{"id":138,"date":"2018-07-27T11:59:46","date_gmt":"2018-07-27T09:59:46","guid":{"rendered":"https:\/\/project.inria.fr\/puma\/?page_id=138"},"modified":"2018-09-25T02:44:22","modified_gmt":"2018-09-25T00:44:22","slug":"miniaturised-antenna","status":"publish","type":"page","link":"https:\/\/project.inria.fr\/puma\/examples\/miniaturised-antenna\/","title":{"rendered":"Miniaturised antenna"},"content":{"rendered":"

We show next an example of matching an antenna’s reflection in the band 870-900 MHz. Before starting, the reflection parameter of the antenna has been saved to a .s1p (touchstone) file called superdirective.s1p.<\/p>\n

Matching problem set up<\/h2>\n

The first step is loading the antenna data and creating the matching object. For that we use the function MultiPort.read<\/em>.
\nAdditionally we interpolate the data obtaining 1000 frequency points from 800MHz to 1GHz. This step is important since a good frequency resolution will be required for the rational approximation<\/p>\n

data = MultiPort.read('superdirective.s1p');\r\ndata = resample(data,linspace(800e6,1e9,1000));<\/pre>\n
Define frequency band object (from 870MHz to 900MHz)<\/p>\n
BAND = FreqBand('Band',[870e6,900e6]);<\/pre>\n
Pick rational approximation order and filter order. We choose A=2 for the order of the rational approximation and M=5 for the order of the matching filter. Thus the global system is of order N=A+M=7.<\/p>\n
A=2;\r\nM=5;<\/pre>\n
Create the matching object specifying the order of the global system, the order of the rational approximation and the desired passband. Also we can provide additional options as parameter-value pairs.<\/p>\n
MATCHING = matching(data,...\r\n                    'SystemOrder',A+M,...\r\n                    'ApproximationOrder',A,...\r\n                    'Passband',BAND,...\r\n                    'Fixpoint',true);<\/pre>\n
Rational approximation<\/span><\/span><\/h2>\n
 Rational approximation of the load is required. The plot<\/em> function can be used to check the quality of the approximation at this stage. <\/span><\/p>\n
MATCHING.rationalApproximation;\r\nfigure\r\nplot(MATCHING)\r\ntitle('Rational approximation');\r\nlegend('show','Location','Best');<\/pre>\n
\"\"<\/p>\n
Solve the matching problem<\/h2>\n
It can be seen that a good fit is obtained in the band of interest with the rational approximation. Therefore we can proceed to solve the problem.<\/p>\n
MATCHING.solve;<\/pre>\n
Extract the results<\/h2>\n
Once the solve method finished we can extract the result from the matching object. The property MATCHING.Results is a structure containing the rational model of the computed matching filter as well as the obtained global system. Moreover the structure MATCHING.ReflectionLevel contains the reflection level corresponding to: a) the lower hard bound, b) the reflection level obtained after the simplification of the blaschke product (fixpoint) if applicable, c) the reflection level obtained after a local optimisation (if it is performed)<\/p>\n
Results = MATCHING.Results;\r\nL = MATCHING.ReflectionLevel<\/pre>\n
L = struct with fields:\r\n     optimal: -8.6620\r\n    fixpoint: -8.5652<\/pre>\n
Verify the results by plotting the scattering parameters of the matching filter and the global system. Also parameter-value pairs can be used to provide additional options. In this case we decided not to plot the rationall approximation again (we already saw it was a very good approximation) and also to plot the filter response with dash (–) lines.<\/p>\n
figure\r\nplot(MATCHING,'PlotApprox',false,...\r\n              'Scale','MHz',...\r\n              'FilterArgs',{'LineStyle','--'});\r\nlegend('show','Location','Best');\r\nylim([-15 0]);\r\nxlim([800 950]);\r\ntitle('Matching of superdirective antenna');<\/pre>\n
<\/p>\n","protected":false},"excerpt":{"rendered":"
We show next an example of matching an antenna’s reflection in the band 870-900 MHz. Before starting, the reflection parameter of the antenna has been saved to a .s1p (touchstone) file called superdirective.s1p. Matching problem set up The first step is loading the antenna data and creating the matching object.\u2026<\/p>\n
 Continue reading<\/span><\/i><\/a> <\/p>\n","protected":false},"author":1445,"featured_media":0,"parent":132,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-138","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/project.inria.fr\/puma\/wp-json\/wp\/v2\/pages\/138","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/project.inria.fr\/puma\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/project.inria.fr\/puma\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/project.inria.fr\/puma\/wp-json\/wp\/v2\/users\/1445"}],"replies":[{"embeddable":true,"href":"https:\/\/project.inria.fr\/puma\/wp-json\/wp\/v2\/comments?post=138"}],"version-history":[{"count":138,"href":"https:\/\/project.inria.fr\/puma\/wp-json\/wp\/v2\/pages\/138\/revisions"}],"predecessor-version":[{"id":896,"href":"https:\/\/project.inria.fr\/puma\/wp-json\/wp\/v2\/pages\/138\/revisions\/896"}],"up":[{"embeddable":true,"href":"https:\/\/project.inria.fr\/puma\/wp-json\/wp\/v2\/pages\/132"}],"wp:attachment":[{"href":"https:\/\/project.inria.fr\/puma\/wp-json\/wp\/v2\/media?parent=138"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}