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<h3>Impedance Parameters &nbsp;&nbsp;
<a href="javascript:void(0);" onClick="var e; if (parseInt(navigator.appVersion)>=4){e=event;}  if (parseInt(navigator.appVersion) >=2 && typeof(PickupDialog_Invoke) == 'function') PickupDialog_Invoke(e,'','Admittance','../../MMI_Reference/Trace/Measure/Admittance/Admittance.htm','Impedance (GUI reference)','../../MMI_Reference/Trace/Measure/Impedance/Impedance.htm','Mixed Mode Parameters','Mixed_Mode_Parameters.htm','Z-Parameters','../../MMI_Reference/Trace/Measure/Z-Parameters/Z_Parameters.htm');return false;" title="Related Topics"><img src="../../ss_btn_related_topics2.gif" border=0 height=17 width=81 alt="Related Topics"></a>

 </h3>

<p>An impedance is the complex ratio between a voltage and a current. The 
 analyzer provides two independent sets of impedance parameters, essentially 
 based on different n-port circuit models:</p>

<ul type="disc" class="whs1">
	
	<li class=kadov-p-CList><p class=List>Matched-circuit <a href="Impedance_Parameters.htm#Converted_Impedances"
															id=A7
															style="/*begin!kadov{{*/ position: relative; /*}}end!kadov*/ ">impedances</a><script 
 type="text/javascript"
	language=JavaScript1.2><!--
kadovInitEffects('A7');
//--></script>, 
 converted from reflection S-parameters</p></li>
	
	<li class=kadov-p-CList><p class=List>Open-circuit <a href="Impedance_Parameters.htm#Open_circuit_impedances"
															id=A8
															style="/*begin!kadov{{*/ position: relative; /*}}end!kadov*/ ">Z-parameters</a><script 
 type="text/javascript"
	language=JavaScript1.2><!--
kadovInitEffects('A8');
//--></script> 
 </p></li>
</ul>


<hr align="center" width="50%" class="whs2">


<h4><a name=Converted_Impedances></a>Converted Impedances</h4>

<p>The converted, matched-circuit impedances describe the impedances of 
 a DUT that is terminated at its outputs with the reference impedance Z<span 
 style="vertical-align: Sub;">0i</span> displayed in the <span style="font-style: italic;"><I><a 
 HREF="../../MMI_Reference/Channel/Mode/Channel_Mode.htm"
	id=A5
	style="/*begin!kadov{{*/ position: relative; /*}}end!kadov*/ ">Port 
 Configuration</a><script type="text/javascript"
												language=JavaScript1.2><!--
kadovInitEffects('A5');
//--></script></I></span> 
 dialog. i numbers the analyzer/DUT port. </p>

<p class=Figure><img src="Impedances_equiv_circuits.gif" width="411px" height="127px" border="0" class="img_whs3"></p>

<p>The analyzer converts the measured S-parameters to determine the matched-circuit 
 impedances.</p>

<p class=Dropdownline><span class=dropspot><a name=Relation_with_S_parameters></a><img src="../../small_images/info_red.jpg" x-maintain-ratio="TRUE" width="32px" height="37px" border="0" class="img_whs4"></span><a class="dropspot" href="javascript:kadovTextPopup(this)" id="a10" style="font-style: normal; /*begin!kadov{{*/ position: relative; /*}}end!kadov*/ ">Relation 
 with S-parameters</a><script type="text/javascript"
													language=JavaScript1.2><!--
kadovInitEffects('a10');
//--></script></p>

