{"id":1597,"date":"2024-07-15T11:06:06","date_gmt":"2024-07-15T05:36:06","guid":{"rendered":"https:\/\/study.madeeasy.in\/?p=1597"},"modified":"2025-07-16T15:06:51","modified_gmt":"2025-07-16T09:36:51","slug":"network-parameters","status":"publish","type":"post","link":"https:\/\/www.madeeasy.in\/study\/ec\/network-theory\/network-parameters","title":{"rendered":"Network Parameters"},"content":{"rendered":"<h2>What is Network Parameters?<\/h2>\n<p style=\"text-align: justify;\">A pair of terminals through which a current may enter or leave a network is known as a port. Most of the circuits we have dealt with so far are two-terminal or one-port circuits, represented in fig. (a). We have considered the voltage across or current through a single pair of terminals-such as the two terminals of a resistor, a capacitor, or an inductor. We have also studied four-terminal or two-port circuit involving op-amps, transistors and transformer as shown in fig. (b). Thus, we can say that a two-port network is an electrical network with separate ports for input and output.<\/p>\n<p style=\"text-align: justify;\">In general, a network may have <em>n <\/em>ports. In this chapter, we are mainly concerned with two-port networks (or simply, two ports).<\/p>\n<p style=\"text-align: justify;\">In two port network four variables are use (i.e., <em>V<\/em><sub>1<\/sub>, <em>V<\/em><sub>2<\/sub>, <em>I<sub>1<\/sub>, <em>I<sub>2<\/sub> ) out of four variable, we can chose two variable in six different way (<sup>4<\/sup>C<sub>2<\/sub>), and hence we have six sets of two-port.<\/em><\/em><\/p>\n<ul style=\"text-align: justify;\">\n<li><em>Z<\/em>-parameters (Impedance parameters)<\/li>\n<li><em>Y<\/em>-parameters (Admittance parameters)<\/li>\n<li><em>ABCD<\/em> parameters (Transmission parameters)<\/li>\n<li><em>A&#8217;<\/em>\u00a0<em>B&#8217;<\/em>\u00a0<em>C&#8217;<\/em>\u00a0<em>D&#8217;<\/em>\u00a0parameters (Inverse transmission parameters)<\/li>\n<li><em>h<\/em>-parameters (Hybrid parameters)<\/li>\n<li><em>g<\/em>-parameters (Inverse hybrid parameters)<\/li>\n<\/ul>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_79_1 ez-toc-wrap-left counter-hierarchy ez-toc-counter ez-toc-light-blue ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.madeeasy.in\/study\/ec\/network-theory\/network-parameters\/#Z-Parameters\" >Z-Parameters<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.madeeasy.in\/study\/ec\/network-theory\/network-parameters\/#Condition-of-Reciprocity-and-Symmetry\" >Condition of Reciprocity and Symmetry<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.madeeasy.in\/study\/ec\/network-theory\/network-parameters\/#Y-parameters\" >Y-parameters<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.madeeasy.in\/study\/ec\/network-theory\/network-parameters\/#Condition-of-Reciprocity-and-Symmetry-2\" >Condition of Reciprocity and Symmetry<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.madeeasy.in\/study\/ec\/network-theory\/network-parameters\/#h-parameters-or-Hybrid-Parameters\" >h-parameters or Hybrid Parameters<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.madeeasy.in\/study\/ec\/network-theory\/network-parameters\/#Condition-of-Reciprocity-and-Symmetry-3\" >Condition of Reciprocity and Symmetry<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/www.madeeasy.in\/study\/ec\/network-theory\/network-parameters\/#g-parameters-or-Inverse-Hybrid-Parameters\" >g-parameters or Inverse Hybrid Parameters<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/www.madeeasy.in\/study\/ec\/network-theory\/network-parameters\/#Condition-of-Reciprocity-and-Symmetry-4\" >Condition of Reciprocity and Symmetry<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/www.madeeasy.in\/study\/ec\/network-theory\/network-parameters\/#Transmission-Parameters-ABCD\" >Transmission Parameters (ABCD)<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/www.madeeasy.in\/study\/ec\/network-theory\/network-parameters\/#Condition-of-Reciprocity-and-Symmetry-5\" >Condition of Reciprocity and Symmetry<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/www.madeeasy.in\/study\/ec\/network-theory\/network-parameters\/#Inverse-Transmission-Parameters\" >Inverse Transmission Parameters<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/www.madeeasy.in\/study\/ec\/network-theory\/network-parameters\/#Inter-Relations-in-Network-Parameters\" >Inter Relations in Network Parameters<\/a><\/li><\/ul><\/nav><\/div>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Z-Parameters\"><\/span><strong><em>Z<\/em>-Parameters<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">The Z-parameter, or impedance parameters, relates current to voltage, as one would expect. The Z-parameters are <img loading=\"lazy\" decoding=\"async\" class=\"alignright wp-image-1599 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/two-port-network.jpg\" alt=\"Two Port Network\" width=\"222\" height=\"109\" \/> the inverse of the Y-parameters in most cases.