From: "Saved by Internet Explorer 11" Subject: fishes eddy (current amps and feedback) | lab jc Date: Thu, 21 Aug 2014 11:36:29 -0700 MIME-Version: 1.0 Content-Type: multipart/related; type="text/html"; boundary="----=_NextPart_000_0000_01CFBD34.264467C0" X-MimeOLE: Produced By Microsoft MimeOLE V6.1.7601.17609 This is a multi-part message in MIME format. ------=_NextPart_000_0000_01CFBD34.264467C0 Content-Type: text/html; charset="utf-8" Content-Transfer-Encoding: quoted-printable Content-Location: file://C:\Users\R&D 1\Documents\Research\Power Amplifiers\Current Feedback Amplifier.htm =EF=BB=BF =20 =20 =20 fishes eddy (current amps and feedback) | lab jc =20 =20 =20 =20 =20 =20 =20 =20

lab jc

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fishes eddy (current amps and feedback)

Posted on =20 by jc =
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it=E2=80=99s been awhile. a tough bunch a months.

at the time of writing this there=E2=80=99s an election looming, in = the usa, that=20 will set the course of the next generation and it=E2=80=99s economic = future. there=E2=80=99s =20 =E2=80=9Cfrankenstorm=E2=80=9D on the american east coast and an = earthquake and tsunami on the=20 west: all matter of unnatural and natural catastrophe. in the usa, very = few=20 seem to realize there are just a few small mistakes left between = generally=20 crappy and a major meltdown. that this was caused by the former = republican=20 president and his advisors has been both completely forgotten and = successfully=20 made vague. =E2=80=9Cit=E2=80=99s the black guy=E2=80=99s = fault=E2=80=9D. the de-distribution of american=20 wealth that began under bush=E2=80=99s watch has continued helter = skelter. never in the=20 history of personal wealth have the wealthy been so rich and in my = opinion, so=20 undeserving of it. many of them make nothing. they speculate, gamble, = con or=20 just plain steal. like goldman sachs. like morgan stanley. like = citigroup. like=20 bain. on the flipside, poverty is now almost mainstream. it is crazy, = to me, no=20 one seems to care how this happened. most just want a slice off the = flank. it=E2=80=99s=20 business as usual. those responsible for informing the public have been = downsized, both teachers and journalists. propagandists have replaced = them, and=20 are actually much more profitable. conspiracy theories, the price of = gas and=20 who gets to boss the vagina around gets more attention than why = it=E2=80=99s that way=20 in the first place. the mainstream media=E2=80=99s open racism and = radical revisionism=20 of all history, and even of science, has tainted the process to the = point where=20 it is actually hard to find out what the fuck IS going on. you have to = watch=20 the fake news to make any sense of it (thank goodness for john stewart = and=20 stephen colbert). comedians, like chris rock, make fake public service=20 announcements that are way more honest and useful than any political=20 organization. it should be funny=E2=80=A6

hanging over the american election: corporate money has utterly = corrupted the=20 democratic process. if romney wins, he will have proved that elections = can be=20 bought in the usa.

and things are hard everywhere! the storm that trashed the east coast = just=20 now, trashed the caribbean before that. there=E2=80=99s no electricity = or safe place to=20 sleep, or sanitary way to take a shit, or a shower=E2=80=A6 for lots of = people there.=20 the eu=E2=80=99s money problems persist and inequality there threatens = to split the=20 union. the arab spring has collapsed. syria, jordan and lebanon are = primed to=20 blow together! beyond the false pride, economics and human costs of the = wars we=20 just can=E2=80=99t seem to =E2=80=9Cwin=E2=80=9D, corporate greed and = avarice have become status=20 values. the answer. things to take comfort in. =E2=80=9Cat least our = billionaires are=20 richer than yours=E2=80=9D, =E2=80=9Cwe=E2=80=9D must be doing = something right? this is how we do=20 business. god bless.

it feels a little odd and even a bit shameful to be thinking about = circuit=20 hacking under the circumstances=E2=80=A6 about art and craft. about = making weird=20 machines. although it is a nice place to escape to. i have friends who = have no=20 lights, heat or water at the moment. it=E2=80=99s getting cold and = there=E2=80=99s a nor-easter=20 on it=E2=80=99s way to nyc. i guess i want to say that i feel = compassion, sadness, and=20 anxiety for the people over there. i am grateful i have a job and a = roof over=20 my family=E2=80=99s head.

i want to go back to a discussion of current amplifiers and also of = current=20 feedback. i=E2=80=99m a little rusty at the blog thing=E2=80=A6. this = will be a good way to=20 ease back into it.

the ee universe is a man=E2=80=99s world, sadly. yes, and a man = worthy of the name,=20 pays attention to the volts. you think i=E2=80=99m joking?! i am simply = stating a fact.=20 ours is a voltage-centric discipline. a =E2=80=9Cthevenized=E2=80=9D = kind of bag. thevenin is=20 the ralph cramden of engineering attitudes, and there is nothing more=20 conventional and everyman than that. CAD relies heavily upon it too, as = nearly=20 all equivalent circuit simplification starts there. if you are not sure = of what=20 i am talking about, please go look it up. it is worth your time and = will help=20 you in your work. i am simply going to the punch line because i need to = get=20 some where else, but i want you to know why. because of thevenin, we = tend to=20 analyze active devices in his terms. an ideal voltage amplifier is a = voltage=20 source with an output impedance of 0 ohms. a short circuit. and it = likes to=20 work UP, into it=E2=80=99s load, which has some finite value.

