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| {{Antennas|Characteristics}}
| | Surely the second option would be more beneficial for any website. You may discover this probably the most time-consuming part of building a Word - Press MLM website. I thought about what would happen by placing a text widget in the sidebar beneath my banner ad, and so it went. s ultimately easy to implement and virtually maintenance free. After activating, you will find their website link and get the activation code from their website. <br><br>In case you have just about any queries relating to where in addition to the best way to utilize [http://dinky.in/?WordpressBackupPlugin682159 wordpress backup], you possibly can contact us from our own web site. Luckily, for Word - Press users, WP Touch plugin transforms your site into an IPhone style theme. If you wish to sell your services or products via internet using your website, you have to put together on the website the facility for trouble-free payment transfer between customers and the company. There are number of web services that offer Word press development across the world. It primarily lays emphasis on improving the search engine results of your website whenever a related query is typed in the search box. Many times the camera is following Mia, taking in her point of view in almost every frame. <br><br>It is also popular because willing surrogates,as well as egg and sperm donors,are plentiful. Word - Press has different exciting features including a plug-in architecture with a templating system. We can active Akismet from wp-admin > Plugins > Installed Plugins. Thousands of plugins are available in Word - Press plugin's library which makes the task of selecting right set of plugins for your website a very tedious task. If you have any questions on starting a Word - Press food blog or any blog for that matter, please post them below and I will try to answer them. <br><br>The next thing I did after installing Wordpress was to find myself a free good-looking Wordpress-theme offering the functionality I was after. php file in the Word - Press root folder and look for this line (line 73 in our example):. Websites that do rank highly, do so becaue they use keyword-heavy post titles. A whole lot worse, your site will likely be useless as well as your merchandise won't sell if no one has the endurance to wait for the web pages to load. Word - Press offers constant updated services and products, that too, absolutely free of cost. <br><br>Someone with a basic knowledge of setting up a website should be able to complete the process in a couple of minutes however even basic users should find they are able to complete the installation in around 20 minutes by following the step by step guide online. Here's a list of some exciting Word - Press features that have created waves in the web development industry:. While deciding couple should consider the expertise of the doctor,clinics success rate,the costs of fertility treatment,including fertility tests and IVF costs and overall ones own financial budget. Word - Press is the most popular personal publishing platform which was launched in 2003. Your topic is going to be the basis of your site's name. |
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| The '''equivalent radius''' of an [[Antenna (radio)|antenna]] conductor is defined as:<ref>E.A. Wolff, ''Antenna Analysis'', Chapter 3, John Wiley & Sons, New York, NY, Second Edition, 1966.</ref>
| |
| <center><math> | |
| r_e = \exp\left\{
| |
| {1\over L^2} \oint_\ell \oint_\ell
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| \ln \vert \boldsymbol{x} - \boldsymbol{y} \vert
| |
| \; dx \; dy
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| \right\}
| |
| </math></center>
| |
| where <math>\scriptstyle\ell</math> denotes the conductor's [[circumference]], <math>\scriptstyle{L}</math> is the length of the circumference, <math>\scriptstyle{\boldsymbol{x}}</math> and <math>\scriptstyle{\boldsymbol{y}}</math> are [[Euclidean vector|vector]]s locating points along the circumference, and <math>\scriptstyle{dx}</math> and <math>\scriptstyle{dy}</math> are differentials segments along it. The equivalent [[radius]] allows the use of analytical formulas or computational or [[experimental data]] derived for antennas constructed from small conductors with uniform, ''circular'' cross-sections to be applied in the analysis of antennas constructed from small conductors with uniform, ''non-circular'' cross-sections. Here "small" means the largest dimension of the cross-section is much less than the wavelength <math>\scriptstyle{\lambda}</math>. | |
| | |
| == Formulas ==
| |
| The following table lists equivalent radii for various conductor cross-sections derived assuming 1) all dimensions are much less than <math>\scriptstyle{\lambda}</math>, 2) for cross-sections composed of multiple conductors, the distances between conductors are much greater than any single conductor dimension. The formula for the flat, infinitely thin conductor is a closed-form solution. Formulas for the square and triangular cross-sections follow from numerical evaluation of the double integral.