<\/p>\n<p style=\"text-align: justify;\">The terminal voltage can be related to the terminal currents as<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1600 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/matrix.jpg\" alt=\"Matrix\" width=\"214\" height=\"88\" \/><\/p>\n<p style=\"text-align: justify;\">The values of the parameters can be evaluated by setting I1 = 0 (input port open-circuit) or I2 = 0. (output port open-circuited). Thus<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1602 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/impedance.jpg\" alt=\"Impedance\" width=\"287\" height=\"113\" \/><\/p>\n<p style=\"text-align: justify;\">where,<\/p>\n<p style=\"text-align: justify;\">Z<sub>11<\/sub> = Open-circuit input impedance<br \/>\nZ<sub>12<\/sub> = Open-circuit transfer impedance<br \/>\nZ<sub>21<\/sub> = Open-circuit transfer impedance from port 2 to port 1<br \/>\nZ<sub>22<\/sub> = Open-circuit output impedance<\/p>\n<p style=\"text-align: justify;\">The equivalent circuit representation of equation (12.1) and (12.2) is in figure shown below, where Z<sub>12<\/sub> I<sub>2<\/sub> and Z<sub>21<\/sub> I<sub>1<\/sub>\u00a0are current-controlled voltage sources (CCVS).<\/p>\n<p style=\"text-align: justify;\">The equivalent circuit for equation (12.1) and (12.2) is given as<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1603 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/two-port-network-1.jpg\" alt=\"Two Port Network\" width=\"305\" height=\"145\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/two-port-network-1.jpg 305w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/two-port-network-1-300x143.jpg 300w\" sizes=\"auto, (max-width: 305px) 100vw, 305px\" \/><\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1604 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/impedance-parameters.jpg\" alt=\"Impedance Parameters\" width=\"656\" height=\"96\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/impedance-parameters.jpg 656w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/impedance-parameters-300x44.jpg 300w\" sizes=\"auto, (max-width: 656px) 100vw, 656px\" \/><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1605 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/linear-network.jpg\" alt=\"Linear network\" width=\"628\" height=\"230\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/linear-network.jpg 628w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/linear-network-300x110.jpg 300w\" sizes=\"auto, (max-width: 628px) 100vw, 628px\" \/><\/p>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Condition-of-Reciprocity-and-Symmetry\"><\/span><strong>Condition of Reciprocity and Symmetry<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>Reciprocity network :<\/strong> A two port network is said to be reciprocal if the ratio of response to excitation remains the same even when there positions are interchanged.<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1609 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/reciprocity-network.jpg\" alt=\"Reciprocity Network\" width=\"310\" height=\"52\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/reciprocity-network.jpg 310w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/reciprocity-network-300x50.jpg 300w\" sizes=\"auto, (max-width: 310px) 100vw, 310px\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Symmetrical Network:<\/strong> Network is said to be symmetrical if the ratio of current and voltage at some (one) port is same as ratio of current and voltage at other port.<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1610 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/symmetrical-network.jpg\" alt=\"Symmetrical Network\" width=\"300\" height=\"57\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Note:<\/strong><\/p>\n<p style=\"text-align: justify;\">For small independent networks symmetry can be identified by the \u201cmirror image property\u201d.<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1612 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/mirror-image-property.png\" alt=\"Mirror Image Property\" width=\"267\" height=\"114\" \/><\/p>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Y-parameters\"><\/span><strong>Y-parameters<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">In the previous section we saw that impedance parameters may not exist for a two-port network. So, there is a need for an alternative means of describing such a network. This need may be met by the second set of parameter which we obtain by expressing the terminal currents in terms of the terminal voltages.