Applications for wide band rf transformers include =
impedance=20
matching, voltage or current transformation, DC isolation, balanced / =
unbalanced=20
mixing, matching, power splitting, coupling, and signal inversion. =
Custom wide=20
band transformers with special combinations of impedance ratio, =
insertion loss,=20
frequency response, and current handling are also =
available."
Wideband rf transformers are simply transfomers designed to provide =
an=20
impedance transformation over a broad frequency range. In amateur radio=20
applications we wind these transformers on ferrite =
toroids. A common impedance transformation is 200 ohms to 50 ohms =
using a=20
bi-filar winding. Here is an example from our broad=20
band amplifiers tutorial.
=20
Figure 1. - wideband rf amplifier with shunt feedback and =
emitter=20
degeneration
Transformer T1 is a broadband rf transformer.=20
Designing wide band rf transformers
In the design of these kinds of wide band rf transformers the primary =
reactance is usually around 5 times the primary impeda=
nce.=20
With a 200 ohms to 50 ohm transformer, we would allow a reactance of =
1,000 ohms=20
at the lowest frequency of interest. Just as an example consider =
we were=20
building a broad band amplifier for the amateur bands and going down as =
low as=20
1.8 Mhz.=20
For this example we would need bi-filar windings which have a reacta=
nce=20
of 1,000 ohms at 1.8 Mhz, this means a required induc=
tance=20
of around 88 uH. A look through the Amidon data book tells me that =
ferrite=20
toroid FT-50-61 as one example can provide me with an AL factor of 68mH =
/ 1000=20
turns.=20
This means if 1,000 turns were wound on the toroid it would give us =
68 mH.=20
Yes that IS milli-henries, these are ferrite toroids.=20
Calculating turns for wide band rf transformers
To wind a wide band rf transformer with an inductance of 88 uH (yes =
that's=20
micro-henries) which is in fact 0.088 mh we use the following formula:=20
Turns =3D 1,000 X SQRT (L in mH / AL factor) =
=3D 1,000 X=20
SQRT (0.088 / 68) =3D 36 turns.=20
Our wide band rf transformer needs 36 turns to achieve an inductance =
of 88=20
uH.=20
Winding the wide band rf transformer
Because this is a bi-filar winding for our wide band rf transformer, =
we need=20
two lengths of wire which we will "twist" together at a "pitch" of 2.5 =
turns per=20
inch or 1 turn per 10 mm. If you anchor one end of the two wires =
together in a=20
bench vise and fix the other ends securely in a hand drill (a bent nail =
or fish=20
hook helps here) you then gently "stretch" the wires first. Then you =
slowly turn=20
the hand drill and notice the two wires "twisting" together, as you =
proceed you=20
will notice more and more twists appearing. Stop when you have about 2.5 =
twists=20
to the inch. Stretch the wires once more.=20
Wind 36 turns through the toroid and that is it! To use in an =
application=20
such as figure 1 above you need to pay attention to the "phasing". =
Notice the=20
two dots on T1 above? They indicate the start of each wire. Use =
an=20
ohmmeter to find the start and finish of one winding, mark it in some =
convenient=20
manner e.g. coloured pen. The other winding should then be obvious.=20
Commercially manufactured wide band rf transformers
Coilcraft is one manufacturer of wide band transformers which provide =
reliable performance.=20
The transformers are offered in tapped or untapped configurations and =
are=20
packaged in a low-profile DIP-style plastic case. All parts are =
available in=20
either a surface mount version or a through-hole version that=92s =
compatible with=20
standard DIP sockets.=20
Applications include impedance matching, voltage or current =
transformation,=20
DC isolation, balanced / unbalanced mixing, matching, power splitting, =
coupling,=20
and signal inversion. Custom wide band transformers with special =
combinations of=20
impedance ratio, insertion loss, frequency response, and current =
handling are=20
also available.=20
Designing wide band rf transformers for different impedances
Alright what if you need something other than a 200 ohm to 50 ohms=20
transformer, how would you go about it?=20
What I tell you here now is applicable from DC to daylight. What that =
means=20
is, it is equally applicable to an audio transformer with a bandwidth of =
100 Hz=20
to 3,000 Hz (for an audio=20
transformer) as it is to a broadband transformer designed to operate =
at say=20
7.00 to 7.50 Mhz. Read on.=20
Firstly you need to pick either a lower 1 dB or 3 dB bandwidth. =
Wozzat???=20
Look at figure 2 below where I present my usual scungy drawing - I'm no =
good at=20
this graphic arts caper, not the program, just my lack of artistic =
talent.=20
=20
Figure 2. - band pass filter characteristics
Here I've crudely depicted a range of frequencies being passed by a =
filter=20
and indicated the 1 dB and 3 db points. A 1 db point is where the power =
output=20
is about 80% of the band pass power or 90% of the voltage level. A 3 db =
point is=20
where the power output is about 50% of the band pass power or 70.7% of =
the=20
voltage level. If you can't understand decibels then you need to look at =
the decibel =
page=20
In your broad band transformer you need to determine the lowest point =
you can=20
tolerate in frequency. Entirely for discussion purposes I've selected 5 =
Mhz for=20
both 1 dB and 3 dB to demonstrate the formulas. Also I'm going to =
construct a =20
broad band tranformer to operate between 14.4 ohms and 50 ohms.=20
For the 1 db point to be 5 Mhz, I use the formula Lp =3D R / ( 2 X Pi =
X Fo) and=20
for the 3 dB point, I use the formula Lp =3D R / ( 4 X Pi X Fo). The =
general=20
formula for any other dB level is a bit difficult to reproduce here but =
contact =
me and I'll give it to anyone who wants it.=20
The first formula simply gives you an inductance equal the reactance =
of R or=20
in our case we're using 14.4 ohms at 5 Mhz. This results in an =
inductance of=20
0.458 uH. The second formula simply produces half that inductance or, =
0.229 uH.=20
Back to the result of 0.458 uH, that could easily be achieved with 10 =
turns=20
on a T-50-2 toroid. Alright we have a T50-2 toroid with 10 turns on it, =
this is=20
supposed to represent 14.4 ohms at 5 Mhz. To match to 50 ohms all we =
have to do=20
is work out the turns ratio. Impedance transforms as "the square of the =
ratio of=20
turns". Then 50 / 14.4 =3D 3.472' and the square root of this is 1.86 so =
we need=20
on the secondary 1.86 times more turns or in our case 19 turns.=20
IF our output were terminated in a genuine 50 ohm load then the =
square of [19=20
/10] being the turns ratio would be reflected back giving (if you work =
it out) a=20
source of 13.85 ohms.=20
The CRITICAL aspects here are: a) turns ratio AND; b) final=20
termination being a genuine 50 ohm load.=20
What is the upper frequency limit of our wide band rf =
transformer?
The high frequency limit is influenced by the leakage inductance Lk =
and=20
distributed capacitance of the inductor forming a second order low pass =
filter=20
and is influenced by a very wide range of factors. The higher the =
inductance,=20
then the lower or flatter the low-frequency end but, this comes at a =
price of=20
higher Lk and distributed capacitance limiting high frequency response. =
Often a=20
compromise is needed for high ratios of frequencies. Although I have =
never=20
tested it, I would imagine at least one octave bandwidth could easily be =
accomodated e.g. 2.5 Mhz to 5 Mhz or 5 Mhz to 10 Mhz.=20
=20
=20
Custom Search =
=20
Got a question on this topic?
If you are involved in electronics then consider joining our "electronics=20
Questions and Answers" news group to ask your question there as well =
as=20
sharing your thorny questions and answers. Help out your colleagues!.=20
The absolute fastest way to get your question answered and yes, I =
DO=20
read most posts.=20
This is a mutual help group with a very professional air about it. =
I've=20
learn't things. It is an excellent learning resource for lurkers as well =
as=20
active contributors. =20
Want to create a page link to me from your =
site? It=20
couldn't be easier. No HTML knowledge required; even the technophobes =
can do=20
it. All you need to do is copy and paste, the following code. All =
links are=20
greatly appreciated; I sincerely thank you for your =
support.
