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t,e){function i(t){f.open(t)}function n(e,i){var =
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r(t,e){if(h.isTwitterURL(t))if(p.get("eventsHub")&&e){var r=3Dnew =
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o(t,e){this.id=3Dt,this.element=3Dthis.srcEl=3De}function =
s(t){this.srcEl=3D[],this.element=3Dt}var =
a,l=3Dt("env/document"),u=3Dt("tfw/widget/base"),c=3Dt("util/util"),d=3Dt=
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bals/twttr"),p=3Dt("globals/private");s.prototype=3Dnew =
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ent":33,"tfw/widget/base":40,"util/promise":60,"util/twitter":63,"util/ut=
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i(){o=3Dn.VALID_COLOR.test(d.val("widgets:link-color"))&&RegExp.$1,a=3Dn.=
VALID_COLOR.test(d.val("widgets:border-color"))&&RegExp.$1,s=3Dd.val("wid=
gets:theme")}function n(t){if(t){var e,i=3Dthis;this.readyPromise=3Dnew =
_(function(t){i.readyResolver=3Dt}),this.renderedPromise=3Dnew =
_(function(t){i.renderResolver=3Dt}),u.apply(this,[t]),e=3Dthis.params(),=
this.targetEl=3Dthis.srcEl&&this.srcEl.parentNode||e.targetEl||l.body,thi=
s.predefinedWidth=3Dn.VALID_UNIT.test(e.width||this.attr("width"))&&RegEx=
p.$1,this.layout(function(){return =
i.containerWidth=3Dv.effectiveWidth(i.targetEl)}).then(function(t){var =
r=3Di.predefinedWidth||t||i.dimensions.DEFAULT_WIDTH;i.height=3Dn.VALID_U=
NIT.test(e.height||i.attr("height"))&&RegExp.$1,i.width=3DMath.max(i.dime=
nsions.MIN_WIDTH,Math.min(r,i.dimensions.DEFAULT_WIDTH))}),this.linkColor=
=3Dn.VALID_COLOR.test(e.linkColor||this.dataAttr("link-color"))?RegExp.$1=
:o,this.borderColor=3Dn.VALID_COLOR.test(e.borderColor||this.dataAttr("bo=
rder-color"))?RegExp.$1:a,this.theme=3De.theme||this.attr("data-theme")||=
s,this.theme=3D/(dark|light)/.test(this.theme)?this.theme:"",this.classAt=
tr.push(y.touch()?"is-touch":"not-touch"),y.ie9()&&this.classAttr.push("i=
e9"),this.sandboxCreated=3Db.createSandbox({"class":this.renderedClassNam=
es,id:this.id,allowfullscreen:""},{position:"absolute",visibility:"hidden=
"},function(t){i.srcEl?i.targetEl.insertBefore(t,i.srcEl):i.targetEl.appe=
ndChild(t)},this.layout).then(function(t){i.setupSandbox(t),new =
m(t.element().contentWindow)}),this.rendered().then(function(t){i.applyVi=
sibleSandboxStyles(t)})}}function r(t,e){return t+e}var =
o,s,a,l=3Dt("env/document"),u=3Dt("tfw/widget/base"),c=3Dt("tfw/widget/in=
tent"),d=3Dt("globals/pagemetadata"),h=3Dt("tfw/util/media"),f=3Dt("scrib=
e/pixel"),m=3Dt("video/video_post_message_interface"),p=3Dt("dom/classnam=
e"),g=3Dt("dom/get"),w=3Dt("dom/delegate"),v=3Dt("dom/size"),b=3Dt("sandb=
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x=3Dt("util/typevalidator"),E=3Dt("util/util"),A=3D[".customisable",".cus=
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ble:focus",".customisable:active",".customisable-highlight:hover",".custo=
misable-highlight:focus","a:hover .customisable-highlight","a:focus =
.customisable-highlight"],I=3D["a:hover .ic-mask","a:focus =
.ic-mask"],N=3D[".customisable-border"],S=3D[".timeline-header =
h1.summary",".timeline-header h1.summary a:link",".timeline-header =
h1.summary a:visited"],D=3D{TWEET:0,RETWEET:10};n.prototype=3Dnew =
u,E.aug(n.prototype,{styleSheetUrl:function(){throw new Error("must set =
styleSheetUrl")},setupSandbox:function(t){var =
e=3Dthis;this.sandbox=3Dt,_.some(e.applyInitialSandboxStyles(t),t.appendC=
ss(".SandboxRoot { display:none =
}"),t.setBaseTarget("_blank"),t.appendStyleSheet(this.styleSheetUrl(this.=
lang))).then(function(){e.readyResolver.fulfill(t)})},ready:function(){re=
turn this.readyPromise},rendered:function(){return =