<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1613 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/y-parameters.jpg\" alt=\"Y-Parameters\" width=\"626\" height=\"97\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/y-parameters.jpg 626w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/y-parameters-300x46.jpg 300w\" sizes=\"auto, (max-width: 626px) 100vw, 626px\" \/><\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1614 size-full aligncenter\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/y-parameters-1.jpg\" alt=\"Y-parameters\" width=\"726\" height=\"606\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/y-parameters-1.jpg 726w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/y-parameters-1-300x250.jpg 300w\" sizes=\"auto, (max-width: 726px) 100vw, 726px\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>The step-by-step methodology to obtain the admittance parameters is given as following:<\/strong><\/p>\n<ul>\n<li style=\"text-align: justify;\"><strong>Step-1 :<\/strong> To obtain Y<sub>11<\/sub> and Y<sub>21<\/sub>, connect a voltage source V1 across the input terminals and short circuit the output terminals as shown below in fig. (a).<\/li>\n<li style=\"text-align: justify;\"><strong>Step-2 :<\/strong> Find I<sub>1<\/sub> and I<sub>2<\/sub> and then Y<sub>11<\/sub> = I<sub>1<\/sub>\/V<sub>1<\/sub> and Y<sub>21<\/sub> = I<sub>2<\/sub>\/V<sub>1<\/sub>.<\/li>\n<li style=\"text-align: justify;\"><strong>Step-3 :<\/strong> To obtain Y<sub>22<\/sub> and Y<sub>12<\/sub>, connect a voltage source V2 across the output terminals and short circuit the input terminals as shown below in fig. (b).<\/li>\n<li style=\"text-align: justify;\"><strong>Step-4 :<\/strong> Find I<sub>1<\/sub> and I<sub>2<\/sub> and then Y<sub>22<\/sub> = I<sub>2<\/sub>\/V<sub>2<\/sub> and Y<sub>12<\/sub> = I<sub>1<\/sub>\/V<sub>2<\/sub>.<\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1616 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/linear-network-1.jpg\" alt=\"Linear Network\" width=\"603\" height=\"169\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/linear-network-1.jpg 603w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/linear-network-1-300x84.jpg 300w\" sizes=\"auto, (max-width: 603px) 100vw, 603px\" \/><\/p>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Condition-of-Reciprocity-and-Symmetry-2\"><\/span><strong>Condition of Reciprocity and Symmetry<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>For reciprocal network:<\/strong><\/p>\n<p style=\"text-align: justify;\">Y<sub>12<\/sub> = Y<sub>21<\/sub><\/p>\n<p style=\"text-align: justify;\"><strong>For symmetrical network:<\/strong><\/p>\n<p style=\"text-align: justify;\">Y<sub>11<\/sub> = Y<sub>22<\/sub><\/p>\n<p style=\"text-align: justify;\"><strong>Note:<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1618 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/condition-reciprocity.png\" alt=\"Condition of Reciprocity\" width=\"556\" height=\"74\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/condition-reciprocity.png 556w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/condition-reciprocity-300x40.png 300w\" sizes=\"auto, (max-width: 556px) 100vw, 556px\" \/><br \/>\n<\/strong><\/p>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"h-parameters-or-Hybrid-Parameters\"><\/span>h-parameters or Hybrid Parameters<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">The Z and Y parameters of two-port network do not always exist. So, there is a need for developing another set of parameters. This third set of parameters is based on making V<sub>1<\/sub> and I<sub>2<\/sub> the dependent variable. Thus, we obtain h parameter which is also known as the hybrid parameters.<\/p>\n<p style=\"text-align: justify;\">The hybrid parameters (h-parameters) would find wide usage in electronic circuits, especially in constructing models for transistors.<\/p>\n<p style=\"text-align: justify;\">The parameters of a transistor cannot be measured either by short-circuit admittance parameter measurement or open-circuit impedance parameter measurement alone, because of the forward bias of the base emitter junction, the device has a very low input resistance. For open-circuit impedance measurement of Z<sub>12<\/sub> and Z<sub>22<\/sub>, it is very difficult to make the input open circuited. Z<sub>11<\/sub> and Z<sub>21<\/sub> can be measured by open-circuit impedance measurements, since the collector-emitter junction is reversed biased.