemf 5 3 1 u 3 B 2 # dl 5 3 L 0 x5, 1 uay 3 Baz 2 # dx ax 5 2uB, 5 220A4 3 1023 2 A0.06 2 5 24.8 mV (c) Both transformer emf and motional emf are present in this case. to be aligned to an 8- or 16-byte boundary. This is the standing wave ratio on the line segment between the stub and the load (see Figure 11.18); s 5 1 to the left of the stub because the line is matched, and s 5 ` along the stub because the stub is shorted. We should note that the pattern in Figure 13.17(c) is not the resultant pattern but the group pattern of the three-element array. Solution: Ae 5 l5 l2 G 1 u, f 2 4p d c 3 3 108 5 5 10 m f 30 3 106 Gd 1 u, f 2 5 h 120p 2 f 21u 2 5 f 1 u 2 5 1.64f 2 1 u 2 pRrad 73p Gd max 5 1.64 Ae max 5 102 1 1.64 2 5 13.05 m2 4p Pr 5 ave Ae 5 5 E20 A 2h e 1 2 3 1023 2 2 13.05 5 69.23 nW 240p PRACTICE EXERCISE 13.8 Determine the maximum effective area of a Hertzian dipole of length 10 cm operating at 100 MHz. are specified. This mode is selected by -mno-shared. Position-independent code requires special support, and therefore works They could be chosen by using eq. These researchers, who were the first to bend waves without any reflection, now plan to further develop the cloak to make it omnidirectional, hiding the object from every angle. 80 bits can speed some programs by 2% or more. Equation (7.33) or (7.34) shows that magnetostatic fields have no sources or sinks.