Sallen Key

Reviewing some old stuff, I crossed the Sallen-Key filter. Analysis of this topology is relatively straightforward, but what I never sussed is the why - what makes it so important? What was the great advance, at that time? And is it still considered so consequential, today?

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Rich
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RichD
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It only requires a single active device to make, e.g. say a single vacuum tube cathode follower. Active devices were expensive back in the day!

I've pressed the buffer Darlington in a LM13700 into service as one it works okay.

It's kinda bad compared to other topologies like the multiple feedback, pretty sensitive to component variation, its performance falls off very rapidly as you approach the gain-bandwidth of the active device due to rising output impedance wrt frequency, you can't set the gain independently of the Q there aren't enough degrees of freedom in component selection.

Reply to
bitrex

I use a lot of SK filters. One nice thing is that it has unity DC gain and zero offset, as good as the opamp, independent of resistor and capacitor values. So it's a good filter for precision measurements.

The general schematic architecture, even if not literally SK, is nice too.

I don't know the details of the history. Wiki says it was introduced in 1955, which is about the dawn of the age of "modern" filter design.

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John Larkin         Highland Technology, Inc 
picosecond timing   precision measurement  
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John Larkin

Seems like it must be older than that, "The circuits described in the following pages were developed and collected to provide an alternative method of realizing sharp cut-off filters at very low frequencies."

note: "collected" so unclear if this was one they "developed" or "collected"

Reply to
bitrex

When applied to electronic circuits that is, the e.g. steam engine ball-governor is much older than that

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bitrex

Here's the original paper.

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GH

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George Herold

Pre WWII, and for some time after, filters were mostly LCs and the design theory was "image parameter", which cascaded LC sections as if they were independent pieces of a telephone system. It didn't work very well.

"Modern network synthesis" waited for computers.

This was a classic, sort of pre-dating Williams.

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John Larkin         Highland Technology, Inc 
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John Larkin

Here's an interesting patent filed 1934, circuit for filtering noise from telegraph signals to prevent spikes of interference from slamming print heads around or something like that. Consider Fig 6, it's not as neat as the topologies in Sallen/Key paper and a transformer is used for coupling as was common at the time, but it looks to me like they're headed in the right direction.

Reply to
bitrex

I would argue that James Clerk Maxwell was the first controls engineer, as such. Among many other things, of course.

It's amazing that such things took so long to disseminate; the analysis of filters was revolutionary in the 1920s (Campbell and Zobel at Bell Labs -- it's in the BSTJ, freely available, take a look!), but at least in principle, the differential equations had been known in various parts for the last century. Just, applied to different things -- mathematics in the abstract, or perhaps practical problems in mechanics and fluid dynamics.

It just goes to show that, no matter how good an idea is, it doesn't mean anything until it achieves circulation, usually by being economically important. (Strictly speaking, mimetic. Since we're talking economically useful ideas, that would seem to be the threshold for this case.)

Which is nice supporting information with the last reply I wrote on this newsgroup.

It wasn't until the 20s that telephone circuits were getting severely congested, while at the same time, electronic amplifiers (tubes) were just being developed, and becoming useful (namely, the combination of the two for frequency multiplex service).

More strictly speaking, it was the incremental cost of adding and maintaining more telephone lines -- more difficult due to spacial competition, as well as rising labor costs I would suppose? -- that made a "smarter" solution have the better ROI.

It's also amazing how far ahead of the times some engineers were, relative to the average. While Fessenden for example was crafting radios, most engineers were... whacking machines with wrenches, I guess? (Not to mention the literal "engine-ers" of the train era, of which there were probably vastly many more.) Or, say, in the 50s when television was new and remarkable to the average tech, but it's rather quaint to EEs today. (Or maybe that's my bias, having a deep understanding of it and many other signals; I really shouldn't speak for the level of understanding of the average EE student, say...)

Tim

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Reply to
Tim Williams

This is what the engineers I worked with used in the 1980's.

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blocher

I'd say more his correspondence-student Oliver Heaviside; from what I've read of Maxwell he was more of a mathematician/academic than much interest in the dirty work of engineering, not the type of guy to sully his beautiful theories with anything so pedestrian as _applications_....

They hadn't come up with tubes yet but as for ah, complexity, dig these photos of telegraph lines from the 1880s and 1890s!

Reply to
bitrex

Congestion, rather

Reply to
bitrex

AoE III page 399, footnote 16: R. P. Sallen and E. L. Key,

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 Thanks, 
    - Win
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Winfield Hill

Me too. There's a lot of mythology out there about component value sensitivity, but the net is that S-K works great as long as you don't ask it to do high-Q sections.

TI put out a very useful tutorial on filters with low component value sensitivity. Their recommendation (unsurprisingly) was to use S-K sections with equal resistors for most of it, and use a biquad for any higher-Q sections that might be required.

