42 0 obj <>/Filter/FlateDecode/ID[]/Index[21 40]/Info 20 0 R/Length 97/Prev 73865/Root 22 0 R/Size 61/Type/XRef/W[1 2 1]>>stream Q BT 0.8572 0 0 1 30.96 728.64 Tm 3 Tr 0 0 0 rg /F0 8.88 Tf 0.5329 Tc -0.2597 Tw (Fig. ) 0000011402 00000 n If this system were simply prepared as a basic RLC circuit, the results would show a very high number of poles in the networks transfer function; SPICE results would actually show the network resonating at the pole frequencies. Watch this episode or listen on the go now. hmo8?ZQVH.E w] !/)$(SxIIB"7Q$^D8gp/D>%8>LI!DH_qxO~"+x,4TSKo]lcN1*ru0Dctb9Fq]&epDKqB~$YA'k|O tf8}jsCT |CT:U]A,v$ kpjG:Wt+!O:!Ykj5/cSjxEN2[B All real power plane arrangements in a PCB have some resonances, and these resonances can be excited by emission of a propagating electromagnetic wave in the structure. His background in scientific research spans topics in nanoparticle lasers, electronic and optoelectronic semiconductor devices, environmental sensors, and stochastics. Thermal stress analysis helps achieve reliability and stability in multilayer PCBs by identifying thermal stress points in the circuit. The standard enthalpy of combustion is the heat energy released when a mole of fuel is burned under standard conditions. 0000032712 00000 n Cadence Design Systems, Inc. All Rights Reserved. Q q 599.04 0 0 25.2 0 264.48 cm /im53 Do endstream endobj 46 0 obj 44 endobj 47 0 obj << /Length 46 0 R >> stream Tj 0 Tr 23.2383 0 TD 3 Tr 0.5429 Tc -0.2714 Tw (2. ) What Is Cross Spectral Density and When Should You Use It? Q q 599.04 0 0 25.2 0 239.28 cm /im54 Do endstream endobj 48 0 obj 44 endobj 49 0 obj << /Length 48 0 R >> stream 0000000999 00000 n Q q 599.04 0 0 25.2 0 617.28 cm /im39 Do endstream endobj 18 0 obj 44 endobj 19 0 obj << /Length 18 0 R >> stream This is because, for the (0, 0, 1) resonance, the resonant frequencies corresponding to the vertical direction are hundreds of GHz. Get started with surface mounted sub-assemblies in this hands-on wireless module designs project.  | , Entry Level, Professional PCB Design Tool, Free PCB design for makers, open source and non-profits, See why and how to switch to Altium from other PCB design tools, Extensive, Easy-to-Use Search Engine for Electronic Parts. Q q 599.04 0 0 25.2 0 163.68 cm /im57 Do endstream endobj 54 0 obj 44 endobj 55 0 obj << /Length 54 0 R >> stream An set of example impedance spectra showing the structural resonances due to the power/ground plane pair arrangement is shown below. If your next system design depends on the natural power-plane capacitance to limit You can analyze multiple layers at a time. This is our cue that the above resonances are all k = 0 resonances, just as we would expect. Q q 599.04 0 0 25.2 0 314.88 cm /im51 Do endstream endobj 42 0 obj 44 endobj 43 0 obj << /Length 42 0 R >> stream Tj 0 Tr 47.8764 0 TD 3 Tr 0.6435 Tc -0.3887 Tw (Table ) Tj 0 Tr 29.9578 0 TD 3 Tr 0.362 Tc -0.0603 Tw (I ) Tj 0 Tr 7.5594 0 TD 3 Tr 0.732 Tc -0.4919 Tw (shows ) Tj 0 Tr 30.7977 0 TD 3 Tr 0.6033 Tc -0.3418 Tw (the ) Tj 0 Tr -280.8192 -10.56 TD 3 Tr 0.6334 Tc -0.377 Tw (resonant ) Tj 0 Tr 43.1168 0 TD 3 Tr 0.6106 Tc -0.3503 Tw (frequencies ) Tj 0 Tr 55.1559 0 TD 3 Tr 0.7239 Tc -0.4825 Tw (and ) Tj 0 Tr 20.4385 0 TD 3 Tr 0.6033 Tc -0.3418 Tw (the ) Tj 0 Tr 18.7586 0 TD 3 Tr 0.6342 Tc -0.3779 Tw (corresponding ) Tj 0 Tr 68.8749 0 TD 3 Tr 0.8044 Tc -0.5764 Tw (mode ) Tj 0 Tr 29.3978 0 TD 3 Tr 0.5745 Tc -0.3083 Tw (indices ) Tj 0 Tr 34.9974 0 TD 3 Tr 0.7239 Tc -0.4825 Tw (up ) Tj 0 Tr 15.6788 0 TD 3 Tr 0.5429 Tc -0.2714 Tw (to ) Tj 0 Tr -285.8588 -11.04 TD 3 Tr 0.732 Tc -0.4919 Tw (3GHz. ) The exact resonant frequencies in a complex structure like the PDN on an integrated circuit or a circuit board shouldnt be treated with circuit models. 0000002460 00000 n Tj 0 Tr -185.6262 -10.8 TD 3 Tr 0.744 Tc -0.506 Tw (As ) Tj 0 Tr 15.1189 0 TD 3 Tr 0.6703 Tc -0.42 Tw (mentioned ) Tj 0 Tr 51.5162 0 TD 3 Tr 0.7239 Tc -0.4825 Tw (and ) Tj 0 Tr 20.4385 0 TD 3 Tr 0.6837 Tc -0.4356 Tw (as ) Tj 0 Tr 12.0391 0 TD 3 Tr 0.4424 Tc -0.1541 Tw (will ) Tj 0 Tr 19.5985 0 TD 3 Tr 0.7239 Tc -0.4825 Tw (be ) Tj 0 Tr 13.999 0 TD 3 Tr 0.5046 Tc -0.2266 Tw (illustrated ) Tj 0 Tr 50.3963 0 TD 3 Tr 0.5027 Tc -0.2245 Tw (in ) Tj 0 Tr 11.7591 0 TD 3 Tr 0.6033 Tc -0.3418 Tw (the ) Tj 0 Tr 17.6387 0 TD 3 Tr 0.5975 Tc -0.3351 Tw (sequel, ) Tj 0 Tr 34.1575 0 TD 3 Tr 0.5932 Tc -0.3301 Tw (only ) Tj 0 Tr 22.3983 0 TD 3 Tr 0.6033 Tc -0.3418 Tw (the ) Tj 0 Tr -280.5392 -10.8 TD 3 Tr 0.7893 Tc -0.5588 Tw (TEM-mode ) Tj 0 Tr 56.2758 0 TD 3 Tr 0.4424 Tc -0.1541 Tw (will ) Tj 0 Tr 19.3186 0 TD 3 Tr 0.7239 Tc -0.4825 Tw (be ) Tj 0 Tr 13.719 0 TD 3 Tr 0.5429 Tc -0.2714 Tw (of ) Tj 0 Tr 10.9192 0 TD 3 Tr 0.6395 Tc -0.384 Tw (importance ) Tj 0 Tr 55.4359 0 TD 3 Tr 0.7009 Tc -0.4557 Tw (between ) Tj 0 Tr 40.597 0 TD 3 Tr 0.6033 Tc -0.3418 Tw (the ) Tj 0 Tr 17.3587 0 TD 3 Tr 0.7078 Tc -0.4638 Tw (power ) Tj 0 Tr 29.9578 0 TD 3 Tr 0.5975 Tc -0.3351 Tw (planes. ) :' ) Tj 0 Tr 9.6811 0 TD 3 Tr 0.2786 Tc -0.0854 Tw ('. ) 0000032978 00000 n Tj 0 Tr -10.6392 -10.56 TD 3 Tr 0.7373 Tc -0.4982 Tw (The ) Tj 0 Tr 22.9583 0 TD 3 Tr 0.6033 Tc -0.3418 Tw (basic ) Tj 0 Tr 28.2779 0 TD 3 Tr 0.5791 Tc -0.3136 Tw (simulation ) Tj 0 Tr 54.036 0 TD 3 Tr 0.6918 Tc -0.445 Tw (space ) Tj 0 Tr 29.9578 0 TD 3 Tr 0.5832 Tc -0.3183 Tw (consists ) Tj 0 Tr 40.877 0 TD 3 Tr 0.5429 Tc -0.2714 Tw (of ) Tj 0 Tr 13.439 0 TD 3 Tr 0.7239 Tc -0.4825 Tw (a ) Tj 0 Tr 9.7993 0 TD 3 Tr 0.5923 Tc -0.329 Tw (rectangular ) Tj 0 Tr 57.6757 0 TD 3 Tr 0.6998 Tc -0.4544 Tw (mesh, ) Tj 0 Tr -268.7801 -10.8 TD 3 Tr 0.5731 Tc -0.3066 Tw (with ) Tj 0 Tr 25.1981 0 TD 3 Tr 0.7239 Tc -0.4825 Tw (an ) Tj 0 Tr 15.1189 0 TD 3 Tr 0.6345 Tc -0.3783 Tw (absorbing ) Tj 0 Tr 49.5563 0 TD 3 Tr 0.6787 Tc -0.4298 Tw (boundary ) Tj 0 Tr 48.9964 0 TD 3 Tr 0.5765 Tc -0.3105 Tw (condition ) Tj 0 Tr 48.4364 0 TD 3 Tr 0.6998 Tc -0.4544 Tw (\(ABC\) ) Tj 0 Tr 34.9974 0 TD 3 Tr 0.5429 Tc -0.2714 Tw (at ) Tj 0 Tr 12.879 0 TD 3 Tr 0.6033 Tc -0.3418 Tw (the ) Tj 0 Tr 19.3186 0 TD 3 Tr 0.6502 Tc -0.3965 Tw (edges, ) Tj 0 Tr 31.6377 0 TD 3 Tr 0.5429 Tc -0.2714 Tw (to ) Tj 0 Tr -286.1388 -10.8 TD 3 Tr 0.5982 Tc -0.3359 Tw (simulate ) Tj 0 Tr 44.5167 0 TD 3 Tr 0.7239 Tc -0.4825 Tw (an ) Tj 0 Tr 16.5188 0 TD 3 Tr 0.4675 Tc -0.1834 Tw (infinite ) Tj 0 Tr 38.0772 0 TD 3 Tr 0.6368 Tc -0.3809 Tw (space. ) power-supply noise, check to see how the round-trip delay across your board compares with This The presence of chip caps on the PDN also helps keep the total impedance low as measured on the chip. graphics look really cool). For our arrangement