this.renderedPromise},contentWidth:function(t){var =
e=3Dthis.dimensions,i=3Dthis.borderless?0:e.BORDERS,n=3Dthis.fullBleedPho=
to?0:this.chromeless&&this.narrow?e.NARROW_MEDIA_PADDING_CL:this.chromele=
ss?e.WIDE_MEDIA_PADDING_CL:this.narrow?e.NARROW_MEDIA_PADDING:e.WIDE_MEDI=
A_PADDING;return(t||this.width)-(n+i)},applyInitialSandboxStyles:function=
(t){var e=3Dthis;return =
t.style({border:"none",maxWidth:"100%",minWidth:e.dimensions.MIN_WIDTH+"p=
x",margin:e.dimensions.MARGIN,padding:"0",display:"block",position:"absol=
ute",visibility:"hidden"},!0)},applyVisibleSandboxStyles:function(t){retu=
rn =
t.style({position:"static",visibility:"visible"})},addSiteStyles:function=
(){function t(t){return("dark"=3D=3De.theme?".thm-dark ":"")+t}var =
e=3Dthis,i=3D[];return =
this.headingStyle&&i.push(S.map(t).join(",")+"{"+this.headingStyle+"}"),t=
his.linkColor&&(i.push(A.map(t).join(",")+"{color:"+this.linkColor+"}"),i=
.push(I.map(t).join(",")+"{background-color:"+this.linkColor+"}")),this.b=
orderColor&&i.push(N.map(t).concat("dark"=3D=3Dthis.theme?[".thm-dark.cus=
tomisable-border"]:[]).join(",")+"{border-color:"+this.borderColor+"}"),i=
.length?this.sandbox.appendCss(i.join("")):void =
0},setNarrow:function(){var t=3Dthis,e=3Dthis.narrow;return =
this.narrow=3Dthis.width0;){if(l--,i=3Da.reduce(r=
,0),!s||!i)return;if(s>i)return;n=3Do[l].getAttribute("data-collapsed-cla=
ss"),n&&(p.add(t.element,n),a[l]=3Do[l].offsetWidth)}})}}),n.VALID_UNIT=3D=
/^([0-9]+)( =
?px)?$/,n.VALID_COLOR=3D/^(#(?:[0-9a-f]{3}|[0-9a-f]{6}))$/i,i(),e.exports=
=3Dn},{"dom/classname":4,"dom/delegate":5,"dom/get":6,"dom/size":7,"env/d=
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v":53,"util/promise":60,"util/twitter":63,"util/typevalidator":64,"util/u=
til":67,"video/video_post_message_interface":71}],45:[function(t,e){funct=
ion i(t){if(t){var =
e,i,n,r,o,a,l,u;s.apply(this,[t]),e=3Dthis.params(),i=3D(e.chrome||this.d=
ataAttr("chrome")||"").split(" =
"),this.preview=3De.previewParams,this.widgetId=3De.widgetId||this.dataAt=
tr("widget-id"),this.instanceId=3D++q,this.cursors=3D{maxPosition:0,minPo=
sition:0},this.override=3D(r=3De.screenName||this.dataAttr("screen-name")=
)||(o=3De.userId||this.dataAttr("user-id"))?{overrideType:"user",override=
Id:o,overrideName:r,withReplies:w.asBoolean(e.showReplies||this.dataAttr(=
"show-replies"))?"true":"false"}:(r=3De.favoritesScreenName||this.dataAtt=
r("favorites-screen-name"))||(o=3De.favoritesUserId||this.dataAttr("favor=
ites-user-id"))?{overrideType:"favorites",overrideId:o,overrideName:r}:((=
r=3De.listOwnerScreenName||this.dataAttr("list-owner-screen-name"))||(o=3D=
e.listOwnerId||this.dataAttr("list-owner-id")))&&((a=3De.listId||this.dat=
aAttr("list-id"))||(l=3De.listSlug||this.dataAttr("list-slug")))?{overrid=
eType:"list",overrideOwnerId:o,overrideOwnerName:r,overrideId:a,overrideN=
ame:l}:(u=3De.customTimelineId||this.dataAttr("custom-timeline-id"))?{ove=
rrideType:"custom",overrideId:u}:{},this.tweetLimit=3Dw.asInt(e.tweetLimi=
t||this.dataAttr("tweet-limit")),this.staticTimeline=3Dthis.tweetLimit>0,=
i.length&&(n=3Dv.contains(i,"none"),this.chromeless=3Dn||v.contains(i,"tr=
ansparent"),this.headerless=3Dn||v.contains(i,"noheader"),this.footerless=
=3Dn||v.contains(i,"nofooter"),this.borderless=3Dn||v.contains(i,"noborde=
rs"),this.noscrollbar=3Dv.contains(i,"noscrollbar")),this.headingStyle=3D=
p.sanitize(e.headingStyle||this.dataAttr("heading-style"),void =
0,!0),this.classAttr.push("twitter-timeline-rendered"),this.ariaPolite=3D=
e.ariaPolite||this.dataAttr("aria-polite")=0A=
}}var =
n=3Dt("env/window"),r=3Dt("assets/css"),o=3Dt("tfw/widget/base"),s=3Dt("t=
