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NEC Features INPUT Geometry Wires & Patches Environment Free Space Perfect Ground Real Earth Sources Voltage & Current Plane Wave C U R R E N T D I S T R I B U T I O N OUTPUT I & Q Distributions ZIN YIN PIN Power Budget PIN PRAD PLOSS Efficiency Fields Near & Far Gain Power, Directive, Average 1 NEC Features (Continued) INPUT LOADING Lumped Impedance Networks Transmission Lines OUTPUT Patterns Transmitting & Receiving Port Currents Network Voltages Coupling Information Scattered Fields 2 NEC Input Options Titles Group of Comments and descriptions Structure Specifications Wires GW Surface Patches SP Geometry Moves & Replications Move, Rotate, Duplicate Rotate, Duplicate (Z-Axis)(w/Symm) Reflect in Coordinate Planes (w/Symm) Scale Dimensions CM GA SM CE GC SC GM GR GX GS 3 NEC Input Options Performance Parameters Alters Matrix Frequency Stepping (Linear, Multipl.) Ground Conditions (P.G., R.C., SOMM) Structure Loading (Lumped, Distrib.) Alters Currents Excitations (XMT or RCV) Networks (Non-Radiative) Transmission Lines (Balanced) FR GN LD EX NT TL 4 NEC Input Options Performance Selection Radiation Patterns/Far Fields/Gain Near Fields Coupling Additional Ground Conditions (Patterns) Receive Currents Charges RP NE CP GD PT PQ NH Repetitive Use of Matrix and Exploit Partial Symmetry Create Numerical Greens Function WG Use Numerical Green’s Function GF 5 NEC Output Features Comments Structure Specifications (Wires and Patches) Segmentation Data Frequency Structure Impedance Loading Network Data Excitation at Network Connection Points Antenna Environment Matrix Timing Currents and Location Power Budget 6 NEC Output Features Charge Densities Near Fields Input Impedance Data Radiation Patterns Average Power Gain Scattering Cross Section Radiated Fields Near Ground Normalized Gain Coupling Data Plane Wave Excitation Receive Pattern 7 NEC2 Ground Conditions Perfectly conducting ground-image Reflection coefficient approximation (wire height > 0.1 ) Sommerfeld solution for wire over lossy earth Wire ground screen approximation Cliff approximations for radiated fields Ground wave calculations 8 Space Wave and Surface Wave x Wave Surface eR, s Observation Point Lossy Earth Direct wave follows free space attenuation Reflected wave path slightly longer + suffers some loss at reflection point Surface wave hugs the interface and decays rapidly 9 Wire Modeling Wire Specifications Example: GW TAG 1 No Segs 5 X1 Y1 Z1 0, 0, 0 X2 Y2 Z2 .5, 0, 0 Radius .001 Default is equal segment lengths ( D ) and uniform radius, but tapered radii (a) and variable segmentation is an option. Arcs are formed as sections of polygons 10 Wire Modeling Tag & Segment numbers help locate loads & sources Segment connections are described by integer arrays “+” Current Ref. Ex. 1 G.P. For automatic segment connection: Separation of segment ends Segment length 2 End 1 Seg# 1 1 2 1 2 3 -4 3 0 -5 4 10003 2 5 < 10-3 End 2 Free e nd Patch 0 11 Wire Modeling Wire Modeling Guidelines Segment Length D relative to wavelength is a key parameter a D D < 0.1 for accuracy in most cases D < 0.05 in critical regions D < 0.2 on long, straight segments Avoid extremely short segments (D < 10-4 ) 12 Wire Modeling a Must be small relative to both and D a < 0.5 D a < 2D a < ~ 0.1 with thin wire kernel with extended T.W. kernel since no transverse current & no variations around the wire are included 13 Wire Modeling Avoid: Large changes in radius (especially on short segments) Sharp bends in thick wires Wires that are connected must contact at segment ends Connection Separation/Length < 10-3 No Connection 14 Wire Modeling Use equal length segment