{"id":8086,"date":"2014-09-06T10:45:13","date_gmt":"2014-09-06T14:45:13","guid":{"rendered":"http:\/\/www.engineeringradio.us\/blog\/?p=8086"},"modified":"2023-03-26T09:39:17","modified_gmt":"2023-03-26T13:39:17","slug":"the-smith-chart","status":"publish","type":"post","link":"https:\/\/www.engineeringradio.us\/blog\/2014\/09\/the-smith-chart\/","title":{"rendered":"The Smith Chart"},"content":{"rendered":"\n<p>I have been fooling around with Smith Charts lately. They look complicated, but are really pretty easy to understand and use, once you get around all those lines and numbers and stuff. Smith charts offer a great way to visualize what is going on with a particular antenna or transmission line. They can be very useful for AM antenna broadbanding.<\/p>\n\n\n\n<figure class=\"wp-block-image alignnone\"><a href=\"https:\/\/www.engineeringradio.us\/blog\/wp-content\/uploads\/2014\/09\/smith-chart.jpg\"><img loading=\"lazy\" decoding=\"async\" width=\"470\" height=\"600\" src=\"https:\/\/www.engineeringradio.us\/blog\/wp-content\/uploads\/2014\/09\/smith-chart-470x600.jpg\" alt=\"Smith chart\" class=\"wp-image-8091\" srcset=\"https:\/\/www.engineeringradio.us\/blog\/wp-content\/uploads\/2014\/09\/smith-chart-470x600.jpg 470w, https:\/\/www.engineeringradio.us\/blog\/wp-content\/uploads\/2014\/09\/smith-chart-117x150.jpg 117w, https:\/\/www.engineeringradio.us\/blog\/wp-content\/uploads\/2014\/09\/smith-chart-235x300.jpg 235w, https:\/\/www.engineeringradio.us\/blog\/wp-content\/uploads\/2014\/09\/smith-chart-400x510.jpg 400w, https:\/\/www.engineeringradio.us\/blog\/wp-content\/uploads\/2014\/09\/smith-chart-39x50.jpg 39w, https:\/\/www.engineeringradio.us\/blog\/wp-content\/uploads\/2014\/09\/smith-chart-900x1148.jpg 900w, https:\/\/www.engineeringradio.us\/blog\/wp-content\/uploads\/2014\/09\/smith-chart.jpg 1200w\" sizes=\"auto, (max-width: 470px) 100vw, 470px\" \/><\/a><figcaption class=\"wp-element-caption\">Smith chart<\/figcaption><\/figure>\n\n\n\n<p>.pdf version available here: <a href=\"https:\/\/www.engineeringradio.us\/blog\/wp-content\/uploads\/2014\/09\/smith-chart.pdf\">smith-chart<\/a>.<\/p>\n\n\n\n<p>The first thing to understand about a Smith chart is normalization. Impedance and reactance are expressed as ratios of value units like VSWR. A ratio of 1:1 is a perfect match. In the center of the Smith chart is point 1, which expresses a perfect match. To normalize, the load resistance and reactance are divided by the input resistance. Thus, if the input resistance is 50 ohms and the load impedance is 50 ohms j0, then the normalized Smith chart point would be 50\/50 or 1. If the load impedance is 85 ohms and the reactance is +j60, then the normalized Smith chart point would be <del>.58<\/del> 1.7,1.2.<\/p>\n\n\n\n<p>More basic Smitch chart usage information in this video:<\/p>\n\n\n\n<p><iframe loading=\"lazy\" src=\"\/\/www.youtube.com\/embed\/hmqM8PnUkmo\" allowfullscreen=\"allowfullscreen\" width=\"640\" height=\"360\" frameborder=\"0\"><\/iframe><\/p>\n\n\n\n<p>I touched on the black art of AM antenna broadbanding before. It is a complex topic, especially where directional antenna systems are concerned, as there are several potential bottlenecks in a directional array. To explain this simply, I will use an example of a single-tower non-directional antenna.<\/p>\n\n\n\n<p>Below is a chart of base impedance from a single tower AM antenna on 1430 KHz.