Copy and paste the following code for a text =
link:=20
YOU ARE HERE: HOME =20
> BASICS =20
> WIDE BAND RF TRANSFORMERS=20
the author Ian C. Purdie, VK2TIP of =
www.electronics-tutorials.com=20
asserts the moral right to be identified as the author of this web site =
and all=20
contents herein. Copyright =A9 2000 =3D 2001, all rights reserved. See =
copying =
and links. These electronic tutorials are provided for individual =
private=20
use and the author assumes no liability whatsoever for the application, =
use,=20
misuse, of any of these projects or electronics tutorials that may =
result in the=20
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tutorials.=20
All materials are provided for free private and public use. =
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prohibited without prior written permission from =
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ja=3Dia.display;if(ja=3D=3D=3D'popup'||ja=3D=3D=3D'touch')return =
'opener';if(ja=3D=3D=3D'dialog'||ja=3D=3D=3D'iframe'||ja=3D=3D=3D'hidden'=
||ja=3D=3D=3D'none')return 'parent';if(ja=3D=3D=3D'async')return =
'parent.frames['+window.name+']';},popup:function(ia){var ja=3Dtypeof =
window.screenX!=3D'undefined'?window.screenX:window.screenLeft,ka=3Dtypeo=
f =
window.screenY!=3D'undefined'?window.screenY:window.screenTop,la=3Dtypeof=
=
window.outerWidth!=3D'undefined'?window.outerWidth:document.documentEleme=
nt.clientWidth,ma=3Dtypeof =
window.outerHeight!=3D'undefined'?window.outerHeight:(document.documentEl=
ement.clientHeight-22),na=3Ds.mobile()?null:ia.size.width,oa=3Ds.mobile()=
?null:ia.size.height,pa=3D(ja<0)?window.screen.width+ja:ja,qa=3DparseInt(=
pa+((la-na)/2),10),ra=3DparseInt(ka+((ma-oa)/2.5),10),sa=3D[];if(na!=3D=3D=
null)sa.push('width=3D'+na);if(oa!=3D=3Dnull)sa.push('height=3D'+oa);sa.p=
ush('left=3D'+qa);sa.push('top=3D'+ra);sa.push('scrollbars=3D1');if(ia.na=
me=3D=3D'permissions.request'||ia.name=3D=3D'permissions.oauth')sa.push('=
location=3D1,toolbar=3D0');sa=3Dsa.join(',');var =
ta;if(ia.post){ta=3Dwindow.open('about:blank',ia.id,sa);if(ta){ha.setLoad=
edNode(ia,ta,'popup');h.submitToTarget({url:ia.url,target:ia.id,params:ia=
.params});}}else{ta=3Dwindow.open(ia.url,ia.id,sa);if(ta)ha.setLoadedNode=
(ia,ta,'popup');}if(!ta)return;if(ia.id in =
ha._defaultCb)ha._popupMonitor();},setLoadedNode:function(ia,ja,ka){if(ia=
.params&&ia.params.display!=3D'popup')ja.fbCallID=3Dia.id;ja=3D{node:ja,t=
ype:ka,fbCallID:ia.id};ha._loadedNodes[ia.id]=3Dja;},getLoadedNode:functi=
on(ia){var ja=3Dtypeof =
ia=3D=3D'object'?ia.id:ia,ka=3Dha._loadedNodes[ja];return =
ka?ka.node:null;},hidden:function(ia){ia.className=3D'FB_UI_Hidden';ia.ro=
ot=3Dh.appendHidden('');ha._insertIframe(ia);},iframe:function(ia){ia.cla=
ssName=3D'FB_UI_Dialog';var =
ja=3Dfunction(){ha._triggerDefault(ia.id);};ia.root=3Dj.create({onClose:j=
a,closeIcon:ia.closeIcon=3D=3D=3D(void =
0)?true:ia.closeIcon,classes:(s.ipad()?'centered':'')});if(!ia.hideLoader=
)j.showLoader(ja,ia.size.width);i.addCss(ia.root,'fb_dialog_iframe');ha._=
insertIframe(ia);},touch:function(ia){if(ia.params&&ia.params.in_iframe){=
if(ia.ui_created){j.showLoader(function(){ha._triggerDefault(ia.id);},0);=
}else ha.iframe(ia);}else =
if(s.nativeApp()&&!ia.ui_created){ia.frame=3Dia.id;n.onready(function(){h=
a.setLoadedNode(ia,n.open(ia.url+'#cb=3D'+ia.frameName),'native');});ha._=
popupMonitor();}else =
if(!ia.ui_created)ha.popup(ia);},async:function(ia){ia.params.redirect_ur=
i=3Dlocation.protocol+'//'+location.host+location.pathname;delete =
ia.params.access_token;p.remote.showDialog(ia.params,function(ja){var =
ka=3Dja.result;if(ka&&ka.e2e){var =
la=3Dj.get(ia.id);la.trackEvents(ka.e2e);la.trackEvent('close');delete =
ka.e2e;}ia.cb(ka);});},getDefaultSize:function(){return =
j.getDefaultSize();},_insertIframe:function(ia){ha._loadedNodes[ia.id]=3D=
false;var ja=3Dfunction(ka){if(ia.id in =
ha._loadedNodes)ha.setLoadedNode(ia,ka,'iframe');};if(ia.post){aa({url:'a=
bout:blank',root:ia.root,className:ia.className,width:ia.size.width,heigh=
t:ia.size.height,id:ia.id,onInsert:ja,onload:function(ka){h.submitToTarge=
t({url:ia.url,target:ka.name,params:ia.params});}});}else =
aa({url:ia.url,root:ia.root,className:ia.className,width:ia.size.width,he=
ight:ia.size.height,id:ia.id,name:ia.frameName,onInsert:ja});},_handleRes=
izeMessage:function(ia,ja){var =
ka=3Dha.getLoadedNode(ia);if(!ka)return;if(ja.height)ka.style.height=3Dja=
.height+'px';if(ja.width)ka.style.width=3Dja.width+'px';u.inform('resize.=
ack',ja||{},'parent.frames['+ka.name+']');if(!j.isActive(ka))j.show(ka);}=
,_triggerDefault:function(ia){ha._xdRecv({frame:ia},ha._defaultCb[ia]||fu=
nction(){});},_popupMonitor:function(){var ia;for(var ja in =
ha._loadedNodes)if(ha._loadedNodes.hasOwnProperty(ja)&&ja in =
ha._defaultCb){var =
ka=3Dha._loadedNodes[ja];if(ka.type!=3D'popup'&&ka.type!=3D'native')conti=
nue;var la=3Dka.node;try{if(la.closed){ha._triggerDefault(ja);}else =
ia=3Dtrue;}catch(ma){}}if(ia&&!ha._popupInterval){ha._popupInterval=3Dset=
Interval(ha._popupMonitor,100);}else =
if(!ia&&ha._popupInterval){clearInterval(ha._popupInterval);ha._popupInte=
rval=3Dnull;}},_xdChannelHandler:function(ia,ja){return =
u.handler(function(ka){var =
la=3Dha.getLoadedNode(ia);if(!la)return;if(ka.type=3D=3D'resize'){ha._han=
dleResizeMessage(ia,ka);}else if(ka.type=3D=3D'hide'){j.hide(la);}else =
if(ka.type=3D=3D'rendered'){var ma=3Dj._findRoot(la);j.show(ma);}else =
if(ka.type=3D=3D'fireevent')k.fire(ka.event);},ja,true,null);},_xdNextHan=
dler:function(ia,ja,ka,la){if(la)ha._defaultCb[ja]=3Dia;return =
u.handler(function(ma){ha._xdRecv(ma,ia);},ka)+'&frame=3D'+ja;},_xdRecv:f=
unction(ia,ja){var =
ka=3Dha.getLoadedNode(ia.frame);if(ka)if(ka.close){try{ka.close();if(/iPh=
one.*Version\/(5|6)/.test(navigator.userAgent)&&RegExp.$1!=3D=3D'5')windo=
w.focus();ha._popupCount--;}catch(la){}}else =
if(i.containsCss(ka,'FB_UI_Hidden')){setTimeout(function(){ka.parentNode.=
parentNode.removeChild(ka.parentNode);},3000);}else =
if(i.containsCss(ka,'FB_UI_Dialog'))j.remove(ka);delete =
ha._loadedNodes[ia.frame];delete ha._defaultCb[ia.frame];if(ia.e2e){var =
ma=3Dj.get(ia.frame);ma.trackEvents(ia.e2e);ma.trackEvent('close');delete=
ia.e2e;}ja(ia);},_xdResult:function(ia,ja,ka,la){return =
(ha._xdNextHandler(function(ma){ia&&ia(ma.result&&ma.result!=3Dha._result=
Token&&ES('JSON','parse',false,ma.result));},ja,ka,la)+'&result=3D'+encod=
eURIComponent(ha._resultToken));},xdHandler:function(ia,ja,ka,la,ma){retu=
rn =
ha._xdNextHandler(g.xdResponseWrapper(ia,la,ma),ja,ka,true);}};p.stub('sh=
owDialog');e.exports=3Dha;},null);=0A=