Cheers

Phil Hobbs

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Dr Philip C D Hobbs 
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Phil Hobbs

There were also "M-derived" filters, which looked a bit like elliptic filters. Both were rehearsed in ARRL handbooks up to the '70s. (I vividly remember being a pre-teen reading my brother's copy of the 1966 ARRL handbook, frustrated that I didn't understand more.)

Well, Bode's 1946 book gave folks something to be going on with--certainly better than constant-K or m-derived filters.

Cheers

Phil Hobbs

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Dr Philip C D Hobbs 
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Reply to
Phil Hobbs

The S-K paper starts out talking about low freq. and crappy inductors. Which is the same reason I/we like good caps and gain/ opamps.

George H.

Reply to
George Herold

Yup. Zverev has an honoured place on my bookshelf. He's still very useful, 50 years on. AFAIK he invented the equiripple group delay filter, which is pretty neat--the constant-delay property extends throughout the transition band, a trick that Bessel and Gauss and that ilk never mastered. ;)

Cheers

Phil Hobbs

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Dr Philip C D Hobbs 
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Phil Hobbs

Gain used to be expensive, at all frequencies. Tubes were big and expensive too, which is why people bothered to use interstage transformers to get voltage gain. The S-K filter acknowledged that tubes were getting cheaper than inductors.

Active filters are easier than LCs to design, too, since 1 and 2-pole sections can be cascaded without interacting. You can cheat a little and do a 3-pole SK with one opamp.

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John Larkin         Highland Technology, Inc 

lunatic fringe electronics
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John Larkin

I like their Filterpro (3.1.0, older version) to pop out active filters with standard component values.

LCs, we either normalize something out of Wilson, or use the NuHertz program. Using theory is the absolute last resort.

My guy Rob does impressive FIR digital filters in FPGAs. I have mapped essentially SK and biquads into uP code, to make IIR filters, which takes less computing than FIRs. It annoys people but it works.

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John Larkin         Highland Technology, Inc 

lunatic fringe electronics
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John Larkin

Comment on remarks by Bitrex. Transcontinental phone lines required many amplifiers to boost the signal o ver such large distances. ?Simple? amplifiers drifted too m uch and caused so much distortion that the signal became unintelligible. It is recorded that ?every hour on the hour? someone had to a djust filament and plate supply voltages of every amplifier to keep the sys tem working. Harold Black invented the idea of negative feedback and showe d practically that stable amplifiers could be built.

Black H.S. (1934): Stabilised Feedback Amplifiers; Bell Syst. Tech. J. 13,

1-18. See also reprint in Proc. IEEE 72, 715-722, 1984.

Black H.S. (1977): Inventing the Negative Feedback Amplifier; IEEE Spectrum 14, 54-60.

Klein R. (1993): Harold Black and the Negative-Feedback Amplifier; IEEE Con trol Systems 13 No.4, 82-85.

This was not generally accepted since the ?theory? at the time was that this could/should not work. Luckily Harry Nyquist examined th e mathematical theory and showed that Black was correct and negative feedba ck did what had been demonstrated.

Nyquist H. (1932): Regeneration Theory; Bell Sys. Tech. J. 13, 126-147.

However the general diffusion of this idea was very slow though some recogn ised the potential:

Terman F.E., Buss R.R., Hewlett W.R., Cahill F.C. (1939): Some Applications of Negative Feedback with Particular Reference to Laboratory Equipment; Pr oc. IRE 27, 649-655

Bode H. W. (1940): Relation Between Attenuation and Phase in Feedback Amp1i fier Design; Bell Syst. Tech. J. 19, 412-454.

and it was not till considerably later (WWII intervening) with the book by Henrik Bode, Network Analysis and Feedback Amplifier Design, that it really caught on. It was fortuitous that these three, Black, Nyquist and Bode, we re colleagues at Bell Labs. It may be noted that probably the first report on what came to be known as negative feedback in electronic systems was the paper:

Miller J.M. (1919): Dependence of the Input Impedance of a Three-Electr ode Vacuum Tube upon the Load in the Plate Circuit; National Bureau of Stan dards Sci. Papers 15, No.351, 367-385.

(the consequence of grid-plate capacity) but in this case it was viewed as a deleterious effect since it decreased the bandwidth of the amplifier. How ever this paper is the origin of the term ?Miller integrator? ? for what we now know as the usual operational integrator. Re the remark s by Bitrex about the very much earlier steam engine ball regulator and Tim Wiliams regarding Maxwell it may be noted that the latter did analyse the regulator:

Maxwell J.C. (1868): On Governors; Proceedings Royal Society 16, 270-283.

Scott.

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Prof78

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