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| The '''return ratio''' of a dependent source in a linear electrical circuit is the ''negative'' of the ratio of the current (voltage) returned to the site of the dependent source to the current (voltage) of a replacement independent source. The terms ''loop gain'' and ''return ratio'' are often used interchangeably; however, they are necessarily equivalent only in the case of a single feedback loop system with unilateral blocks. <ref name=Spencer>
| | 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. Change the site's theme and you have essentially changed the site's personality. Dead links are listed out simply because it will negatively have an influence on the website's search engine rating. In the most current edition you can customize your retailer layout and display hues and fonts similar to your site or blog. <br><br>These websites can be easily customized and can appear in the top rankings of the major search engines. When you write a new post, you'll see a small bar that goes across the text input area. Which is perfect for building a mobile site for business use. Now, I want to anxiety that not every single query will be answered. Now a days it has since evolved into a fully capable CMS platform which make it, the best platform in the world for performing online business. <br><br>The entrepreneurs can easily captivate their readers by using these versatile themes. Note: at a first glance WP Mobile Pro themes do not appear to be glamorous or fancy. Use this section to change many formatting elements. The first thing you need to do is to choose the right web hosting plan. Search engine optimization pleasant picture and solution links suggest you will have a much better adjust at gaining considerable natural site visitors. <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. Find more information about Design To Wordpress here. Websites that do rank highly, do so becaue they use keyword-heavy post titles. So, we have to add our social media sharing buttons in website. The popularity of Word - Press has increased the demand for Word - Press themes and these themes sells like hot cake on the internet. <br><br>Instead, you can easily just include it with our bodies integration field in e - Panel. If you adored this article and you simply would like to receive more info concerning [http://webilyst.com/basicdemo/HHatchett/tab:info backup plugin] nicely visit the site. When you sign up with Wordpress, you gain access to several different templates and plug-in that allow you to customize your blog so that it fits in with your business website design seamlessly. You can select color of your choice, graphics of your favorite, skins, photos, pages, etc. Word - Press is an open source content management system which is easy to use and offers many user friendly features. As for performing online business, websites and blogs are the only medium that are available to interact with customers and Word - Press perform this work with the help of cross-blog communication tools, comments and full user registration plug-ins. |
| {{cite book
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| |author=Richard R Spencer & Ghausi MS
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| |title=Introduction to electronic circuit design
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| |page=723
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| |year= 2003
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| |publisher=Prentice Hall/Pearson Education
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| |location=Upper Saddle River NJ
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| |isbn=0-201-36183-3}}
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| </ref>
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| | |
| ==Calculating the return ratio==
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| [[File:Bipolar transresistance amplifier.PNG|thumbnail|200px|Figure 1: Collector-to-base biased bipolar amplifier]]
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| The steps for calculating the return ratio of a source are as follows:<ref name=Gray-Meyer>
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| {{cite book
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| |author=Paul R. Gray, Hurst P J Lewis S H & Meyer RG
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| |title=Analysis and design of analog integrated circuits
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| |page=§8.8 pp. 599–613
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| |year= 2001
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| |edition=Fourth Edition
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| |publisher=Wiley
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| |location=New York
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| |isbn=0-471-32168-0}}
| |
| </ref> | |
| # Set all independent sources to zero.
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| # Select the [[dependent source]] for which the return ratio is sought.
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| # Place an independent source of the same type (voltage or current) and polarity in parallel with the selected dependent source.
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| # Move the dependent source to the side of the inserted source and cut the two leads joining the dependent source to the independent source.
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| # For a '''voltage source''' the return ratio is minus the ratio of the voltage across the dependent source divided by the voltage of the independent replacement source.
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| # For a '''current source''', short-circuit the broken leads of the dependent source. The return ratio is minus the ratio of the resulting short-circuit current to the current of the independent replacement source.
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| | |
| === Other Methods ===
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| These steps may not be feasible when the dependent sources inside the devices are not directly accessible, for example when using built-in "[[black box]]" [[SPICE]] models or when measuring the return ratio experimentally.
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| For [[SPICE]] simulations, one potential workaround is to manually replace [[non-linear]] devices by their small-signal equivalent model, with exposed dependent sources. However this will have to be redone if the bias point changes.