__d("sdk.ui",["Assert","sdk.Impressions","Log","sdk.PlatformVersioning","=
sdk.Runtime","sdk.UIServer","sdk.feature"],function(a,b,c,d,e,f,g,h,i,j,k=
,l,m){b.__markCompiled&&b.__markCompiled();function =
n(o,p){g.isObject(o);g.maybeFunction(p);if(k.getIsVersioned()){j.assertVe=
rsionIsSet();if(o.version){j.assertValidVersion(o.version);}else =
o.version=3Dk.getVersion();}o=3DES('Object','assign',false,{},o);if(!o.me=
thod){i.error('"method" is a required parameter for FB.ui().');return =
null;}if(o.method=3D=3D'pay.prompt')o.method=3D'pay';var =
q=3Do.method;if(o.redirect_uri){i.warn('When using FB.ui, you should not =
specify a redirect_uri.');delete =
o.redirect_uri;}if((q=3D=3D'permissions.request'||q=3D=3D'permissions.oau=
th')&&(o.display=3D=3D'iframe'||o.display=3D=3D'dialog'))o.display=3Dl.ch=
eckOauthDisplay(o);var r=3Dm('e2e_tracking',true);if(r)o.e2e=3D{};var =
s=3Dl.prepareCall(o,p||function(){});if(!s)return null;var =
t=3Ds.params.display;if(t=3D=3D=3D'dialog'){t=3D'iframe';}else =
if(t=3D=3D=3D'none')t=3D'hidden';var u=3Dl[t];if(!u){i.error('"display" =
must be one of "popup", '+'"dialog", "iframe", "touch", "async", =
"hidden", or "none"');return =
null;}if(r)s.dialog.subscribe('e2e:end',function(v){v.method=3Dq;v.displa=
y=3Dt;i.debug('e2e: =
%s',ES('JSON','stringify',false,v));h.log(114,{payload:v});});u(s);return=
s.dialog;}e.exports=3Dn;},null);=0A=
__d("legacy:fb.auth",["sdk.Auth","sdk.Cookie","copyProperties","sdk.Event=
","FB","Log","sdk.Runtime","sdk.SignedRequest","sdk.ui"],function(a,b,c,d=
,e,f,g,h,i,j,k,l,m,n,o){b.__markCompiled&&b.__markCompiled();k.provide(''=
,{getLoginStatus:function(){return =
g.getLoginStatus.apply(g,arguments);},getAuthResponse:function(){return =
g.getAuthResponse();},getAccessToken:function(){return =
m.getAccessToken()||null;},getUserID:function(){return =
m.getUserID()||m.getCookieUserID();},login:function(p,q){if(q&&q.perms&&!=
q.scope){q.scope=3Dq.perms;delete q.perms;l.warn('OAuth2 specification =
states that \'perms\' '+'should now be called \'scope\'. Please =
update.');}var =
r=3Dm.isEnvironment(m.ENVIRONMENTS.CANVAS)||m.isEnvironment(m.ENVIRONMENT=
S.PAGETAB);o(i({method:'permissions.oauth',display:r?'async':'popup',doma=
in:location.hostname},q||{}),p);},logout:function(p){o({method:'auth.logo=
ut',display:'hidden'},p);}});g.subscribe('logout',ES(j.fire,'bind',true,j=
,'auth.logout'));g.subscribe('login',ES(j.fire,'bind',true,j,'auth.login'=
));g.subscribe('authresponse.change',ES(j.fire,'bind',true,j,'auth.authRe=
sponseChange'));g.subscribe('status.change',ES(j.fire,'bind',true,j,'auth=
.statusChange'));j.subscribe('init:post',function(p){if(p.status)g.getLog=
inStatus();if(m.getClientID())if(p.authResponse){g.setAuthResponse(p.auth=
Response,'connected');}else if(m.getUseCookie()){var =
q=3Dh.loadSignedRequest(),r;if(q){try{r=3Dn.parse(q);}catch(s){h.clearSig=
nedRequestCookie();}if(r&&r.user_id)m.setCookieUserID(r.user_id);}h.loadM=
eta();}});},3);=0A=
__d("sdk.Canvas.IframeHandling",["DOMWrapper","sdk.RPC"],function(a,b,c,d=
,e,f,g,h){b.__markCompiled&&b.__markCompiled();var i=3Dnull,j;function =
k(){var =
o=3Dg.getWindow().document,p=3Do.body,q=3Do.documentElement,r=3DMath.max(=
p.offsetTop,0),s=3DMath.max(q.offsetTop,0),t=3Dp.scrollHeight+r,u=3Dp.off=
setHeight+r,v=3Dq.scrollHeight+s,w=3Dq.offsetHeight+s;return =
Math.max(t,u,v,w);}function l(o){if(typeof o!=3D'object')o=3D{};var =
p=3D0,q=3D0;if(!o.height){o.height=3Dk();p=3D16;q=3D4;}if(!o.frame)o.fram=
e=3Dwindow.name||'iframe_canvas';if(j){var =
r=3Dj.height,s=3Do.height-r;if(s<=3Dq&&s>=3D-p)return =
false;}j=3Do;h.remote.setSize(o);return true;}function =
m(o,p){if(p=3D=3D=3D(void 0)&&typeof =
o=3D=3D=3D'number'){p=3Do;o=3Dtrue;}if(o||o=3D=3D=3D(void =
0)){if(i=3D=3D=3Dnull)i=3DsetInterval(function(){l();},p||100);l();}else =
if(i!=3D=3Dnull){clearInterval(i);i=3Dnull;}}h.stub('setSize');var =
n=3D{setSize:l,setAutoGrow:m};e.exports=3Dn;},null);=0A=
__d("sdk.Canvas.Navigation",["sdk.RPC"],function(a,b,c,d,e,f,g){b.__markC=
ompiled&&b.__markCompiled();function =
h(j){g.local.navigate=3Dfunction(k){j({path:k});};g.remote.setNavigationE=
nabled(true);}g.stub('setNavigationEnabled');var =
i=3D{setUrlHandler:h};e.exports=3Di;},null);=0A=
__d("sdk.Canvas.Plugin",["Log","sdk.RPC","sdk.Runtime","sdk.UA","sdk.api"=
,"createArrayFromMixed"],function(a,b,c,d,e,f,g,h,i,j,k,l){b.__markCompil=
ed&&b.__markCompiled();var =
m=3D'CLSID:D27CDB6E-AE6D-11CF-96B8-444553540000',n=3D'CLSID:444785F1-DE89=
-4295-863A-D46C3A781394',o=3Dnull,p=3Dj.osx()&&j.osx.getVersionParts(),q=3D=
!((p&&p[0]>10&&p[1]>10)&&(j.chrome()>=3D31||j.webkit()>=3D537.71||j.firef=
ox()>=3D25));function =
r(ba){ba._hideunity_savedstyle=3D{};ba._hideunity_savedstyle.left=3Dba.st=
yle.left;ba._hideunity_savedstyle.position=3Dba.style.position;ba._hideun=
ity_savedstyle.width=3Dba.style.width;ba._hideunity_savedstyle.height=3Db=
a.style.height;ba.style.left=3D'-10000px';ba.style.position=3D'absolute';=
ba.style.width=3D'1px';ba.style.height=3D'1px';}function =
s(ba){if(ba._hideunity_savedstyle){ba.style.left=3Dba._hideunity_savedsty=
le.left;ba.style.position=3Dba._hideunity_savedstyle.position;ba.style.wi=
dth=3Dba._hideunity_savedstyle.width;ba.style.height=3Dba._hideunity_save=
dstyle.height;}}function =
t(ba){ba._old_visibility=3Dba.style.visibility;ba.style.visibility=3D'hid=
den';}function u(ba){ba.style.visibility=3Dba._old_visibility||'';delete =
ba._old_visibility;}function v(ba){var =
ca=3Dba.type?ba.type.toLowerCase():null,da=3Dca=3D=3D=3D'application/x-sh=
ockwave-flash'||(ba.classid&&ba.classid.toUpperCase()=3D=3Dm);if(!da)retu=
rn false;var =
ea=3D/opaque|transparent/i;if(ea.test(ba.getAttribute('wmode')))return =
false;for(var fa=3D0;fa1/l||m=3D=3D'*'||~ES(m,'indexOf',true,j.getClientID()=
))return;setTimeout(p,30000);}function r(u){n=3Du;}function =
s(u){o.push(u);}var =
t=3D{COLLECT_AUTOMATIC:k.AUTOMATIC,COLLECT_MANUAL:k.MANUAL,addStaticResou=
rce:s,setCollectionMode:r,_maybeSample:q};e.exports=3Dt;},null);=0A=
__d("legacy:fb.canvas.prefetcher",["FB","sdk.Canvas.Prefetcher","sdk.Even=
t","sdk.Runtime"],function(a,b,c,d,e,f,g,h,i,j){b.__markCompiled&&b.__mar=
kCompiled();g.provide('Canvas.Prefetcher',h);i.subscribe('init:post',func=
tion(k){if(j.isEnvironment(j.ENVIRONMENTS.CANVAS))h._maybeSample();});},3=
);=0A=
__d("legacy:fb.compat.ui",["copyProperties","FB","Log","sdk.ui","sdk.UISe=
rver"],function(a,b,c,d,e,f,g,h,i,j,k){b.__markCompiled&&b.__markCompiled=
();h.provide('',{share:function(l){i.error('share() has been deprecated. =
Please use FB.ui() =
instead.');j({display:'popup',method:'stream.share',u:l});},publish:funct=
ion(l,m){i.error('publish() has been deprecated. Please use FB.ui() =