fw/widget/syndicatedbase"),a=3Dt("util/datetime"),l=3Dt("anim/transition"=
),u=3Dt("performance/perf-timers"),c=3Dt("tfw/util/data"),d=3Dt("tfw/util=
/media"),h=3Dt("scribe/audience"),f=3Dt("scribe/frame"),m=3Dt("tfw/util/p=
arams"),p=3Dt("util/css"),g=3Dt("util/env"),w=3Dt("util/typevalidator"),v=
=3Dt("util/util"),b=3Dt("dom/delegate"),y=3Dt("dom/classname"),_=3Dt("dom=
/get"),T=3Dt("util/donottrack"),x=3Dt("util/document"),E=3Dt("globals/twt=
tr"),A=3Dt("globals/private"),I=3D{CLIENT_SIDE_USER:0,CLIENT_SIDE_APP:2},=
N=3D".timeline",S=3D".new-tweets-bar",D=3D".timeline-header",R=3D".timeli=
ne-footer",k=3D".stream",L=3D".h-feed",P=3D".tweet",C=3D".detail-expander=
",M=3D".expand",O=3D".permalink",F=3D".no-more-pane",j=3D"expanded",H=3D"=
pending-scroll-in",W=3D"pending-new-tweet-display",U=3D"pending-new-tweet=
",q=3D0;i.prototype=3Dnew =
s,v.aug(i.prototype,{renderedClassNames:"twitter-timeline =
twitter-timeline-rendered",dimensions:{DEFAULT_HEIGHT:"600",DEFAULT_WIDTH=
:"520",NARROW_WIDTH:"320",maxHeight:"375",MIN_WIDTH:"180",MIN_HEIGHT:"200=
",MARGIN:"0",WIDE_MEDIA_PADDING:81,NARROW_MEDIA_PADDING:16,WIDE_MEDIA_PAD=
DING_CL:60,NARROW_MEDIA_PADDING_CL:12,BORDERS:2},styleSheetUrl:r.timeline=
,create:function(t){var =
e,i,n,r,o=3Dthis,s=3Dthis.sandbox.createElement("div"),a=3D[];return =
s.innerHTML=3Dt.body,(e=3Ds.children[0]||!1)?(this.reconfigure(t.config),=
this.discardStaticOverflow(e),this.sandbox.setTitle(e.getAttribute("data-=
iframe-title")||"Timeline"),d.retinize(e),this.constrainMedia(e),this.sea=
rchQuery=3De.getAttribute("data-search-query"),this.profileId=3De.getAttr=
ibute("data-profile-id"),this.timelineType=3De.getAttribute("data-timelin=
e-type"),r=3Dthis.getTweetDetails(s.querySelector(L)),v.forIn(r,function(=
t){a.push(t)}),n=3Dthis.baseScribeData(),n.item_ids=3Da,n.item_details=3D=
r,this.timelineType&&f.clientEvent({page:this.timelineType+"_timeline",co=
mponent:"timeline",element:"initial",action:a.length?"results":"no_result=
s"},n,!0),f.clientEvent({page:"timeline",component:"timeline",element:"in=
itial",action:a.length?"results":"no_results"},n,!0),h.scribeTimelineAudi=
enceImpression(),f.flush(),"assertive"=3D=3Dthis.ariaPolite&&(i=3De.query=
Selector(S),i.setAttribute("aria-polite","assertive")),e.id=3Dthis.id,e.c=
lassName+=3D" "+this.classAttr.join(" =
"),e.lang=3Dthis.lang,this.ready().then(function(t){t.appendChild(e).then=
(function(){o.renderResolver.fulfill(o.sandbox)}),t.style({display:"inlin=
e-block"}),o.layout(function(){o.srcEl&&o.srcEl.parentNode&&o.srcEl.paren=
tNode.removeChild(o.srcEl),o.predefinedWidth=3Do.width,o.predefinedHeight=
=3Do.height,o.width=3Dt.width(o.width),o.height=3Dt.height(o.height)}).th=
en(function(){o.setNarrow(),o.sandbox.onresize(o.handleResize.bind(o)),o.=
completeResolver.fulfill(o.sandbox.element())})}),e):void =
0},render:function(){var t=3Dthis;return =
this.preview||this.widgetId?(this.rendered().then(this.staticTimeline?fun=
ction(e){t.layout(function(){e.height(t.height=3Dt.element.offsetHeight)}=
),o.doLayoutAsync()}:function(){t.recalculateStreamHeight(),o.doLayoutAsy=
nc()}),this.preview?this.getPreviewTimeline():this.getTimeline(),this.com=
pleted().then(this.scribePerformance.bind(this)),this.completed()):(this.=
completeResolver.reject(400),this.completed())},scribePerformance:functio=
n(){u.endAndTrack("render","widgets-js-load","timeline",this.baseScribeDa=
ta())},getPreviewTimeline:function(){var =
t=3Dthis;c.timelinePreview({success:function(e){t.ready().then(function()=
{t.element=3Dt.create(e),t.readTranslations(),t.bindInteractions(),t.upda=
teCursors(e.headers,{initial:!0}),o.doLayoutAsync()})},error:function(e){=
return e&&e.headers?void =
t.completeResolver.reject(e.headers.status):void =