<div class="droptext" id="POPUP293634647" style="display: 'none'; " x-ss-type="dropdown">
 <p>It is possible to express the matched-circuit impedances Z<span style="vertical-align: Sub;">ii</span> 
 in terms of the reflection <a href="S-Parameters.htm"
								id=a12
								style="/*begin!kadov{{*/ position: relative; /*}}end!kadov*/ ">S-parameters</a> 
 S<span style="vertical-align: Sub;">ii</span> and vice versa. The reflection 
 parameters are calculated according to: </p>
 <p class=List
	style="margin-left: 40px;"><img src="Z_reflex.gif" width="110px" height="41px" border="0" class="img_whs5"></p>
 <p>where i numbers the analyzer/DUT port. The transmission parameters are 
 calculated according to: </p>
 <p class=List
	style="margin-left: 40px;"><img src="../../MMI_Reference/Trace/Measure/Impedance/Z_formula_trans.gif" width="265px" height="51px" border="0" class="img_whs6"></p>
 <p>The two sets of reflection S-parameters and input/output impedances 
 provide equivalent descriptions of the reflection in a linear n-port network. 
 Another set of equivalent parameters is given by the matched-circuit <a href="../../MMI_Reference/Trace/Measure/Admittance/Admittance.htm" id="a16" style="/*begin!kadov{{*/ position: relative; /*}}end!kadov*/ ">admittances</a>, 
 defined as the inverse of the impedances. </p>
</div>
<p><span style="font-weight: bold;"><B>Examples:</B></span> </p>

<ul type="disc" class="whs1">
	
	<li class=kadov-p-CList><p class=List>Z<span style="vertical-align: Sub;">11</span> 
 is the input impedance of a 2-port DUT that is terminated at its output 
 with the reference impedance Z<span style="vertical-align: Sub;">0</span> 
 (matched -circuit impedance measured in a forward reflection measurement). 
 &nbsp;</p></li>
	
	<li class=kadov-p-CList><p class=List>The extension of the impedances 
 to more ports and mixed mode measurements is analogous to S-parameters. 
 Z<span style="vertical-align: Sub;">dd44</span> is the differential mode 
 input impedance at port 4 of a DUT that is terminated at its other ports 
 with the reference impedance Z<span style="vertical-align: Sub;">0</span>. 
 See <span style="font-style: italic;"><I><a HREF="../../MMI_Reference/Trace/Measure/Impedance/Impedance.htm#More_Z_Parameters" id="A6" style="/*begin!kadov{{*/ position: relative; /*}}end!kadov*/ ">More 
 Impedances</a><script type="text/javascript"
											language=JavaScript1.2><!--
kadovInitEffects('A6');
//--></script></I></span> 
 for detailed information. </p></li>
</ul>

<p><img src="../../small_images/tip.jpg" x-maintain-ratio="TRUE" width="36px" height="37px" border="0" class="img_whs7">You can also read the converted impedances in a reflection 
 coefficient measurement from the <a HREF="../Screen_Elements/Display_Formats_and_Diagram_Types.htm#Smith_Chart" id="A13" style="/*begin!kadov{{*/ position: relative; /*}}end!kadov*/ ">Smith 
 chart</a><script type="text/javascript"
										language=JavaScript1.2><!--
kadovInitEffects('A13');
//--></script>. 
 &nbsp;</p>


<hr align="center" width="50%" class="whs2">


<h4><a name=Open_circuit_impedances></a>Z-Parameters</h4>

<p>The Z-parameters describe the impedances of a DUT with open output ports 
 (I = 0). The analyzer provides the full set of open-circuit impedances 
 including the transfer impedances (i.e. the complete nxn Z-matrix for 
 an n port DUT). </p>

<p>This means that Z-parameters can be used as an alternative to S-parameters 
 (or <a HREF="Admittance_Parameters.htm#Short_circuit_admittances"
		id=A4
		style="/*begin!kadov{{*/ position: relative; /*}}end!kadov*/ ">Y-parameters</a><script 
 type="text/javascript"
	language=JavaScript1.2><!--
kadovInitEffects('A4');
//--></script>) 
 in order to completely characterize a linear n-port network. </p>


<hr align="center" width="50%" class="whs2">


<h5><a name=2_port_Z_parameters></a>2-Port Open-Circuit Z-Parameters</h5>

<p>In analogy to <a HREF="S-Parameters.htm"
					id=A1
					style="/*begin!kadov{{*/ position: relative; /*}}end!kadov*/ ">S-parameters</a><script 
 type="text/javascript"
	language=JavaScript1.2><!--
kadovInitEffects('A1');
//--></script>, 
 Z-parameters are expressed as Z<span style="vertical-align: Sub;">&lt;out&gt;&lt; 
 in&gt;</span>, where &lt;out&gt; and &lt;in&gt; denote the output and 
 input port numbers of the DUT. </p>

