R. F. Harrington, Time-Harmonic Electromagnetic Fields. Hoboken, NJ: Wiley, 2001, ch. 3.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....term is the scattered field off the j th subscatterer. Therefore, the amplitude of the third term must be related to the total amplitude of the first two terms via the isolated scatterer T matrix of the j th subscatterer, i.e. T j(1) Here, T j(1) is diagonal for the spherical scatterer [31] [33] [34] Consequently, we have a j = T j(1) Delta 6 4ff js Delta e s 7 5 total impinging field amplitude at j th subscatterer ; j = 1; Delta Delta Delta ; N: 11) Essentially, we match the boundary condition at the surface of the j th subscatterer instead of at the center of the ....

....lm (k; r) Psi (r )fi ;lm : 17) Efficient recurrence relations have been derived for fi ;lm such that it can be derived from fi ;00 [38] There are only 6 independent elements in ff ij . The T matrix for the sphere can be found from transition coefficients, which are given by [31] [33] [34] l (k b a) j l (k s a) Gamma h l (k b a) j ; 34) j l (k s a) Gamma h l (k b a) j ; 35) where t lm is the transition coefficient of TE to r mode, and t lm is the transition coefficient of TM to r mode. j l (x) xj l (x) h l (x) xh l (x) and a is the ....

R. F. Harrington, Time-Harmonic Electromagnetic Fields. New York: McGrawHill, 1961.

....t r and t a are the thicknesses of the ruby and air dielectrics. An air gap of 0.01 mm results in an e#ective dielectric constant of 9.18. 7 Alternatively, the e#ect of the air gap can be calculated using the formula for the change in resonant frequency of a cavity due to a material perturbation [11]. The values of the e#ective dielectric constants obtained by using the two di#erent approaches are in close agreement. The resonant frequencies of the cavity near 32 GHz (signal) and 66.4 GHz (pump) can be shifted in several ways. Changing the e#ective dielectric constant shifts the signal and ....

R. F. Harrington, Time-Harmonic Electromagnetic Fields, New York: McGrawHill Book Company, 1961.

....4 ) 4.25 Table 1. Experimental timings for option price modeling (in seconds) 12 G. Cheng, G. C. Fox, T. Lin, and T. Haupt 5. A Computational Electromagnetic Application 5.1. Introduction and Problem Description Electromagnetic scattering is a widely encountered problem in electromagnetics [8], with important applications in industry such as microwave equipment, radar, antenna, aviation, and electromagnetic compatibility design. Figure 5 illustrates the EMS problem we are modeling, as well as physical parameters tunable by a user. Above an infinite conductor plane there is an incident ....

....versions on a high speed workstation[9] Parallel models on high performance systems provide a unique opportunity to interactively visualize EMS simulation in real time. This problem requires a response time of the simulation cycle that is not possible on conventional hardware. The moment method [8] is used as the numerical model for the EMS problem, which can be represented as: f Theta Y a Theta Y b g V = I ; Theta H = Lff ( V ; M ; Theta H 2 0 )g where Theta Y a : equivalent admittance matrix of the free space; Theta Y b : equivalent ....

R. F. Harrington, Time-Harmonic Electromagnetic Fields, McGraw-Hill Book Company, New York (1961).

....our performance prediction may be optimistically biased. For clarity, this paper focuses on estimation of a cylindrical symmetric target (whose profile is constant along the axis) with perfect electric conducting boundary, using transverse magnetic (TM) polarized incident plane waves [1] [22]. This setup gives rise to a relatively simple two dimensional (2 D) imaging problem using the scalar Helmholtz equation. The extension to transverse electric (TE) polarized incident plane waves is in principle similar and is briefly addressed. Section II sets up the parametric formulation of the ....

....TO PASSIVE RADAR 777 Fig. 3. Geometry of the first example. A cylinder of radius ae is illuminated from direction d = cos ; sin ) using a TM polarized plane wave. The CRB for the radius is computed by rotating a receiver located in x = R cos ; R sin ) The scattered wave is given by [22], 39] 36) where denotes the Bessel function of order . The gradient of with respect to can be computed by (37) using the properties of Bessel functions. Hence, for a sensor at location in (35) with noise variance , the CRB (14) on radius estimation is given by (38) where the superscript ....

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R. F. Harrington, Time-Harmonic Electromagnetic Fields. New York: McGraw-Hill, 1961.