<\/p>\n<p style=\"text-align: justify;\">By making a short-circuit admittance parameter measurement, Y<sub>12<\/sub> and Y<sub>22<\/sub> can be measured by short circuiting the input port, but Y<sub>11<\/sub> and Y<sub>21<\/sub> cannot be measured since the collector-emitter junction is reverse biased.<\/p>\n<p style=\"text-align: justify;\">Some kind of parameter representation is required by which some parameters are measured by open circuiting the input port, while the rest of the parameters can be measured by short-circuiting the output port. This is the so-called hybrid parameter representation. This parameter representation is a hybrid of short-circuit admittance and open-circuit impedance measurement.<\/p>\n<p style=\"text-align: justify;\">One set of equations result when the voltage of the input port and the current of the output port are expressed in terms of the current of the input port and the voltage of the output port [Refer Figure (a)], in the form<\/p>\n<p style=\"text-align: justify;\"><em>V<sub>1<\/sub> = h<sub>11<\/sub>I<sub>1<\/sub> + h<sub>12<\/sub> V<sub>2<\/sub><\/em><\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1620 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/equivalent-network.jpg\" alt=\"Equivalent Network\" width=\"655\" height=\"430\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/equivalent-network.jpg 655w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/equivalent-network-300x197.jpg 300w\" sizes=\"auto, (max-width: 655px) 100vw, 655px\" \/><\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1621 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/hybrid-parameters.jpg\" alt=\"Hybrid Parameters\" width=\"638\" height=\"328\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/hybrid-parameters.jpg 638w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/hybrid-parameters-300x154.jpg 300w\" sizes=\"auto, (max-width: 638px) 100vw, 638px\" \/><\/p>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Condition-of-Reciprocity-and-Symmetry-3\"><\/span>Condition of Reciprocity and Symmetry<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1623 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/reciprocal.jpg\" alt=\"Reciprocal\" width=\"464\" height=\"72\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/reciprocal.jpg 464w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/reciprocal-300x47.jpg 300w\" sizes=\"auto, (max-width: 464px) 100vw, 464px\" \/><\/p>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"g-parameters-or-Inverse-Hybrid-Parameters\"><\/span><strong>g-parameters or Inverse Hybrid Parameters<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">A set of parameters closely related to the h-parameters are the g-parameters or inverse hybrid parameter. These are used to describe the terminal currents and voltage as<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1626 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/g-parameter.jpg\" alt=\"G Parameter\" width=\"716\" height=\"493\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/g-parameter.jpg 716w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/g-parameter-300x207.jpg 300w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/g-parameter-130x90.jpg 130w\" sizes=\"auto, (max-width: 716px) 100vw, 716px\" \/><\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1628 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/output-terminals.jpg\" alt=\"Output Terminals\" width=\"627\" height=\"298\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/output-terminals.jpg 627w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/output-terminals-300x143.jpg 300w\" sizes=\"auto, (max-width: 627px) 100vw, 627px\" \/><\/p>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Condition-of-Reciprocity-and-Symmetry-4\"><\/span>Condition of Reciprocity and Symmetry<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignleft wp-image-1631 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/reciprocity.jpg\" alt=\"Reciprocity\" width=\"434\" height=\"76\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/reciprocity.jpg 434w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/reciprocity-300x53.jpg 300w\" sizes=\"auto, (max-width: 434px) 100vw, 434px\" \/><\/p>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Transmission-Parameters-ABCD\"><\/span>Transmission Parameters (ABCD)<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">Since, there are no restrictions on which terminal voltage and current should be considered independent and which should be dependent variables, we expect to be able to generate many set of parameters. Another set\u00a0 of parameter relates the variable at the input port to those at the output port.