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线性坐标系到对数坐标系的变换——EMC测试曲线的绘制

 
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<meta http-equiv="Content-Type" content="text/html; charset=utf-8"> <meta name="ProgId" content="Word.Document"> <meta name="Generator" content="Microsoft Word 12"> <meta name="Originator" content="Microsoft Word 12"> <link rel="File-List" href="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_filelist.xml"> <link rel="themeData" href="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_themedata.thmx"> <link rel="colorSchemeMapping" href="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_colorschememapping.xml"> <!--[if gte mso 9]><xml> <w:WordDocument> <w:View>Normal</w:View> <w:Zoom>0</w:Zoom> <w:TrackMoves /> <w:TrackFormatting /> <w:PunctuationKerning /> <w:DrawingGridVerticalSpacing>7.8 磅</w:DrawingGridVerticalSpacing> <w:DisplayHorizontalDrawingGridEvery>0</w:DisplayHorizontalDrawingGridEvery> <w:DisplayVerticalDrawingGridEvery>2</w:DisplayVerticalDrawingGridEvery> <w:ValidateAgainstSchemas /> 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16 0 262145 0;} @font-face {font-family:"Cambria Math"; panose-1:2 4 5 3 5 4 6 3 2 4; mso-font-charset:0; mso-generic-font-family:roman; mso-font-pitch:variable; mso-font-signature:-1610611985 1107304683 0 0 159 0;} @font-face {font-family:Calibri; panose-1:2 15 5 2 2 2 4 3 2 4; mso-font-charset:0; mso-generic-font-family:swiss; mso-font-pitch:variable; mso-font-signature:-1610611985 1073750139 0 0 159 0;} @font-face {font-family:"/@宋体"; panose-1:2 1 6 0 3 1 1 1 1 1; mso-font-charset:134; mso-generic-font-family:auto; mso-font-pitch:variable; mso-font-signature:3 135135232 16 0 262145 0;} /* Style Definitions */ p.MsoNormal, li.MsoNormal, div.MsoNormal {mso-style-unhide:no; mso-style-qformat:yes; mso-style-parent:""; margin:0cm; margin-bottom:.0001pt; text-align:justify; text-justify:inter-ideograph; mso-pagination:none; mso-hyphenate:none; font-size:10.5pt; mso-bidi-font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-fareast-font-family:宋体; mso-bidi-font-family:Calibri; mso-font-kerning:.5pt; mso-fareast-language:AR-SA;} .MsoChpDefault {mso-style-type:export-only; mso-default-props:yes; font-size:10.0pt; mso-ansi-font-size:10.0pt; mso-bidi-font-size:10.0pt; mso-ascii-font-family:"Times New Roman"; mso-fareast-font-family:宋体; mso-hansi-font-family:"Times New Roman"; mso-font-kerning:0pt;} /* Page Definitions */ @page {mso-page-border-surround-header:no; mso-page-border-surround-footer:no;} @page Section1 {size:612.0pt 792.0pt; margin:72.0pt 90.0pt 72.0pt 90.0pt; mso-header-margin:36.0pt; mso-footer-margin:36.0pt; mso-paper-source:0;} div.Section1 {page:Section1;} --> </style>
绘制测试曲线的核心函数为
CEMCView::DrawFrameCurve()函数。该函数可以根据测试的频段和该频段的测试数据在对数坐标系的对应位置绘制测试曲线。DrawFrameCurve()函数绘制曲线的流程图如图1所示:


图1 测试流程图



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图2 R3131A屏幕显示的线性坐标系


每次测试,Advantest R3131A频谱仪都会对所测频段采样501个点,每个点对应的测试值不小于512,如图3-29所示。大于3392的数值不在频谱仪屏幕上显示,但会记录下这个值,因为这个值也是有效的。Advantest R3131A频谱仪默认纵轴每格代表10dB,因此频谱仪的测试值3392-512=2880对应着80dB。对于在计算机上绘制的对数坐标系而言,若纵轴表示0M dB,因此对数坐标系纵坐标最大值对应的频谱仪测试值为:


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<!--[endif]--><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1273091893"> </o:OLEObject> </xml><![endif]-->