as with everything else under the sun, there is another side of the = tracks=E2=80=A6 =20 and it is called norton. the bald headed goofy well-meaning = idiot-savant.=20 emphasis on savant. well educated EEs will of course point out, and = rightfully=20 so, that in the end, thevenin and norton are simply flipsides of the = same=20 insight: that no matter what kind of electrical circuit you have, it = can be=20 simplified into one relationship between volts, current and impedance = right=20 where the source of power meets the circuit. they come to the same = conclusion.=20 one pushes a bus and the other works in the sewer. yes yes=E2=80=A6 = well said.

i say, there is a practical limit there which tends to be pushed = aside in our=20 haste to get to the end of the job well done. there isn=E2=80=99t a = practical=20 amplifying device made today that is a short circuit or reliably drives = one.

on the other hand, norton has a different perspective of these = things. the=20 current-centric view. and a current source can be viewed, ala` norton, = as an=20 infinite impedance looking DOWN into a finite load. so what? as noted, = you wind=20 up with the same result. the big difference is that all of the = practical=20 devices we have to work with today are much more reliable, or how about = =E2=80=9Chappier=E2=80=9D, as open circuits than they are as shorts. = vacuum tubes in=20 particular, and especially tetrodes/pentodes, could be said to fit this = view=20 very nicely.

voltage feedback and current feedback have some related twists = relating to=20 thevenin and norton practically, but as my perspective is = controversial, i am=20 going to save most of that for another day. it is uncontroversial to = say that=20 voltage feedback and current feedback transform practical amplifiers in = slightly different ways. there can be advantages to current feedback in = the way=20 it handles impedance transformation=E2=80=A6 even though in the end you = have the =E2=80=9Csame=E2=80=9D=20 result.

below is a simple example of one of the most basic ways to return = negative=20 current feedback to the first stage. most modern voltage feedback op = amps are=20 actually based on this exact arrangement. the main difference is that = this is=20 half of the circuit. the op amp would have a differential input. but in = this=20 case, the =E2=80=9Cinput=E2=80=9D for the feedback circuit is low = impedance=E2=80=A6 the cathode. the=20 input for the signal is very high impedance, the grid. i think this is=20 accurately describes a current feedback amplifier. i also believe = modern=20 current feedback op amps are different in that they respond to current = at the=20 inverting input. but that shouldn=E2=80=99t change this discussion. = we=E2=80=99ll see who yells=20 at me for all this=E2=80=A6

here, you see two grounded cathode inverting gain stages, plus a = cathode=20 follower buffer, which returns it=E2=80=99s current variations (the = swing through it=E2=80=99s=20 Rk) back to the cathode resistor of the first stage. these current = variations=20 are in opposite phase to those in the first stage. consider what = happens when=20 the cathode follower has to dump extra current into a load=E2=80=A6. = loading it down.=20 there is less current variation in Rk. less CFB. more voltage into the = buffer.=20 this tends to stabilize the output. this is classic negative feedback = error=20 correction, done with current. one fabulous feature is that the error = signal is=20 DC coupled.

above is a very fancy practical hybrid version with metal pentodes = and=20 extraordinary performance. the 6SJ7 (triode wired) is set for a gain of = 24 dB.=20 and the C3g is a Gm amp, with a gain of 65 dB. that is roughly 90 dB of = gain=20 for the two. the bandwidth is DC to -3 dB at 18KHz open loop. the = buffer is a=20 depletion mode mosfet with 10mA going though it. that is probably not = enough=20 but it is what i have in the supply. there are better parts for this = job=E2=80=A6 yes,=20 this combination is sure to piss off a few! of course that=E2=80=99s = why i do it. i=20 will wire up a version with submini tubes (solder leads) under the hood = for=20 comparison. here, i have dialed in 58dB of current feedback for a = closed loop=20 gain of 32 dB. the 20pF compensation cap is for stability. below is a = view of=20 the prototype. the heatsinks are for the current source and buffer = mosfets.

here=20 are some measurements for you. first is a 250 Vpp sine wave at 20KHz. = it looks=20 like a sine wave but nice and big. 50 volts per centimeter. the next = image is=20 much more impressive. it is an X/Y measurement of the same signal. note = the=20 simple straight line. it is completely closed. without a distortion = analyzer or=20 phase meter i can still say that this 250 Vpp is provided with well = under 1%=20 distortion, and well under 1 degree of phase shift. probably under 0.1% = and 0.5=20 degrees.

that this was accomplished with 5 active devices is pretty cool. the = two gain=20 stages are tubed. it could be all tube, but that would put a bunch more = holes=20 on the top panel, and there isn=E2=80=99t any real advantage. the = current source and=20 the buffer don=E2=80=99t have to be tubes. also, to do this in only = solid state is not=20 that easy. most of the practical devices available have too much input=20 capacitance (and the C is too voltage variable) and the high voltage = would=20 cause problems. you could go to more devices and get to the same place = where=20 this design is=E2=80=A6 cascode high voltage transistors, or mosfets. = but there would=20 be a great deal more phase shift at 20KHz with any 2 high voltage = transistors=20 and the same mosfets. the tubes i use here have very low input C and = and are=20 voltage controlled.

most tube circuits aren=E2=80=99t expected to work this well. = especially in the DIY=20 world. but also in the =E2=80=9Chigh end=E2=80=9D world=E2=80=A6 of = course, there will be many who=20 immediately ask, =E2=80=9Cbut, how does it sound?=E2=80=9D. = =E2=80=9Cfeedback! what the fuck!=E2=80=9D =E2=80=9Cwho=20 needs it to be that good!=E2=80=9D and, =E2=80=9Cit ain=E2=80=99t = natural=E2=80=9D (for some reason i hear=20 jeffrey jackson saying this to me=E2=80=A6). look, electronics is the = antithesis of=20 natural. i say, it all depends on what you use it for=E2=80=A6 i plan = to drive some big=20 globe 50 tubes with it. i=E2=80=99m pretty happy about it. i=E2=80=99ll = have more to say about=20 this=E2=80=A6 later.

