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November 3, 2016 / consort3

Index

I am always tweaking this blog. Unfortunately I tend to edit existing posts, so it is worth re-checking pages you are interested in, if you have visited before.

November 3, 2016 / consort3

Some History of technology

Where it began, for our purposes, little known Elizabethan physician Gilbert

http://www.edn.com/electronics-blogs/all-things-measured/4441206/The-actual-father-of-electricity

Thought Morse invented the Telegraph? Francis Ronalds invented it in 1816. Unfortunately no-one wanted it.

http://www.theiet.org/resources/library/archives/biographies/ronalds.cfm

It has been 150 years since Maxwell presented his equations:

http://spectrum.ieee.org/telecom/wireless/the-long-road-to-maxwells-equations

The history of Maxwells equations

http://rsta.royalsocietypublishing.org/content/366/1871/1849

My friend has summarised them here:

Maxwells Equ

Heaviside’s conflict with Preece “Theory versus practice”

83Hunt

A worthy biography of Heaviside is “Oliver Heaviside”   by Paul Nahin

Another 150th anniversary George Boole. Boole like Heaviside was self -taught.

http://www.irishtimes.com/news/science/how-george-boole-s-zeroes-and-ones-changed-the-world-1.2014673

http://blogs.scientificamerican.com/guest-blog/the-bicentennial-of-george-boole-the-man-who-laid-the-foundations-of-the-digital-age/

There is more to Boole than Boolean

http://georgeboole.com/boole/

Interesting article about a contemporary of Maxwell and Boole, namely Babbage

http://blog.plan28.org/2014/11/babbages-language-of-thought.html?m=1

More detail on the invention

http://athena.union.edu/~hemmendd/Courses/cs80/an-engine.pdf

Article about Babbages friend, the first programmer, Ada

http://www.leftlion.co.uk/articles.cfm/title/the-dilettante-society–augusta-ada-lovelace/id/7225

Great piece on Ada and Babbage by Wolfram

http://blog.stephenwolfram.com/2015/12/untangling-the-tale-of-ada-lovelace/#

Another contemporary British invention, the Bessemer process

http://hackaday.com/2015/04/07/retrotechtacular-the-bessemer-converter/#comment-2518

A quartet of Victorian engineers beginning with B

http://en.wikipedia.org/wiki/Isambard_Kingdom_Brunel

I had to make it a quintet of people beginning with B. Thomas Bayes came up with Bayes’ Theorem, a basic law of probability governing how to modify one’s beliefs when new evidence arrives. Are you Bayesian or Boolean?

In the Boolean worldview, the world is organised into basic situations such as Sydney being north of Melbourne. Such situations are facts. Truth is correspondence to facts. That is, if a belief matches a fact, it is objectively true; if not, it is objectively false. If you and I disagree, one of us must be right, the other wrong; and if I know I’m right, then I know you’re wrong. Totally wrong.

In the Bayesian worldview, beliefs are not simply true or false, but more or less probable. That is, we can be more or less confident that they are true, given how they relate to our other beliefs and how confident we are in them. If you and I disagree about the cause of climate change, it is not a matter of me being wholly right and you being wholly wrong, but about the differing levels of confidence we have in a range of hypotheses. Dare I say it, shades of grey!

http://www.york.ac.uk/depts/maths/histstat/bayesholland.pdf

Good explantion of Bayes Theorem

http://blogs.scientificamerican.com/cross-check/bayes-s-theorem-what-s-the-big-deal/

Another question, are you Babylonian or Balkan in your Philosophy? Feynman used to say that there were two kinds of Physicists, the Babylonians and the Greeks. He was referring to the opposing philosophies of those ancient civilizations. The Babylonians made western civilization’s first great strides in understanding numbers and equations, and in geometry.
Yet it was the later Greeks – in particular Thales, Pythagoras, and Euclid – whom we credit with inventing Mathematics. This is because the Babylonians cared only whether or not a method of calculation worked – that is, adequately described a real physical situation – and not whether it was exact, or fitted into any greater logical system. Thales and his Greek followers, on the other hand, invented the idea of theorem and proof – and required that for a statement to be considered thorough, it had to be an exact logical consequence of a system of explicitly stated axioms or assumptions. To put it simply, the Babylonians focused on phenomena, the Greeks on the underlying order.”
Nevertheless, the existence of Babylonian method has actually a deep sense: axiomatic approach can be formulated only if satisfactory number of facts, needed for the generalization, is accumulated.