instead.');l=3Dl||{};j(g({display:'popup',method:'stream.publish',preview=
:1},l||{}),m);},addFriend:function(l,m){i.error('addFriend() has been =
deprecated. Please use FB.ui() =
instead.');j({display:'popup',id:l,method:'friend.add'},m);}});k.Methods[=
'auth.login']=3Dk.Methods['permissions.request'];},3);=0A=
__d("mergeArrays",[],function(a,b,c,d,e,f){b.__markCompiled&&b.__markComp=
iled();function g(h,i){for(var =
j=3D0;j0)||(typeof =
s=3D=3D'string'&&/^[0-9a-f]{21,}$|^[0-9]{1,21}$/.test(s));if(t)return =
s.toString();j.warn('Invalid App Id: Must be a number or numeric string =
representing '+'the application id.');return null;}function =
r(s){if(n.getInitialized())j.warn('FB.init has already been called - =
this could indicate a =
problem');if(n.getIsVersioned()){if(Object.prototype.toString.call(s)!=3D=
=3D'[object Object]')throw new k('Invalid =
argument');if(s.authResponse)j.warn('Setting authResponse is not =
supported');if(!s.version)s.version=3Do(location.href).getQueryData().sdk=
_version;l.assertValidVersion(s.version);n.setVersion(s.version);}else{if=
(/number|string/.test(typeof s)){j.warn('FB.init called with invalid =
parameters');s=3D{apiKey:s};}s=3DES('Object','assign',false,{status:true}=
,s||{});}var =
t=3Dq(s.appId||s.apiKey);if(t!=3D=3Dnull)n.setClientID(t);if('scope' in =
s)n.setScope(s.scope);if(s.cookie){n.setUseCookie(true);if(typeof =
s.cookie=3D=3D=3D'string')g.setDomain(s.cookie);}if(s.kidDirectedSite)n.s=
etKidDirectedSite(true);n.setInitialized(true);i.fire('init:post',s);}set=
Timeout(function(){var =
s=3D/(connect\.facebook\.net|\.facebook\.com\/assets.php).*?#(.*)/;ES(p(d=
ocument.getElementsByTagName('script')),'forEach',true,function(t){if(t.s=
rc){var u=3Ds.exec(t.src);if(u){var v=3Dm.decode(u[2]);for(var w in =
v)if(v.hasOwnProperty(w)){var =
x=3Dv[w];if(x=3D=3D'0')v[w]=3D0;}r(v);}}});if(window.fbAsyncInit&&!window=
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__d("legacy:fb.init",["FB","sdk.init"],function(a,b,c,d,e,f,g,h){b.__mark=
Compiled&&b.__markCompiled();g.provide('',{init:h});},3);=0A=
__d("legacy:fb.json",["FB","ManagedError"],function(a,b,c,d,e,f,g,h){b.__=
markCompiled&&b.__markCompiled();g.provide('JSON',{stringify:function(i){=
try{return ES('JSON','stringify',false,i);}catch(j){throw new =
h(j.message,j);}},parse:function(i){try{return =
ES('JSON','parse',false,i);}catch(j){throw new h(j.message,j);}}});},3);=0A=
__d("legacy:fb.ua",["FB","sdk.UA"],function(a,b,c,d,e,f,g,h){b.__markComp=
iled&&b.__markCompiled();g.provide('UA',{nativeApp:h.nativeApp});},3);=0A=
__d("legacy:fb.ui",["FB","sdk.ui"],function(a,b,c,d,e,f,g,h){b.__markComp=
iled&&b.__markCompiled();g.provide('',{ui:h});},3);=0A=
__d("runOnce",[],function(a,b,c,d,e,f){b.__markCompiled&&b.__markCompiled=
();function g(h){var i,j;return =
function(){if(!i){i=3Dtrue;j=3Dh();}return j;};}e.exports=3Dg;},null);=0A=
__d("XFBML",["Assert","sdk.DOM","Log","ObservableMixin","sdk.UA","createA=
rrayFromMixed","runOnce"],function(a,b,c,d,e,f,g,h,i,j,k,l,m){b.__markCom=
piled&&b.__markCompiled();var n=3D{},o=3D{},p=3D0,q=3Dnew j();function =
r(y,z){return ES((y[z]+''),'trim',true);}function s(y){return =
y.scopeName?(y.scopeName+':'+y.nodeName):'';}function t(y){return =
n[r(y,'nodeName').toLowerCase()]||n[s(y).toLowerCase()];}function =
u(y){var =
z=3DES(r(y,'className').split(/\s+/),'filter',true,function(aa){return =
o.hasOwnProperty(aa);});if(z.length=3D=3D=3D0)return (void =
0);if(y.getAttribute('fb-xfbml-state')||!y.childNodes||y.childNodes.lengt=
h=3D=3D=3D0||(y.childNodes.length=3D=3D=3D1&&y.childNodes[0].nodeType=3D=3D=
=3D3)||(y.children.length=3D=3D=3D1&&r(y.children[0],'className')=3D=3D=3D=
'fb-xfbml-parse-ignore'))return o[z[0]];}function v(y){var =
z=3D{};ES(l(y.attributes),'forEach',true,function(aa){z[r(aa,'name')]=3Dr=
(aa,'value');});return z;}function w(y,z,aa){var =
ba=3Ddocument.createElement('div');h.addCss(y,z+'-'+aa);ES(l(y.childNodes=
),'forEach',true,function(ca){ba.appendChild(ca);});ES(l(y.attributes),'f=
orEach',true,function(ca){ba.setAttribute(ca.name,ca.value);});y.parentNo=
de.replaceChild(ba,y);return ba;}function =
x(y,z,aa){g.isTrue(y&&y.nodeType&&y.nodeType=3D=3D=3D1&&!!y.getElementsBy=
TagName,'Invalid DOM node passed to =
FB.XFBML.parse()');g.isFunction(z,'Invalid callback passed to =
FB.XFBML.parse()');var ba=3D++p;i.info('XFBML Parsing Start %s',ba);var =
ca=3D1,da=3D0,ea=3Dfunction(){ca--;if(ca=3D=3D=3D0){i.info('XFBML =
Parsing Finish %s, %s tags =
found',ba,da);z();q.inform('render',ba,da);}g.isTrue(ca>=3D0,'onrender() =
has been called too many =
times');};ES(l(y.getElementsByTagName('*')),'forEach',true,function(ga){i=
f(!aa&&ga.getAttribute('fb-xfbml-state'))return;if(ga.nodeType!=3D=3D1)re=
turn;var =
ha=3Dt(ga)||u(ga);if(!ha)return;if(k.ie()<9&&ga.scopeName)ga=3Dw(ga,ha.xm=
lns,ha.localName);ca++;da++;var ia=3Dnew =
ha.ctor(ga,ha.xmlns,ha.localName,v(ga));ia.subscribe('render',m(function(=
){ga.setAttribute('fb-xfbml-state','rendered');ea();}));var =
ja=3Dfunction(){if(ga.getAttribute('fb-xfbml-state')=3D=3D'parsed'){q.sub=
scribe('render.queue',ja);}else{ga.setAttribute('fb-xfbml-state','parsed'=
);ia.process();}};ja();});q.inform('parse',ba,da);var =
fa=3D30000;setTimeout(function(){if(ca>0)i.warn('%s tags failed to =
render in %s ms',ca,fa);},fa);ea();}q.subscribe('render',function(){var =
y=3Dq.getSubscribers('render.queue');q.clearSubscribers('render.queue');E=
S(y,'forEach',true,function(z){z();});});ES('Object','assign',false,q,{re=
gisterTag:function(y){var =
z=3Dy.xmlns+':'+y.localName;g.isUndefined(n[z],z+' already =
registered');n[z]=3Dy;o[y.xmlns+'-'+y.localName]=3Dy;},parse:function(y,z=
){x(y||document.body,z||function(){},true);},parseNew:function(){x(docume=
nt.body,function(){},false);}});e.exports=3Dq;},null);=0A=
__d("PluginPipe",["sdk.Content","sdk.feature","guid","insertIframe","Miny=
","ObservableMixin","JSSDKPluginPipeConfig","sdk.Runtime","sdk.UA","UrlMa=
p","XFBML"],function(a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q){b.__markCompiled&=
&b.__markCompiled();var r=3Dnew l(),s=3Dm.threshold,t=3D[];function =
u(){return !!(h('plugin_pipe',false)&&n.getSecure()!=3D=3D(void =
0)&&(o.chrome()||o.firefox())&&m.enabledApps[n.getClientID()]);}function =
v(){var =
x=3Dt;t=3D[];if(x.length<=3Ds){ES(x,'forEach',true,function(aa){j(aa.conf=
ig);});return;}var y=3Dx.length+1;function =
z(){y--;if(y=3D=3D=3D0)w(x);}ES(x,'forEach',true,function(aa){var =
ba=3D{};for(var ca in =
aa.config)ba[ca]=3Daa.config[ca];ba.url=3Dp.resolve('www',n.getSecure())+=
'https://www.schematicsforfree.com/plugins/plugin_pipe_shell.php';ba.onload=3Dz;j(ba);});z();}q.subscribe(=
'parse',v);function w(x){var =
