The tools required for calculating the vales in an L Network come from the following equations that can be found in the ARRL Handbook.
\nXS = QRs and Xp=Rp\/Q
\nQ=Xs\/Rs and Q=Rp\/Xp
\nRp=Rs(Q^2+1)
\nRs=Rp\/\u3016(Q\u3017^2+1)
\nQ=\u221a(RP\/Rs-1)
\nThe L network is based on a technique known as series to parallel transformations.
\nSuppose we have measured the impedance of an antenna we have constructed with an antenna analyzer and found it to be 21 + J5\u2126. We are going to match this impedance to a 50\u2126 line.
\nWe first give the larger impedance the designation of Rp then determine the Q. We will put the +J5\u2126 aside for the moment.
\nSo Q= \u221a(50\/21-1) = 1.715
\nWe now find the parallel reactance required to be placed across the 50\u2126 .
\nXp=Rp\/Q =50\/1.715 =42.55 We now have our parallel form 50\u2126 in parallel with a 42.55\u2126 reactance. This reactance could be chosen as an inductor or a capacitor however in some circumstances the values may become quite ridiculous so try the other option. What is a 42.55\u2126 reactance? I shall choose a working frequency of 14.2MHz for my example. I am going to choose a capacitor for my reactance. The reactance of a capacitor can be calculated using the following formula C=1\/2\u220fFXc where Xc is the reactance an f in this case 14.2MHz. In our case this gives a capacitor of 260 PF.
\nNow we convert to series equivalent. Xs = QRs Rs is the 21\u2126 we are trying to match. So Xs =1.175 x 21 = 24.675\u2126. As we chose a capacitor for our parallel reactance we will now place a series inductor with a reactance of 24.675\u2126 in series to cancel the remaining reactance. The reactance of an inductor is calculated using the following equation Xs=2\u220fFL rearranging we have L= Xs\/2\u220fF. In our case at 14.2MHz this is an inductance of 276nH. Remember we put the +J5\u2126 aside now when we take it into consideration we can subtract this reactance from our required reactance. The reactance of 5 ohms we need to subtract from the 24.675\u2126 we calculated for Xs. So in fact our required reactance is actually 19.675\u2126 or an inductor of 220 nH.
\nTo summarize we place a 260PF capacitor across the 50 ohms and form an L network by placing a 220 nH inductor in series. The 21+J5\u2126 with the L network in place will have a combined impedance of 50+J0\u2126.<\/p>\n","protected":false},"excerpt":{"rendered":"
The tools required for calculating the vales in an L Network come from the following equations that can be found in the ARRL Handbook. XS = QRs and Xp=Rp\/Q Q=Xs\/Rs and Q=Rp\/Xp Rp=Rs(Q^2+1) Rs=Rp\/\u3016(Q\u3017^2+1) Q=\u221a(RP\/Rs-1) The L network is based on a technique known as series to parallel transformations.<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[12],"tags":[],"class_list":["post-187","post","type-post","status-publish","format-standard","hentry","category-antennas"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p8ympN-31","jetpack-related-posts":[],"_links":{"self":[{"href":"https:\/\/vk8bn.me\/info\/wp-json\/wp\/v2\/posts\/187","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vk8bn.me\/info\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/vk8bn.me\/info\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/vk8bn.me\/info\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/vk8bn.me\/info\/wp-json\/wp\/v2\/comments?post=187"}],"version-history":[{"count":2,"href":"https:\/\/vk8bn.me\/info\/wp-json\/wp\/v2\/posts\/187\/revisions"}],"predecessor-version":[{"id":189,"href":"https:\/\/vk8bn.me\/info\/wp-json\/wp\/v2\/posts\/187\/revisions\/189"}],"wp:attachment":[{"href":"https:\/\/vk8bn.me\/info\/wp-json\/wp\/v2\/media?parent=187"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vk8bn.me\/info\/wp-json\/wp\/v2\/categories?post=187"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vk8bn.me\/info\/wp-json\/wp\/v2\/tags?post=187"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}