the square wave pic simply shows that the X/Y plot is very real. it = is boring=20 in it=E2=80=99s simplicity. no ringing, no rounded edges=E2=80=A6 = it=E2=80=99s just a plain old 1 KHz=20 square wave. 22 Vpp with half a volt in.

now for an interesting variation, imagine making the 3rd stage a = transformer=20 coupled grounded cathode stage=E2=80=A6 but what about the phase? it is = an inverting=20 stage at the plate but the current variations through the tube are the = same as=20 for the cathode follower. it is still negative cfb returned to the = first stage.=20 but in this case, the output impedance at the plate will be increased. = the=20 unbypassed resistance of the first stage=E2=80=99s Rk (which is in = series with the=20 output stage=E2=80=99s Rk), times the gain against the error signal = there. variations=20 in load impedance will have the opposite behavior of the typical = voltage amp.=20 with the source impedance (the amp) higher than the load=E2=80=99s, the = output current=20 will tend to be regulated by the feedback, and the voltage will track = the=20 impedance.

now why would that be cool?

well, imagine you are interested in driving a =E2=80=9Cfull = range=E2=80=9D speaker (a=20 misnomer) or a compression driver connected to a horn. both of these = speakers=20 have difficulties at the bottom (near resonance) and at the top (roll = off from=20 the mass of the piston). a traditional voltage feedback power amp (with = an =20 =E2=80=9Cinfinitely=E2=80=9D low source impedance) would have a good = =E2=80=9Cdamping factor=E2=80=9D and would=20 dump more current into the load as it approached 0 ohms, and less as it = increased. it would have to do this in order to keep the output voltage = =20 =E2=80=9Cregulated=E2=80=9D as compared to the input signal. but, this = would result in a loss of=20 bass and treble into both =E2=80=9Cfull range=E2=80=9D speakers and = compression drivers, as the=20 impedance is rising at both of these frequencies=E2=80=A6 and the = efficiency is fading=20 at the low frequency end, at the same time. a current amplifier, with = it=E2=80=99s=20 higher source impedance, would look at these particular loads quite=20 differently. the output voltage would track the impedance of the = speaker. and=20 you would have extension of both the bass and the treble.

this is interesting for me as i use manger drivers in my system. = mangers are=20 complicated drivers. they are bending wave drivers above 400 Hz, really = inefficient piston drivers below, and beamy laser beams above 1 KHz. i = have a=20 love/hate thing with them, for sure. but they do one thing better than = all=20 standard moving coil dynamic drivers: their impulse response is almost=20 perfectly in time with the drive signal. if you can cross them over to = a bass=20 driver low enough, and keep the woofer output out of the midrange as = much as=20 possible, and then deal with the beaminess=E2=80=A6 (i have gone the = way of the=20 diffusor), you have something pretty special. at least for a small to = mid sized=20 room. they do make excellent monitors for recording as there is no = appreciable=20 group delay or phase shift over the range of 150 to 30KHz (!). they can = reproduce a square wave. the number of speakers ever made that can, can = be=20 counted on one hand.

if=20 i could get a bit more extension at the low end of the manger, it would = help me=20 with the crossover to the woofer=E2=80=A6 i want as little woofer = output as possible=20 mixed in with the manger. so i put the woofers on the sides of the = baffle, with=20 an electronic crossover (18dB/octave). this will be steeper in practice = with=20 the mechanical crossover of the baffle added in=E2=80=A6 also, i can = use the back wall=20 as a boundary reinforcement, to get a boost in the very low = frequencies. this=20 allows use of smaller woofers (2 of them). but the fact is the manger = starts to=20 crap out at 400 Hz. and X max is 2mm. they are easy to blow up, and = crazy=20 expensive. we have had a great deal of experience with them at = silbatone.

so, back to the current amplifier. i have made one using an 807 beam = tetrode.=20 it drives the manger safely to 100 Hz, and drops off. at the top, i get = a 3dB=20 rise in output up around 9KHz with the amp, which flattens out when the = diffusor is installed. it=E2=80=99s a touch dull with the regular amps. = i=E2=80=99ve been=20 listening to it full range for a few months now and it is wonderful. a = good mix=20 of compromises. the diffusor was designed by MJ Chung. it works very = nicely. no=20 more laser beam.

but this isn=E2=80=99t the only thing i am working on=E2=80=A6 i = think the most useful place=20 to use a current amp is on compression drivers. the big advantage now = shifts to=20 the high frequency end of things=E2=80=A6 because of mass roll off, = many compression=20 drivers, especially older ones, are limited to a fundamental range of = about 6=20 to 12 KHz. think of a WE555 or an altec 288. modern drivers have wacky = tricks=20 to extend the range by use of resonance and peaking. it has never = impressed me=20 as a sound approach. the classic approach was equalizing the driver and = using a=20 super tweeter. a current amp offers a middle way. the output rises with = impedance. the amp equalizes the output. it is very natural and not = anywhere as=20 harsh as what you get with the modern beryllium peaking types. i have = only=20 heard this on a an altec 288A. but plan to test out some things soon on = the=20 WE555 and WE594. more on that, later. the real interest for me is with = full=20 range horns. and drivers like the WE555. the vitavox low resonance = freq.=20 compression drivers are also very interesting to me.

obviously, if you are into =E2=80=9Cfull range=E2=80=9D drivers, = current amps are something=20 to check out. by the way, nelson pass has been into this for some time. = way=20 longer than me. he has a bunch of really interesting stuff on his = website along=20 these lines. i do have to control my gag reflex when it comes to = lowthers, but=20 many people like them. a current amp could (nothing can save those = pieces of=20 shit) help=E2=80=A6?

here is the 807 current amp design adapted for 2A3s. i have = substituted more=20 common tubes than i used. i can recommend the 2A3 EH (made in russia), = but=20 6B4Gs or any of the extended family would do=E2=80=A6 or even a 6AV5 or = 6550 could be=20 crowbarred in there. i used one electron output trannies for this test = and they=20 didn=E2=80=99t disappoint. you can use whatever you can get=E2=80=A6 = fun, and interesting.