y=3Ddocument.createElement('span');g.appendHidden(y);var =
z=3D{};ES(x,'forEach',true,function(ea){z[ea.config.name]=3D{plugin:ea.ta=
g,params:ea.params};});var =
aa=3DES('JSON','stringify',false,z),ba=3Dk.encode(aa);ES(x,'forEach',true=
,function(ea){var =
fa=3Ddocument.getElementsByName(ea.config.name)[0];fa.onload=3Dea.config.=
onload;});var =
ca=3Dp.resolve('www',n.getSecure())+'/plugins/pipe.php',da=3Di();j({url:'=
about:blank',root:y,name:da,className:'fb_hidden =
fb_invisible',onload:function(){g.submitToTarget({url:ca,target:da,params=
:{plugins:ba.lengthja&&ia>ha)=
{this._iframe.style.left=3DparseInt(h.getStyle(this._iframe,'width'),10)-=
ha+'px';this._isRepositioned=3Dtrue;la.type=3D'reposition';}else =
if(this._isRepositioned&&(ka-ha)!=3D=3D0){this._iframe.style.left=3D'0px'=
;this._isRepositioned=3Dfalse;la.type=3D'restore';}else =
return;t.sendToFacebook(this._iframe.name,{method:'xd/reposition',params:=
ES('JSON','stringify',false,la)});},updateLift:function(){var =
ha=3Dthis._iframe.style.width=3D=3D=3Dthis._iframeOptions.root.style.widt=
h&&this._iframe.style.height=3D=3D=3Dthis._iframeOptions.root.style.heigh=
t;h[ha?'removeCss':'addCss'](this._iframe,'fb_iframe_widget_lift');}},k);=
ga.getVal=3Dca;ga.withParams=3Dfunction(ha,ia){return =
ga.extend({getParams:function(){return ha;},getConfig:function(){return =
ia?ia:{};}});};e.exports=3Dga;},null);=0A=
__d("PluginConfig",["sdk.feature"],function(a,b,c,d,e,f,g){b.__markCompil=
ed&&b.__markCompiled();var =
h=3D{messengerpreconfirmation:{mobile_fullsize:true},messengeraccountconf=
irmation:{mobile_fullsize:true},messengertoggle:{mobile_fullsize:true},po=
st:{fluid:g('fluid_embed',false),mobile_fullsize:true},video:{fluid:true,=
full_width:true}};e.exports=3Dh;},null);=0A=
__d("PluginTags",[],function(a,b,c,d,e,f){b.__markCompiled&&b.__markCompi=
led();var =
g=3D{activity:{filter:'string',action:'string',max_age:'string',linktarge=
t:'string',header:'bool',recommendations:'bool',site:'hostname'},composer=
:{action_type:'string',action_properties:'string'},create_event_button:{}=
,degrees:{href:'url'},facepile:{href:'string',action:'string',size:'strin=
g',max_rows:'string',show_count:'bool'},follow:{href:'url',layout:'string=
',show_faces:'bool'},like:{href:'url',layout:'string',show_faces:'bool',s=
hare:'bool',action:'string',send:'bool'},like_box:{href:'string',show_fac=
es:'bool',header:'bool',stream:'bool',force_wall:'bool',show_border:'bool=
',id:'string',connections:'string',profile_id:'string',name:'string'},pag=
e:{href:'string',hide_cover:'bool',show_facepile:'bool',show_about:'bool'=
,show_posts:'bool'},open_graph:{href:'url',layout:'string',show_faces:'bo=
ol',action_type:'string',action_properties:'string'},open_graph_preview:{=
action_type:'string',action_properties:'string'},messengerpreconfirmation=
:{messenger_app_id:'string'},messengeraccountconfirmation:{messenger_app_=
id:'string',state:'string'},messengertoggle:{messenger_app_id:'string',to=
ken:'string'},page_events:{href:'url'},post:{href:'url',show_border:'bool=
'},privacy_selector:{},profile_pic:{uid:'string',linked:'bool',href:'stri=
ng',size:'string',facebook_logo:'bool'},recommendations:{filter:'string',=
action:'string',max_age:'string',linktarget:'string',header:'bool',site:'=
hostname'},share_button:{href:'url',layout:'string',type:'string'},shared=
_activity:{header:'bool'},send:{href:'url'},send_to_mobile:{max_rows:'str=
ing',show_faces:'bool',size:'string'},story:{href:'url',show_border:'bool=
'},topic:{topic_name:'string',topic_id:'string'},video:{allowfullscreen:'=
bool',href:'url'},want:{href:'url',layout:'string',show_faces:'bool'}},h=3D=
{subscribe:'follow',fan:'like_box',likebox:'like_box',friendpile:'facepil=
e'};ES(ES('Object','keys',false,h),'forEach',true,function(i){g[i]=3Dg[h[=
i]];});e.exports=3Dg;},null);=0A=
__d("sdk.Arbiter",[],function(a,b,c,d,e,f){b.__markCompiled&&b.__markComp=
iled();var =
g=3D{BEHAVIOR_EVENT:'e',BEHAVIOR_PERSISTENT:'p',BEHAVIOR_STATE:'s'};e.exp=
orts=3Dg;},null);=0A=
__d("sdk.XFBML.Element",["sdk.DOM","Type","ObservableMixin"],function(a,b=
,c,d,e,f,g,h,i){b.__markCompiled&&b.__markCompiled();var =
j=3Dh.extend({constructor:function(k){this.parent();this.dom=3Dk;},fire:f=
unction(){this.inform.apply(this,arguments);},getAttribute:function(k,l,m=
){var n=3Dg.getAttr(this.dom,k);return =
n?m?m(n):n:l;},_getBoolAttribute:function(k,l){var =
m=3Dg.getBoolAttr(this.dom,k);return =
m=3D=3D=3Dnull?l:m;},_getPxAttribute:function(k,l){return =
this.getAttribute(k,l,function(m){var n=3DparseInt(m,10);return =
isNaN(n)?l:n;});},_getLengthAttribute:function(k,l){return =
this.getAttribute(k,l,function(m){if(m=3D=3D=3D'100%')return m;var =
n=3DparseInt(m,10);return =
isNaN(n)?l:n;});},_getAttributeFromList:function(k,l,m){return =
this.getAttribute(k,l,function(n){n=3Dn.toLowerCase();return =
(ES(m,'indexOf',true,n)>-1)?n:l;});},isValid:function(){for(var =
k=3Dthis.dom;k;k=3Dk.parentNode)if(k=3D=3Ddocument.body)return =
true;},clear:function(){g.html(this.dom,'');}},i);e.exports=3Dj;},null);=0A=
__d("sdk.XFBML.IframeWidget",["sdk.Arbiter","sdk.Auth","sdk.Content","sdk=
.DOM","sdk.Event","sdk.XFBML.Element","guid","insertIframe","QueryString"=
,"sdk.Runtime","sdk.ui","UrlMap","sdk.XD"],function(a,b,c,d,e,f,g,h,i,j,k=
,l,m,n,o,p,q,r,s){b.__markCompiled&&b.__markCompiled();var =
t=3Dl.extend({_iframeName:null,_showLoader:true,_refreshOnAuthChange:fals=
e,_allowReProcess:false,_fetchPreCachedLoader:false,_visibleAfter:'load',=
_widgetPipeEnabled:false,_borderReset:false,_repositioned:false,getUrlBit=
s:function(){throw new Error('Inheriting class needs to implement =
getUrlBits().');},setupAndValidate:function(){return =
true;},oneTimeSetup:function(){},getSize:function(){},getIframeName:funct=
ion(){return this._iframeName;},getIframeTitle:function(){return =
'Facebook Social =
Plugin';},getChannelUrl:function(){if(!this._channelUrl){var =
x=3Dthis;this._channelUrl=3Ds.handler(function(y){x.fire('xd.'+y.type,y);=
},'parent.parent',true);}return =
this._channelUrl;},getIframeNode:function(){return =
this.dom.getElementsByTagName('iframe')[0];},arbiterInform:function(event=
,x,y){s.sendToFacebook(this.getIframeName(),{method:event,params:ES('JSON=
','stringify',false,x||{}),behavior:y||g.BEHAVIOR_PERSISTENT});},_arbiter=
Inform:function(event,x,y){var =
z=3D'parent.frames["'+this.getIframeNode().name+'"]';s.inform(event,x,z,y=
);},getDefaultWebDomain:function(){return =
r.resolve('www');},process:function(x){if(this._done){if(!this._allowRePr=
ocess&&!x)return;this.clear();}else =
this._oneTimeSetup();this._done=3Dtrue;this._iframeName=3Dthis.getIframeN=
ame()||this._iframeName||m();if(!this.setupAndValidate()){this.fire('rend=