lengths next to sources D * D ~ * D No voltage sources or loads at a wire open end ~ 15 Wire Modeling Source Modeling Guidelines Balanced: Source “gap” is a segment with E-field on it Unbalanced: Coax Feed Multiple: YIN YIN = Y1+Y2+Y3 16 Wire Modeling Computational Checks for RIN & Gain Find Radiated Power by integrating the far field: E PRAD Input Power: r2 = 2 r 1 PIN = VI 2 4p E h dW * For a Lossless Antenna 2 PIN = PRAD NEC prints “Average Power Gain” GAVE = 1 P G P d W = RA D when W = 4p WW PIN 17 Wire Modeling For a loss-free antenna, average gain is a check on solution accuracy Source voltage Vo V S NEC solves for current I (s) 1 Input power PIN = Re V 0 I * (0) o 2 PIN is sensitive to errors in I(s) Integrate radiated power over sphere in far field PRAD is a stationary function of I (s) For Loss-Free Antenna PRAD = PIN 18 Wire Modeling Average Power Gain G AVE = GPd W W W 1 G P = ( 4p Re E x H * / PIN 2 G A V E = kPRA D / PIN k = 1 for free space ( = 2 for perfect ground Corrected PIN = Computed PIN x (GAVE/k) Corrected Input Resistance = 2 GAVE PIN k | I (0)| 2 = Computed RIN x (GAVE/k) Corrected Gain = Computed Gain x (k/GAVE) 19 Wire Modeling Wires near lossy earth Reflection coefficient approximation is reasonable for: vertical wires at least 0.1 to 0.2 above the ground horizontal wires at least 0.4 above earth Sommerfeld/Norton works for: wires as close as 10-6 height should be several time radius {h2 + a2} 1/2 > 10-6 , h > ~ 3a 20 Surface Modeling Surface Specifications Area A Arbitrary Shape Patch has area & normal direction Center of Patch Input data: Coordinates of patch center, a, b, Area Other Options: Rectangular Triangular Quadrilateral 3 corners (RHR) “ 4 corners 21 Surface Modeling Area should be less than 0.04 2 (.2 x .2 ) Since no defined shape, avoid long, thin patches Since currents defined at center only, not good for edge currents Where radius of curvature is small, use smaller patches Surface must be closed and not too thin (no plates, no fins or wings) Wires must connect at patch centers Increase definition at connection points 22 Surface Modeling Wire Grid Modeling Use wire grids where edge connections are needed Wire grid = surface if mesh is “small enough” Problem: - can’t afford real fine meshes - sparse meshes have too much L, not enough C Possible Solutions: - negative L distributed loading - fat, rod-like wires 23 Surface Modeling Wire gridding is acceptable for thin structures, plates, wings, etc. and for far field responses / not for surface charge or currents Grid size not too critical (~ 0.1 at midband) D/a not critical (10< D/a < 30 good for wires attaching to surface) Use equal radii and segmentation at junctions 24 Patch vs. Wire Grid/Resources L W Patch: 2LW Grid: 2LW + L + W But Patch can be .2 on a side … 2 LG (2 x WG 2 ) LW 2 Ex: 4x2 grid 20x20 grid Patch: 4 Grid: 22 Patch: 200 Grid: 840 Usually find patch model will save about 40% on computational resources 25 GC -- Wire Radius/Segment Tapering Set radius = 0 on the GW card > follow with a GC card RDEL -- Ratio of adjacent segment lengths RAD 1, RAD 2 -- Radius of 1st segment, radius of last segment Make RDEL < 2 and adjacent segments radii ratio < 2 26 GE -- Geometry End (Gound Plane Options) Options (sets symmetry w.r.t. ground plane) 0 -- No ground plane (free space) 1 -- Ground plane present “touch” wires connected -1 -- Ground plane present “touch” wires insulated GE 1 GE-1 current current 27 GX -- Reflections Exploit symmetry for faster solutions Tag number increment GW1 GW2 GW3 GW4 Tag GW5 Increment GW6 by 4 GW7 GW8 Reflection control Reflect along ( x y z Axis ( in y-z plane in x-z plane in x-y plane 28 GX -- Reflection