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| The '''Second Order Intercept Point''', also known as the '''SOI''', '''IP2''', or '''IIP2''' (Input Intercept Point), is a measure of linearity that quantifies the second-order distortion generated by [[nonlinear system]]s and devices. Examples of frequently used devices that are concerned with this measure are [[amplifiers]] and [[Frequency mixer|mixers]]. It is related to the [[third-order intercept point]], which is generally used for quantifying degree of nonlinearity of a nonlinear system or it can also be used to estimate the nonlinear products present at the output of such a system.<!-- Image with unknown copyright status removed: [[ Image:1st_2nd_order_slopes.png | thumb | 200px | Graph of 1st- and 2nd-order response]] -->
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| ==Definition==
| | Right starting from social media support to search engine optimization, such plugins are easily available within the Word - Press open source platform. You may either choose to link only to the top-level category pages or the ones that contain information about your products and services. It allows Word - Press users to easily use HTML5 the element enable native video playback within the browser. This is identical to doing a research as in depth above, nevertheless you can see various statistical details like the number of downloads and when the template was not long ago updated. This can be done by using a popular layout format and your unique Word - Press design can be achieved in other elements of the blog. <br><br>The entrepreneurs can easily captivate their readers by using these versatile themes. After sending these details, your Word - Press blog will be setup within a few days. You've got invested a great cope of time developing and producing up the topic substance. These frequent updates have created menace in the task of optimization. If you've hosted your Word - Press website on a shared hosting server then it'll be easier for you to confirm the restricted access to your site files. <br><br>Whether your Word - Press themes is premium or not, but nowadays every theme is designed with widget-ready. I have compiled a few tips on how you can start a food blog and hopefully the following information and tips can help you to get started on your food blogging creative journey. Some examples of its additional features include; code inserter (for use with adding Google Analytics, Adsense section targeting etc) Webmaster verification assistant, Link Mask Generator, Robots. Contact Infertility Clinic Providing One stop Fertility Solutions at:. Fortunately, Word - Press Customization Service is available these days, right from custom theme design, to plugin customization and modifying your website, you can take any bespoke service for your Word - Press development project. <br><br>You will know which of your Word - Press blog posts are attracting more unique visitors which in turn will help you develop better products and services for your customers. Here's a list of some exciting Word - Press features that have created waves in the web development industry:. It can be concluded that white label SEO comprise of a third party who resells a contract involving IT expert or consultant, SEO professional and end user. with posts or testimonials updated as they are uploaded to a particular section of the website. Press CTRL and the numbers one to six to choose your option. |
| <!-- Image with unknown copyright status removed: [[ Image:SOI_point.png | thumb | 200px | ISOI and OSOI points ]] -->
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| At low power levels, the fundamental output power rises in a one-to-one ratio (in terms of [[Decibel|dB]]) of the input power, while the second-order output power rises in a two-to-one ratio. If the input power is high enough for the device to reach saturation, the output power flattens out in both the first- and second-order cases.
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| The second order intercept point is the output power point at which the extrapolated first- and second-order lines intersect on a plot, since the actual power levels will flatten off due to saturation at much lower power level typically. In other words, the response is assumed to be perfect all the way to infinity. There are actually values for both the input and output SOI (known as the ISOI & OSOI or IIP2 & OIP2) of a device or system, being related by the small signal gain of the device or system. The OSOI in dB is simply the ISOI in dB plus the small signal gain of the device or system.
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| ==Derivation==
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| To determine the second-order characteristics of a device, a strong signal is put through the device, and the output are measured. Both single- and two-tone techniques can be used, and while there will be frequencies components off to infinity, for SOI analysis the fundamental and second-order distortion products are the desired results.
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| ===Single-tone analysis===
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| <!-- Image with unknown copyright status removed: [[ Image:Single_tone_analysis.png | thumb | 200px | single-tone analysis ]] --> | |
| In single-tone analysis, one tone at the desired frequency is generated and put through the device. There will be output at the fundamental, and the output due to second-order effects will be at DC and twice the input frequency. The derivation follows:
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| :<math>V_{in} = A\cos(wt)</math>
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| :<math>V_{out,2nd order} = k_{2}A^{2}\cos^{2}(wt)</math>
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| :<math>V_{out,2nd order} = \frac{k_{2}A^{2}}{2} + \frac{k_{2}A^{2}}{2}\cos(2wt)</math>
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| ===Two-tone analysis===
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| <!-- Image with unknown copyright status removed: [[ Image:Two_tone_analysis.png | thumb | 200px | two-tone analysis ]] -->
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| Single-tone analysis fails to illustrate several common linearity problems, therefore in two-tone analysis, two tones of approximately equal strength are put through the device. There will be output at the fundamental frequencies, and the output due to second-order effects will be at DC, twice the input frequencies, and the sum and difference of the input frequencies. The derivation follows:
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| :<math>V_{in} = A_{1}\cos(w_{1}t) + A_{2}\cos(w_{2}t)</math>
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| :<math>V_{out,2nd order} = k_{2}[A_{1}\cos(w_{1}t) + A_{2}\cos(w_{2}t)]^{2}</math>
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| :<math>V_{out,2nd order} = k_{2}\{\frac{A_{1}^{2} + A_{2}^{2}}{2} + \frac{A_{1}^{2}\cos(2w_{1}t)}{2} + \frac{A_{2}^{2}\cos(2w_{2}t)}{2} + A_{1}A_{2}\cos[(w_{1}+w_{2})t] + A_{1}A_{2}\cos[(w_{1}-w_{2})t] \}</math>
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| ==Cascade gain==
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| If multiple devices are connected in cascade, and their individual ISOI and OSOI are known, it is possible to calculate the ISOI and OSOI of the entire system. It is helpful to think of how they are derived in the following ways. For the ISOI, the second-order distortion components can be "moved" to the beginning of the cascade, where the ISOI of the first component is unaffected by any gain, the ISOI of the second component is divided by the gain of the first component, and this process continues to the end of the cascade. In this case the gain of the last device has no effect on the cascade ISOI.