 

 

addendum!

after a great deal of trouble driving the output stage with the = current=20 feedback driver stage shown above, i had to back up and get some = help=E2=80=A6 2 quick=20 conversations with morgan jones and frank bl=C3=B6hbaum (at etf) helped = enormously.=20 i blew up a bunch of fancy depletion mode mos, and normal run of the = mill=20 hexfet enhancement mode mosfets too. it was hard to see what the = failure=20 mechanism was (morgan was extolling the virtues of inexpensive digital=20 oscilloscopes for the ability to record events=E2=80=A6 i guess now i = have one on my=20 christmas wish list). it eventually turned out to be the gate charge = and the=20 extremely high impedance of the gM amp (the C3g stage). you learn = something new=20 every day. i had diodes and up to 5k gate stopper. boom. especially on = big=20 transients. i ended up using an IRF730 with a 10k gate stopper (!), a = 12 volt=20 zener from gate to source, and a 100 ohm source resistor in order to = make it=20 reliable. but the performance is affected. the much lower C in of the = IXCP45MS=20 allowed a large amount of current feedback (58 dB) with relatively = modest=20 compensation. the much larger value of input C on a hexfet changed = everything.=20 it was much harder to manage it without oscillation. i ended up = increasing the=20 compensation cap to 420pF! it had been 20p. and it is still just stable = at=20 clipping=E2=80=A6 i will work on making the fancy mos more reliable. = while this=20 measures and sounds excellent, it can be better. it makes me appreciate = tubes=20 all the more.

i switched to a submini tube as a cathode follower (because a solder = lead=20 tube fit under the chassis and i didn=E2=80=99t need to drill any more = holes) and=20 everything was perfectly stable with much less compensation. it is so = easy to=20 compensate tubes, at least if you know them=E2=80=A6 but the insertion = loss was 50=20 volts! the mos dropped 5. my 250 volts of swing became 200 just like = that.=20 tubes just don=E2=80=99t have the transconductance to make really good = simple buffers.=20 they need help. they sound good, don=E2=80=99t get me wrong, but solid = state does=20 buffers without losing so much level. at line level, who cares. but for = lots of=20 volts, they eat up swing.

so back to the mosfets. i have been compensating the driver stage by = using a=20 shunt cap to ground from the C3g plate. this is supposed to help define = the=20 pole associated with this stage and prevent it from screwing with the = other=20 poles=E2=80=A6 particularly the buffer and opt tube. i have switched to = using a=20 =E2=80=9Cmiller=E2=80=9D compensation scheme (basically the cap goes = from plate to grid)=20 instead and everything works much better=E2=80=A6 why throw bandwidth = away for=20 stability without getting anything for it? miller effect is negative = feedback.=20 you get the compensation needed AND distortion is reduced in the = attenuation=20 band. now, even the fancy depletion mos is stable and i don=E2=80=99t = need more than=20 22p of C.

i meant to drive a 50 tube and test something i have wanted to for = years.=20 50=E2=80=B2s are tough to drive because they have a largely variable = input admittance.=20 for this reason, they expressly do not recommend fixed bias and most of = the=20 amps you will ever find that used them were transformer coupled to the = grid=20 (low impedance) and self-biased. the grid current varies from negative = to=20 positive quite a bit from cutoff to saturation. with fixed bias, there = is=20 nothing to prevent runaway if the bias shifts due to clipping or = asymmetrical=20 waveforms of large amplitude (drums and synth pulses from dance = music=E2=80=A6). i want=20 to push the envelope and see what i can get away with. the problem is = the=20 resistor connecting the 50 grid to the source of bias: for cap = coupling, this=20 is usually on the order of 100k to 500k. this allows a cap of = reasonable size=20 to be used, typically .047uF to .47uF, for low frequency performance. = this=20 maximum requirement is always reduced for fixed bias=E2=80=A6 an EL34 = in fixed bias=20 shouldn=E2=80=99t have it=E2=80=99s Rg exceed 50K. most amp = manufacturers have no clue. this is=20 a major source of failure in the musical instrument amp business. a 50k = grid=20 resistor would need a minimum of 1uF and probably more like 2uF for = anything=20 quality in an RC coupled fixed bias amp, if you wanted a reasonable low = frequency performance. that is a big and expensive part.

i have always got around it by direct coupling. no cap is the best = cap. but i=20 wanted to know just what the range was=E2=80=A6 and my contrary nature = began to tug at=20 me: who says it can=E2=80=99t be done! so i want to make a reliable cap = coupled fixed=20 biased 50 amp. driven with metal pentodes and very high performance. = fixed bias=20 gives a bit more power. when you are talking about a 4 watt amp, an = extra watt=20 doesn=E2=80=99t hurt.