er');return;}if(this._showLoader)this._addLoader();j.addCss(this.dom,'fb_=
iframe_widget');if(this._visibleAfter!=3D'immediate'){j.addCss(this.dom,'=
fb_hide_iframes');}else =
this.subscribe('iframe.onload',ES(this.fire,'bind',true,this,'render'));v=
ar =
y=3Dthis.getSize()||{},z=3Dthis.getFullyQualifiedURL();if(y.width=3D=3D'1=
00%')j.addCss(this.dom,'fb_iframe_widget_fluid');this.clear();n({url:z,ro=
ot:this.dom.appendChild(document.createElement('span')),name:this._iframe=
Name,title:this.getIframeTitle(),className:p.getRtl()?'fb_rtl':'fb_ltr',h=
eight:y.height,width:y.width,onload:ES(this.fire,'bind',true,this,'iframe=
.onload')});this._resizeFlow(y);this.loaded=3Dfalse;this.subscribe('ifram=
e.onload',ES(function(){this.loaded=3Dtrue;if(!this._isResizeHandled)j.ad=
dCss(this.dom,'fb_hide_iframes');},'bind',true,this));},generateWidgetPip=
eIframeName:function(){u++;return =
'fb_iframe_'+u;},getFullyQualifiedURL:function(){var =
x=3Dthis._getURL();x+=3D'?'+o.encode(this._getQS());if(x.length>2000){x=3D=
'about:blank';var =
y=3DES(function(){this._postRequest();this.unsubscribe('iframe.onload',y)=
;},'bind',true,this);this.subscribe('iframe.onload',y);}return =
x;},_getWidgetPipeShell:function(){return =
r.resolve('www')+'/common/widget_pipe_shell.php';},_oneTimeSetup:function=
(){this.subscribe('xd.resize',ES(this._handleResizeMsg,'bind',true,this))=
;this.subscribe('xd.resize',ES(this._bubbleResizeEvent,'bind',true,this))=
;this.subscribe('xd.resize.iframe',ES(this._resizeIframe,'bind',true,this=
));this.subscribe('xd.resize.flow',ES(this._resizeFlow,'bind',true,this))=
;this.subscribe('xd.resize.flow',ES(this._bubbleResizeEvent,'bind',true,t=
his));this.subscribe('xd.refreshLoginStatus',function(){h.getLoginStatus(=
function(){},true);});this.subscribe('xd.logout',function(){q({method:'au=
th.logout',display:'hidden'},function(){});});if(this._refreshOnAuthChang=
e)this._setupAuthRefresh();if(this._visibleAfter=3D=3D'load')this.subscri=
be('iframe.onload',ES(this._makeVisible,'bind',true,this));this.subscribe=
('xd.verify',ES(function(x){this.arbiterInform('xd/verify',x.token);},'bi=
nd',true,this));this.oneTimeSetup();},_makeVisible:function(){this._remov=
eLoader();j.removeCss(this.dom,'fb_hide_iframes');this.fire('render');},_=
setupAuthRefresh:function(){h.getLoginStatus(ES(function(x){var =
y=3Dx.status;k.subscribe('auth.statusChange',ES(function(z){if(!this.isVa=
lid())return;if(y=3D=3D'unknown'||z.status=3D=3D'unknown')this.process(tr=
ue);y=3Dz.status;},'bind',true,this));},'bind',true,this));},_handleResiz=
eMsg:function(x){if(!this.isValid())return;this._resizeIframe(x);this._re=
sizeFlow(x);if(!this._borderReset){this.getIframeNode().style.border=3D'n=
one';this._borderReset=3Dtrue;}this._isResizeHandled=3Dtrue;this._makeVis=
ible();},_bubbleResizeEvent:function(x){var =
y=3D{height:x.height,width:x.width,pluginID:this.getAttribute('plugin-id'=
)};k.fire('xfbml.resize',y);},_resizeIframe:function(x){var =
y=3Dthis.getIframeNode();if(x.reposition=3D=3D=3D"true")this._repositionI=
frame(x);x.height&&(y.style.height=3Dx.height+'px');x.width&&(y.style.wid=
th=3Dx.width+'px');this._updateIframeZIndex();},_resizeFlow:function(x){v=
ar =
y=3Dthis.dom.getElementsByTagName('span')[0];x.height&&(y.style.height=3D=
x.height+'px');x.width&&(y.style.width=3Dx.width+'px');this._updateIframe=
ZIndex();},_updateIframeZIndex:function(){var =
x=3Dthis.dom.getElementsByTagName('span')[0],y=3Dthis.getIframeNode(),z=3D=
y.style.height=3D=3D=3Dx.style.height&&y.style.width=3D=3D=3Dx.style.widt=
h,aa=3Dz?'removeCss':'addCss';j[aa](y,'fb_iframe_widget_lift');},_reposit=
ionIframe:function(x){var =
y=3Dthis.getIframeNode(),z=3DparseInt(j.getStyle(y,'width'),10),aa=3Dj.ge=
tPosition(y).x,ba=3Dj.getViewportInfo().width,ca=3DparseInt(x.width,10);i=
f(aa+ca>ba&&aa>ca){y.style.left=3Dz-ca+'px';this.arbiterInform('xd/reposi=
tion',{type:'horizontal'});this._repositioned=3Dtrue;}else =
if(this._repositioned){y.style.left=3D'0px';this.arbiterInform('xd/reposi=
tion',{type:'restore'});this._repositioned=3Dfalse;}},_addLoader:function=
(){if(!this._loaderDiv){j.addCss(this.dom,'fb_iframe_widget_loader');this=
._loaderDiv=3Ddocument.createElement('div');this._loaderDiv.className=3D'=
FB_Loader';this.dom.appendChild(this._loaderDiv);}},_removeLoader:functio=
n(){if(this._loaderDiv){j.removeCss(this.dom,'fb_iframe_widget_loader');i=
f(this._loaderDiv.parentNode)this._loaderDiv.parentNode.removeChild(this.=
_loaderDiv);this._loaderDiv=3Dnull;}},_getQS:function(){return =
ES('Object','assign',false,{api_key:p.getClientID(),locale:p.getLocale(),=
sdk:'joey',kid_directed_site:p.getKidDirectedSite(),ref:this.getAttribute=
('ref')},this.getUrlBits().params);},_getURL:function(){var =
x=3Dthis.getDefaultWebDomain(),y=3D'';return =
x+'/plugins/'+y+this.getUrlBits().name+'.php';},_postRequest:function(){i=
.submitToTarget({url:this._getURL(),target:this.getIframeNode().name,para=
ms:this._getQS()});}}),u=3D0,v=3D{};function w(){var x=3D{};for(var y in =
v){var =
z=3Dv[y];x[y]=3D{widget:z.getUrlBits().name,params:z._getQS()};}return =
x;}e.exports=3Dt;},null);=0A=
__d("sdk.XFBML.Comments",["sdk.Event","sdk.XFBML.IframeWidget","QueryStri=
ng","sdk.Runtime","JSSDKConfig","sdk.UA","UrlMap","sdk.feature"],function=
(a,b,c,d,e,f,g,h,i,j,k,l,m,n){b.__markCompiled&&b.__markCompiled();var =
o=3Dh.extend({_visibleAfter:'immediate',_refreshOnAuthChange:true,setupAn=
dValidate:function(){var =
p=3D{channel_url:this.getChannelUrl(),colorscheme:this.getAttribute('colo=
rscheme'),skin:this.getAttribute('skin'),numposts:this.getAttribute('num-=
posts',10),width:this._getLengthAttribute('width'),href:this.getAttribute=
('href'),permalink:this.getAttribute('permalink'),publish_feed:this.getAt=
tribute('publish_feed'),order_by:this.getAttribute('order_by'),mobile:thi=
s._getBoolAttribute('mobile'),version:this.getAttribute('version')};if(!p=
.width&&!p.permalink)p.width=3D550;if(k.initSitevars.enableMobileComments=
&&l.mobile()&&p.mobile!=3D=3Dfalse){p.mobile=3Dtrue;delete =
p.width;}if(!p.skin)p.skin=3Dp.colorscheme;if(!p.href){p.migrated=3Dthis.=
getAttribute('migrated');p.xid=3Dthis.getAttribute('xid');p.title=3Dthis.=
getAttribute('title',document.title);p.url=3Dthis.getAttribute('url',docu=
ment.URL);p.quiet=3Dthis.getAttribute('quiet');p.reverse=3Dthis.getAttrib=
ute('reverse');p.simple=3Dthis.getAttribute('simple');p.css=3Dthis.getAtt=
ribute('css');p.notify=3Dthis.getAttribute('notify');if(!p.xid){var =
q=3DES(document.URL,'indexOf',true,'#');if(q>0){p.xid=3DencodeURIComponen=
t(document.URL.substring(0,q));}else =
p.xid=3DencodeURIComponent(document.URL);}if(p.migrated)p.href=3Dm.resolv=