t.completeResolver.fulfill(t.srcEl)},params:this.preview})},getTimeline:f=
unction(){var =
t=3Dthis;f.init(),c.timeline(v.aug({id:this.widgetId,instanceId:this.inst=
anceId,dnt:T.enabled(),lang:this.lang,success:function(e){t.ready().then(=
function(){t.element=3Dt.create(e),t.readTranslations(),t.bindInteraction=
s(),t.updateTimeStamps(),t.updateCursors(e.headers,{initial:!0}),e.header=
s.xPolling&&/\d/.test(e.headers.xPolling)&&(t.pollInterval=3D1e3*e.header=
s.xPolling),t.staticTimeline||t.schedulePolling(),o.doLayoutAsync()})},er=
ror:function(e){return e&&e.headers?void =
t.completeResolver.reject(e.headers.status):void =
t.completeResolver.fulfill(t.srcEl)}},this.override))},reconfigure:functi=
on(t){this.lang=3Dt.lang,this.theme||(this.theme=3Dt.theme),"dark"=3D=3Dt=
his.theme&&this.classAttr.push("thm-dark"),this.chromeless&&this.classAtt=
r.push("var-chromeless"),this.borderless&&this.classAttr.push("var-border=
less"),this.headerless&&this.classAttr.push("var-headerless"),this.footer=
less&&this.classAttr.push("var-footerless"),this.staticTimeline&&this.cla=
ssAttr.push("var-static"),!this.linkColor&&t.linkColor&&s.VALID_COLOR.tes=
t(t.linkColor)&&(this.linkColor=3DRegExp.$1),!this.height&&s.VALID_UNIT.t=
est(t.height)&&(this.height=3DRegExp.$1),this.height=3DMath.max(this.dime=
nsions.MIN_HEIGHT,this.height?this.height:this.dimensions.DEFAULT_HEIGHT)=
,this.preview&&this.classAttr.push("var-preview"),this.narrow=3Dthis.widt=
h<=3Dthis.dimensions.NARROW_WIDTH,this.narrow&&this.classAttr.push("var-n=
arrow"),this.addSiteStyles()},getTweetDetails:function(t){var =
e,i=3Dthis,n=3D{};return =
e=3Dt&&t.children||[],v.toRealArray(e).forEach(function(t){v.aug(n,i.extr=
actTweetScribeDetails(t))}),n},baseScribeData:function(){return{widget_id=
:this.widgetId,widget_origin:x.rootDocumentLocation(),widget_frame:x.isFr=
amed()&&x.currentDocumentLocation(),message:this.partner,query:this.searc=
hQuery,profile_id:this.profileId}},bindInteractions:function(){var =
t=3Dthis,e=3Dthis.element,i=3D!0;this.bindIntentHandlers(),b.delegate(e,"=
click",".load-tweets",function(e){i&&(i=3D!1,t.forceLoad(),b.stop(e))}),b=
.delegate(e,"click",".display-sensitive-image",function(i){t.showNSFW(_.c=
losest(P,this,e)),b.stop(i)}),b.delegate(e,"mouseover",N,function(){t.mou=
seOver=3D!0}),b.delegate(e,"mouseout",N,function(){t.mouseOver=3D!1}),b.d=
elegate(e,"mouseover",S,function(){t.mouseOverNotifier=3D!0}),b.delegate(=
e,"mouseout",S,function(){t.mouseOverNotifier=3D!1,n.setTimeout(function(=
){t.hideNewTweetNotifier()},3e3)}),this.staticTimeline||(b.delegate(e,"cl=
ick",M,function(i){i.altKey||i.metaKey||i.shiftKey||(t.toggleExpando(_.cl=
osest(P,this,e)),b.stop(i))}),b.delegate(e,"click","A",function(t){b.stop=
Propagation(t)}),b.delegate(e,"click",".with-expansion",function(e){t.tog=
gleExpando(this),b.stop(e)}),b.delegate(e,"click",".load-more",function()=
{t.loadMore()}),b.delegate(e,"click",S,function(){t.scrollToTop(),t.hideN=
ewTweetNotifier(!0)}))},scrollToTop:function(){var =
t=3Dthis.element.querySelector(k);t.scrollTop=3D0,t.focus()},update:funct=
ion(){var =
t=3Dthis,e=3Dthis.element.querySelector(L),i=3De&&e.children[0],n=3Di&&i.=
getAttribute("data-tweet-id");this.updateTimeStamps(),this.requestTweets(=
n,!0,function(e){e.childNodes.length>0&&t.insertNewTweets(e)})},loadMore:=
function(){var =
t=3Dthis,e=3Dv.toRealArray(this.element.querySelectorAll(P)).pop(),i=3De&=
&e.getAttribute("data-tweet-id");this.requestTweets(i,!1,function(e){var =
n=3Dt.element.querySelector(F),r=3De.childNodes[0];return =
n.style.cssText=3D"",r&&r.getAttribute("data-tweet-id")=3D=3Di&&e.removeC=
hild(r),e.childNodes.length>0?void =
