4nec2 models

4nec2 models. 77 & -14 dbi Spot on frequency. Introduction. It is very useful for those designing home made antennas for their RTL-SDR or other radio, or for those just trying to understand how antennas work. Presentation about Practical Antenna Modeling Using the NEC Codes with examples of HF wire antennas and 4NEC2. The antennas were modeled with 4nec2 at 0. It says "Geometry builder to create cylindric, patch, plane, box, helix and parabola shaped structures using auto-segmentation and/or equal-area rules. Paul McMahon VK3DIP. Rating: 2022-02-05. * Drag and drop style Geometry Editor to assist the starting antenne modeller. As a baseline, I already had a model for the DB2 bowtie antenna, so I ran this simulation first. Feb 20, 2021 · Ive been trying to model this in 4nec2 to get a similar result to what my nano vna shows, but not able to get there. Under the "Plot" option is the option to plot Forw-gain, R-in (real), X-in (imag). ca gang. If the Gain correction is too large the results will be in red indicating the model needs to be corrected. These parameters may be modified automatically by optimiser later when it is started. 4. SY L=0. Feb 5, 2024 · 4nec2 seems to be able to do the meshing for you. KK4OBI model - EFHW Inverted-L. g. EZNEC is feature rich and can be used for very detailed models. To remove overlapping wires, use ‘Geometry-edit’, select and remove wires one by one or select more wires by dragging a rectangle around them and remove them as a whole. I am very new to 4Nec2 and need to do a simulation of a half-wave dipole antenna for 433 MHz. on Box over Perfect Ground: Model, Results 96 o Example 5: Log-Periodic Antenna 100 + Model, Results 100, 101 o Example 6: Cylinder with Attached Wires 106 Nov 6, 2023 · Includes 4NEC2 models and recipes to build your own. You can see this for yourself by modeling an antenna made of copper and then writing down the gain, and then changing the antenna model to use a lossier material such as iron. 001 'Pitch. The PSO parameters are: Particle Swarm size is 22, and the gbest model using ϕ = 4. 4 and 5. –EZNEC or 4nec2 are the most popular –Start with the best basic features, get fancy later –Try both with a basic model to see which you like •Add more references –Antenna Book, Antenna Experimenters Guide (G3LDO) –L. The 4nec2 program then outputs a Imp. Two versions are presented below, one without and one WITH the Open Matching Stub Line found directly. 4NEC2 can be a complicated piece This paper describes 4nec2 model analysis of the expected performance of 2. net/4nec2 Jun 4, 2020 · 4NEC2 Modeling Log Periodic Dipole Array (LPDA) - alternate modeling method. Jan 4, 2014 · 4nec2 NEC based antenna modeler and optimizer by Arie Voors Download site http://www. Nec2dXS executable (engine) files to run models containing up to 11000 segments, using virtual memory. Everyone now gets the Pro/2 version. 144 MHz stacked Cebik Triangle Antenna horizontal polarization radiation pattern calculated by NEC Model. How to define and edit the models, Running the simulations, Work some examples, Variables usage, Deal with Feed Lines and ground. exe etc. Using the editor, I lifted both ends up 1 meter (on the Z-Axis). Get A=3. 2MHz; no conductor loss; real ground assumed to have conductivity=0. The parameters may be declared using a special SY-command: The 4nec2 is a completely free Nec2, Nec4 and windows based tool for creating, viewing, optimizing and checking 2D and 3D style antenna geometry structures and generate, display and/or compare near/far-field radiation patterns for both the starting and experienced antenna modeler. Run 4NEC2 and click Open and load the file you just made. 6. 4]. The accuracy of your results will depend on the size of the segments relative to the wavelength of operation. Also note that the Feedpoint Gap is between the two Zig-Zag Elements, running Horizontal for Horizontally Polarized Antennas as shown here. NOTE: Due to complexity limits in 4nec2 modeling program, most FF4 & FF6 Reflector models were forced to use. It should be the only file inside the zip file you downloaded. This simple antenna system is a great sandbox for learning the tricks of the NEC codes and some of the basic principles of antenna design, and to find all the pitfalls of this nice idea. You can simulate the load impedance attached to the second antenna by placing a load in the second antenna's appropriate segment. MMANA is simple to use and provides easy to understand graphs. But, I want to build an 8-element version of the ELK (5-element) 2m / 70cm Satellite Antenna that uses a loading coil at the base. " lems, an external optimiser is included in the 4NEC2 package and may be used in a very versatile way. Highlight and copy (Ctrl C) the program control codes (CM, CE, SY, etc). Resonant frequency: 28. How to start adding coils into 4NEC2. Click that green calculator looking icon to bring up the next screen, choose frequency sweep and check the start and end . Listing of the files. 