\u00a0 The tower is skirted, 125.6 degrees tall.\u00a0 An AM tower that is expressed in electrical degrees is denoting wavelength.\u00a0 A 1\/4-wave tower (typical for AM) is 90 degrees tall. A 1\/2 wave tower is 180 degrees tall.\u00a0 Thus this tower is slightly taller than 1\/4 wavelength.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>Frequnecy(khz)<\/td><td>Reactance<\/td><td>Reactance (normalized)<\/td><td>Resistance<\/td><td>Resistance(normalized)<\/td><\/tr><tr><td>1390<\/td><td>-j 139<\/td><td>-2.78<\/td><td>405<\/td><td>8.1<\/td><\/tr><tr><td>1395<\/td><td>-j 143<\/td><td>-2.86<\/td><td>400<\/td><td>8.0<\/td><\/tr><tr><td>1400<\/td><td>-j 147<\/td><td>-2.94<\/td><td>350<\/td><td>7.0<\/td><\/tr><tr><td>1405<\/td><td>-j 146<\/td><td>-2.92<\/td><td>310<\/td><td>6.2<\/td><\/tr><tr><td>1410<\/td><td>-j 142<\/td><td>-2.84<\/td><td>270<\/td><td>5.4<\/td><\/tr><tr><td>1415<\/td><td>-j 132<\/td><td>-2.64<\/td><td>236<\/td><td>4.72<\/td><\/tr><tr><td>1420<\/td><td>-j 125<\/td><td>-2.50<\/td><td>210<\/td><td>4.2<\/td><\/tr><tr><td>1425<\/td><td>-j 118<\/td><td>-2.36<\/td><td>190<\/td><td>3.8<\/td><\/tr><tr><td><strong>1430<\/strong><\/td><td><strong>-j 112<\/strong><\/td><td><strong>-2.24<\/strong><\/td><td><strong>170<\/strong><\/td><td><strong>3.4<\/strong><\/td><\/tr><tr><td>1435<\/td><td>-j 106<\/td><td>-2.12<\/td><td>155<\/td><td>3.1<\/td><\/tr><tr><td>1440<\/td><td>-j 100<\/td><td>-2.00<\/td><td>138<\/td><td>2.76<\/td><\/tr><tr><td>1445<\/td><td>-j 93<\/td><td>-1.86<\/td><td>125<\/td><td>2.5<\/td><\/tr><tr><td>1450<\/td><td>-j 86<\/td><td>-1.72<\/td><td>114<\/td><td>2.28<\/td><\/tr><tr><td>1455<\/td><td>-j 79<\/td><td>-1.58<\/td><td>104<\/td><td>2.08<\/td><\/tr><tr><td>1460<\/td><td>-j 75<\/td><td>-1.50<\/td><td>95<\/td><td>1.9<\/td><\/tr><tr><td>1465<\/td><td>-j 70<\/td><td>-1.4<\/td><td>92<\/td><td>1.84<\/td><\/tr><tr><td>1470<\/td><td>-j 65<\/td><td>-1.3<\/td><td>85<\/td><td>1.7<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>The base impedance is not too far out of line from what is expected for a tower this tall.&nbsp; Plotted on a Smith Chart:<\/p>\n\n\n\n<figure class=\"wp-block-image alignnone\"><a href=\"https:\/\/www.engineeringradio.us\/blog\/wp-content\/uploads\/2014\/09\/1430-smith-chart.jpg\"><img loading=\"lazy\" decoding=\"async\" width=\"496\" height=\"600\" src=\"https:\/\/www.engineeringradio.us\/blog\/wp-content\/uploads\/2014\/09\/1430-smith-chart-496x600.jpg\" alt=\"1430 base impedance plotted on a Smith chart\" class=\"wp-image-8096\" srcset=\"https:\/\/www.engineeringradio.us\/blog\/wp-content\/uploads\/2014\/09\/1430-smith-chart-496x600.jpg 496w, https:\/\/www.engineeringradio.us\/blog\/wp-content\/uploads\/2014\/09\/1430-smith-chart-124x150.jpg 124w, https:\/\/www.engineeringradio.us\/blog\/wp-content\/uploads\/2014\/09\/1430-smith-chart-248x300.jpg 248w, https:\/\/www.engineeringradio.us\/blog\/wp-content\/uploads\/2014\/09\/1430-smith-chart-400x483.jpg 400w, https:\/\/www.engineeringradio.us\/blog\/wp-content\/uploads\/2014\/09\/1430-smith-chart-41x50.jpg 41w, https:\/\/www.engineeringradio.us\/blog\/wp-content\/uploads\/2014\/09\/1430-smith-chart-900x1086.jpg 900w, https:\/\/www.engineeringradio.us\/blog\/wp-content\/uploads\/2014\/09\/1430-smith-chart.jpg 1200w\" sizes=\"auto, (max-width: 496px) 100vw, 496px\" \/><\/a><figcaption class=\"wp-element-caption\">1430 base impedance plotted on a Smith chart<\/figcaption><\/figure>\n\n\n\n<p>One of the first principles behind broadbanding an AM antenna is to distribute the sideband energy evenly and have a symmetrical VSWR.