t.appendTweets(e):(y.add(t.element,"no-more"),void =
n.focus())})},forceLoad:function(){var =
t=3Dthis,e=3D!!this.element.querySelectorAll(L).length;this.requestTweets=
(1,!0,function(i){i.childNodes.length&&(t[e?"insertNewTweets":"appendTwee=
ts"](i),y.add(t.element,"has-tweets"))})},schedulePolling:function(t){var=
=
e=3Dthis;null!=3D=3Dthis.pollInterval&&(t=3DA.get("timeline.pollInterval"=
)||t||this.pollInterval||1e4,t>-1&&n.setTimeout(function(){e.isUpdating||=
e.update(),e.schedulePolling()},t))},updateCursors:function(t,e){(e||{}).=
initial?(this.cursors.maxPosition=3Dt.maxPosition,this.cursors.minPositio=
n=3Dt.minPosition):(e||{}).newer?this.cursors.maxPosition=3Dt.maxPosition=
||this.cursors.maxPosition:this.cursors.minPosition=3Dt.minPosition||this=
.cursors.minPosition},requestTweets:function(t,e,i){var =
n=3Dthis,r=3D{id:this.widgetId,instanceId:this.instanceId,screenName:this=
.widgetScreenName,userId:this.widgetUserId,withReplies:this.widgetShowRep=
lies,dnt:T.enabled(),lang:this.lang};e&&this.cursors.maxPosition?r.minPos=
ition=3Dthis.cursors.maxPosition:!e&&this.cursors.minPosition?r.maxPositi=
on=3Dthis.cursors.minPosition:e?r.sinceId=3Dt:r.maxId=3Dt,r.complete=3Dfu=
nction(){n.isUpdating=3D!1},r.error=3Dfunction(t){if(t&&t.headers){if("40=
4"=3D=3Dt.headers.status)return =
void(n.pollInterval=3Dnull);if("503"=3D=3Dt.headers.status)return =
void(n.pollInterval*=3D1.5)}},r.success=3Dfunction(t){var =
r,o,s=3Dn.sandbox.createDocumentFragment(),a=3Dn.sandbox.createElement("o=
l"),l=3D[];if(n.updateCursors(t.headers,{newer:e}),t&&t.headers&&t.header=
s.xPolling&&/\d+/.test(t.headers.xPolling)&&(n.pollInterval=3D1e3*t.heade=
rs.xPolling),t&&void =
0!=3D=3Dt.body){if(a.innerHTML=3Dt.body,a.children[0]&&"LI"!=3Da.children=
[0].tagName)return;for(o=3Dn.getTweetDetails(a),v.forIn(o,function(t){l.p=
ush(t)}),l.length&&(r=3Dn.baseScribeData(),r.item_ids=3Dl,r.item_details=3D=
o,r.event_initiator=3De?I.CLIENT_SIDE_APP:I.CLIENT_SIDE_USER,n.timelineTy=
pe&&f.clientEvent({page:n.timelineType+"_timeline",component:"timeline",e=
lement:"initial",action:l.length?"results":"no_results"},r,!0),f.clientEv=
ent({page:"timeline",component:"timeline",element:e?"newer":"older",actio=
n:"results"},r,!0),f.flush()),d.retinize(a),n.constrainMedia(a);a.childre=
n[0];)s.appendChild(a.children[0]);i(s)}},c.timelinePoll(v.aug(r,this.ove=
rride))},insertNewTweets:function(t){var =
e,i=3Dthis,r=3Dthis.element.querySelector(k),o=3Dr.querySelector(L),s=3Do=
.offsetHeight;return =
o.insertBefore(t,o.firstChild),e=3Do.offsetHeight-s,E.get("events").trigg=
er("timelineUpdated",{target:this.sandbox.element(),region:"newer"}),r.sc=
rollTop>40||this.mouseIsOver()?(r.scrollTop=3Dr.scrollTop+e,this.updateTi=
meStamps(),void =
this.showNewTweetNotifier()):(y.remove(this.element,H),o.style.cssText=3D=
"margin-top: =
-"+e+"px",n.setTimeout(function(){r.scrollTop=3D0,y.add(i.element,H),g.cs=
sTransitions()?o.style.cssText=3D"":l.animate(function(t){o.style.cssText=
=3De>t?"margin-top: =
-"+(e-t)+"px":""},e,500,l.easeOut)},500),this.updateTimeStamps(),void("cu=
stom"!=3Dthis.timelineType&&this.gcTweets(50)))},appendTweets:function(t)=
{var =
e=3Dthis.element.querySelector(L);e.appendChild(t),this.updateTimeStamps(=
),E.get("events").trigger("timelineUpdated",{target:this.sandbox.element(=
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e,i=3Dthis.element.querySelector(L),n=3Di.children.length;for(t=3Dt||50;n=
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=20
=20
=
=20
=20
=
=20
=20
=20
=20
Build Your Own Transfomer
When the right off-the-shelf part just can=E2=80=99t be found, you = may want to=20 consider designing a custom transformer to fit your specific=20 requirements.