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| | |
| {| class="wikitable"
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| |-
| |
| ! align="center"| Cross-Section
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| ! width="250pt" align="center"| Description
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| ! width="330pt" align="center"| Equivalent Radius
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| |-
| |
| |-
| |
| | align="center"|[[File:two-conductor antenna cross-section.png|200px]]
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| ! align="center"| Two circular conductors,<br> equal radii
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| | align="center"| <math> \sqrt{rs} </math>
| |
| |-
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| | align="center"|[[File:two-diff-conductor antenna cross-section.png|200px]]
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| ! align="center"| Two circular conductors,<br> unequal radii
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| | align="center"| <math> \exp\left\{ { r_1^2 \ln r_1 + r_2^2 \ln r_2 + 2r_1r_2 \ln S \over (r_1+r_2)^2} \right\} </math>
| |
| |-
| |
| | align="center"| [[File:three-conductor antenna cross-section.png|200px]]
| |
| ! align="center"| Equilateral triangle,<br> identical circular conductors
| |
| | align="center"| <math> \left( rs^2 \right)^{1/3} </math>
| |
| |-
| |
| | align="center"| [[File:four-conductor antenna cross-section.png|200px]]
| |
| ! align="center"| Square,<br> identical circular conductors
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| | align="center"| <math> \left( \sqrt{2}\,rs^3 \right)^{1/4} </math>
| |
| |-
| |
| | align="center"| [[File:five-conductor antenna cross-section.png|200px]]
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| ! align="center"| Pentagon,<br> identical circular conductors
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| | align="center"| <math> \left( 2.62\,rs^4 \right)^{1/5} </math>
| |
| |-
| |
| | align="center"| [[File:six-conductor antenna cross-section.png|200px]]
| |
| ! align="center"| Hexagon,<br> identical circular conductors
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| | align="center"| <math> \left( 6\,rs^5 \right)^{1/6} </math>
| |
| |-
| |
| | align="center"| [[File:multiple-conductor antenna cross-section.png|230px]]
| |
| ! align="center"| Approximate cylinder, <br> identical circular conductors,<br> conductors uniformly spaced,<br> <math>N \gg 6 </math>
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| | align="center"| <math> \displaystyle{ r^{1/N} R^{1-1/N} } </math>
| |
| |-
| |
| | align="center"| [[File:flat thin conductor antenna cross-section.png|200px]]
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| ! align="center"| Flat conductor,<br> infinitely thin
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| | align="center"| <math> \displaystyle{ We^{-3/2} \approx 0.22\, W} </math>
| |
| |-
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| | align="center"| [[File:square conductor antenna cross-section.png|200px]]
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| ! align="center"| Square conductor
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| | align="center"| <math> \displaystyle{ 0.58\, W } </math>
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| |-
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| | align="center"| [[File:triangular conductor antenna cross-section.png|200px]]
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| ! align="center"| Equilateral triangle conductor
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| | align="center"| <math> \displaystyle{ 0.41\, W } </math>
| |
| |}
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| | |
| ==Derivation==
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| The equivalent radius is derived by equating the average potential at the surface of a charged conductor of arbitrary cross-section with the electric potential on the surface of a charged cylinder.
| |
| | |
| Because a conductor's cross-section dimensions are small compared to the wavelength, the current distribution slowly varies along the conductor's length, charge is uniformly distributed along its circumference (owing to the [[skin effect]]) and the electric field is perpendicular to the surface. Furthermore, only the charge in a neighborhood around any point on the conductor significantly contributes to the electric potential at that point. Time dependence is ignored, as it may be incorporated by multiplying the current distribution by a time-varying sinusoid. These conditions imply that an electrostatic condition exists and that the geometry is, effectively, one of an infinitely long conductor with a constant surface charge density <math>\scriptstyle{Q}</math> (charge per area), thereby reducing a three-dimensional problem to a two-dimensional one.