....in Table C.7. Thus, T s = 0:015 0:085 4:05 4:25 4 0:9 = 12:0, and we calculate an expected speed up of S = 12:0=3:642 = 3:3. C.2 A Computational Electromagnetic Application C.2. 1 Problem Description Electromagnetic scattering is a widely encountered problem in electromagnetics [32, 69, 77], with important applications in industry such as microwave equipment, radar, APPENDIX C. CASE STUDIES IN CHAPTER 4 168 antenna, aviation, and electromagnetic compatibility design. Figure C.6 illustrates the EMS problem we are modeling. Above an infinite conductor plane there is an incident EM ....

R. F. Harrington. Time-Harmonic Electromagnetic Fields, McGraw-Hill Book Company, New York (1961).

....order for Lagrange multiplier is equal to p h in one direction and p v in the other, then K = p h (p v 1) p h 1)p v ; L = 2(p h p v ) p h Gamma 1) p v Gamma 1) 3. 14) The choice of functions n ; ff n is dictated by the form of the exact solution outside of the truncating sphere [12, 21, 8]. They are of the following form. n (r) 8 : i a r j e jk(r Gammaa) for n = 0 i a r j n 1 Gamma i a r j e jk(r Gammaa) for n 0; 3.15) ff n (r) a r n 2 e jk(r Gammaa) 3.16) Notice that, consistently with the exact solution representation, the leading ....

....of a plane wave on a perfectly conducting sphere, the closed form solution The incident electric field is assumed in the form of a plane wave polarized in xz plane and traveling in the z direction: E inc = E 0 e Gammaj kz ; 0; 0) 5. 1) The wave admits the following series representation: [12, 8, 21] E = 1 X n=0 X m= Gamma1;1 GammaA m n j n (kr) x Theta r s Y m n ( x) B m n ( n j n (kr) kr Y m n ( x) x j n (kr) kr j 0 n (kr) # r s Y m n ( x) 5.2) where A 1 n = Gamma E0 2 j Gamma(n 1) 2n 1 n(n 1) A Gamma1 n = GammaA 1 n n = 1; 2; ....

R.F. Harrington, Time-Harmonic Electromagnetic Fields, McGraw-Hill Book Co., New York, 1961.

....R 1,mn # 1,mn T 2,mn # 1 R 2,mn # 2,mn 1 R 1,mn # 1,mn # gmn (3.40) dmn = # R 2,mn # 2,mn T 2,mn # gmn (3.41) fmn = # 1 T 2,mn # gmn . 3.42) The solution for gmn is found using the Lorentz reciprocity theorem which is applied next. The Lorentz reciprocity theorem is stated as follows [125]: # S (E b H a E a H b ) n ds = ## (E a J b H a M b E b J a H b M a ) dv (3.43) where the independent electric and magnetic source currents J a , M a and J b , M b produce the electric and magnetic fields E a , H a and E b , H b in a volume# which is bounded by ....

R. F. Harrington, Time-Harmonic Electromagnetic Fields, New York: McGraw-Hill, 1961.

....of the structure to be analyzed is shown in figure 1. represents the area of the fictitious outer boundary to be used for terminating the FEM computational domain and represents the area of the input plane. The electric field inside the compuational domain satisfies the vector wave equation[4] (1) where and are the relative permittivity and relative permeability of the medium. The time dependency of is assumed through out this report. To facilitate the suitable solution of the partial differential equation in (1) via FEM, multiply equation (1) with a vector testing function and ....

....the computational volume and the equivalent magentic and electric current densities on the surface terminating the computational domain. Using the equivalent electric and magnetic current densities on the surface terminating the computational domain, the radiated electric far field is computed as [4] (24) where are the spherical coordinates of the observation point. The solution of equation (23) will also enables the calculation of electric field at the input plane, which can be used to calculte the reflection coefficient at the input plane [9] The input admittance is then calculated as ....

R.F.Harrington, Time Harmonic Electromagnetic Fields, McGraw Hill Inc, 1961.

....dense complex symmetric matrix, b(k) is the excitation vector, and e(k) is the unknown electric field coefficient vector. A(k) is evaluated as a sum of three matrices. 4) where (5) 6) 7) 8) Equations (6) and (7) are obtained by making use of the equivalence principle and image theory [23] and follow the procedure given in [24] and R is the distance between source point and the observation point. M is the equivalent magnetic current over the aperture . indicates del operation over the source coordinates and indicates the surface integration over the source region. Equation (8) is ....