above, we would have the following formula for the eigenfrequencies of the plane pair waveguide: Theoretically, there is an infinite set of possible frequencies, and these are indexed by the set of integers (i, j, k). Tj 0 Tr 33.3175 0 TD 3 Tr 0.7139 Tc -0.4708 Tw (They ) Tj 0 Tr 27.9979 0 TD 3 Tr 0.6301 Tc -0.3731 Tw (are ) Tj 0 Tr 17.6387 0 TD 3 Tr 0.5631 Tc -0.2949 Tw (sur- ) Tj 0 Tr -278.0194 -10.8 TD 3 Tr 0.6837 Tc -0.4356 Tw (rounded ) Tj 0 Tr 41.4369 0 TD 3 Tr (by ) Tj 0 Tr 14.8389 0 TD 3 Tr 0.7239 Tc -0.4825 Tw (a ) Tj 0 Tr 8.9593 0 TD 3 Tr 0.5108 Tc -0.2339 Tw (dielectric ) Tj 0 Tr 45.9166 0 TD 3 Tr 0.5731 Tc -0.3066 Tw (material ) Tj 0 Tr 41.9969 0 TD 3 Tr (with ) Tj 0 Tr 24.6382 0 TD 3 Tr 0.7239 Tc -0.4825 Tw (a ) Tj 0 Tr 8.1194 0 TD 3 Tr 0.5228 Tc -0.248 Tw (relative ) Tj 0 Tr 38.0772 0 TD 3 Tr 0.5128 Tc -0.2362 Tw (permittivity ) Tj 0 Tr 59.9156 0 TD 3 Tr 0.6435 Tc -0.3887 Tw (E?, ) Tj 0 Tr -283.619 -10.8 TD 3 Tr 0.6837 Tc -0.4356 Tw (as ) Tj 0 Tr 12.879 0 TD 3 Tr 0.4625 Tc -0.1776 Tw (is ) Tj 0 Tr 10.3592 0 TD 3 Tr 0.7481 Tc -0.5107 Tw (shown ) Tj 0 Tr 32.4776 0 TD 3 Tr 0.5027 Tc -0.2245 Tw (in ) Tj 0 Tr 12.5991 0 TD 3 Tr 0.5329 Tc -0.2597 Tw (Fig. ) Within the PDN in a PCB, excitation of resonances can occur inside the parallel plane structure, leading to strong emission at the edge of the board. 0000007319 00000 n Tj 0 Tr 15.9588 0 TD 3 Tr 0.5872 Tc -0.323 Tw (Point ) Tj 0 Tr 29.9578 0 TD 3 Tr 0.362 Tc -0.0603 Tw (I ) Tj 0 Tr 8.3994 0 TD 3 Tr 0.6998 Tc -0.4544 Tw (marks ) Tj 0 Tr 32.7576 0 TD 3 Tr 0.6033 Tc -0.3418 Tw (the ) Tj 0 Tr 19.5985 0 TD 3 Tr 0.5803 Tc -0.315 Tw (current ) Tj 0 Tr 38.0772 0 TD 3 Tr 0.609 Tc -0.3485 Tw (source. ) 2%,8`5s. Tj 0 Tr 14.3878 0 TD 3 Tr 0.5618 Tc -0.312 Tw (Transfer ) Tj 0 Tr 37.7341 0 TD 3 Tr 0.674 Tc -0.4389 Tw (impedance ) Tj 0 Tr 47.7785 0 TD 3 Tr 0.4853 Tc -0.2254 Tw (of ) Tj 0 Tr 10.8587 0 TD 3 Tr 0.5392 Tc -0.2864 Tw (the ) Tj 0 Tr 16.5596 0 TD 3 Tr 0.4275 Tc -0.16 Tw (finite ) Tj 0 Tr 24.7036 0 TD 3 Tr 0.5893 Tc -0.343 Tw (planes ) Tj 0 Tr ET BT 0.8572 0 0 1 307.44 269.76 Tm 3 Tr /F0 8.88 Tf 0.6435 Tc -0.3887 Tw (Since ) Tj 0 Tr 27.9979 0 TD 3 Tr 0.925 Tc -0.7171 Tw (R ) Tj 0 Tr 11.7591 0 TD 3 Tr 0.4625 Tc -0.1776 Tw (is ) Tj 0 Tr 11.4791 0 TD 3 Tr 0.6133 Tc -0.3535 Tw (very ) Tj 0 Tr 24.0782 0 TD 3 Tr 0.6033 Tc -0.3418 Tw (close ) Tj 0 Tr 25.7581 0 TD 3 Tr 0.5429 Tc -0.2714 Tw (to ) Tj 0 Tr 13.999 0 TD 3 Tr 0.6334 Tc -0.377 Tw (one, ) Tj 0 Tr 23.5183 0 TD 3 Tr 0.7239 Tc -0.4825 Tw (a ) Tj 0 Tr 9.2393 0 TD 3 Tr (good ) Tj 0 Tr 26.598 0 TD 3 Tr 0.6249 Tc -0.3671 Tw (approximation ) Tj 0 Tr 72.7946 0 TD 3 Tr 0.4625 Tc -0.1776 Tw (is ) Tj 0 Tr 10.9192 0 TD 3 Tr 0.5429 Tc -0.2714 Tw (to ) Tj 0 Tr 13.999 0 TD 3 Tr 0.4826 Tc -0.201 Tw (ig- ) Tj 0 Tr -283.619 -10.8 TD 3 Tr 0.6535 Tc -0.4004 Tw (nore ) Tj 0 Tr 24.0782 0 TD 3 Tr 0.6033 Tc -0.3418 Tw (the ) Tj 0 Tr 18.7586 0 TD 3 Tr 0.6971 Tc -0.4513 Tw (second ) Tj 0 Tr 34.9974 0 TD 3 Tr 0.6435 Tc -0.3887 Tw (term ) Tj 0 Tr 26.0381 0 TD 3 Tr 0.5027 Tc -0.2245 Tw (in ) Tj 0 Tr 13.159 0 TD 3 Tr 0.6033 Tc -0.3418 Tw (the ) Tj 0 Tr 19.0386 0 TD 3 Tr 0.6787 Tc -0.4298 Tw (boundary ) Tj 0 Tr 48.9964 0 TD 3 Tr 0.555 Tc -0.2855 Tw (condition, ) Tj 0 Tr 50.9562 0 TD 3 Tr 0.6234 Tc -0.3653 Tw (reducing ) Tj 0 Tr 44.2367 0 TD 3 Tr 0.6033 Tc -0.3418 Tw (the ) Tj 0 Tr -280.2592 -10.8 TD 3 Tr 0.6665 Tc -0.4155 Tw (problem ) Tj 0 Tr 41.9969 0 TD 3 Tr 0.5429 Tc -0.2714 Tw (to ) Tj 0 Tr 14.2789 0 TD 3 Tr 0.7239 Tc -0.4825 Tw (a ) Tj 0 Tr 9.2393 0 TD 3 Tr 0.5688 Tc -0.3016 Tw (perfect ) Tj 0 Tr 36.3973 0 TD 3 Tr 0.6122 Tc -0.3522 Tw (resonator ) Tj 0 Tr 48.4364 0 TD 3 Tr 0.5731 Tc -0.3066 Tw (with ) Tj 0 Tr 25.1981 0 TD 3 Tr 0.5631 Tc -0.2949 Tw (four ) Tj 0 Tr 23.2383 0 TD 3 Tr 0.5688 Tc -0.3016 Tw (perfect ) Tj 0 Tr 37.2372 0 TD 3 Tr 0.5966 Tc -0.334 Tw (magnetically ) Tj 0 Tr -236.0225 -10.8 TD 3 Tr 0.6274 Tc -0.3699 Tw (conducting ) Tj 0 Tr 53.756 0 TD 3 Tr 0.5711 Tc -0.3043 Tw (walls ) Tj 0 Tr 26.318 0 TD 3 Tr 0.7239 Tc -0.4825 Tw (and ) Tj 0 Tr 19.5985 0 TD 3 Tr 0.6703 Tc -0.42 Tw (two ) Tj 0 Tr 20.1585 0 TD 3 Tr 0.5688 Tc -0.3016 Tw (perfect ) Tj 0 Tr 35.2774 0 TD 3 Tr 0.5128 Tc -0.2362 Tw (electric ) Tj 0 Tr 36.3973 0 TD 3 Tr 0.6354 Tc -0.3793 Tw (conductors ) Tj 0 Tr 54.8759 0 TD 3 Tr 0.5631 Tc -0.2949 Tw (\(the ) Tj 0 Tr 21.2784 0 TD 3 Tr 0.7078 Tc -0.4638 Tw (power ) Tj 0 Tr -267.6602 -10.8 TD 3 Tr 0.5781 Tc -0.3125 Tw (planes\). )