Thousands of ready-made off-the-shelf transformers out in the market = are=20 available to be designed into electronic or electrical circuits. = However, when=20 the right part just can=E2=80=99t be found, you may want to consider = designing a custom=20 transformer to fit your specific requirements.
| Download=20
this article in .PDF format = This=20 file type includes high resolution graphics and schematics when=20 applicable. |
You need to determine a few things before you can start to design a=20 transformer, though. At the minimum, these include the input voltage(s) = and=20 frequency, and the output voltage(s) and current(s). There may very well = be=20 other parameters to consider, both physical and electrical, such as = available=20 space for mounting, mounting style, isolation requirements, leakage = currents,=20 etc. Environmental conditions may also be a consideration.
Note: At this step, it=E2=80=99s important to point out = that all of the=20 decisions made concerning the design will be verified through = calculations that=20 can only be made after many =E2=80=9Crules of thumbs=E2=80=99=E2=80=9D = and =E2=80=9Ceducated guesses=E2=80=9D are used=20 to get us to that point.
Selecting the Core
The first step is to determine the type of core for the design. You = should=20 consult with a core manufacturer to obtain the specific characteristics = and=20 power-handling capabilities for each type and size of core. However, a = general=20 starting point is:
=E2=80=A2 When less than 400 Hz, a silicon steel lamination is = generally used.
=E2=80=A2 At 400 to 2000 Hz, consider a tape-wound or nickel-alloy = core.
=E2=80=A2 Above 2000 Hz, look at ferrite.
Remember this is only a guideline; it=E2=80=99s not uncommon to go = outside of these=20 ranges (e.g., audio transformers can use silicon steel laminations and = operate=20 from 20 to 20,000 Hz). There are many other core types, and many sizes, = shapes,=20 and material grades within the cores listed above. The exact core chosen = may=20 depend on board spacing, location, mounting style, or any of a number of = physical and electrical parameters that only you can decide.
Most core types will also need a winding bobbin to fit the core that = you=20 choose, and possibly assist in the mounting of the finished product. = Make sure a=20 sufficient bobbin style and material is available, and that you have all = of the=20 mechanical measurements to determine winding details later on in the = design.=20 Certain cores don=E2=80=99t require a bobbin, but we=E2=80=99ll save = those for another=20 discussion.
After selecting a core and bobbin, you need to calculate the correct = number=20 of primary turns needed using formula 1 or 2 (see =E2=80=9CBasic = Design Formulas,=E2=80=9D=20 below). There are several variables to consider when using these = formulas;=20 you will need to consult the core manufacturer=E2=80=99s data for = answers to=20 specifications such as flux density and stacking factor.