005S, εr=13, of course results are dependent on these values; conductors are ~10m long, 20mm diameter; bottom fed vertical half wave uses a 10m x 20mm vertical driven ground electrode; Jul 27, 2021 · Welcome back after five years! The only way to know if a model is a good model is to make a model, and then compare its predictions to real-world measured results. Mar 2, 2016 · 4nec2 takes the radiation efficiency into account when it calculates the gain. Jan 5, 2013 · The antennas were modeled with 4nec2 at 0. EZNEC is now FREE and runs on Linux/WINE! Time Owned: more than 12 months. Below some 4nec2 specific tutorials I found on the Internet or were sent by email: (I would especially like to thank all the contributors !!) English. Followed by the construction of a sample antenna, measuring its char-acteristics and comparison with the simulation. Bob used a mast diameter about 1" to 1. Go to "File, Save as" and name your new antenna model. Sep 23, 2009 · RawGain = Gain output given by 4nec2 at the specific frequency The Raw Gain, Real Impedance, and Imaginary Impedance data can be obtained when a Frequency Sweep is calculated. Figure 2: View of 4NEC2 when first installed. Furthermore, EZNEC in comparison to 4nec2 indicates that the antenna needs to be slightly longer, namely: 40. 2 model description: 14. This allows automatic optimization to find the best value for parameters such as length, width, feed point elevation, SWR, impedance and reactance. 73 is adopted in the UHF 16-Element Yagi with 6 Reflector Rod Corner Reflector, approximate 4nec2 Model for Wade CYD-1446, analyzed using 4nec2 Antenna Modeling Program. I’ve included some Some 4Nec2 features. 3. 19% at 475 kHz. In the case of the horizontal wires, it is necessary to observe a height over the ground of at least one tenth of the working Apr 21, 2016 · We would like to show you a description here but the site won’t allow us. I built the model in 4NEC2 and ran some frequency sweeps using various parameter sets from published sources and some of my own. This is a collection of my antenna simulation files in MMANA-GAL and 4NEC2 - handiko/AntennaFiles-OLD May 4, 2017 · To merge one or more structures to an existing model, open both the created *. My NEC description for this vertical antenna model is located here, to use with 4NEC2 available here. If normal 1"Hx2"W Grid Size is used, F/B and F/R Ratios are significantly improved. New UHF Band is 470-698 MHz. 1 with constriction coefficient k = 0. – tomnexus. In these models the value of the tuning inductor was adjusted to maintain resonance as L and H were changed. To study the characteristics of the Bow Tie Dipole an updated version of the L. 04, Effic. Simulation van Drahtantennen. 144 MHz 2 stacked Halo Antennas horizontal polarization radiation pattern calculated by NEC Model. Chireix antennas are similar, but with a GAP at the tips. For that case I think it would work well. 75 m (55 ft), VSWR is hardly influenced by ground quality. 6 ohms, SWR= 1. On 3 March 2012, Peter van Latum PA0PVL from the Netherlands wrote and sent his 4nec2 model and pictures for the Cushcraft R5 vertical antenna (similar to the R7 but without the 7 and 10 MHz bands). " GitHub is where people build software. Applying these dimensions to the 4NEC2 Model at a feedpoint elevation of 5 meters, we get: A bit off tune but very good. When this is the case however, execution time is exponentially increased. qsl. Mar 24, 2021 · A 4nec2 model is also available. 7)” under the “Downloads” header. 