Ytop<!--[if gte vml 1]><v:shape id="_x0000_i1026" type="#_x0000_t75" style='width:20.25pt;height:18.75pt' o:ole=""> <v:imagedata src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image003.wmz" o:title="" /> </v:shape><![endif]--><!--[if !vml]--><!--[endif]--><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1026" DrawAspect="Content" ObjectID="_1273091894"> </o:OLEObject> </xml><![endif]-->为对数坐标系左上角对应的计算机屏幕上的纵坐标值,<!--[if gte vml 1]><v:shape id="_x0000_i1027" type="#_x0000_t75" style='width:20.25pt;height:18.75pt' o:ole=""> <v:imagedata src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image005.wmz" o:title="" /> </v:shape><![endif]-->Ybot表示对数坐标系左下角对应的计算机屏幕上的纵坐标值,y<!--[endif]--><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1028" DrawAspect="Content" ObjectID="_1273091896"> </o:OLEObject> </xml><![endif]-->表示对数坐标系中某个测试点对应的计算机屏幕上的纵坐标值,d<!--[endif]--><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1029" DrawAspect="Content" ObjectID="_1273091897"> </o:OLEObject> </xml><![endif]-->表示该测试点对应的频谱仪测试值,对数坐标系纵坐标从0开始,则:

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因此,

<!--[if gte vml 1]><v:shape id="_x0000_i1031" type="#_x0000_t75" style='width:117pt;height:36.75pt' o:ole=""> <v:imagedata src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image013.wmz" o:title="" /> </v:shape><![endif]--><!--[if !vml]-->

(3-1)

对于横坐标,如果已知测试的起始频率为<!--[if gte vml 1]><v:shape id="_x0000_i1032" type="#_x0000_t75" style='width:24pt;height:18pt' o:ole=""> <v:imagedata src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image015.wmz" o:title="" /> </v:shape><![endif]--><!--[if !vml]-->fstart,起始频率对应的计算机横坐标为<!--[if gte vml 1]><v:shape id="_x0000_i1033" type="#_x0000_t75" style='width:24pt;height:18pt' o:ole=""> <v:imagedata src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image017.wmz" o:title="" /> </v:shape><![endif]--><!--[if !vml]-->xstart,测试终止频率为<!--[if gte vml 1]><v:shape id="_x0000_i1034" type="#_x0000_t75" style='width:23.25pt;height:18.75pt' o:ole=""> <v:imagedata src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image019.wmz" o:title="" /> </v:shape><![endif]--><!--[if !vml]-->fstop,测试终止频率对应的计算机横坐标为<!--[if gte vml 1]><v:shape id="_x0000_i1035" type="#_x0000_t75" style='width:21.75pt;height:18.75pt' o:ole=""> <v:imagedata src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image021.wmz" o:title="" /> </v:shape><![endif]--><!--[if !vml]-->xstop,该频段的起始频率为<!--[if gte vml 1]><v:shape id="_x0000_i1036" type="#_x0000_t75" style='width:35.25pt;height:18.75pt' o:ole=""> <v:imagedata src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image023.wmz" o:title="" /> </v:shape><![endif]--><!--[if !vml]-->ffrmstart,结合图3-16可得该频段起始频率对应的计算机坐标<!--[if gte vml 1]><v:shape id="_x0000_i1037" type="#_x0000_t75" style='width:33.75pt;height:18.75pt' o:ole=""> <v:imagedata src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image025.wmz" o:title="" /> </v:shape><![endif]--><!--[if !vml]-->有:


<!--[if gte vml 1]><v:shape id="_x0000_i1038" type="#_x0000_t75" style='width:198pt;height:36.75pt' o:ole=""> <v:imagedata src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image027.wmz" o:title="" /> </v:shape><![endif]--><!--[if !vml]--><!--[endif]--><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1038" DrawAspect="Content" ObjectID="_1273091906"> </o:OLEObject> </xml><![endif]-->

因此

<!--[if gte vml 1]><v:shape id="_x0000_i1039" type="#_x0000_t75" style='width:212.25pt;height:75.75pt' o:ole=""> <v:imagedata src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image029.wmz" o:title="" /> </v:shape><![endif]--><!--[if !vml]--><!--[endif]--><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1039" DrawAspect="Content" ObjectID="_1273091907"> </o:OLEObject> </xml><![endif]-->