Examples 3 Basic Wires X, Y, Z Directed from (A, B, C) Z Z GX 100 Right Upper A One Corner Right, Upper, Front 2B C A Y B C Y A C X Z GX 111 X Z GX 110 2A 2B 2B 2A C C 2A 2B Upper 2B 2A 2C 2C C 2C Y Y 2A 2C 2B 2A X X 29 RP - Radiation Patterns RP 0: Space wave = direct + reflected RP 1 : Ground wave = spacewave + surface wave. Must specify observation point(s) Space wave (or sky wave) dominates in ionospheric propagation Surface wave decays rapidly with distance and frequency 30 NT -- Networks + V1 - Connection between 2 segments containing admittances (impedances) Segments do not have to be nearby (not so in real life) 2-port Y-parameters Example: I1 Y11 Y12 Y22 I2 + V2 - Y11V1 Y12V2 = I1 Y12V1 Y22V2 = I 2 R Y11 = Y22 = Y12 = - Series Resistor 1 R 31 1 R TL -- Transmission Lines NEC’s transmission lines are equations, not wires If transmission line (TL), load (LD), and voltage source (Ex) are on the same segment … V Segment ZL = load on LD ZT ZL ZT = load on TL Transmission Line 32 Transmission Line Application Transmission line equations are for balanced conditions only! OK! NOT BALANCED! 33 Crossed Feeds Turnstile radiators present a challenge at the feed point V jV Dipoles Co-Planar Feeds Displaced Slight Vertical Displacement j V/2 V/2 V/2 j V/2 4 Feeds, Centers Connected 34 Current Directions Positive current flows from END 1 to END 2 I X1, Y1 , Z1 X2, Y2 , Z2 35 Current Directions Ex: VEE dipole, fed at corner B A 2 B A 2 - + C + - + + C - - 1 GW 1, 4, X C , YC , Z C , X B , YB , Z B , a GW 2, 4, X C , YC , Z C , X A , YA , Z A , a 1 GW 1, 4, X C , YC , Z C , X B , YB , Z B , a GW 2, 4, X A , YA , Z A , X C , YC , Z C , a 36 E- and H-Fields for a Desired Power NEC uses peak values for voltage, current, and fields We usually apply 1 volt to an unknown Zin E rms = E peak / 2 E rms = Desired Power E NEC 1 volt source NEC Power for 2 1 volt source 37 NEC User Notes Feeding of Arrays Problem: Array excitations are in terms of feed point currents (amplitude & phase) NEC does not allow current drives, only voltage (amplitude & phase) at feed points You can’t drive a feed with a specified current unless you know the driving point impedance. But the driving point impedance depends on the current drive and, of course, the physical arrangement of the array elements. You could possibly “iterate” yourself to an approximate solution by twiddling voltage drives 23 38 NEC User Notes Feeding of Arrays Solution: Current generators are realizable by high impedance, high voltage series source: ~1 AMP into circuits whose input impedance is <104W If you use in NEC, the large numbers used will swamp out the drive segment voltage and you won’t be able to use the results Can overcome this problem by replacing the series resistor by an appropriate network but there is an easier method….. 39 NEC User Notes Feeding of Arrays Details: The NT card(s) are used thusly: I One feed segment of array Cards: Far-Way Segment I1 V1 - I2 YC YA YB V2 - ~ V “Extra” added segment to support the generator. Use GW 901, 1, …, or similar large tag number. Set: Y11 = YA + YC = Y22 = 0 Y12 = -YC = j I = - I1 = - jV NT (Tag, Seg Seg), ), 901, 1, 0, 0 0, 1 0, 0 EX 0, 901, 1, 0, (j x FEED PT. CURRENT) GW 901, 1, 103, 0, 0, (103 + slightly more), 0, 0, (RADIUS) } One set per feed Make sure these GW900’s do not interact with each other / squirt them off in all directions (LATEST VIEWER ALLOWS YOU TO ELIMINATE A RANGE OF SEGMENTS FROM THE VIEW!) 40 43 NEC User Notes Feeding of Arrays Process: Set up enough GW900 cards for far-out feed segments, one for each array element. Make them very short w.r.t a wavelength so they will not radiate. Put them after any GS scaling to maximize