40m dipole at 20m; Nov 5, 2019 · This is available directly from 4NEC2 by driving the first antenna as specified and observing the current in the second antenna (which does not include a source). For the 160m monopole which is 5m tall with a simple capacity hat and base loading coil, In a model with several wires, it is advisable not to connect short segments with long segments [Ref. Programs for common antennas and some experimental, includes, dipoles, quad, Yagi, verticals Feb 4, 2017 · At present the binary gain data for the anntenas is generated from MMANA-GAL, switching to 4nec2 would make things easier for others to produce these models and the data format is easier to work with and could provide better simulation information. Just make a wire of 3 or 4 segments, 3 mm diameter, 20 mm long, load in the middle and source on one end. 4nec2 Model Analysis of Quadcopter "Range Extender" Antennas. exe, build. That means for the 80 m Band that the smallest segment is about 8 cm long. Antenna Over Ground: Model, Results 91 + Example 4, T Ant. I have included some nec2 input files as examples. I'm familiar with tools such as 4nec2, but from what I can tel this fourth and final installment of our series designed to get you started in modeling with NEC, we’ll look at two disparate areas of modeling. 2"Hx2"W). * Line-chart visualization for freq-sweep Gain, F/B, F/R, SWR and impedance data. 8 GHz "Parabolic" reflectors, Yagi-Uda antennas, and combination "ParaYagi" antennas for quadcopter radio control links. Can be interfaced to HFwin32 propagation To associate your repository with the 4nec2 topic, visit your repo's landing page and select "manage topics. Add a comment. Tasks: Update C++ signal processing to use the new format. Don, I don't know anything about 4NEC2, but it seems like there should be some model on there which shows your complex antenna impedance at a specific frequency. In Windows Explorer, right-click on your new model and "Rename" the file to end as ". Scroll down, and find “Latest 4nec2 version (5. Run the program, 4nec2. The program can be used to model an antenna, and then determine through simulation properties such as the radiation pattern and SWR of the modelled antenna. When run with 4nec2, this model is resonant at 7. You just do that and click the Generate Model button and save a file ready to open in 4NEC2. com –Tutorials by Cebik and Ordy W8WWV online Jan 29, 2022 · There are two free modeling softwares that I’m aware are used frequently for antenna modeling: MMANA and EZNEC (EZNEC was a paid program and had several free variations, but EZNEC is now free). Nov 30, 2020 · Justin G0KSC downloads, installs and then talks through the basics of 4NEC2, opening and viewing a Yagi, running polar plots, SWR sweeps and a 3D view of the Sep 14, 2015 · 4NEC2 is a freeware antenna simulation software program. B. On the left is the main screen, and on the right is a view of the current geometry. " The equal-area rule recommends a segment radius that makes the total area of the wire mesh, the same as the area of the metal sheet it replaces. 144 MHz stacked Turnstile Antenna horizontal polarization radiation pattern calculated by NEC Model. 5λ and 1λ above a simulated ground. Jul 19, 2017 · The 4NEC2 software provides the Automatic Gain Test (AGT) check box when you Generate (F7) the results of your model. Aug 1, 2016 · 20mHW-HCA – centre fed horizontal at 5m height above ground; NEC 4. I've read a couple of tutorials and I understand most of it so far, still, my simulation doesn't make sense. The 4nec2 software is at https://www. Since 1/1/2022, EZNEC has been free to download. Bi-Quad Antennas, including Double Bi-Quad and Bi-Quad Yagis analyzed using 4nec2. Fast ground. Jun 8, 2022 · This is beginner's intro to designing simple HF vertical antenna for 20 mtr Amateur Radio band. 5. 4 . Feb 23, 2021 · Show activity on this post. You can click and drag in the geometry screen to view the current antenna from different angles. Nec tutorial. 4 MHz, Z=51. Note that the outer tips of a Bi-Quad connect to each other. The article shows how a Helix antenna can be sketched with the 4NEC2 soft-ware. For the example below, I used the Create > Loop feature of EZNEC to produce numbered segments, each of which is further broken down (see the green MODEL The 4nec2 modeling program1 contains a model of an 18-sided vertical magnetic loop with an 18-sided coupling loop in the sample file named "models\HFshort\Magnetic. Currents are roughly balanced on the two parallel lines of the J as shown in Apr 23, 2022 · About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features NFL Sunday Ticket Press Copyright Aug 4, 2016 · The 4NEC2 software was used to run the NEC file produced by MATLAB, to derive the SWR, gain, and F/R ratio, while the convergence diagram figures were derived directly from the optimization algorithms. The first arena involves a pair of auxiliary facilities built into NEC: the ability to model reactive (capacitive and/or inductive) loads and the ability to model transmission lines—both within limits. Today is 2/5/2022, and in the last couple of days, Roy W7EL released Pro/2 v. Summary. 