RF MODULE

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or in more detail, with K = 0, where u y,test = ∂u test /∂y and similarly for the other test function derivatives. The dot product in the domain integral is interpreted as a dot product operating on the rows of the matrices so that where 280 | CHAPTER 4: OPTICS AND PHOTONICS MODELS ∫ Ω ∫ ∫ 0 = vσndΓ – ∇v⋅ σdΩ + v⋅KdΩ ∫ ∂Ω Ω 0 = utest vtest wtest – ∂Ω ∫ Ω ∫ Ω σx τxy 0 τyx σy 0 0 0 σz n x n y n z dΓ ⎛ ⎞ ⎜ ux, test uy, test uz, test σx τxy 0 ⎟ ⎜ vx, test vy, test v ⋅ z, test τyx σy 0 ⎟dΩ ⎜ ⎟ ⎜ ⎝ wx, test wy, test wz, test 0 0 σ ⎟ z ⎠ ⎛ ⎞ ⎜ ux, test uy, test uz, test σx τxy 0 ⎟ ⎜ vx, test vy, test v ⋅ z, test τyx σy 0 ⎟dΩ ⎜ ⎟ ⎜ ⎝ wx, test wy, test wz, test 0 0 σ ⎟ z ⎠ = ∫ Ω ⎛ ⎝ + + ux, test vx, test wx, test uy, test vy, test wy, test uz, test vz, test ⋅ ⋅ wz, test σ x τ xy 0 ⋅ τ yx σ y 0 00σ z ⎠ ⎞ dΩ σx = -------------------------------------- E ( ( 1 – ν)ε ( 1 + ν) ( 1 – 2ν) x + νεy + νεz – ( 1 + ν)α( T– Tref) ) σy = -------------------------------------- E ( νε ( 1 + ν) ( 1 – 2ν) x + ( 1 – ν)εy+ νεz – ( 1 + ν)α( T– Tref) ) σz = -------------------------------------- E ( νε ( 1 + ν) ( 1 – 2ν) x + νεy + ( 1 – ν)εz– ( 1 + ν)α( T– Tref) ) τxy -------------------------------------- E 1 2ν ( 1 + ν) ( 1 – 2ν) – = ⎛---------------γ ⎞ ⎝ 2 xy⎠
and εx ∂u = ∂x εy ∂v = ∂y εz = ∂w ∂z γxy ∂u ∂v = + ∂y ∂x Note that the displacement variable w in the z direction is not available in the Plane Strain application mode. However, it is not needed since the generalized formulation assumes a certain fix shape of the deformation in the z direction. The same relations hold for the test functions, γxy, test εx, test εy, test εz, test u x test , In COMSOL Multiphysics, the test functions u test and v test are denoted u_test and v_test, respectively. Their derivatives u x,test, u y,test, v x,test, and v y,test are denoted ux_test, uy_test, vx_test, and vy_test, respectively. Note that the z components of the test functions are not available in the Plane Strain application mode. Using this notation, the weak form of Navier’s equation becomes (with K = 0) ∫ 0 = vσndΓ – ∂Ω ∫ Ω = This expression for the weak equation shows which terms you must add as weak terms to generalize the plane strain formulation. To see the difference compared to the ordinary plane strain formulation, the equation for σ z can be separated out according to = = = uy, test vy, test wz, test + vx, test ( τxy) dΩ εx, testσx + εy, testσy + εz, testσz + γxy, test STRESS-OPTICAL EFFECTS WITH GENERALIZED PLANE STRAIN | 281
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COMSOL Multiphysics RF MODULE V ERS
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CONTENTS Chapter 1: Introduction Mo
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Results and Discussion. . . . . . .
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Chapter 4: Optics and Photonics Mod
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1 Introduction The RF Module Model
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highlights. The categories here inc
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TABLE 1-1: RF MODULE MODEL LIBRARY
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2 Tutorial Models This chapter cont
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Results and Discussion Figure 2-1 s
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4 Draw a square with corners at (
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COMPUTING THE SOLUTION Click the So
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Results and Discussion The dipole a
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PHYSICS SETTINGS Variables 1 Choose
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5 Click OK to close the dialog box
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Model Library path: RF_Module/Tutor
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4 From the Solve menu, open the Sol
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them from the eigenvalues. The appl
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5 On the Port page, set the values
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5 On the Port page, enter 36.4 in t
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Waveguide Optimization Introduction
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Results and Discussion Figure 2-3 s
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Modeling Using the Graphical User I
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3 Select Boundary 7 and set the Con
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POSTPROCESSING AND VISUALIZATION Fo
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The solution takes a few minutes to
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Night side Earth surface Ionosphere
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Results and Discussion The model pr
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4 Select both spheres and click the
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RF and Microwave Models In this cha
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measure of the transmittance and re
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y 1 cm is at about 7.5 GHz. At the
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By feeding the circulator at a diff
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Importing the Geometry from a Binar
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MESH GENERATION This model uses the
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It is more instructive to look at t
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Note: When displaying S-Parameter v
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Monoconical RF Antenna Introduction
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50 Ω, to obtain maximum transmiss
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Figure 3-7 shows the antenna radiat
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2 Select the RF Module>Electromagne
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13 Zoom in around (0, 0) using the
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4 In the Contour levels area, click
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2 Clear the Keep current plot check
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6 Click the Solve button on the Mai
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Results and Discussion The figure b
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PHYSICS SETTINGS Point Settings Def
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2 In the x-axis area, select the Ex
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Because the impedance is inversely
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4 From the Space dimension list, se
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2 Select Boundaries 1, 2, 4, and 6.