Interesting reflections on Feynman:

http://www.planetanalog.com/author.asp?section_id=3049&doc_id=563898

Comments on the Feynman minority report of the shuttle disaster, interesting blog BTW

Feynman’s Minority Report and Top-Down Design | The Multidisciplinarian

How ARM happened

http://www.bloomberg.com/bw/articles/2014-02-24/the-unlikely-tale-of-how-arm-came-to-rule-the-world#p1

More on the history of ARM

http://community.arm.com/groups/processors/blog/2015/04/22/a-brief-history-of-arm-part-1

http://armdevices.net/

Arm 25th anniversary

http://blog.visual6502.org/2015/11/the-visual-arm1.html

350 years of scientific publishing. The Royal Society

http://www.theguardian.com/science/grrlscientist/2015/mar/06/royal-society-celebrates-350-years-of-scientific-publishing

Contemporary work showing interest in Science from the nobility

http://www.tor.com/2016/09/21/discover-the17th-century-science-fiction-of-duchess-margaret-cavendish/

A good summary of the basics of electronics:

http://lcamtuf.coredump.cx/electronics/

Germanium is making a comeback:

http://forum.eetasia.com/BLOG_ARTICLE_22875.HTM

The hacker hacked

http://aeon.co/magazine/technology/how-yuppies-hacked-the-original-hacker-ethos/

The history of spreadsheets or the first killer app:

http://www.theguardian.com/commentisfree/2016/jan/03/visicalc-software-first-killer-app-john-naughton

Unsung computing hero Douglas Englebart

http://media.bemyapp.com/douglas-engelbart/?utm_source=bemyapp&utm_medium=ycombin&utm_content=&utm_campaign=media

The engineering approach to innovation in science

http://serious-science.org/principles-of-invention-3679

More on this idea

https://en.wikipedia.org/wiki/TRIZ

Review of TRIZ for dummies

https://www.amazon.co.uk/gp/reader/1119107474/?tag=foxebook-21#reader_1119107474

How to engineer serendipity

http://time.com/3951029/engineer-serendipity/

Divisions of time

http://curious.astro.cornell.edu/physics/161-our-solar-system/the-earth/day-night-cycle/761-why-is-a-day-divided-into-24-hours-intermediate

Talking astronomy, where Jocelyn Bell discovered the Quasar. She, Lise Meitner and Rosalind Franklin are more famous female scientists than if they were Nobel Laureates:

http://www.theregister.co.uk/2016/02/12/geeks_guide_to_britain_mullard_radio_astronomy_observatory/?page=1

Talking of Rosalind Franklin here is the story of the how the structure of DNA was discovered:

http://blogs.scientificamerican.com/the-curious-wavefunction/the-structure-of-dna-61-years-later-how-they-did-it/

Lest I be accused of eurocentrism in the history of science

https://thonyc.wordpress.com/2015/09/30/political-correctness-and-the-history-of-science/

Sorry its creeping back in. Horrocks

https://thonyc.wordpress.com/2009/11/24/an-important-anniversary-in-the-history-of-science/

Restoring the balance, Martin Bernal and Black Athena

http://www.news.cornell.edu/stories/2007/10/martin-bernal-revisits-black-athena-controversy-lecture

https://aeon.co/ideas/arabic-translators-did-far-more-than-just-preserve-greek-philosophy

More balance, Sanskrit and the periodic table

http://swarajyamag.com/ideas/sanskrit-and-mendeleevs-periodic-table-of-elements/

Erdos and the Egyptian fraction problem:

https://www.simonsfoundation.org/uncategorized/new-erdos-paper-solves-egyptian-fraction-problem/

Computers can lead to experiments not being repeatable:

http://gizmodo.com/how-computers-broke-science-and-what-we-can-do-to-fix-i-1741649207

The future of the professions

http://www.oxfordtoday.ox.ac.uk/opinion/future-professions-0

Philosophy and work/life balance

https://www.brainpickings.org/2015/08/10/leisure-the-basis-of-culture-josef-pieper/

Lord Nuffields philanthropy

http://www.oxfordtoday.ox.ac.uk/features/humble-philanthropist-how-modest-multimillionaire-lord-nuffield-saved-many-oxford-college