4NEC2 antenna modeler. Curves must be broken into a series of straight segments. The reduced half sloper reduced half sloper adds a loading coil and May 15, 2020 · This tutorial makes broadside and endfire array of 4 dipoles using 4nec2 A 4nec2 Model for a Linked Inverted V Dipole. To remove overlapping wires, use ‘Geometry-edit’, select and remove wires one by one or select more wires by dragging a rectangle around KK4OBI model - EFHW Inverted-L. 812 m. 144 MHz 2 stacked Turnstile Antennas horizontal polarization Oct 27, 2020 · The J-pole is a monoband antenna so I developed a simple NEC model that has just a couple of parameters that allow for optimization for a given design frequency. EZNEC and other similar antenna modeling packages, with few exceptions, are wrappers for the NEC (Numerical Electromagnetics Code) engines. 5 - 0. Jul 19, 2020 · The wires of a model can touch the perfect ground. The design elements of a 160m Half sloper are very simple. So, I have successfully modeled 8-element LPDA antennas in EZNEC and 4NEC2 using no boom, 8 full length elements and 7 transmission lines between element pairs. 4NEC2. Nov 9, 2021 at 13:56. 7 which adds some features and improvements. + Example 1, Center-Fed Linear Antenna: Model, Results 83 + Example 2, Center-Fed Linear Antenna: Model, Results 86 + Example 3, Vert. nec and your 4nec2 file using Notepad and cut/paste the required cards/lines into your model. These engines date back to the 1970’s, and were written in Fortran to run on mainframe computers. Then you should have some way to set your SWR reference impedance. 4nec2 is a completely free Nec2, Nec4 and windows based tool for creating, viewing, optimizing and checking 2D and 3D style antenna geometry structures and generate, display and/or compare near/far-field radiation patterns for both the starting and experienced antenna modeler. One limitation is the lack of high accuracy ground, that starts to matter (sometimes a lot) when you model low (under 1/2 wave length above ground) antennas, or antenna which have a low horizontal component (e. This article represents the revised and extended version of a lecture at the UKW conference 2010 in Bensheim. 7]. Use this in the early stages of modeling. 1 Edit Nov 11, 2020 · Look at the image above and see I have selected Format NEC on the right. com/channel/UCtcVL8MFCcEHPH87zeDsn-A/pl Nov 8, 2021 · 1. Run the install file. * Full Nec2 and Nec4 command support Cushcraft R7 4nec2 Model Files In free space at 5 feet above good ground Cushcraft R7 Videos Feedback: Cushcraft R5 NEC Model. . Practical Antenna Modeling with 4NEC2. Electric Dipole Antenna Simulation. NEC (= Numerical Electric Code) is a simulation method for wire antennas, developed by the Lawrence Livermore Laboratory in 1981 or the Navy. Details. 8 MHz / 160m. This is where using the NEC model really helps to extend our design beyond the single band case. Cebik, W4RNL (SK) model was created in the 4NEC2 program using symbol variables rather than fixed numbers. 50" inches. Table 1 lists the elements of the model from top to bottom, and for clarity, the velocity factor applicable to each one from Collis's article. Simulation of wire antennas. Created: 16 March 2014. With the fast ground type, NEC-2 uses a method based on complex reflection coefficients. I use 4NEC2 software for these designs available at https://w Nov 5, 2019 · I'm interested in modeling the radiation pattern of wire antennas for hf before I invest the resources necessary to erect the antenna. First, some parameters (variables) need to be declared and be applied in suitable commands. Sloper: The Model. 0205 'Length of helix. These engine files also contain an integrated SomNec calculation engine thus enabling the use of a Sommerfeld-Norton ground when requesting a frequency sweep. Using 4nec2 and running your unedited . To realize this an antenna is divided into “short segments” with linear variation of current and voltage (like SPICE when simulating circuits). First, let us look at a square 40m loop antenna with NEC. exe, 4nec2X. Last Updated: 16 March 2014. (The version number may be different) 3. result in the 4nec2 display includes losses based on the amount of the originally-radiated r-f energy remaining after propagating along an infinite, flat ground plane having the conductivity defined for the wire model as analyzed. Now optimize the A dimension (Radiator and Reflector) for 28. /SWR/Gain (F5) Line Chart. Sep 23, 2015 · The antenna resonances, and the feed line resonances are likely to interact in ways that are hard to predict. Right out the gate upon using and experimenting with the software you'll notice that 4NEC2 supports by default roughly 500 different segments. The 4nec2 modeling program 1 contains a model of an 18-sided vertical magnetic loop with an 18-sided coupling loop in the sample file named "models\HFshort\Magnetic. Naturally, the power in the load is Z*I^2. exe and View. With these points and in free space, the modeled antenna will have the appearance shown in Fig. Open your new model to alter the L-height (hgh), L-bend ratio (R), angle of upward wire (lat2). 