Basic Design Formulas
1) N(p) =3D (V x 108) / (4.44 B A f K) sine wave
2) N(p) =3D (V x 108) / (4 B A f K) square wave
3) N(s) =3D V(s) / V(p) x N(p)
4) I(p) =3D (VA(s) + losses) / V(p)
5) I(s) =3D P(out) / V(out)
6) Open circuit voltage (Voc) =3D N(s)/N(p) x V(p)
7) Loaded voltage (Vld) =3D Voc-[IR(sec) + (IR(pri) x = (N(s)/N(p))]
8) Temp rise (T(C)) =3D (losses/(0.008 x surface area))
N(p) =3D Primary turns
N(s) =3D Secondary turns
B =3D Flux density in gauss
A =3D Core area in centimeters squared
f =3D Frequency
K =3D Stacking factor
L =3D Inductance
A(l) =3D Inductance per turn squared for a given core
Windings and Wire
The primary winding current and wire size needs to be determined. The = primary=20 current will be equal to the total output power plus transformer power = losses,=20 divided by the primary voltage. For power losses, I start at a 10% = increase in=20 the input power, assuming a 90% efficient transformer. For example, a=20 transformer with a 12-V, 2-A output at 120 V input would be:
12 V x 2 A =3D 24 VA; 24 VA x 1.10 (110%) =3D 26.4 VA needed in the =
primary=20
winding;
26.4 VA/120 V =3D 0.22 A in =
the primary=20
winding
The next step will be a subject for debate and adjustment depending = on the=20 transformer characteristics: I generally start at approximately 500 = circular=20 mills (cm) per amp to choose the starting wire gauge. This number may be = smaller=20 for small transformers, and larger for large power transformers; that = decision=20 is again up to the designer. Using the example above, 0.22 A x 500cm/A = =3D 110cm;=20 I would start with a 29 gauge wire (127.7cm) for the primary.
You now need to determine the number of turns that will be required = for each=20 secondary winding. The first step is to use formula 3 (N(s) =3D V(s) / = V(p) x=20 N(p)) to determine the turns for a perfect transformer. This number then = needs=20 to be increased to account for the losses in the coils. As a rule of = thumb=20 again, I start with a 10% increase in the number of turns, assuming a = 90%=20 efficient transformer: N(s) x 1.10 =3D N Turns. This percentage will = vary=20 depending on the characteristics of your design. Use the same method to=20 determine the secondary wire gauge(s) that you used for the primary.
Now you need to see if the windings fit into your winding area and = determine=20 the actual losses of the coils. Start by determining the winding width = (ww) of=20 the bobbin, the winding height (wh) of the bobbin, and the mean length = of turns=20 (mlt) from the mechanical drawing (see the figure).
With this information, you can now calculate how many turns of wire = can fit=20 in each layer of winding for each different winding. After that, = determine how=20 many layers of each wire gauge used it will take to wind the calculated = number=20 of turns for each given winding. Finally, calculate the total height of = all of=20 the windings wound concentrically. Remember to include the insulation = used=20 between the windings in figuring your total winding height.
Verification
The next step is to verify your design. Will it fit in the allowable = winding=20 height with enough =E2=80=9Cplay=E2=80=9D to allow for error? Keep in = mind that the windings=20 will not be perfectly layered, so you must allow for some bowing of the = copper=20 wire as it bends around each corner of the bobbin. I use a maximum of = 85% fill=20 (or build) when comparing the actual winding height to the allowable = bobbin=20 winding height:
(Actual winding height/Allowable winding height) =C3=97 100 =3D < = 85%
A build of around 75% is more desirable, and will make the = transformer easier=20 to manufacture in the long run.
Next, you need to calculate the resistance of each winding, and the = loaded=20 voltage losses in the winding to determine loaded output voltages. = First, the=20 resistance of each winding is calculated by multiplying the mean length = of turn=20 by the number of turns. This gives the total length of the wire = conductor.=20 Whatever unit of measure you are using, convert this length to thousands = of feet=20 (K ft); for example, a length of 400 in./12000 =3D 0.03 K ft. Now from a = magnet=20 wire chart, you can get resistance of each gauge of wire in thousands of = feet.=20 For our example, 29 gauge has a resistance of 81.21 =CE=A9/K ft, so a = 400-in. wire=20 would have a resistance of 0.03 K ft =C3=97 81.21 =CE=A9 /K ft =3D 2.44 = =CE=A9.
Once you have the resistance of a winding, you simply calculate the = voltage=20 drop across that winding by multiplying the resistance by the current in = the=20 winding. In this primary it would be 2.44 =CE=A9 x 0.22 A =3D 0.540 V. = Calculate the=20 voltage drop across each winding in the same manner.
The next step is to calculate the open-circuit voltage of each = secondary=20 using formula 6 and the loaded voltage using formula 7 of (see = =E2=80=9CBasic Design=20 Formulas=E2=80=9D). I put these together because I usually do both = calculations on=20 each secondary winding before moving on to multiple windings if I have = them.
The key thing to note here is that the primary voltage drop is = reflected into=20 the secondary loaded voltage by the ratio of the turns. After that, = it=E2=80=99s added=20 to the secondary voltage drop. The sum of the two is then subtracted = from the=20 open circuit voltage of the given secondary. This gives you the loaded = output=20 voltage of that secondary (I realize the formula could be mathematically = simplified, but this format allows me easier use with a calculator; = again, my=20 opinion).
If the voltage is not what you want, divide the desired output = voltage by the=20 calculated output for an error ratio. Use this ratio multiplied by the = number of=20 turns on the given secondary and recalculate everything starting at the = number=20 of layers of winding.