| |
| | |
| First, consider the potential at a fixed point <math>\scriptstyle{\boldsymbol{y}}</math> on the circumference of the arbitrary cross-section. With the circumference divided into differential segments <math>\scriptstyle{dx}</math>, the charge distribution may be approximated by placing a vertical line charge within each segment, each with a linear charge density of <math> \scriptstyle{Q\, dx} </math> (charge per length). It is well known that the potential of such a line charge is <math> \scriptstyle{-2k_e \, Q\, dx \ln \vert \boldsymbol{x} - \boldsymbol{y} \vert} </math>, where <math>\scriptstyle{k_e}</math> is Coulomb’s constant. The potential at <math>\scriptstyle{\boldsymbol{y}}</math> is the sum of the potentials for all the strips, which is
| |
| <center><math>
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| V(\boldsymbol{y}) = -2k_e Q
| |
| \oint_\ell
| |
| \ln \vert \boldsymbol{x} - \boldsymbol{y} \vert
| |
| \; dx .
| |
| </math></center>
| |
| The average potential is then
| |
| <center><math>
| |
| \bar{V}
| |
| = {1 \over L} \oint_\ell
| |
| V(\boldsymbol{y}) \; dy \,
| |
| = -2k_e Q
| |
| {1 \over L} \oint_\ell \oint_\ell
| |
| \ln \vert \boldsymbol{x} - \boldsymbol{y} \vert
| |
| \; dx \; dy .
| |
| </math></center>
| |
| Now consider the case of cylinder with the same linear charge density as the conductor of arbitrary cross-section. It is also well known that the potential at any point on its surface, which is also equal its average potential, is
| |
| <center><math>
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| V_c = -2k_e QL
| |
| \ln \left( r_e \right) .
| |
| </math></center>
| |
| Equating <math>\scriptstyle{\bar{V}}</math> and <math>\scriptstyle{V_c}</math> yields
| |
| <center><math>
| |
| \ln\left( r_e \right)
| |
| = {1\over L^2} \oint_\ell \oint_\ell
| |
| \ln \vert \boldsymbol{x} - \boldsymbol{y} \vert
| |
| \; dx \; dy .
| |
| </math></center>
| |
| Exponentiation of both side leads to the formula for the equivalent radius.
| |
| | |
| The formula for the equivalent radius provides consistent results. If the conductor cross-section dimensions are scaled by a factor <math>\scriptstyle{\alpha}</math>, the equivalent radius is scaled by <math>\scriptstyle{|\alpha |}</math>. Also, the equivalent radius of a cylindrical conductor is equal to the radius of the conductor.
| |
| | |
| ==References==
| |
| {{Reflist|33em}}
| |
| | |
| {{DEFAULTSORT:Antenna Equivalent Radius}}
| |
| [[Category:Antennas (radio)]]
| |
Surely the second option would be more beneficial for any website. You may discover this probably the most time-consuming part of building a Word - Press MLM website. I thought about what would happen by placing a text widget in the sidebar beneath my banner ad, and so it went. s ultimately easy to implement and virtually maintenance free. After activating, you will find their website link and get the activation code from their website.
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It is also popular because willing surrogates,as well as egg and sperm donors,are plentiful. Word - Press has different exciting features including a plug-in architecture with a templating system. We can active Akismet from wp-admin > Plugins > Installed Plugins. Thousands of plugins are available in Word - Press plugin's library which makes the task of selecting right set of plugins for your website a very tedious task. If you have any questions on starting a Word - Press food blog or any blog for that matter, please post them below and I will try to answer them.
The next thing I did after installing Wordpress was to find myself a free good-looking Wordpress-theme offering the functionality I was after. php file in the Word - Press root folder and look for this line (line 73 in our example):. Websites that do rank highly, do so becaue they use keyword-heavy post titles. A whole lot worse, your site will likely be useless as well as your merchandise won't sell if no one has the endurance to wait for the web pages to load. Word - Press offers constant updated services and products, that too, absolutely free of cost.
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