3%, a factor of 6. Back KK4OBI Bent Dipoles This is the 4NEC2 antenna bend model for: EFHW Straight To use this model: Below. Not sure this is the right software or approach to use. Even a small amount of top-loading increases efficiency. 8X! Sloper: The Model. Height for a model over ground needs to be one-half wavelength for optimum In this section Justin describes how to change all existing parameters into symbols in preparation for the optimiser, opens the optimiser and details how to Jan 4, 2024 · The most frequent installation filenames for the program are: 4nec2. UHF Multi-Bay Comparison Charts (17 Aug 2009) Old (Ch14-69) UHF Band is from 470-806 MHz. However, it also features options Modelling the Hoverman Antenna with 4NEC2. 05 MHz with an impedance of 1. * Graphical 2D and 3D visualization of Far- and Near-field data and Geometry strutures (including circular polarization view). Open Windows Wordpad and copy (Ctrl V) the control codes into Wordpad. 4NEC2 is an NEC2, NEC4, Windows based antenna modeler and optimizer by Arie Voors. a vertical with elevated radials just above ground) the results are not as accurate, sometimes quite miss-leading (too good to be true). When running frequency sweeps, linear or logarithmic style SWR, Gain If the Lab is able to verify that the model accurately represents the design of the antenna, the advertiser may then advertise the antenna gain figures in ARRL publications. This is instead what I am getting: The antenna looks like this: The nec file is: CE. Tutorium zur Antennensimulation Jan 3, 2011 · Make the mast inside the antenna 197" to 220" inches long (1/2 wave) and then put a suitable short insulator (1" to 4" inches) at the bottom that connects the support mast going to the ground. The model uses a single GW element for the array, and segment numbers are calculated for connection of transmission line connections and source. When a link was provided to the second Hoverman antenna patent #3,148,371, I modelled it using Arie’s 4NEC2 software, with some variations suggested by the DigitalHome. nec". net/4nec2/ 4nec2 YouTube videos by dx2hunt Quick tour Apr 29, 2019 · By request. Justin covers the opening of a Yagi model within 4NEC2, how to switch between the NEC2 and NEC4 calculation engines (assuming you have an NEC4 license) and t Apr 25, 2021 · Here the simple technique presented to design Helical Antenna using 4NEC2 Simulator Jan 11, 2008 · But is this an accurate model? One limitation of 4nec2 (or better: the nec-2 algorithm) is, that the segment length must be greater than 1/1000 of the wave length. 5λ and 1λ above a simulated ground with spacing optimized for minimum gain at 90º elevation and maximum gain at 15º elevation. youtube. This will be a reasonable model of the helical antenna for the purpose of radiation, coupling etc. 15 ohms and Nov 1, 2021 · 0. Back KK4OBI Bent Dipoles This is the 4NEC2 antenna bend model for: EFHW Sloping To use this model: Below. The wires of the model cannot touch the fast ground. After reading Tony’s write-up on his portable linked inverted V dipole ( April 2017 Nerg News) I was motivated to see if I could do a workable model for the antenna in a general purpose antenna modelling package, for me the best choice for this is 4nec2, it is free, and has many features even the paid for packages don’t offer. From the developer: 4nec2 is a completely free Nec2, Nec4 and windows based tool for creating, viewing, optimizing and checking 2D and 3D style antenna geometry structures and generate, display and/or compare near/far-field radiation 4Nec2 tutorials . 