如果每个测试频段有<!--[if gte vml 1]><v:shape id="_x0000_i1040" type="#_x0000_t75" style='width:14.25pt;height:14.25pt' o:ole=""> <v:imagedata src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image031.wmz" o:title="" /> </v:shape><![endif]--><!--[if !vml]-->N个采样点,也即有<!--[if gte vml 1]><v:shape id="_x0000_i1041" type="#_x0000_t75" style='width:14.25pt;height:14.25pt' o:ole=""> <v:imagedata src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image033.wmz" o:title="" /> </v:shape><![endif]--><!--[if !vml]-->N个测试数据,那么该频段中第<!--[if gte vml 1]><v:shape id="_x0000_i1042" type="#_x0000_t75" style='width:6.75pt;height:12.75pt' o:ole=""> <v:imagedata src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image034.wmz" o:title="" /> </v:shape><![endif]--><!--[if !vml]-->i个数据对应的频率为<!--[if gte vml 1]><v:shape id="_x0000_i1043" type="#_x0000_t75" style='width:12.75pt;height:18pt' o:ole=""> <v:imagedata src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image036.wmz" o:title="" /> </v:shape><![endif]--><!--[if !vml]--><!--[endif]--><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1043" DrawAspect="Content" ObjectID="_1273091911"> </o:OLEObject> </xml><![endif]-->fi,且

<!--[if gte vml 1]><v:shape id="_x0000_i1044" type="#_x0000_t75" style='width:168pt;height:33pt' o:ole=""> <v:imagedata src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image038.wmz" o:title="" /> </v:shape><![endif]--><!--[if !vml]--><!--[endif]--><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1045" DrawAspect="Content" ObjectID="_1273091913"> </o:OLEObject> </xml><![endif]-->

式中, <!--[if gte vml 1]><v:shape id="_x0000_i1046" type="#_x0000_t75" style='width:33pt;height:18.75pt' o:ole=""> <v:imagedata src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image042.wmz" o:title="" /> </v:shape><![endif]--><!--[if !vml]-->ffrmstop——测试频段的终止频率。

<!--[if gte vml 1]><v:shape id="_x0000_i1047" type="#_x0000_t75" style='width:6.75pt;height:12.75pt' o:ole=""> <v:imagedata src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image034.wmz" o:title="" /> </v:shape><![endif]--><!--[if !vml]-->i个数据对应的计算机横坐标为:

<!--[if gte vml 1]><v:shape id="_x0000_i1048" type="#_x0000_t75" style='width:179.25pt;height:75pt' o:ole=""> <v:imagedata src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image044.wmz" o:title="" /> </v:shape><![endif]--><!--[if !vml]--> (3-2)

如果在某个测试频段内的第<!--[if gte vml 1]><v:shape id="_x0000_i1050" type="#_x0000_t75" style='width:6.75pt;height:12.75pt' o:ole=""> <v:imagedata src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image034.wmz" o:title="" /> </v:shape><![endif]--><!--[if !vml]-->i个数据的测试值为<!--[if gte vml 1]><v:shape id="_x0000_i1051" type="#_x0000_t75" style='width:11.25pt;height:14.25pt' o:ole=""> <v:imagedata src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image009.wmz" o:title="" /> </v:shape><![endif]--><!--[if !vml]--><!--[endif]--><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1051" DrawAspect="Content" ObjectID="_1273091919"> </o:OLEObject> </xml><![endif]-->d,则该点对应的计算机屏幕坐标为(xi,yi)<!--[if gte vml 1]><v:shape id="_x0000_i1052" type="#_x0000_t75" style='width:36.75pt;height:18pt' o:ole=""> <v:imagedata src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image046.wmz" o:title="" /> </v:shape><![endif]--><!--[if !vml]--><!--[endif]--><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1052" DrawAspect="Content" ObjectID="_1273091920"> </o:OLEObject> </xml><![endif]--><!--[if gte vml 1]><v:shape id="_x0000_i1053" type="#_x0000_t75" style='width:12pt;height:18pt' o:ole=""> <v:imagedata src="file:///C:/DOCUME~1/ADMINI~1/LOCALS~1/Temp/msohtmlclip1/01/clip_image048.wmz" o:title="" /> </v:shape><![endif]--><!--[if !vml]-->xi、yi<!--[endif]--><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1054" DrawAspect="Content" ObjectID="_1273091922"> </o:OLEObject> </xml><![endif]-->可分别根据式(3-1)和式(3-2)求出。

PS:

CSDN不支持把Word中的公式自动保存为图片实在是太难用了,每次都要自己先把公式转化为图片然后再插入到文章里,麻烦!

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