Babylonian maths more advanced than we previously thought:

https://www.inverse.com/article/10792-ancient-babylonians-used-calculus-to-track-jupiter-1-400-years-before-anyone-else

http://www.maa.org/press/periodicals/convergence/the-best-known-old-babylonian-tablet

On the other hand:

http://www.theatlantic.com/science/archive/2016/02/babylonians-scientists/462150/

The clock on most computers started theoretically on 1st Jan  1970. Someone has worked out when the clock on the Anti-Kythera mechanism started, for solar eclipses it is 12 May 205BC.

https://assets.documentcloud.org/documents/1386117/on-the-epoch-of-the-antikthera-mechansim.pdf

ancient-computer-lg

The age of enlightenment has become the age of entanglement

http://jods.mitpress.mit.edu/pub/enlightenment-to-entanglement

Newtons recipe for the Philosophers stone

http://www.livescience.com/54162-newton-recipe-for-philosophers-stone-rediscovered.html

The extraordinary career of William Dampier

https://scolarcardiff.wordpress.com/2016/05/16/william-dampier-pirate-navigator-naturalist-and-explorer/

Richard Hakluyt and his early travel book

http://publicdomainreview.org/2016/10/26/richard-hakluyt-and-early-english-travel/

The silicon revolution started at  Shockley Semiconductor in April 1956 at Santa Clara which was the year Shockley got the Nobel prize for Physics for inventing the transistor. However by 1957 a number of staff he had recruited left to join Fairchild. More here:

http://silicongenesis.stanford.edu/about.html

How Silicon Valley got the name in 1971:

http://www.computerhistory.org/atchm/who-named-silicon-valley/

Unfortunately, all those manufacturing plants in Silicon Valley have left a toxic legacy in the groundwater.

The is/ ought problem

https://en.wikipedia.org/wiki/Is%E2%80%93ought_problem

The above was written by Enlightenment philosopher David Hume who may have got some of his ideas from Buddism

http://www.alisongopnik.com/papers_alison/gopnik_humestudies_withtoc.pdf

Salvation by algorithm!

http://www.newstatesman.com/politics/uk/2016/09/salvation-algorithm-god-technology-and-new-21st-century-religions

A scientific look at religon

http://sciencereligionspectrum.org/blog-posts/edward-burnett-tylor-and-the-evolution-of-religion/

Smartphones and social media are supposed to connect us. What happens when we are so constantly connected that forget how to be alone?

http://nymag.com/selectall/2016/09/andrew-sullivan-technology-almost-killed-me.html

How information technology affects capitalism:

https://medium.com/mosquito-ridge/postcapitalism-and-the-city-6dda80bc201d#.uqgdt8usf

November 3, 2016 / consort3

Shakespeare Scrapbook

Another alliterative professor (see 741) was Ephraim Everitt who came up with the radical idea that Shakespeare had written more plays and suggested some. His idea was pooh-poohed at the time but these days there is more of an academic consensus that the bard wrote Edward III. Everitt also reckoned that the manuscript of Edmund Ironside was in Shakespeare’s own hand.

http://ericsams.org/index.php/on-shakespeare/essays-and-reviews/396-edmund-ironside-a-reappraisal

Well this is interesting. Kims FFP technique produced the following table:

shakespeare-phylogeny-tree

Which shows Edward III to be more like Marlowe than Shakespeare. Also interesting is that the  Henry VI part 2 and 3 plays are grouped with Marlowe, possible collaboration when they were both working for Stanley, but part 1 is elsewhere, possibly Nashe had some involvement. Dido, Queen of Carthage is also in the same area, might Shakespeare be the collaborator with Marlowe back in 1587. So keen is Shakespeare on the story of Dido, the Queen of Carthage,  that he mentions her four times in The Tempest, twice in Titus Andronicus, and once each in The Merchant of Venice2 Henry VI, Antony and CleopatraHamlet, and Romeo and Juliet.