<p>The open-circuit Z-parameters for a two-port are based on a circuit 
 model that can be expressed with two linear equations: </p>

<p class=Figure><img src="../../MMI_Reference/Trace/Measure/Z-Parameters/Z_Y_Circuit.gif" width="338px" height="118px" border="0" class="img_whs8"></p>

<p class=Figure><img src="../../MMI_Reference/Trace/Measure/Z-Parameters/Z_Formula.gif" width="121px" height="44px" border="0" class="img_whs9"></p>

<p class=Dropdownline><img src="../../small_images/info_red.jpg" x-maintain-ratio="TRUE" width="32px" height="37px" border="0" class="img_whs4"><a class="dropspot" href="javascript:kadovTextPopup(this)" id="a2" style="font-style: normal; /*begin!kadov{{*/ position: relative; /*}}end!kadov*/ ">Meaning 
 of Z-parameters</a><script type="text/javascript"
												language=JavaScript1.2><!--
kadovInitEffects('a2');
//--></script></p>

<div class="droptext" id="POPUP294079185" style="display: 'none'; " x-ss-type="dropdown">
 <p class=Dropdowntext>The <span style="x-condition:ZVB_A_T; ">four </span>2-port open-circuit Z-parameters 
 can be interpreted as follows:</p>
 <ul type="disc" class="whs1">
  <li class=kadov-p-CList>
  <p class=List>Z<span style="vertical-align: Sub;">11</span> 
 is the input impedance, defined as the ratio of the voltage V<span style="vertical-align: Sub;">1</span> 
 to the current I<span style="vertical-align: Sub;">1</span>, measured 
 at port 1 (forward measurement with open output, I<span style="vertical-align: Sub;">2</span> 
 = 0). </p></li>
  <li style="x-condition:ZVB_A_T; " class="kadov-p-CList">
  <p class=List>Z<span style="vertical-align: Sub;">21</span> 
 is the forward transfer impedance, defined as the ratio of the voltage 
 V<span style="vertical-align: Sub;">2</span> to the current I<span style="vertical-align: Sub;">1</span> 
 (forward measurement with open output, I<span style="vertical-align: Sub;">2</span> 
 = 0).</p></li>
  <li style="x-condition:ZVB_A_T; " class="kadov-p-CList">
  <p class=List>Z<span style="vertical-align:Sub; x-condition:ZVB_A_T; ">12</span> 
 is the reverse transfer impedance, defined as the ratio of the voltage 
 V<span style="vertical-align:Sub; x-condition:ZVB_A_T; ">1</span> to the 
 current I<span style="vertical-align:Sub; x-condition:ZVB_A_T; ">2</span> 
 (reverse measurement with open input, I<span style="vertical-align:Sub; x-condition:ZVB_A_T; ">1</span> 
 = 0).</p></li>
  <li class=kadov-p-CList>
  <p class=List>Z<span style="vertical-align: Sub;">22</span> 
 is the output impedance, defined as the ratio of the voltage V<span style="vertical-align: Sub;">2</span> 
 to the current I<span style="vertical-align: Sub;">2</span>, measured 
 at port 2 (reverse measurement with open input, I<span style="vertical-align: Sub;">1</span> 
 = 0). </p></li>
 </ul>
</div>
<p>Z-parameters can be easily extended to describe circuits with more than 
 two ports or several modes of propagation<span style="x-condition:OLH; ">; 
 see section </span><span style="font-style:italic; x-condition:OLH; "><I><a 
 href="../../MMI_Reference/Trace/Measure/Z-Parameters/Z_Parameters.htm#More_Z_Parameters"
	id=a14
	style="/*begin!kadov{{*/ position: relative; /*}}end!kadov*/ ">More 
 Z-Parameters</a><script type="text/javascript"
											language=JavaScript1.2><!--
kadovInitEffects('a14');
//--></script></I></span>. 
 </p>


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