R.F.Harrington, Time Harmonic Electromagnetic Fields, McGraw Hill Inc, 1961.

....the boundary conditions of the problem. These requirements lead to a (usually large) set of linear equations that are solved for the source strengths. These are very useful methods in their niches. Like the methods of ray tracing, however, they cannot account for non local phenomena. In Harrington [1], methods were developed for the solutions of time harmonic waves by writing the fields in terms of vector potentials that are governed by the Helmholtz equation. Exact solutions for varied but geometrically simple devices, such as rectangular and circular wave guides and posts, are given as a ....

....G TE;r b z j = Y 2 i G TM;t n t;y b x Gamma G TE;t b z j (2.48) Without loss of generality, each wave can be assumed to have the functional form G(x; y; z; t) f xn x yn y zn z c Gamma (2. 49) Then the usual functional dependence argument can be made on the surface [1], resulting in the deduction n i;x = n r;x (2.50) and Snell s law, n i;x c 1 = n t;x c 2 (2.51) As usual, these relationships (and the fact that all b n are unit vectors) can be used to uniquely determine b n r and b n t . Knowing the longitudinal directions b n for each wave, 26 equation ....

R. F. Harrington, Time-Harmonic Electromagnetic Fields. New York: McGrawHill, 1961.

....in this paper will be presented in terms of the electric field E; the parallel development for the magnetic field H is obtained by making the substitutions E H and ffl. It is well known that the field solution in a three dimensional cavity can be formulated in a variational form [10]. If the cavity contains only lossless materials, the variational functional in terms of E can be written as F ( E) Z Omega 1 r k r Theta E k 2 Gammak 2 ffl r k E k 2 d Omega (7) From the functional (7) we note that both r Theta E and E need to be square ....

R. F. Harrington, Time Harmonic Electromagnetic Fields, New York: McGraw-Hill, 1961.

....we consider only current sources, but the extension to magnetic sources is straightforward. Therefore, we can write a rigorous solution as follows: G = T V dr r J r r r E (1) where ) r r G is the tensor Green s function subject to the appropriate boundary conditions [4]. Figure 1: Communication with EM waves between a transmitting and receiving domains in the presence of material bodies (B) V T V R Jr( E(r) B 111 Our first goal is to evaluate the degrees of freedom for communication with EM waves. We consider the space of vectors of functions [ ....

R. Harrington, Time harmonic electromagnetic fields ( ).

....the j th magnetic layer. The four vertical walls are metal. gation at the interface of two adjacent dielectrics with relative permitivities # 1 and # 2 as shown in Fig. 3.6. The equivalence principal is applied to obtain separate representation for the field in region 1 (Z 0) and region 2 (Z 0) [72,73] by short circuiting the aperture (covering the aperture by an electric conductor) Assuming a propagating wave H i is incident from region 1 into region 2. The field in region 1 is determined by the incident field and the equivalent magnetic current M over the aperture area produced by the ....

Harrington, R. F., Time-Harmonic electromagnetic fields. McGraw-Hill Book Co., New York 1961, pp. 106-120.

....the complex conjugate of the impedance functional, Z#k## Z # #k# 1 . If the integrating surface is chosen to coincide with the plane of the screen where E 1 satisfies the boundary condition n # E 1 #0,Zreduces to Z # Z H 1 # #n #E 2 #dS# (10) By using Rumsey s reaction concept [3] [4], we can derive the variational expression for Z as [5] Z # 1 4j## h R Sa H i # #n #E a #dS i 2 R Sa R Sa #n #E a #r## # G 0 #rjr 0 # # #n # E a #r 0 ##dSdS 0 # (11) where H i is the incident magnetic field on the screen (previously denoted as H 1 ) E a is the ....

Harrington, R. F., Time Harmonic Electromagnetic Fields, McGraw-Hill Book Company, Inc., New York, 1961.

....or what is the e#ect of the transmitter and receiver locations. For clarity, this paper focuses on estimation of a cylindrical symmetric target (whose profile is constant along the z axis) with perfect electric conducting boundary, using transverse magnetic (TM) polarized incident plane waves [1, 22]. This setup gives rise to a relatively simple twodimensional imaging problem using the scalar Helmholtz equation. The extension to non symmetric three dimensional targets with arbitrary polarized incident waves is in principle similar and is currently under investigation. Section 2 sets up the ....