One issue I have with Kims FFP technique is the spelling or lack of consistency in Shakespeares time:

http://blog.shakespearesworld.org/2016/01/20/ffor-heavens-sak-whi-wolde-a-pson-euer-spelle-yt-yt-waye/

Co-author with Marlowe of Henry VI ?

http://www.vox.com/culture/2016/11/4/13480052/shakespeare-marlowe-henry-vi

Another play to add to the canon?

http://www.independent.co.uk/arts-entertainment/theatre-dance/news/fake-shakespeare-play-double-falsehood-is-genuine-after-all-10167657.html

Amazing what people can derive from a few lines of Shakespeare

http://www.theatlantic.com/entertainment/archive/2015/01/by-heart-measure-for-measure/384252/

Shakespeare Hackfest

https://shkspr.mobi/blog/2014/12/shakespearean-hackfest/

Shakespeare as it would have been pronounced in 1600

http://www.youtube.com/watch?feature=player_embedded&v=gPlpphT7n9s

Translate your text to Shakespearean dialogue!

http://www.shmoop.com/shakespeare-translator/

Cumberbatch does Hamlet

https://theconversation.com/the-lure-of-hamlet-why-this-is-the-test-of-a-lifetime-for-benedict-cumberbatch-45455

Not a lot of people know that Shakespeare translated Hamlet from the original Klingon. For too long, readers throughout the Federation have been exposed to The Tragedy of Khamlet, Son of the Emperor of Qo’nos, that classic work of Klingon™ literature, only through inadequate and misleading English translations. Now at last, thanks to the tireless efforts of the Klingon Language Institute, this powerful drama by the legendary Klingon playwright, Wil’yam Shex’pir, can be appreciated in the elegance and glory of its original tongue. khamcov

Talking Sci-Fi I realised I had just missed towel day:

http://en.wikipedia.org/wiki/Towel_Day

I have an obscure connection with Douglas Adams and it’s not that I once drove a Ford Prefect! There is a related obscure connection between Adams and the renaissance in that Douglas lived in the same small village as William Byrd, the medieval composer.

Consorts conjectures The absence of information about the ‘lost years’ of the Bard has led me to make some informed guesses about those lost years.

1578 Shakespeare leaves school early due to his father’s financial downfall and becomes teaching assistant at a noble house. He develops playwriting and acting skills teaching children. The noble house could have been the Stanley family place at Lathom. I think he could have developed into Stanleys Poet as it was fashionable then for noble people to have your own tame poet. When Stanley formed his own acting troupe in 1587 Shakespeare would have been in a good position to join the troupe. Stanley was  a lawyer and he might have doubled as Stanleys scrivener..

1582 Aged 18, he marries Anne Hathaway and they have a child (this is known)

1585 After his twins are born moves to London. Possibly with Stanley at his London base (Cannon Row).

1587 He becomes so useful to acting company that he is invited to join, writing plays from scratch.

One more alliterative professor Hildegard Hammerschmidt-Hummel and Shakespeares portraits

http://www.new.hammerschmidt-hummel.de/Pages/EN/AuthenticPortraits.html

A history channel documentary covered this (50 mins in)

http://www.youtube.com/watch?v=6yf6lLaxBY4

Modern re-creation of Shakespeares portrait

http://www.dailymail.co.uk/news/article-3456973/What-having-squire-New-accurate-portrait-William-Shakespeare-400-years-death-looks-like-chap-pub.html

The lack of evidence of Shakespeares life has led to some notorious forgeries:

https://en.wikipedia.org/wiki/William_Henry_Ireland

https://en.wikipedia.org/wiki/John_Payne_Collier

These are extensively covered by yet another alliterative Professor, Samuel Schoenbaum’s in Shakespeares lives. Schoenbaum dominated Shakespeares studies and was intolerant of others views, yet with so little factual evidence there is only speculation. Ian Wilson in “Shakespeare the evidence” has a convincing argument that Shakespeare was under the patronage of Ferdinando Stanley.

The worldwide following of Shakespeare

http://www.theguardian.com/books/2015/sep/25/shakespeare-world-anti-apartheid-hero-nazi-favourite-bollywood

Another attempt to rewrite the Bard

http://www.newyorker.com/books/page-turner/why-we-mostly-stopped-messing-with-shakespeares-language

Where did Shakespearean Londoners go when they wanted a day out? To Brentford Staines or Ware according to Middleton and Dekkers Roaring girl of 1612. In Jacobean times the Thames was tidal up to Staines, so they would go up river on a flood tide and back downriver on an ebb tide. The journey to Ware was more difficult up the River Lea. Edmund Spenser described the river in his epic poem The Faerie Queene as “the wanton Lea that oft doth lose his way”. The Lea could confuse travellers with its twisting, splitting course.