so here it is. after a bunch of head scratching, it works fine. not = only is=20 it fixed bias, but cap coupled. it sounds fabulous as it = should=E2=80=A6 it makes just=20 under 6 watts at 2% thd. almost 1 and a half more watts. i even tested = an=20 electrolytic coupling cap (4.7uF 400V, bypassed with a silver mica = .001) and it=20 still sounds and tests excellent. look, i just can=E2=80=99t help = it=E2=80=A6 tell me i can=E2=80=99t=20 or shouldn=E2=80=99t and i just have to try. panasonic won again, by = the way, over=20 sprague and illinois. but now i am using a 2uF film and foil. i worry = about=20 such big AC swings across an electrolytic=E2=80=A6 if it = weren=E2=80=99t such a rare output=20 tube, i would let it rip. the grid resistor is 12K. i started out with = 5k (and=20 the 4.7uF electrolytic). the drop across the resistor at clipping is = 0.4 volts=E2=80=A6=20 not enough to worry about. at 50k, this would be 3 volts less bias. = 100K would=20 be 5 or 6. you see the problem. the grid current and the voltage drop = across=20 the grid resistor would destroy the tube.

and=20 finally, here is a look at the top. now i have to make the other = channel=E2=80=A6 bleh!=20 i need an intern. more soon=E2=80=A6