e('www')+'/plugins/comments_v1.php?'+'app_id=3D'+j.getClientID()+'&xid=3D=
'+encodeURIComponent(p.xid)+'&url=3D'+encodeURIComponent(p.url);}else{var=
=
r=3Dthis.getAttribute('fb_comment_id');if(!r){r=3Di.decode(document.URL.s=
ubstring(ES(document.URL,'indexOf',true,'?')+1)).fb_comment_id;if(r&&ES(r=
,'indexOf',true,'#')>0)r=3Dr.substring(0,ES(r,'indexOf',true,'#'));}if(r)=
{p.fb_comment_id=3Dr;this.subscribe('render',ES(function(){if(!window.loc=
ation.hash)window.location.hash=3Dthis.getIframeNode().id;},'bind',true,t=
his));}}if(!p.version)p.version=3Dj.getVersion();this._attr=3Dp;return =
true;},oneTimeSetup:function(){this.subscribe('xd.commentCreated',ES(this=
._handleCommentCreatedMsg,'bind',true,this));this.subscribe('xd.commentRe=
moved',ES(this._handleCommentRemovedMsg,'bind',true,this));},getSize:func=
tion(){if(!this._attr.permalink)return =
{width:this._attr.mobile?'100%':this._attr.width,height:100};},getUrlBits=
:function(){return =
{name:'comments',params:this._attr};},getDefaultWebDomain:function(){if(t=
his._attr.mobile&&!n('one_comment_controller',false)&&this._attr.version!=
=3D=3D'v2.3')return m.resolve('m',true);return =
m.resolve('www',true);},_handleCommentCreatedMsg:function(p){if(!this.isV=
alid())return;var =
q=3D{href:p.href,commentID:p.commentID,parentCommentID:p.parentCommentID,=
message:p.message};g.fire('comment.create',q);},_handleCommentRemovedMsg:=
function(p){if(!this.isValid())return;var =
q=3D{href:p.href,commentID:p.commentID};g.fire('comment.remove',q);}});e.=
exports=3Do;},null);=0A=
__d("sdk.XFBML.CommentsCount",["ApiClient","sdk.DOM","sdk.XFBML.Element",=
"sprintf"],function(a,b,c,d,e,f,g,h,i,j){b.__markCompiled&&b.__markCompil=
ed();var =
k=3Di.extend({process:function(){h.addCss(this.dom,'fb_comments_count_zer=
o');var =
l=3Dthis.getAttribute('href',window.location.href);g.scheduleBatchCall('/=
v2.1/'+encodeURIComponent(l),{fields:'share'},ES(function(m){var =
n=3D(m.share&&m.share.comment_count)||0;h.html(this.dom,j('%s',n));if(n>0)h.removeCss(this.dom,'f=
b_comments_count_zero');this.fire('render');},'bind',true,this));}});e.ex=
ports=3Dk;},null);=0A=
__d("sdk.Helper",["sdk.ErrorHandling","sdk.Event","UrlMap","safeEval","sp=
rintf"],function(a,b,c,d,e,f,g,h,i,j,k){b.__markCompiled&&b.__markCompile=
d();var l=3D{isUser:function(m){return =
m<2.2e+09||(m>=3D1e+14&&m<=3D100099999989999)||(m>=3D8.9e+13&&m<=3D899999=
99999999)||(m>=3D6.000001e+13&&m<=3D60000019999999);},upperCaseFirstChar:=
function(m){if(m.length>0){return =
m.substr(0,1).toUpperCase()+m.substr(1);}else return =
m;},getProfileLink:function(m,n,o){if(!o&&m)o=3Dk('%s/profile.php?id=3D%s=
',i.resolve('www'),m.uid||m.id);if(o)n=3Dk('%s',o,n);return =
n;},invokeHandler:function(m,n,o){if(m)if(typeof =
m=3D=3D=3D'string'){g.unguard(j)(m,o);}else =
if(m.apply)g.unguard(m).apply(n,o||[]);},fireEvent:function(m,n){var =
o=3Dn._attr.href;n.fire(m,o);h.fire(m,o,n);},executeFunctionByName:functi=
on(m){var =
n=3DArray.prototype.slice.call(arguments,1),o=3Dm.split("."),p=3Do.pop(),=
q=3Dwindow;for(var r=3D0;r"'\/]/g,h=3D{'&':'&','<':'<','>':'>','"':'"',"'":=
''','/':'/'};function i(j){return =
j.replace(g,function(k){return h[k];});}e.exports=3Di;},null);=0A=
__d("sdk.XFBML.Name",["ApiClient","escapeHTML","sdk.Event","sdk.XFBML.Ele=
ment","sdk.Helper","Log","sdk.Runtime"],function(a,b,c,d,e,f,g,h,i,j,k,l,=
m){b.__markCompiled&&b.__markCompiled();var =
n=3D({}).hasOwnProperty,o=3Dj.extend({process:function(){ES('Object','ass=
ign',false,this,{_uid:this.getAttribute('uid'),_firstnameonly:this._getBo=
olAttribute('first-name-only'),_lastnameonly:this._getBoolAttribute('last=
-name-only'),_possessive:this._getBoolAttribute('possessive'),_reflexive:=
this._getBoolAttribute('reflexive'),_objective:this._getBoolAttribute('ob=
jective'),_linked:this._getBoolAttribute('linked',true),_subjectId:this.g=
etAttribute('subject-id')});if(!this._uid){l.error('"uid" is a required =
attribute for ');this.fire('render');return;}var =
p=3D[];if(this._firstnameonly){p.push('first_name');}else =
if(this._lastnameonly){p.push('last_name');}else =
p.push('name');if(this._subjectId){p.push('gender');if(this._subjectId=3D=
=3Dm.getUserID())this._reflexive=3Dtrue;}i.monitor('auth.statusChange',ES=
(function(){if(!this.isValid()){this.fire('render');return =
true;}if(!this._uid||this._uid=3D=3D'loggedinuser')this._uid=3Dm.getUserI=
D();if(!this._uid)return;g.scheduleBatchCall('/v1.0/'+this._uid,{fields:p=
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dget","sdk.Runtime","UrlMap"],function(a,b,c,d,e,f,g,h,i,j,k){b.__markCom=
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skinnyWidth:520,_skinnyBaseHeight:173,_skinnyFieldHeight:52,setupAndValid=
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b_register:this._getBoolAttribute('fb-register',false),fields:this.getAtt=
ribute('fields'),height:this._getPxAttribute('height'),redirect_uri:this.=
getAttribute('redirect-uri',window.location.href),no_footer:this._getBool=
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lidate:this.getAttribute('onvalidate'),width:this._getPxAttribute('width'=
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n=3DES('JSON','parse',false,m.value),o=3DES(function(q){this.arbiterInfor=
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s));return true;},getSize:function(){return =
{width:this._attr.width,height:this._getHeight()};},_getHeight:function()=
{if(this._attr.height)return this._attr.height;var =
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if (!_uVG()) return;=0A=
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var s=3D"&utmt=3Dvar&utmn=3D"+r;=0A=
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i2.src=3D_ugifpath2+"?"+"utmwv=3D"+_uwv+s+"&utmac=3D"+_uacct+"&utmcc=3D"+=
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var t,c=3D"",dc=3D_ubd.cookie;=0A=
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var n=3D"";=0A=
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var c=3Dnew =
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Content-Type: text/html;
charset="Windows-1252"
Content-Transfer-Encoding: quoted-printable
Content-Location: http://www.electronics-tutorials.com/basics/wide-band-rf-transformers.htm
wide band rf transformers=20
=20
=20
=20
=20
=20
=20
Applications for wide band rf transformers include =
impedance=20
matching, voltage or current transformation, DC isolation, balanced / =
unbalanced=20
mixing, matching, power splitting, coupling, and signal inversion. =
Custom wide=20
band transformers with special combinations of impedance ratio, =
insertion loss,=20
frequency response, and current handling are also =
available."