Parody of “Shall I compare thee to a summers day”

http://photodharma.tripod.com/sonnet18.htm

Discussing memorable Shakespeare lines with a friend and he remembered “What news on the Rialto” from the Merchant of Venice. This had resonances with me as I am restoring a Reliant Rialto car! Another line from the same play he remembered was “Do  cream and mantle like a standing pond”

The poisons, potions and charms of Shakespeare

http://hyperallergic.com/285463/the-poisons-potions-and-charms-of-shakespeares-plays/

On the 400th anniversary this seems apposite:

http://www.theguardian.com/commentisfree/2014/nov/02/sharkespeare-marxism-feudalism-capitalism

Which is Shakespeares most popular play:

https://priceonomics.com/what-is-shakespeares-most-popular-play/

Interesting that King Lear does not appear in the top ten in the US but is popular in the UK, perhaps we have more ageing thespians.

Shakespeare web-comic

http://goodticklebrain.com/

There is a link between the rythym of  Rap music and iambic pentameter which I have only just realised, thanks to Lenny Henry.

Restoration of Religious paintings John Shakespeare supposedly whitewashed

https://theconversation.com/why-did-shakespeares-father-paint-over-iconic-medieval-murals-69537

Not alliterative but Oxford professors CS Lewis, Tolkien and Lewis Carroll turned Christianity, Anglo Saxon and mathematics into successful works of fiction.

Cornish influence on medieval Theatre:

http://www.oxfordtoday.ox.ac.uk/news/2015-05-11-dramatic-discovery-bodleian

November 1, 2016 / consort3

80 years of BBC TV

On Nov 2 1936 the BBC started TV broadcasts from Alexandra Palace. There were 2 systems the Baird and the Marconi-EMI and both systems were tried, the Marconi system winning. That decision was made in March 1937. On May 12th 1937 the first British outside broadcast was made, the Coronation of George VI. You could buy these sets at launch:
Ekco-Scophony
Marconiphone
HMV
Cossor
GEC
Pye
Ferranti
Baird
Murphy
RGD
Ultra
By September 1938 KB and Philips sets were also available
These were household names back until the 1980’s, when Sony, Hitachi (GEC) Toshiba(Rank), Panasonic, Sanyo(Philips/Pye) and Tatung (Decca)  took over. The bracketed make is the factory that the Japanese took over. Pedants will point out that Tatung was from Taiwan. Funny how the Japanese made a success of TV production in the UK when the Brits could not.
A BBC programme covers the start up:
http://www.bbc.co.uk/mediacentre/proginfo/2016/44/televisions-opening-night
The Baird work was not wasted as the flying spot Telecine became a useful piece of kit.
The 1953 coronation of the present Queen provided a major boost for TV. A lot of the population finding a place to view a TV set. My father in law built a DIY one for the occasion.

August 13, 2016 / consort3

TTL & Microprocessors

TTL (that is transistor – transistor logic) is 50 years old

http://www.embedded.com/electronics-blogs/break-points/4431173/TTL-turns-50–more-or-less–in-2014-

Good article on the history of TTL

http://www.computerhistory.org/atchm/the-rise-of-ttl-how-fairchild-won-a-battle-but-lost-the-war/

A 4bit microprocessor built in TTL

http://www.bigmessowires.com/nibbler/

An even simpler TTL processor

http://www.bradrodriguez.com/papers/piscedu2.htm

A more complex TTL microprocessor

http://www.mycpu.eu/

A TTL processor that does not use the 74181 ALU also interesting web-ring

http://www.galacticelectronics.com/Simple4BitCPU.HTML

Not a lot of people remember the Signetics 8200 series and the AMD 9300 series TTL

While I am on a historical bent, this site is good on old microprocessors etc.

http://www.cpushack.com/

The z80 versus the 6502

http://www.luke.maurits.id.au/blog/post/on-choosing-the-z80-over-the-6502.html

The development of the 6502

http://www.commodore.ca/commodore-history/the-rise-of-mos-technology-the-6502/

and this on the 70s and 80s personal computer boom

http://www.filfre.net/about-me/sitemap/

Historical computer designs index

https://people.cs.clemson.edu/~mark/hist.html

The modern way of designing a microprocessor using VHDL

http://labs.domipheus.com/blog/designing-a-cpu-in-vhdl-part-1-rationale-tools-method/

People still use DOS

https://opensource.com/life/16/9/interview-jim-hall-freedos

The 16 bit (2 byte) microprocessor came out in the mid seventies

222222

I have not been paying attention to what can be squeezed into the humble 8 pin DIL package. How about the NXP LPC810M, a 32 bit ARM microcontroller or the Microchip 128K X 8 serial SRAM? Are they the most complex chips put in the package?