the distance between dummy and actual geometry. Add an NT card for connection between each GW900 and its companion feed point segment. Put the correct current values on the EX0, 900 cards to match the array design. The input impedance at the feed points is in the Network Excitation Table instead of under antenna input impedance. Choose the dummies to be just one segment and set the radius so D/a 10 or more. 41 NEC User Notes -Feeding Equivalent Radius for Nonof Arrays (Example) Circular Cross-Sections /4 /4 I1 = 1 CE GW GW GW GW GE GN NT NT EX EX ~ I2 = -j ~ 2 Phased Verticals -- Current Source Fed 1, 5, 0, 0, 0, 0, 0, 0.25, .001 2, 5, 0.25, 0, 0, 0.25, 0, 0.25, .001 901, 1, 999, 999, 999, 999, 999.001, 999, .0001 Dummy 1 902, 1, -999, 999, 999, -999, 999.001, 999, .0001 Dummy 2 1 1 901, 1, 1, 1, 0, 0, 0, 1, 0, 0 902, 1, 1, 1, 0, 0, 0, 1, 0, 0 0, 901, 1, 0, 0, 1 0, 902, 1, 0, 0, -1 42 47 47 NEC User Notes -Equivalent Radius for NonUsing NT as Loads Circular Cross-Sections R 4 1 7 1 4 Y11 = 1/R Place load here (50 W, 300 W) NT Y22 = 1, 4, 1, 6, 0.02, 0, 0, 0, 1, 4, 1, 6, .00333, 0, 6 NT 1e10, 0 XQ NT 0, 0 1e10, 0 XQ EN 43 47 NEC User Notes -Equivalent Radius for NonMinimum Segment Lengths at BentCross-Sections Wire Junctions Circular Wire 2 (Radius a2) a = angle between wires Match points from each wire at intersection a Wire 1 (Radius a1) D1/2 • Match points for both wires must lie outside the volumes • Set a segment length limit to enforce this THUS : ALSO : a a a a D1 > 2 1 2 and D 2 > 2 1 2 tan a sin a sin a tan a D1 D2 > 8(or 2 and > 8(or 2 (with EK, 0.5 a1 a2 44 Equivalent Radius for NonCircular Cross-Sections Equivalent radius must lie between inscribed and circumscribed circles which bound the conductor boundary. Best fit: Circles formed with same area and perimeter as the conductor boundary. Inner circle : ai = A / p Outer circle : a0 = P / 2p 45 Equivalent Radius for NonCircular Cross-Sections A P ae p 2p Choose the mean: A ae P p 2p 2 46 Equivalent Radius for NonCircular Cross-Sections ae = 0.2 A .0P S • TRIANGLE: S ae = 0.425 S S • SQUARE: S S ae = 0.65 S • RECTANGLE OR STRIP: T W W/T 1 2 3 5 10 100 ae 0.6 w 0.44 w 0.37 w 0.32 w 0.26 w 47 47 Modeling Guidelines Estimate runtime Accuracy checks Vary segmentation -- check convergence Check reciprocity Test for average gain Check grids vs. patches Size problem in wavelengths Locate functional parts before modeling Don’t forget the coupling to baluns, etc. by near fields 48 Modeling Guidelines Always exploit symmetry for large problems Model the radiators first Check the literature Duplicate literature before approaching the full problem Strip out details/simplify structure Transmission lines and connections Supporting structures Environmental interactions 49 Modeling Guidelines Wire grid modeling Outline corners Grid size approximately 0.1 nominal Try “equal area” rule Try two segments/side Minimize D and a changes (< 2:1) at key junctions (near feedpoints) Use denser gridding (2x) at connection points of wires and surfaces 50 Modeling Guidelines Surface patch modeling Make sure surface is closed Maximum patch size: (0.2 0.2 ) Avoid long narrow patches Use large patches on smooth surfaces: smaller patches on curved areas 51 Modeling Guidelines Vary segmentation, grid size, patch size and note results -- look for convergence Consider possible problem areas Sharp bends in thick wires Changes in wire radius Wires connected to lossy ground Wires too thick? 52 Modeling Guidelines Determine number of segments needed D/ < 0.1 in most cases D/ too small? Low frequency limit D/ too small? Pencil lead vs. poker chips “Thin Wire” ( a << D ) “Tuna Can” (aD) “Poker Chip” ( a >> D ) 53