Wideband rf transformers are simply transfomers designed to provide =
an=20
impedance transformation over a broad frequency range. In amateur radio=20
applications we wind these transformers on ferrite =
toroids. A common impedance transformation is 200 ohms to 50 ohms =
using a=20
bi-filar winding. Here is an example from our broad=20
band amplifiers tutorial.
=20
Figure 1. - wideband rf amplifier with shunt feedback and =
emitter=20
degeneration
Transformer T1 is a broadband rf transformer.=20
Designing wide band rf transformers
In the design of these kinds of wide band rf transformers the primary =
reactance is usually around 5 times the primary impeda=
nce.=20
With a 200 ohms to 50 ohm transformer, we would allow a reactance of =
1,000 ohms=20
at the lowest frequency of interest. Just as an example consider =
we were=20
building a broad band amplifier for the amateur bands and going down as =
low as=20
1.8 Mhz.=20
For this example we would need bi-filar windings which have a reacta=
nce=20
of 1,000 ohms at 1.8 Mhz, this means a required induc=
tance=20
of around 88 uH. A look through the Amidon data book tells me that =
ferrite=20
toroid FT-50-61 as one example can provide me with an AL factor of 68mH =
/ 1000=20
turns.=20
This means if 1,000 turns were wound on the toroid it would give us =
68 mH.=20
Yes that IS milli-henries, these are ferrite toroids.=20
Calculating turns for wide band rf transformers
To wind a wide band rf transformer with an inductance of 88 uH (yes =
that's=20
micro-henries) which is in fact 0.088 mh we use the following formula:=20
Turns =3D 1,000 X SQRT (L in mH / AL factor) =
=3D 1,000 X=20
SQRT (0.088 / 68) =3D 36 turns.=20
Our wide band rf transformer needs 36 turns to achieve an inductance =
of 88=20
uH.=20
Winding the wide band rf transformer
Because this is a bi-filar winding for our wide band rf transformer, =
we need=20
two lengths of wire which we will "twist" together at a "pitch" of 2.5 =
turns per=20
inch or 1 turn per 10 mm. If you anchor one end of the two wires =
together in a=20
bench vise and fix the other ends securely in a hand drill (a bent nail =
or fish=20
hook helps here) you then gently "stretch" the wires first. Then you =
slowly turn=20
the hand drill and notice the two wires "twisting" together, as you =
proceed you=20
will notice more and more twists appearing. Stop when you have about 2.5 =
twists=20
to the inch. Stretch the wires once more.=20
Wind 36 turns through the toroid and that is it! To use in an =
application=20
such as figure 1 above you need to pay attention to the "phasing". =
Notice the=20
two dots on T1 above? They indicate the start of each wire. Use =
an=20
ohmmeter to find the start and finish of one winding, mark it in some =
convenient=20
manner e.g. coloured pen. The other winding should then be obvious.=20
Commercially manufactured wide band rf transformers
Coilcraft is one manufacturer of wide band transformers which provide =
reliable performance.=20
The transformers are offered in tapped or untapped configurations and =
are=20
packaged in a low-profile DIP-style plastic case. All parts are =
available in=20
either a surface mount version or a through-hole version that=92s =
compatible with=20
standard DIP sockets.=20
Applications include impedance matching, voltage or current =
transformation,=20
DC isolation, balanced / unbalanced mixing, matching, power splitting, =
coupling,=20
and signal inversion. Custom wide band transformers with special =
combinations of=20
impedance ratio, insertion loss, frequency response, and current =
handling are=20
also available.=20
Designing wide band rf transformers for different impedances
Alright what if you need something other than a 200 ohm to 50 ohms=20
transformer, how would you go about it?=20
What I tell you here now is applicable from DC to daylight. What that =
means=20
is, it is equally applicable to an audio transformer with a bandwidth of =
100 Hz=20
to 3,000 Hz (for an audio=20
transformer) as it is to a broadband transformer designed to operate =
at say=20
7.00 to 7.50 Mhz. Read on.=20
Firstly you need to pick either a lower 1 dB or 3 dB bandwidth. =
Wozzat???=20
Look at figure 2 below where I present my usual scungy drawing - I'm no =
good at=20
this graphic arts caper, not the program, just my lack of artistic =
talent.=20
=20
Figure 2. - band pass filter characteristics
Here I've crudely depicted a range of frequencies being passed by a =
filter=20
and indicated the 1 dB and 3 db points. A 1 db point is where the power =
output=20
is about 80% of the band pass power or 90% of the voltage level. A 3 db =
point is=20
where the power output is about 50% of the band pass power or 70.7% of =
the=20
voltage level. If you can't understand decibels then you need to look at =
the decibel =
page=20
In your broad band transformer you need to determine the lowest point =
you can=20
tolerate in frequency. Entirely for discussion purposes I've selected 5 =
Mhz for=20
both 1 dB and 3 dB to demonstrate the formulas. Also I'm going to =
construct a =20
broad band tranformer to operate between 14.4 ohms and 50 ohms.=20
For the 1 db point to be 5 Mhz, I use the formula Lp =3D R / ( 2 X Pi =
X Fo) and=20
for the 3 dB point, I use the formula Lp =3D R / ( 4 X Pi X Fo). The =
general=20
formula for any other dB level is a bit difficult to reproduce here but =
contact =
me and I'll give it to anyone who wants it.=20
The first formula simply gives you an inductance equal the reactance =
of R or=20
in our case we're using 14.4 ohms at 5 Mhz. This results in an =
inductance of=20
0.458 uH. The second formula simply produces half that inductance or, =
0.229 uH.=20
Back to the result of 0.458 uH, that could easily be achieved with 10 =
turns=20
on a T-50-2 toroid. Alright we have a T50-2 toroid with 10 turns on it, =
this is=20
supposed to represent 14.4 ohms at 5 Mhz. To match to 50 ohms all we =
have to do=20
is work out the turns ratio. Impedance transforms as "the square of the =
ratio of=20
turns". Then 50 / 14.4 =3D 3.472' and the square root of this is 1.86 so =
we need=20
on the secondary 1.86 times more turns or in our case 19 turns.=20
IF our output were terminated in a genuine 50 ohm load then the =
square of [19=20
/10] being the turns ratio would be reflected back giving (if you work =
it out) a=20
source of 13.85 ohms.=20
The CRITICAL aspects here are: a) turns ratio AND; b) final=20
termination being a genuine 50 ohm load.=20
What is the upper frequency limit of our wide band rf =
transformer?
The high frequency limit is influenced by the leakage inductance Lk =
and=20
distributed capacitance of the inductor forming a second order low pass =
filter=20
and is influenced by a very wide range of factors. The higher the =
inductance,=20
then the lower or flatter the low-frequency end but, this comes at a =
price of=20
higher Lk and distributed capacitance limiting high frequency response. =
Often a=20
compromise is needed for high ratios of frequencies. Although I have =
never=20
tested it, I would imagine at least one octave bandwidth could easily be =
accomodated e.g. 2.5 Mhz to 5 Mhz or 5 Mhz to 10 Mhz.=20
=20
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