<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1634 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/transmission-parameters.jpg\" alt=\"Transmission Parameters\" width=\"628\" height=\"85\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/transmission-parameters.jpg 628w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/transmission-parameters-300x41.jpg 300w\" sizes=\"auto, (max-width: 628px) 100vw, 628px\" \/><\/p>\n<p style=\"text-align: justify;\">Equations (12.11) and (12.12) relate the input variables (V<sub>1<\/sub> and I<sub>1<\/sub>) to the output variables (V<sub>2<\/sub> and \u2013I<sub>2<\/sub>). Notice that in computing the transmission parameter, <em>\u2013I<sub>2<\/sub><\/em> is used rather than <em>I<sub>2<\/sub><\/em>, because the current is considered to be leaving the network, as shown in below figure.<br \/>\nThe transmission parameters are<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1666 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/transmission-parameters-1.jpg\" alt=\"Transmission Parameters\" width=\"648\" height=\"491\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/transmission-parameters-1.jpg 648w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/transmission-parameters-1-300x227.jpg 300w\" sizes=\"auto, (max-width: 648px) 100vw, 648px\" \/><\/p>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Condition-of-Reciprocity-and-Symmetry-5\"><\/span>Condition of Reciprocity and Symmetry<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignleft wp-image-1668 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/symmetrical-network-1.jpg\" alt=\"Symmetrical Network\" width=\"592\" height=\"53\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/symmetrical-network-1.jpg 592w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/symmetrical-network-1-300x27.jpg 300w\" sizes=\"auto, (max-width: 592px) 100vw, 592px\" \/><\/p>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Inverse-Transmission-Parameters\"><\/span><strong> Inverse Transmission Parameters<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">Our last set of parameters may be defined by expressing the variables at the output port in terms of the variables at the input port we obtain<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1679 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/inverse-transmission.jpg\" alt=\"Inverse Transmission\" width=\"662\" height=\"436\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/inverse-transmission.jpg 662w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/inverse-transmission-300x198.jpg 300w\" sizes=\"auto, (max-width: 662px) 100vw, 662px\" \/><\/p>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Inter-Relations-in-Network-Parameters\"><\/span>Inter Relations in Network Parameters<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1682 size-full aligncenter\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/network-parameters.jpg\" alt=\"Network Parameters\" width=\"538\" height=\"520\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/network-parameters.jpg 538w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/network-parameters-300x290.jpg 300w\" sizes=\"auto, (max-width: 538px) 100vw, 538px\" \/><\/p>\n<p style=\"text-align: center;\"><a class=\"btn btn-danger\" role=\"button\" href=\"https:\/\/study.madeeasy.in\/ec\/network-theory\/maximum-power-transfer\/\" target=\"_blank\" rel=\"noopener\">&lt;&lt; Previous<\/a> | <a class=\"btn btn-success\" role=\"button\" href=\"https:\/\/study.madeeasy.in\/subjects\/what-is-network-theory\/\" target=\"_blank\" rel=\"noopener\"> Next &gt;&gt;<\/a><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>What is Network Parameters? A pair of terminals through which a current may enter or leave a network is known<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[421,6],"tags":[453,450,454,452,455,449,451],"class_list":["post-1597","post","type-post","status-publish","format-standard","hentry","category-network-theory","category-ec","tag-g-parameter","tag-impedance-parameters","tag-output-terminals","tag-reciprocal","tag-transmission-parameters","tag-two-port-network","tag-y-parameters"],"_links":{"self":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/1597","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/comments?post=1597"}],"version-history":[{"count":0,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/1597\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/media?parent=1597"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/categories?post=1597"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/tags?post=1597"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}