August 12, 2016 / consort3

Beer

There has been a renaissance in beer brewing in the UK and US. I think it started with the Campaign for real ale (CAMRA) in the UK and spread to the US where it is called craft beer.  Dissatisfaction with the products of the large breweries in each country started the trend. With 1400 breweries in the UK and about 4200 in the US it has taken off.

http://edsbeer.blogspot.com/2011/11/brief-history-of-cultivated-hops-in.html

http://www.hertsmemories.org.uk/content/herts-history/work/the-brewing-industry/malting-in-hertfordshire-in-the-mid-17th-century

http://theappendix.net/issues/2013/7/come-hear-this-ditty-seventeenth-century-drinking-songs-and-hearing-the-past

http://www.hotrumcow.co.uk/beer-yeast-genetic-research/

http://munchies.vice.com/articles/what-if-you-could-detox-from-drinking-beer

http://www.wired.com/2015/03/the-very-best-beer/

http://news.yahoo.com/california-craft-beer-brewers-balance-drafts-drought-144310975–finance.html

http://www.cbsnews.com/news/renowned-belgian-beer-brewer-cantillon-says-its-a-victim-of-climate-change/

http://arstechnica.com/science/2016/06/5000-year-old-pay-stub-shows-that-ancient-workers-were-paid-in-beer/

http://www.vice.com/en_uk/read/brilliant-news-doing-two-hours-a-week-of-exercise-offsets-all-the-horror-you-do-to-your-body-with-drinking

http://www.economist.com/blogs/graphicdetail/2016/09/daily-chart-7

I recently found the best brown ale,  Lewes Castle Brown by Harvey’s of Sussex. I must go and see the Widmer Bros Brewery in Portland, Oregon since it combines 2 of my interests beer and trains.

http://www.natgeotraveller.co.uk/smart-travel/features/on-the-real-ale-trail/

Maybe us Brits know something about beer

http://draftmag.com/science-session-abv-processing/

Beer and a statistics pioneer

http://priceonomics.com/the-guinness-brewer-who-revolutionized-statistics/

Reddit beer forum

https://www.reddit.com/r/beer/

I am only going out for one

drink

This guy likes beer

beef
http://www.golfdigest.com/story/my-shot-andrew-beef-johnston

June 1, 2016 / consort3

Sallen & Key slope

The humble unity gain Sallen and Key filter can be versatile. Don Lancaster’s Active filter cookbook showed me some of the filter shapes you could get. By varying the damping you can get upward and downward slopes to the frequency response . A nice article by Kenneth Kuhn showed me how to calculate the component values given the damping and the frequency.

http://www.kennethkuhn.com/students/ee431/sallen_key_low_pass_filter.pdf

At step 4, here is where I deviate from the above by using this website

http://sim.okawa-denshi.jp/en/OPseikiLowkeisan.htm

Enter the capacitor values and it will compute R1 and R2 as 6.2k and 18K respectively, as per Kuhn’s analysis. Here is a Ltspice analysis of the circuit showing the 6dB peak of the underdamped case, even though the op-amp is configured as unity gain! By swapping the capacitors we get an overdamped case.

salkey

Or you could use a Quad style tilt equaliser, if your overall system has a problem.

http://www.edn.com/design/analog/4368935/Implement-an-audio-frequency-tilt-equalizer-filter

http://www.keith-snook.info/wireless-world-magazine/Wireless-World-1970/Tone-balance%20Control%20DCD.pdf

Very nice article by the late great Chu Moy on headphone equalisers including the tilt type

headwize-project-designi

Talking of headphones, Bose Qc35

http://www.theverge.com/2016/6/21/11975496/bose-qc-35-bluetooth-wireless-headphones-quietcomfort-flawed

Back to Sallen and Key. an interesting analysis:

http://www.edn.com/design/analog/4312748/A-new-set-of-Sallen-Key-filter-equations