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| In the OSOI case, a similar process can be performed, except the distortion components are moved to the end of the cascade. Here, the OSOI of the first device is affected by the gain of all subsequent devices, and so on. For the OSOI, the gain of the first device has no effect on the cascade OSOI.
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| Both coherent and non-coherent derivations of these equations exist, due to the possible phase differences of the distortion components. In the coherent case, all of the components are exactly in phase, and their voltages simply add, while in the non-coherent case the phases are random and the distortion powers add together. The coherent case represents the most conservative (i.e. worst-case) answer, and the non-coherent case is generally a more accurate description for most systems.
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| ===Coherent SOI cascade equations===
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| <math>\frac{1}{\sqrt{ISOI_{cas}}} = \frac{1}{\sqrt{ISOI_{1}}} + \frac{1}{\sqrt{ISOI_{2}/G_{p,1}}} + . . . + \frac{1}{\sqrt{ISOI_{n}/G_{p,1}G_{p,2}G_{p,3}. . .G_{p,n-1}}}</math>
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| <math>\frac{1}{\sqrt{OSOI_{cas}}} = \frac{1}{\sqrt{G_{p,2}G_{p,3}G_{p,4}. . .G_{p,n}OSOI_{1}}} + \frac{1}{\sqrt{G_{p,3}G_{p,4}. . .G_{p,n}OSOI_{2}}} + . . . + \frac{1}{\sqrt{OSOI_{n}}}</math>
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| ===Non-Coherent SOI cascade equations===
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| <math>\frac{1}{ISOI_{cas}} = \frac{1}{ISOI_{1}} + \frac{1}{ISOI_{2}/G_{p,1}} + . . . + \frac{1}{ISOI_{n}/G_{p,1}G_{p,2}G_{p,3}. . .G_{p,n-1}}</math>
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| <math>\frac{1}{OSOI_{cas}} = \frac{1}{G_{p,2}G_{p,3}G_{p,4}. . .G_{p,n}OSOI_{1}} + \frac{1}{G_{p,3}G_{p,4}. . .G_{p,n}OSOI_{2}} + . . . + \frac{1}{OSOI_{n}}</math> | |
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| ==Useful second order equations==
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| <!-- Image with unknown copyright status removed: [[ Image:SOI_power.png | thumb | 200px | Definition of <math>\bigtriangleup_{SO,dB}</math> ]] -->
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| In the following equations ''f'' refers to the fundamental frequency, and ''2f'' refers to the second-order distortion component frequencies.
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| :''OSOI''<sub>''dBm''</sub> = ''ISOI''<sub>''dBm''</sub>+''G''<sub>''dB''</sub>
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| :''P''<sub>''out,f,dBm''</sub> = ''P''<sub>''in,f,dBm''</sub> - ''ISOI''<sub>''dBm''</sub> + ''OSOI''<sub>''dBm''</sub>
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| :''P''<sub>''out,2f,dBm''</sub> = ''2P''<sub>''in,f,dBm''</sub> - ''2ISOI''<sub>''dBm''</sub> + ''OSOI''<sub>''dBm''</sub>
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| :''P''<sub>''in,2f,dBm''</sub> = ''2P''<sub>''in,f,dBm''</sub> - ''ISOI''<sub>''dBm''</sub> | |
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| :''P''<sub>''out,2f,dBm''</sub> = ''2P''<sub>''out,f,dBm''</sub> - ''OSOI''<sub>''dBm''</sub>
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| <math>\bigtriangleup_{SO,dB}</math> is the difference in power between the fundamental output and the output of the second-order components, as shown on the figure to the right.
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| :<math>\bigtriangleup_{SO,dB} = P_{out,f,dBm}-P_{out,2f,dBm}</math>
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| :<math>\bigtriangleup_{SO,dB} = ISOI_{dBm} - P_{in,f,dBm}</math>
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| :<math>\bigtriangleup_{SO,dB} = OSOI_{dBm} - P_{out,f,dBm}</math>
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| ==See also==
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| * [[Intermodulation Intercept Point]]
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| * [[Third-order intercept point]]
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| ==References==
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| * [http://www.rfdesignline.com/howto/205800662 Understanding RF Power Amplifiers]
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| * [http://www.matrixtest.com/Literat/mtn109.htm The Relationship of Intercept Points and Composite Distortions]
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| {{DEFAULTSORT:Second-Order Intercept Point}}
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| [[Category:Amplifiers]]
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If you are looking for a specific plugin, then you can just search for the name of the plugin. Good luck on continue learning how to make a wordpress website. Step-4 Testing: It is the foremost important of your Plugin development process. If you liked this short article and you would such as to obtain even more information relating to backup plugin kindly check out our own internet site. Out of the various designs of photography identified these days, sports photography is preferred most, probably for the enjoyment and enjoyment associated with it. The top 4 reasons to use Business Word - Press Themes for a business website are:.
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