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=20 =
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margin-bottom: 0px; margin-left: 1.5em; } li > ol { margin-bottom: 0px; margin-left: 1.5em; } dt { font-weight: bold; } dd { margin: 0px 1.5em 1.5em; } b { font-weight: bold; } strong { font-weight: bold; } dfn { font-style: italic; } cite { font-style: italic; } em { font-style: italic; } i { font-style: italic; } blockquote { margin: 0px 1.5em; } address { margin: 0px 0px 1.5em; } pre { background: rgb(238, 238, 238); padding: 1.6em; line-height: 1.6; = overflow: auto; font-family: "Courier 10 Pitch", Courier, monospace; = font-size: 1.5rem; margin-bottom: 1.6em; max-width: 100%; } code { font: 15px/normal Monaco, Consolas, "Andale Mono", "DejaVu Sans Mono", = monospace; font-size-adjust: none; font-stretch: normal; } kbd { font: 15px/normal Monaco, Consolas, "Andale Mono", "DejaVu Sans Mono", = monospace; font-size-adjust: none; font-stretch: normal; } tt { font: 15px/normal Monaco, Consolas, "Andale Mono", "DejaVu Sans Mono", = monospace; font-size-adjust: none; font-stretch: normal; } var { font: 15px/normal Monaco, Consolas, "Andale Mono", "DejaVu Sans Mono", = monospace; font-size-adjust: none; font-stretch: normal; } abbr { border-bottom-color: rgb(102, 102, 102); border-bottom-width: 1px; = border-bottom-style: dotted; cursor: help; } acronym { border-bottom-color: rgb(102, 102, 102); border-bottom-width: 1px; = border-bottom-style: dotted; cursor: help; } mark { background: rgb(255, 249, 192); text-decoration: none; } ins { background: rgb(255, 249, 192); text-decoration: none; } sup { height: 0px; line-height: 0; font-size: 75%; vertical-align: baseline; = position: relative; } sub { height: 0px; line-height: 0; font-size: 75%; vertical-align: baseline; = position: relative; } sup { bottom: 1ex; } sub { top: 0.5ex; } small { font-size: 75%; } big { font-size: 125%; } figure { margin: 0px; } table { margin: 0px 0px 1.5em; width: 100%; } th { font-weight: bold; } img { height: auto; max-width: 100%; } button { margin: 0px; font-size: 100%; vertical-align: baseline; } input { margin: 0px; font-size: 100%; vertical-align: baseline; } select { margin: 0px; font-size: 100%; vertical-align: baseline; } textarea { margin: 0px; font-size: 100%; vertical-align: baseline; } button { line-height: normal; } input { line-height: normal; } button { background: rgb(230, 230, 230); border-width: 1px; border-style: solid; = border-color: rgb(204, 204, 204) rgb(204, 204, 204) rgb(187, 187, 187); = padding: 0.6em 1em 0.4em; border-radius: 3px; border-image: none; color: = rgba(0, 0, 0, 0.8); line-height: 1; font-size: 1.2rem; cursor: pointer; = box-shadow: inset 0px 1px 0px rgba(255,255,255,0.5), inset 0px 15px 17px = rgba(255,255,255,0.5), inset 0px -5px 12px rgba(0,0,0,0.05); = text-shadow: 0px 1px 0px rgba(255,255,255,0.8); -webkit-appearance: = button; } html input[type=3D'button'] { background: rgb(230, 230, 230); border-width: 1px; border-style: solid; = border-color: rgb(204, 204, 204) rgb(204, 204, 204) rgb(187, 187, 187); = padding: 0.6em 1em 0.4em; border-radius: 3px; border-image: none; color: = rgba(0, 0, 0, 0.8); line-height: 1; font-size: 1.2rem; cursor: pointer; = box-shadow: inset 0px 1px 0px rgba(255,255,255,0.5), inset 0px 15px 17px = rgba(255,255,255,0.5), inset 0px -5px 12px rgba(0,0,0,0.05); = text-shadow: 0px 1px 0px rgba(255,255,255,0.8); -webkit-appearance: = button; } input[type=3D'reset'] { background: rgb(230, 230, 230); border-width: 1px; border-style: solid; = border-color: rgb(204, 204, 204) rgb(204, 204, 204) rgb(187, 187, 187); = padding: 0.6em 1em 0.4em; border-radius: 3px; border-image: none; color: = rgba(0, 0, 0, 0.8); line-height: 1; font-size: 1.2rem; cursor: pointer; = box-shadow: inset 0px 1px 0px rgba(255,255,255,0.5), inset 0px 15px 17px = rgba(255,255,255,0.5), inset 0px -5px 12px rgba(0,0,0,0.05); = text-shadow: 0px 1px 0px rgba(255,255,255,0.8); -webkit-appearance: = button; } input[type=3D'submit'] { background: rgb(230, 230, 230); border-width: 1px; border-style: solid; = border-color: rgb(204, 204, 204) rgb(204, 204, 204) rgb(187, 187, 187); = padding: 0.6em 1em 0.4em; border-radius: 3px; border-image: none; color: = rgba(0, 0, 0, 0.8); line-height: 1; font-size: 1.2rem; cursor: pointer; = box-shadow: inset 0px 1px 0px rgba(255,255,255,0.5), inset 0px 15px 17px = rgba(255,255,255,0.5), inset 0px -5px 12px rgba(0,0,0,0.05); = text-shadow: 0px 1px 0px rgba(255,255,255,0.8); -webkit-appearance: = button; } button:hover { border-color: rgb(204, 204, 204) rgb(187, 187, 187) rgb(170, 170, 170); = box-shadow: inset 0px 1px 0px rgba(255,255,255,0.8), inset 0px 15px 17px = rgba(255,255,255,0.8), inset 0px -5px 12px rgba(0,0,0,0.02); } html input[type=3D'button']:hover { border-color: rgb(204, 204, 204) rgb(187, 187, 187) rgb(170, 170, 170); = box-shadow: inset 0px 1px 0px rgba(255,255,255,0.8), inset 0px 15px 17px = rgba(255,255,255,0.8), inset 0px -5px 12px rgba(0,0,0,0.02); } input[type=3D'reset']:hover { border-color: rgb(204, 204, 204) rgb(187, 187, 187) rgb(170, 170, 170); = box-shadow: inset 0px 1px 0px rgba(255,255,255,0.8), inset 0px 15px 17px = rgba(255,255,255,0.8), inset 0px -5px 12px rgba(0,0,0,0.02); } input[type=3D'submit']:hover { border-color: rgb(204, 204, 204) rgb(187, 187, 187) rgb(170, 170, 170); = box-shadow: inset 0px 1px 0px rgba(255,255,255,0.8), inset 0px 15px 17px = rgba(255,255,255,0.8), inset 0px -5px 12px rgba(0,0,0,0.02); } button:focus { border-color: rgb(170, 170, 170) rgb(187, 187, 187) rgb(187, 187, 187); = box-shadow: inset 0px -1px 0px rgba(255,255,255,0.5), inset 0px 2px 5px = rgba(0,0,0,0.15); } html input[type=3D'button']:focus { border-color: rgb(170, 170, 170) rgb(187, 187, 187) rgb(187, 187, 187); = box-shadow: inset 0px -1px 0px rgba(255,255,255,0.5), inset 0px 2px 5px = rgba(0,0,0,0.15); } input[type=3D'reset']:focus { border-color: rgb(170, 170, 170) rgb(187, 187, 187) rgb(187, 187, 187); = box-shadow: inset 0px -1px 0px rgba(255,255,255,0.5), inset 0px 2px 5px = rgba(0,0,0,0.15); } input[type=3D'submit']:focus { border-color: rgb(170, 170, 170) rgb(187, 187, 187) rgb(187, 187, 187); = box-shadow: inset 0px -1px 0px rgba(255,255,255,0.5), inset 0px 2px 5px = rgba(0,0,0,0.15); } button:active { border-color: rgb(170, 170, 170) rgb(187, 187, 187) rgb(187, 187, 187); = box-shadow: inset 0px -1px 0px rgba(255,255,255,0.5), inset 0px 2px 5px = rgba(0,0,0,0.15); } html input[type=3D'button']:active { border-color: rgb(170, 170, 170) rgb(187, 187, 187) rgb(187, 187, 187); = box-shadow: inset 0px -1px 0px rgba(255,255,255,0.5), inset 0px 2px 5px = rgba(0,0,0,0.15); } input[type=3D'reset']:active { border-color: rgb(170, 170, 170) rgb(187, 187, 187) rgb(187, 187, 187); = box-shadow: inset 0px -1px 0px rgba(255,255,255,0.5), inset 0px 2px 5px = rgba(0,0,0,0.15); } input[type=3D'submit']:active { border-color: rgb(170, 170, 170) rgb(187, 187, 187) rgb(187, 187, 187); = box-shadow: inset 0px -1px 0px rgba(255,255,255,0.5), inset 0px 2px 5px = rgba(0,0,0,0.15); } input[type=3D'checkbox'] { padding: 0px; box-sizing: border-box; } input[type=3D'radio'] { padding: 0px; box-sizing: border-box; } input[type=3D'search'] { box-sizing: content-box; -webkit-appearance: textfield; = -webkit-box-sizing: content-box; -moz-box-sizing: content-box; } input[type=3D'text'] { border-radius: 3px; border: 1px solid rgb(204, 204, 204); border-image: = none; color: rgb(102, 102, 102); } input[type=3D'email'] { border-radius: 3px; border: 1px solid rgb(204, 204, 204); border-image: = none; color: rgb(102, 102, 102); } input[type=3D'url'] { border-radius: 3px; border: 1px solid rgb(204, 204, 204); border-image: = none; color: rgb(102, 102, 102); } input[type=3D'password'] { border-radius: 3px; border: 1px solid rgb(204, 204, 204); border-image: = none; color: rgb(102, 102, 102); } input[type=3D'search'] { border-radius: 3px; border: 1px solid rgb(204, 204, 204); border-image: = none; color: rgb(102, 102, 102); } textarea { border-radius: 3px; border: 1px solid rgb(204, 204, 204); border-image: = none; color: rgb(102, 102, 102); } input[type=3D'text']:focus { color: rgb(17, 17, 17); } input[type=3D'email']:focus { color: rgb(17, 17, 17); } input[type=3D'url']:focus { color: rgb(17, 17, 17); } input[type=3D'password']:focus { color: rgb(17, 17, 17); } input[type=3D'search']:focus { color: rgb(17, 17, 17); } textarea:focus { color: rgb(17, 17, 17); } input[type=3D'text'] { padding: 3px; } input[type=3D'email'] { padding: 3px; } input[type=3D'url'] { padding: 3px; } input[type=3D'password'] { padding: 3px; } input[type=3D'search'] { padding: 3px; } textarea { width: 98%; overflow: auto; padding-left: 3px; vertical-align: top; } a { color: rgb(121, 203, 94); text-decoration: none; } a:visited { =09 } a:hover { text-decoration: underline; } a:focus { text-decoration: underline; } a:active { text-decoration: underline; } .alignleft { margin-right: 1.5em; float: left; display: inline; } .alignright { margin-left: 1.5em; float: right; display: inline; } .aligncenter { margin: 0px auto; clear: both; display: block; } .screen-reader-text { position: absolute !important; clip: rect(1px, 1px, 1px, 1px); } .screen-reader-text:hover { padding: 15px 23px 14px; border-radius: 3px; left: 5px; top: 5px; = width: auto; height: auto; color: rgb(33, 117, 155); line-height: = normal; font-size: 14px; font-weight: bold; text-decoration: none; = display: block; z-index: 100000; clip: auto !important; box-shadow: 0px = 0px 2px 2px rgba(0,0,0,0.6); background-color: rgb(241, 241, 241); } .screen-reader-text:active { padding: 15px 23px 14px; border-radius: 3px; left: 5px; top: 5px; = width: auto; height: auto; color: rgb(33, 117, 155); line-height: = normal; font-size: 14px; font-weight: bold; text-decoration: none; = display: block; z-index: 100000; clip: auto !important; box-shadow: 0px = 0px 2px 2px rgba(0,0,0,0.6); background-color: rgb(241, 241, 241); } .screen-reader-text:focus { padding: 15px 23px 14px; border-radius: 3px; left: 5px; top: 5px; = width: auto; height: auto; color: rgb(33, 117, 155); line-height: = normal; font-size: 14px; font-weight: bold; text-decoration: none; = display: block; z-index: 100000; clip: auto !important; box-shadow: 0px = 0px 2px 2px rgba(0,0,0,0.6); background-color: rgb(241, 241, 241); } .clear::before { display: table; content: ""; } .clear::after { display: table; content: ""; } [class*=3D'content']::before { display: table; content: ""; } [class*=3D'content']::after { display: table; content: ""; } [class*=3D'site']::before { display: table; content: ""; } [class*=3D'site']::after { display: table; content: ""; } .clear::after { clear: both; } [class*=3D'content']::after { clear: both; } [class*=3D'site']::after { clear: both; } .sticky { =09 } .hentry { margin: 0px 0px 1.5em; } .byline { display: none; } .updated { display: none; } .single .byline { display: inline; } .group-blog .byline { display: inline; } .page-content { margin: 1.5em 0px 0px; } .entry-content { margin: 1.5em 0px 0px; } .entry-summary { margin: 1.5em 0px 0px; } .page-links { margin: 0px 0px 1.5em; clear: both; } .blog .format-aside .entry-title { display: none; } .archive .format-aside .entry-title { display: none; } .page-content img.wp-smiley { padding: 0px; border: currentColor; border-image: none; margin-top: = 0px; margin-bottom: 0px; } .entry-content img.wp-smiley { padding: 0px; border: currentColor; border-image: none; margin-top: = 0px; margin-bottom: 0px; } .comment-content img.wp-smiley { padding: 0px; border: currentColor; border-image: none; margin-top: = 0px; margin-bottom: 0px; } .wp-caption { border: 1px solid rgb(204, 204, 204); border-image: none; = margin-bottom: 1.5em; max-width: 100%; } .wp-caption img[class*=3D'wp-image-'] { margin: 1.2% auto 0px; display: block; max-width: 98%; } .wp-caption-text { text-align: center; } .wp-caption .wp-caption-text { margin: 0.8em 0px; } .site-main .gallery { margin-bottom: 1.5em; } .gallery-caption { =09 } .site-main .gallery a img { border: currentColor; border-image: none; height: auto; max-width: 90%; } .site-main .gallery dd { margin: 0px; } .site-main .gallery-columns-4 .gallery-item { =09 } .site-main .gallery-columns-4 .gallery-item img { =09 } embed { max-width: 100%; } iframe { max-width: 100%; } object { max-width: 100%; } .site-main [class*=3D'navigation'] { margin: 0px 0px 1.5em; overflow: hidden; } [class*=3D'navigation'] .nav-previous { width: 50%; float: left; } [class*=3D'navigation'] .nav-next { width: 50%; text-align: right; float: right; } .comment-content a { -ms-word-wrap: break-word; } .bypostauthor { =09 } .widget { margin: 0px 0px 1.5em; } .widget select { max-width: 100%; } .widget_search .search-submit { display: none; } .infinite-scroll .paging-navigation { display: none; } .infinite-scroll.neverending .site-footer { display: none; } .infinity-end.neverending .site-footer { display: block; } body { font-family: "Lato", Helvetica, Arial, sans-serif; } header#masthead { margin: auto; width: 1100px; } .site-branding { padding: 30px 0px; width: 40%; float: left; } h1.site-title a { margin: 20px 0px; color: rgb(72, 72, 72); font-size: 36px; font-weight: = bold; text-decoration: none; display: block; } .logo-container { top: -15px; margin-bottom: -15px; position: relative; } .main_logo { display: block; max-height: 125px; max-width: 360px; } @media screen and (max-width:360px) { .main_logo { height: auto; display: block; max-width: 320px; } } .main-navigation { background: rgb(234, 234, 234); width: 100%; clear: both; = margin-bottom: 30px; float: left; display: block; } #nav-container { margin: auto; width: 1100px; } .main-navigation ul { list-style: none; margin: 0px; padding-left: 0px; } .main-navigation li { float: left; position: relative; } .main-navigation a { padding: 20px; color: rgb(85, 85, 85); font-weight: bold; = text-decoration: none; display: block; } .main-navigation a:hover { background: rgb(243, 243, 243); padding-top: 16px; border-top-color: = rgb(0, 204, 153); border-top-width: 4px; border-top-style: solid; } .main-navigation .current_page_item > a { background: rgb(221, 221, 221); padding-top: 17px; border-top-color: = rgb(34, 34, 34); border-top-width: 3px; border-top-style: solid; } .main-navigation ul ul { background: rgb(243, 243, 243); left: 0px; top: 4em; float: left; = display: none; position: absolute; z-index: 99999; } .main-navigation ul ul ul { left: 100%; top: 0px; } .main-navigation ul ul a { padding: 8px 20px; width: 200px; color: rgb(85, 85, 85); font-size: = 14px; font-weight: 400; } .main-navigation ul ul a:hover { background: rgb(51, 51, 51); padding: 8px 20px; color: rgb(238, 238, = 238); border-top-color: currentColor; border-top-width: medium; = border-top-style: none; } .main-navigation ul ul li { =09 } .main-navigation li:hover > a { background: rgb(243, 243, 243); padding-top: 16px; border-top-color: = rgb(0, 204, 153); border-top-width: 4px; border-top-style: solid; } .main-navigation ul ul li:hover > a { background: rgb(51, 51, 51); padding: 8px 20px; color: rgb(238, 238, = 238); border-top-color: currentColor; border-top-width: medium; = border-top-style: none; } .main-navigation ul ul :hover > a { =09 } .main-navigation ul ul a:hover { =09 } .main-navigation ul li:hover > ul { display: block; } .main-navigation li.current_page_item a { =09 } .main-navigation li.current-menu-item a { =09 } .menu-toggle { display: none; cursor: pointer; } @media screen and (max-width:600px) { .menu-toggle { display: block; } .main-navigation.toggled .nav-menu { display: block; } .main-navigation ul { display: none; } } #content { margin: auto; width: 1100px; } #primary { background: rgb(247, 247, 247); padding: 0px 15px 15px; width: 64%; = float: left; } .primary-full { margin: auto auto 100px; width: 100% !important; float: none; } #secondary { background: rgb(255, 255, 255); padding: 10px; width: 29%; float: = right; } h1.page-title { background: rgb(234, 234, 234); padding: 10px; font-weight: bold; = margin-top: 15px; border-bottom-color: rgb(221, 221, 221); = border-bottom-width: 1px; border-bottom-style: solid; } h1.entry-title a { color: rgb(102, 102, 102); font-size: 40px; } h1.entry-title { color: rgb(102, 102, 102); font-size: 40px; } h1.entry-title a:hover { color: rgb(121, 203, 94); text-decoration: none; } .entry-meta { background: rgb(241, 241, 241); padding: 3px 5px; font-size: 12px; } .entry-meta a { color: rgb(153, 153, 153); } span.comments-link { float: right; } #featured_image { margin: 20px 10px 15px 3px; width: 150px; clear: left; float: left; } #featured_image img { width: 125px; box-shadow: 0px 3px 3px -3px #333; } .entry-content { margin-top: 19px; } article.post { background: url("images/divider.png") repeat-x left bottom; = padding-bottom: 50px; } entry-meta .comments-link { float: right; } h1.widget-title { background: url("images/divider.png") repeat-x left bottom; color: = rgb(153, 153, 153); text-transform: uppercase; padding-top: 10px; = padding-bottom: 20px; font-family: "Lucida Grande", "Lucida Sans = Unicode", "Lucida Sans", "DejaVu Sans", Verdana, sans-serif; font-size: = 12px; margin-bottom: 15px; } .widget > ul { list-style: none; margin-left: 2px; } .widget ul li { border-bottom-color: rgb(238, 238, 238); border-bottom-width: 1px; = border-bottom-style: solid; } .widget a { padding: 3px 0px; color: rgb(102, 102, 102); display: inline-block; } .widget a:hover { color: rgb(121, 203, 94); } .widget ul ul li { border-bottom-color: currentColor; border-bottom-width: medium; = border-bottom-style: none; } #colophon { background: rgb(255, 255, 255); padding: 10px; width: 98%; = border-top-color: rgb(204, 204, 204); border-top-width: 1px; = border-top-style: solid; } #footer-container { margin: auto; width: 1100px; } #footertext { margin-bottom: 20px; float: left; } .site-info { width: 49%; font-size: 14px; float: left; } #footer-navigation { width: 49%; text-align: right; float: right; } #footer-navigation ul { 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0, 0); padding: 10px 5px; color: rgb(17, 170, 0); } article table tr:nth-child(2n) { background: rgb(238, 238, 238); border-bottom-color: rgb(221, 221, = 221); border-bottom-width: 1px; border-bottom-style: solid; } article table tr:nth-child(2n+1) { background: rgb(234, 234, 234); border-bottom-color: rgb(221, 221, = 221); border-bottom-width: 1px; border-bottom-style: solid; } article table td { border-bottom-color: rgb(221, 221, 221); border-bottom-width: 1px; = border-bottom-style: solid; } article ul ul { list-style: circle; } article ul ul ul { =09 } article ol ol { list-style: lower-roman; } article ol ol ol { list-style: lower-alpha; } h2.comments-title { text-transform: uppercase; font-size: 26px; margin-bottom: 50px; } .comment-list { list-style: none; margin: 0px; padding: 0px; } li.comment { clear: both; display: block; } .comment-meta { width: 125px; text-align: center; clear: none; margin-top: 20px; = margin-right: 10px; float: left; display: inline-block; } .comment-meta 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