Temp Calculations
After calculating the turns, you need to know the calculated = temperature=20 rise. There are two main causes of temperature rise in a transformer: = core power=20 losses and winding power losses. To determine the core power losses, = refer to=20 manufacturer=E2=80=99s datasheets and the flux density used in your = design. Winding=20 power losses are easily calculated by multiplying the voltage drop = across the=20 winding again by the current in the winding (I2R). The sum of = the=20 power losses in the windings, primary(s), and secondary(s) is multiplied = by 1.33=20 (I=E2=80=99ll be honest, I don=E2=80=99t fully know where this factor = came from, but it has to=20 do with heat transfer and concentric windings, and it works) to give the = total=20 effective heating losses of the windings. Add the core losses to the = winding=20 losses for total power dissipation.
To determine how well the transformer dissipates power losses, we = need to=20 calculate the surface area of the completed device. This simply requires = looking=20 at all of the surfaces that will be exposed to air and adding them up in = inches=20 squared. Now use formula 8 from the design formulas to calculate the = estimated=20 temperature rise of the transformer.
| Download=20
this article in .PDF format = This=20 file type includes high resolution graphics and schematics when=20 applicable. |
Once again, what constitutes an acceptable temperature rise depends = on the=20 application and the designer. I always use 50=C2=BAC as my maximum = rise=20 allowed. Keep in mind that forced air cooling or heat sinks may be used = in the=20 end product, which could push that number higher.
Now that you=E2=80=99ve made all of your decisions on the design = aspects, based on=20 =E2=80=9Crules of thumb=E2=80=9D and =E2=80=9Ceducated guesses,=E2=80=9D = you should be able to confirm the=20 choices made using the formulas and calculations discussed in the = article. If=20 things anywhere along the way don=E2=80=99t work, you have to go back, = make the=20 appropriate changes, and start over. This includes the temperature-rise=20 calculation.
=20
=20
=20
=20
=20
=20
Discuss this Article 7 = =20
=20You haven't included anything about determining the correct amount of = air gap=20 in the core to allow, if you don't have one for a power transformer you = may get=20 saturation and unacceptable losses, for a signal transformer this will = manifest=20 itself as unacceptable distortion at certain frequency and power levels. = I think=20 you're trying to vastly oversimplify a field of design that it takes = most people=20 an entire career to master.
- Log In =
or
But if you include an air-gap, inductance will drop ... requiring = more turns=20 to restore a reasonable "excitation current" in the primary. It's = generally=20 better to just use more core material to avoid saturation. The only = transformers=20 that normally use air gaps are those that have substantial DC current in = primary=20 or secondary ... so they're generally used only in switch-mode power = supplies or=20 single-ended signal (audio) transformers. All else being equal, they'll = have=20 poorer low-frequency response. Also, any transformer that operates near = core=20 saturation (as do most 50/60 Hz power transformers are to make them = cheap) will=20 also radiate a substantial external field ... making them troublesome = neighbors=20 for nearby equipment. Designing transformers is truly "a world of = trade-offs." =20 Bill Whitlock, Technology Manager, Jensen Transformers, Inc.
- Log In =
or
=20
=20
I have a line isolation TRF (<500W with @16cm2 core) and wanna = modify it=20 to fuse rods of small diameter (max. 10mm2). Do you know how to workout = the=20 current to fuse metals and at what voltage?
- Log In =
or
Advertisement
I'd love to meet you guys for lunch once a week, to kick this subject = around.
- Log In =
or
" I think you're trying to vastly oversimplify a field of design that = it=20 takes most people an entire career to master."
Profoundly true, and it takes some courage to write in one article a=20 transformer design guide. A few additional hand-waves:
1. To optimize transfer power, full core utilization is the goal. The = core=20 should be run at both its power-loss and saturation limits (with design = margins). Then the smallest volume core can be used. Transfer power = applies to=20 coupled inductors, but the same basic utilization criteria apply to=20 transformers.
2. To optimize power transfer, the winding and core power losses = should be=20 about the same. The goal is to maximize power transfer through the = transductor=20 (transformer or coupled inductor) by adjusting the design for winding to = core=20 power loss such that output power / input power is maximized. This = happens=20 neither at equal core and winding loss nor at minimum loss but = in-between the=20 two.
Core and winding losses can be traded off by adjusting turns and wire = size.=20 However, circuit design constraints also affect both. Wire size is = fairly easy=20 to choose from a wire table and circuit current requirements. The = optimal turns=20 is the geometric mean between the max-power-loss minimum and the = saturation=20 maximum.
- Log In =
or
the pdf available for download seems to be corrupted.
The start of =
each=20
page has omissions.
It stops after the table on page 4.
- Log In =
or
Andrew: copy and paste into word doc works great.
- Log In =
or
Please Log In or = Register=20 to post comments.
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