....# centered at the origin. We think of # as a scalar parameter that parameterizes the shape of the object. Let d = cos # 0 , sin # 0 ) We observe a noisy version of the scattered wave u s (x) using a single sensor at the location x = R cos #, R sin #) 55) The scattered wave is given by [22, 36] u s (x) # # n= # j n J n (k#) H (1) n (k#) H (1) n (kR)e jn(# #o ) 56) where J n ( denotes the Bessel function of order n. The gradient of u s (x) with respect to # can be computed by #u s (x) ## = # # n= # j n kJ # n (k#)H (1) n (k#) kJ n (k#)H # ....

R. F. Harrington, Time-Harmonic Electromagnetic Fields. McGraw-Hill Book Co., 1961.

....equation (1) can be written in weak form as [1] 2) where is the vector testing function, is the aperture surface, and is the input surface (see fig. 1) is the magnetic field at the aperture and is the magnetic field at the input surface. In accordance with the equivalence principle [9], the fields inside the cavity can be decoupled to the fields outside the cavity by closing the aperture with a Perfect Electric Conductor (PEC) and introducing the equivalent magnetic current. 3) over the extent of the aperture. Making use of the image theory, the integrals over in equation (2) ....

R.F.Harrington, Time Harmonic Electromagnetic Fields, McGraw Hill Inc, 1961.

....One can distinguish very well the scattered wave on the right side. No deterioration of the solution appears at the corners of the square section cylinder. 3. 2 Time harmonic results Some bistatic RCS simulations are presented for infinite circular cylinders and compared with exact solutions [17]. TE and TM results are shown both in perfectly conducting and coated cases. The bodies are illuminated by a continuous harmonic incident wave and the calculations are performed until the solution reaches a sinusoidal steady state. We use a criterion based on the energy (section 2) We compute ....

HARRINGTON R.F., Time-harmonic electromagnetic fields, Mc Graw-Hill (1961)

....of the structure to be analyzed is shown in figure 1. represents the outer surface of the 3D object, represents the area of the fictitious outer boundary to be used for terminating the FEM computational domain. The electric field inside the compuational domain satisfies the vector wave equation[5] (1) where and are the relative permittivity and relative permeability of the medium. The time dependency of is assumed through out this report. To facilitate the suitable solution of the partial differential equation in (1) via FEM, multiply equation (1) with a vector testing function and ....

....the computational volume and the equivalent magentic and electric current densities on the surface terminating the computational domain. Using the equivalent electric and magnetic current densities on the surface terminating the computational domain, the scattered electric far field is computed as [5] (33) where are the spherical coordinates of the observation point. The radar cross section is given by (34) F 1 e F 2 I 0 = F 1 1 r T ( E ( dv . V k o 2 e r T Edv . V = F 2 T J . s d S o = F 1 F 2 M 1 M 2 e I ....

R.F.Harrington, Time Harmonic Electromagnetic Fields, McGraw Hill Inc, 1961.

....for EMS, including decomposition of computation, system integration, interstage communication and concurrent control, and a high level DVE based distributed programming model. 2 The Electromagnetic Scattering Problem Electromagnetic scattering is a widely encountered problem in electromagnetics [7, 10, 21], with important applications in industry such as microwave equipment, radar, antenna, aviation, and electromagnetic compatibility design. Figure 1 illustrates the EMS problem we are modeling. Above an infinite conductor plane, there is an incident EM field in free space. Two slots of equal width ....

R. F. Harrington, Time-Harmonic Electromagnetic Fields, McGraw-Hill Book Company, New York (1961).

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R. F. Harrington, Time-Harmonic Electromagnetic Fields. Hoboken, NJ: Wiley, 2001, ch. 3.

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R. F. Harrington. Time-Harmonic Electromagnetic Fields. McGraw Hill, New York, 1961.

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R. F. Harrington, Time-Harmonic Electromagnetic Fields. New York: McGraw-Hill, 1961, pp. 348--355.

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Roger F. Harrington, Time-Harmonic Electromagnetic Fields, McGRAW-HILL, New York, 1961.

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R. F. Harrington, Time-Harmonic Electromagnetic Fields. New York: McGraw-Hill, 1961, pp. 152--155.

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Harrington, Roger F.: Time-Harmonic Electromagnetic Fields. McGraw-Hill Book Co., Inc., 1961.

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