4NEC2 and NEC-4. To merge one or more structures to an existing model, open both the created *. sparse Grid Size (e. The NEC files may be used with any of the NEC-2 or NEC-4 programs such as 4NEC2, GNEC or cocoaNEC, however some of them with tapered elements may only be simulated Sep 11, 2021 · 4 Simulation of an Antenna Model with 4Nec2 The control points (Table 1 ) have been entered into the 4Nec2 software. If you live in a large building then I will guess that you don't know the exact construction of the wall, and that you're not allowed to drill holes to discover what is inside. Ve3sqb Antenna Programs. " After all, this is a tutorial about modeling with EZNEC, not general modeling. As you can see, the antenna is outside the pattern. These files may also be imported into 4NEC2 by Arie Voors. 8223 m. Source code and windows executables are available to download. 1. Mar 29, 2020 · The value for the Radiat-eff. Download and extract its contents. 2. nec file after selecting the "Run Average Gain May 8, 2016 · NEC Model Library The following files and links point to NEC/AO/YO models of various Ham antennas that I have simulated and/or tested over the past 30 years as an antenna designer. Cebik W4RNL’s website on antennex. This is a free space model with fixed coordinates and perfect conductors. 4 MHz. Another pro with 4NEC2 is the allowance of graphical entries of models that are used by antennae. This new policy was introduced in an article that appeared in the April, 1998 issue of QST , " Antenna Ads in ARRL Publications . Jul 11, 2019 · 4nec2 is easy to use and comes with a basic 3D editor to help novices create antenna models, compare field patterns, generate SWR charts and learn in the process. B. 7 cm in diameter. You can enter in initials and variables far faster than you would normally. More than 100 million people use GitHub to discover, fork, and contribute to over 420 million projects. MMANA is a good modeler to learn. Keeping H=20' but adding a 40' top-wire, η=1. Some programs may impose conditions in this regard. 51%, Gain=9. Wire antenna modelling . Follow @twitterapi. Running the model and looking at the current distribution immediately illuminates how the antenna radiates. 8 with a gain between 2 and 3 dBi. Contents. It is now possible to create a 4nec2 model with one of these equations and use it to set the rf resistance of a coil automatically whilst the optimiser is adjusting the coil inductance for the best SWR. The rendition on the right is produced by the very nice 3D viewer in 4NEC2. Dimensions were provided by Choclab, with some of his photos below. For example, in 4Nec2, for two connected segments “i” and “j” the condition Lsi <= 5 x Lsj must be fulfilled [Ref. =66. Apr 9, 2019 · The basic idea of the G5RV is a balanced 80m half-wave resonant antenna with a section of high impedance line at the feed point to aid in matching the antenna to the rest of the coax transmission line to the source. SY S=0. I am trying to model a simple helix antenna with 4nec2 program but I am getting very different results from the datasheet specs: in particular SWR is stated to be less than 1. A coax cable is about 0. 8. From comparison with previous modelling above very poor city ground, one may conclude that, at least at a height of 16. Category : Antennas/Theory. As an example, for L=0 and H=20', η=0. German. When running frequency sweeps, linear or logarithmic style SWR, Gain Apr 21, 2016 · With 4NEC2 I model because I can. If the Lab is able to verify that the model accurately represents the design of the antenna, the advertiser may then advertise the antenna gain figures in ARRL publications. If its possible id like some tips, or advice on more suitable software. Antenna simulations with 4NEC2 including an application Applying these dimensions to the 4NEC2 Model at a feedpoint elevation of 5 meters, we get: A bit off tune but very good. So 6 dBi is 6 dBi no matter what the radiation efficiency of the antenna may be. Nov 30, 2020 · This 4nec2 antenna model is designed to fit in an 11 x 7 inch brownie baking pan. To create a new antenna, we focus on the buttons along the top of the main window (on the left in Figure 2). Big Wires – A 160 / 80 / 40 Meter Multi-band Antenna 2/16/2021 This is a full size inverted L antenna that is designed to be pulled up into some tall trees. Generate data for the currently used Nov 5, 2019 · 1. #12 wire conductors are assumed. 1 were used for modelling. For Playlists of related videos click this link: https://www. Once settling on 4NEC2 as the modeling software, I started fiddling with the new antenna itself. 160m low dipole; 7 MHz / 40m. The second area is composed of model testing Antenna Scatterers Analysis Program, is a Free general purpose antenna analysis software program for numerical electromagnetic antenna design, modeling and analysis. xz zc va jn fi zv uy dc gn we