\u00a0 The antenna tuning unit will match the line impedance to the load impedance and cancel out the reactance.\u00a0 Having the proper phase advance or phase retard rotation will distribute the sideband energy symmetrically about the carrier.\u00a0\u00a0 To determine phase rotation, the cusp of the plotted graph is rotated to face either the 3 o&#8217;clock or 9 o&#8217;clock position (0\u00b0 or 180\u00b0).\u00a0 The cusp is where the direction of the line changes, which in this case is the carrier frequency, 1430 KHz.\u00a0 The above example, the line is fairly shallow, which is typical of a skirted tower.\u00a0 Thus, the best phase rotation to start with is +79\u00b0.\u00a0 This will likely be close but will need to be tweaked a bit to find the optimum bandwidth.\u00a0 After looking at the plotted Smith chart, my first inclination would be to reduce the rotation, more tower +75\u00b0 as a first step in tweaking.<\/p>\n\n\n\n<p>When working with AM systems, the bandwidth of the entire system needs to be examined.\u00a0 That means that final bandwidth observations will need to be made at the transmitter output terminal or in some cases, the input to the matching network.\u00a0 It varies on system design, but things like switches, contactors, mating connectors, ATU enclosures, etc can also add VSWR and asymmetry.\u00a0 Broadbanding even a simple one-tower AM antenna can require quite a bit of time and some trial and error.<\/p>\n\n\n\n<p>I will touch on ATU design in the next post.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>I have been fooling around with Smith Charts lately. They look complicated, but are really pretty easy to understand and use, once you get around all those lines and numbers and stuff. Smith charts offer a great way to visualize what is going on with a particular antenna or transmission line. They can be very &hellip; <a href=\"https:\/\/www.engineeringradio.us\/blog\/2014\/09\/the-smith-chart\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">The Smith Chart<\/span><\/a><\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[284,45],"class_list":["post-8086","post","type-post","status-publish","format-standard","hentry","category-tech-stuff","tag-am-tower","tag-rf"],"_links":{"self":[{"href":"https:\/\/www.engineeringradio.us\/blog\/wp-json\/wp\/v2\/posts\/8086","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.engineeringradio.us\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.engineeringradio.us\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.engineeringradio.us\/blog\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/www.engineeringradio.us\/blog\/wp-json\/wp\/v2\/comments?post=8086"}],"version-history":[{"count":9,"href":"https:\/\/www.engineeringradio.us\/blog\/wp-json\/wp\/v2\/posts\/8086\/revisions"}],"predecessor-version":[{"id":11246,"href":"https:\/\/www.engineeringradio.us\/blog\/wp-json\/wp\/v2\/posts\/8086\/revisions\/11246"}],"wp:attachment":[{"href":"https:\/\/www.engineeringradio.us\/blog\/wp-json\/wp\/v2\/media?parent=8086"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.engineeringradio.us\/blog\/wp-json\/wp\/v2\/categories?post=8086"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.engineeringradio.us\/blog\/wp-json\/wp\/v2\/tags?post=8086"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}