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| A result by Rosenstark shows that return ratio can be calculated by breaking the loop at any unilateral point in the circuit. The problem is now finding how to break the loop without affecting the [[bias point]] and altering the results. Middlebrook<ref>[http://www.informaworld.com/smpp/content~content=a771365730~db=all Middlebrook, RD:''Loop gain in feedback systems 1''; Int. J. of Electronics, vol. 38, no. 4, (1975) pp. 485-512 ]</ref>and Rosenstark<ref>[http://www.informaworld.com/smpp/content~content=a777774065~db=all Rosenstark, Sol: ''Loop gain measurement in feedback amplifiers''; Int. J. of Electronics, vol. 57, No. 3 (1984) pp.415-421]</ref> have proposed several methods for experimental evaluation of return ratio (loosely referred to by these authors as simply ''loop gain''), and similar methods have been adapted for use in [[SPICE]] by Hurst.<ref>[http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=99170 Hurst, PJ: ''Exact simulation of feedback circuit parameters''; IEEE Trans. on Circuits and Systems, vol. 38, No. 11 (1991) pp.1382-1389]</ref> See [http://www.spectrum-soft.com/news/spring97/loopgain.shtm Spectrum user note] or Roberts, or Sedra, and especially Tuinenga.<ref name=Roberts>
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| {{cite book
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| |author=Gordon W. Roberts & Sedra AS
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| |title=SPICE
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| |edition=Second Edition
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| |year= 1997
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| |pages=Chapter 8; pp. 256–262
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| |publisher=Oxford University Press
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| |location=New York
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| |isbn=0-19-510842-6}}
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| </ref><ref name=Sedra>
| |
| {{cite book
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| |author=Adel S Sedra & Smith KC
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| |title=Microelectronic circuits
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| |edition=Fifth Edition
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| |year= 2004
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| |pages=Example 8.7; pp. 855–859
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| |publisher=Oxford University Press
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| |location=New York
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| |isbn=0-19-514251-9}}
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| </ref><ref name=Tuinenga>
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| {{cite book
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| |author=Paul W Tuinenga
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| |title=SPICE: a guide to circuit simulation and analysis using PSpice
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| |edition=Third Edition
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| |year= 1995
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| |pages=Chapter 8: ''Loop gain analysis''
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| |publisher=Prentice-Hall
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| |location=Englewood Cliffs NJ
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| |isbn=0-13-436049-4}}
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| </ref>
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| | |
| ==Example: Collector-to-base biased bipolar amplifier==
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| [[File:Inserting return ratio source.PNG|700px|thumb|center|Figure 2: Left - small-signal circuit corresponding to Figure 1; center - inserting independent source and marking leads to be cut; right - cutting the [[dependent source]] free and short-circuiting broken leads]]
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| Figure 1 (top right) shows a bipolar amplifier with feedback bias resistor ''R<sub>f</sub>'' driven by a [[Norton's theorem|Norton signal source]]. Figure 2 (left panel) shows the corresponding small-signal circuit obtained by replacing the transistor with its [[hybrid-pi model]]. The objective is to find the return ratio of the dependent current source in this amplifier.<ref name=Spencer2>
| |
| {{cite book
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| |author=Richard R Spencer & Ghausi MS
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| |title=Example 10.7 pp. 723-724
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| |isbn=0-201-36183-3}}
| |
| </ref> To reach the objective, the steps outlined above are followed. Figure 2 (center panel) shows the application of these steps up to Step 4, with the dependent source moved to the left of the inserted source of value ''i<sub>t</sub>'', and the leads targeted for cutting marked with an ''x''. Figure 2 (right panel) shows the circuit set up for calculation of the return ratio ''T'', which is
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| ::<math> T = - \frac {i_r} {i_t} \ . </math>
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| The return current is
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| ::<math> i_r = g_m v_{\pi} \ . </math>
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| The feedback current in ''R<sub>f</sub>'' is found by [[current division]] to be:
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| ::<math>i_f = \frac {R_D//r_O} {R_D//r_O +R_F +r_{\pi}// R_S} \ i_t \ . </math>
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| The base-emitter voltage ''v<sub>π</sub>'' is then, from [[Ohm's law]]:
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| ::<math> v_{\pi} = -i_f \ ( r_{\pi}// R_S ) \ . </math>
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| Consequently,
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| ::<math> T = g_m (r_{\pi}// R_S ) \ \frac {R_D//r_O} {R_D//r_O +R_F +r_{\pi}// R_S}\ . </math>
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| === Application in asymptotic gain model ===
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| The overall [[Electronic_amplifier#Input_and_output_variables|transresistance gain]] of this amplifier can be shown to be:
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| ::<math> G = \frac {v_{out}} {i_{in}} = \frac {(1-g_m R_F)R_1 R_2} {R_F+R_1+R_2+g_m R_1R_2} \ , </math>
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| with ''R<sub>1</sub> = R<sub>S</sub> || r<sub>π</sub>'' and ''R<sub>2</sub> = R<sub>D</sub> || r<sub>O</sub>''.
| |
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| This expression can be rewritten in the form used by the [[asymptotic gain model]], which expresses the overall gain of a feedback amplifier in terms of several independent factors that are often more easily derived separately than the overall gain itself, and that often provide insight into the circuit. This form is:
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| ::<math> G = \ G_{ \infty } \frac {T} {1+T} + G_0 \frac {1} { 1+T} \ \ , </math>
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| where the so-called '''asymptotic gain''' ''G<sub>∞</sub>'' is the gain at infinite ''g<sub>m</sub>'', namely:
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| ::<math> G_{\infty} = - R_F \ , </math>
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| and the so-called '''feed forward''' or '''direct feedthrough''' ''G<sub>0</sub>'' is the gain for zero ''g<sub>m</sub>'', namely: | |
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| ::<math> G_{0} = \frac { R_1 R_2 } {R_F +R_1 +R_2}\ . </math>
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| For additional applications of this method, see [[Asymptotic gain model#Return ratio|asymptotic gain model]].
| |
| | |
| ==References==
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| <references/>
| |
| | |
| ==See also==
| |
| | |
| [[Category:Control theory]]
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| [[Category:Signal processing]]
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| [[Category:Electronic feedback]]
| |
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