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4 On the Pointwise Constraints page
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12 Click the Solve button on the Ma
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Module. The electromagnetic cavity
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EIGENFREQUENCY VS. TEMPERATURE By r
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GEOMETRY MODELING 1 Go to the Draw
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3 Set dx, dy, and dz to u, v, and w
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20 Select the Solve using solver se
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Computing the Solution Using a Para
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8 Click Solve. 9 When the parametri
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H-Bend Waveguide with S-parameters
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Model Library path: RF_Module/RF_an
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1 From the Postprocessing menu, cho
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The rectangular port is excited by
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Figure 3-16 shows a single-mode wav
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Figure 3-18: The S 21 parameter (in
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PHYSICS SETTINGS First set up the b
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FREEZING THE BOUNDARY MODE ANALYSIS
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Microwave Cancer Therapy Introducti
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The model takes advantage of the pr
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DOMAIN AND BOUNDARY EQUATIONS—HEA
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Figure 3-23: The computed microwave
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solutions for both the electromagne
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4 Select Subdomain 1, then enter th
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1 Click the Plot Parameters button
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sar_in_human_head_interp.txt. That
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The bioheat equation produces a sim
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3 Click OK. 4 From the Options menu
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17 In the Work-Plane Settings dialo
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SETTINGS SUBDOMAIN 19 epsilonr_brai
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4 Click the Init tab and type 0 in
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POSTPROCESSING AND VISUALIZATION 1
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The walls of the oven and the waveg
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Figure 3-29: Temperature in the cen
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3 Click the block symbol again and
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2 At the waveguide end, Boundary 23
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4 Click OK to generate the plot bel
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Because the filter cutoff should be
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the force is applied. Figure 3-32 d
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6 Then the ECAD Import Options dial
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PHYSICS SETTINGS Subdomain Settings
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solver takes more steps than it sto
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3 Select Subdomain 1 and clear the
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Balanced Patch Antenna for 6 GHz In
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k0 = ω ε0 µ 0 All metallic objec
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divided by the input power. In Figu
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Reference 1. E. Recht and S. Shiran
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10 Select the objects SQ2, CO1, and
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43 Specify two spheres with the fol
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inputs are feeding the antenna, lik
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the width of the PML is equal to λ
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a toggle button that shifts between
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5 Select Coarse solver from the tre
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maxE = max(EdB); minE = min(EdB); E
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exterior of the PML that shows a ve
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13 Choose Extrude from the Draw men
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2 Click the Settings button. 3 In t
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Sea Bed Logging Introduction The Se
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Figure 3-39: Electric field magnitu
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PHYSICS SETTINGS Scalar Variables 1
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5 Click the General tab. From the P
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Optics and Photonics Models In this
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Model Definition The model is built
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Model Library path: RF_Module/Optic
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PHYSICS SETTINGS Scalar Variables S
Page 237 and 238: POSTPROCESSING AND VISUALIZATION By
Page 239 and 240: Model Definition The geometry is a
Page 241 and 242: 2 In the list of application modes,
Page 243 and 244: Because the refractive index of GaA
Page 245 and 246: 5 Click OK twice to see the followi
Page 247 and 248: Bandgap Analysis of a Photonic Crys
Page 249 and 250: a 2 a 3 × b1 = 2π----------------
Page 251 and 252: The five lowest bands for the (1, 1
Page 253 and 254: Modeling Using the Graphical User I
Page 255 and 256: Subdomain Settings 1 Open the Subdo
Page 257 and 258: 3 Click the Parametric tab. Select
Page 259 and 260: 3 Click OK to see the following plo
Page 261 and 262: fem.appl{1}.prop.analysis = 'harmon
Page 263 and 264: Model Definition The mode analysis
Page 265 and 266: 2 Select the RF Module>Perpendicula
Page 267 and 268: 4 On the Contour page, give Magneti
Page 269 and 270: includes only two independent param
Page 271 and 272: OPTIONS AND SETTINGS 1 Open the Con
Page 273 and 274: The problem becomes well-posed by a
Page 275 and 276: POSTPROCESSING AND VISUALIZATION Th
Page 277 and 278: 7 Click OK. 8 From the Postprocessi
Page 279 and 280: the computed propagation constants
Page 281 and 282: 3 The default eigenmode is the one
Page 283 and 284: Compare these ideal values of the p
Page 285 and 286: Stress-Optical Effects with General
Page 287: The PDE solved is Navier’s equati
Page 291 and 292: Model Library path: RF_Module/Optic
Page 293 and 294: NAME EXPRESSION DESCRIPTION B2 0.65
Page 295 and 296: 2 In the Subdomain Expressions dial
Page 297 and 298: 4 Initialize the mesh in this geome
Page 299 and 300: Note: This model includes an extens
Page 301 and 302: 3 Enter 1.46 in the text field Sear
Page 303 and 304: In these expressions, w 0 is the mi
Page 305 and 306: After 90 fs the pulse has reached t
Page 307 and 308: 4 Select the RF Module>In-Plane Wav
Page 309 and 310: Boundary Conditions 1 From the Phys
Page 311 and 312: 6 Click the Remesh button; when the
Page 313 and 314: 2 On the General page, make sure th
Page 315 and 316: Propagation of a 3D Gaussian Beam L
Page 317 and 318: Figure 4-15: After 20 fs the pulse
Page 319 and 320: 7 Click the Delete Interior Boundar
Page 321 and 322: Boundary Conditions 1 From the Phys
Page 323 and 324: 5 From the Options menu, select Sup
Page 325 and 326: INDEX 3D electromagnetic waves mode
Page 327 and 328: efractive index 222, 254 resistance
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RF MODULE

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