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Old 22nd April 2013, 06:33 AM   #1
Stee is offline Stee  Italy
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Default the Golden Gain Ratio

In mathematics and the arts, two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one.
The golden ratio is also called the golden section (Latin: sectio aurea) or golden mean.Other names include extreme and mean ratio,medial section, divine proportion, divine section (Latin: sectio divina), golden proportion, golden cut, and golden number.
In audio art design this number is 24/40
The following discussion is provided, recognizing that
not all measured performance behavior explains or
correlates with listening tests by audio experts. The
design of the Gold gain ratio amp included consideration of both
objective performance measurements, as well as an
awareness of widely held theory on the success and
failure of previous amp designs.
the concept is important to break through the wall of the Natural Gain
(open loop gain)
SOUND QUALITY
The sound quality of an golden amp is often the crucial
selection criteria—even when a data sheet claims
exceptional distortion performance.
By its nature, sound quality is subjective.
Furthermore, results of listening
tests can vary depending on application and circuit
configuration. Even experienced listeners in controlled
tests often reach different conclusions.
Many audio experts believe that the sound quality of a
high performance FET buffer is superior to that of
bipolar op amps. A possible reason for this is that
bipolar designs generate greater odd-order harmonics
than FETs. To the human ear, odd-order harmonics
have long been identified as sounding more unpleasant
than even-order harmonics. FETs, like vacuum
tubes, have a square-law I-V transfer function which is
more linear than the exponential transfer function of a
bipolar transistor. As a direct result of this square-law
characteristic, FETs produce predominantly even-order
harmonics.
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Old 22nd April 2013, 09:59 AM   #2
DF96 is offline DF96  England
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Good to see Stee maintaining his usual standards!

The golden ratio is (1+sqrt(5))/2 ~= 1.618. 40/24 is 1.667 so does not even come close. Starting from a false premise is rarely a good way to approach engineering design.
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Old 23rd April 2013, 10:34 AM   #3
Stee is offline Stee  Italy
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the concept is important to break through the wall of the Natural Gain
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Old 23rd April 2013, 12:08 PM   #4
JMFahey is offline JMFahey  Argentina
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Quote:
Originally Posted by DF96 View Post
Good to see Stee maintaining his usual standards!

The golden ratio is (1+sqrt(5))/2 ~= 1.618. 40/24 is 1.667 so does not even come close. Starting from a false premise is rarely a good way to approach engineering design.
Fully agree and add: it's even worse than that: the Golden Ratio applies to ***linear*** dimensions; Stee is comparing ***Logarithmic*** ones which does not make sense.

Example: as a side Hobby I'm a Photographer, and must be aware of Composition Rules .
Often use the "Rule of Thirds" to quickly find the "points of interest" in a picture.
Now, I must (mentally) divide the space in ***linear*** thirds.
Using a Log scale would be ridiculous and produces whacky composed Pictures.
Which is what Elvee suggests.

By the way ..... what is "natural gain?"
Curious concept with no match in reality
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Old 23rd April 2013, 01:03 PM   #5
coluke is offline coluke  Italy
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Quote:
Originally Posted by DF96 View Post
Good to see Stee maintaining his usual standards!
Nope, he's going far beyond - take a look at the OPA604 ds, page 12...

L.
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Old 23rd April 2013, 03:01 PM   #6
Stee is offline Stee  Italy
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natural gain IS OPEN LOOP VALUE
it's so difficult to understand?
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Old 23rd April 2013, 04:44 PM   #7
JMFahey is offline JMFahey  Argentina
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No, you are wrong.
Natural Gain is not open loop gain but a certain gain setting which produces "Natural" or "Perfect" amplification, where the amplified end product bears a harmonious relation to the original one.
Open Loop gain is anything *but* that.
Clearly you are not even aware of the concept.

By the way, you *still* don't answer about your mistaken comparison of non linear (Log) dimensions instead of the proper linear ones.
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Old 23rd April 2013, 05:44 PM   #8
GoatGuy is offline GoatGuy  United States
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Um... its just silly to say that the Golden Ratio is somehow the most glorious amplification level. Directly, its just as pointless as saying that the proper number of eggs to put in a package is 12. (In fact, isn't the Grand Metrification having Europe as its Leader, down-converting eggs to 10-to-the-box? What about wine? seems 12 is a case, the world around. No "five-packs" of beer yet, nor 10-packs for that matter. Hmmm....)

Let me take this someplace where Stee hasn't.

Optics.

We've all seen the lenses that are used in cameras. Maybe some of us remember back to the nicer cameras of the 1950s ... relatively tiny lenses, maybe one-surface multicoated, no zoom, no autofocus. But they worked. By the year 2010, lenses (on DSLRs) are much bigger hunks of plastic, way more elements, Zoom, autofocus, everything. Very cool, that somehow they don't cost more in constant dollars than the 1950s lenses.

Then there are these lenses that we never get to see, but upon which all electronics now depends: the chip-making photolithography lenses. They cost upward of $1,000,000 (some even as high as $3,000,000!). They have dozens of elements (individual lenses cemented together). Why so many?

EXACTLY ANALOGOUS to "amplification", lenses bend light through a series of angles, through materials that are imperfect in well known ways at dispersing the light itself. The tighter the bends, the fewer the number of lens-groups, but the poorer is the ultimate focus of the image plane. The big multimillion dollar chipmaking lenses use dozens of groups, so as to bend the light as little as possible within the design-framework. thus, they're able to almost entirely cancel out the various aberrations that would otherwise ruin their utility in making sub-optical wavelength images.

Connecting these dots, I have myself harbored the notion that if we just "throw out the 'economic principle'" of trying to deliver the "best" for the "most reasonable price" (whatever-the-hell that means), then an optimal amplifier would, like the multimillion dollar lenses, amplifier the signal the smallest reasonable amount per stage - with additive stage noise binding the lower limit. Indeed in the old tube-based oscilloscopes (with their "armies" of carefully matched dual-triode tubes), each stage was required to do very little amplification. This in turn preserved both bandwidth and absolute signal integrity.

Because... let's be clear: the amplification required from line-level signals to output is on the order of 30x to 300x - whether for Class D, B, AB, A, tube, transistor or anything between. That 1 volt of input becomes 30 volts (P2P) becomes about 15 watts at the low end; at 300 volts, its 1,500 watts. Amplifiers, though rarely "remembered" to have been designed such, amplify voltage up front near the input, then current in later stages, to give power.

I built an amplifier using all FETs (because I like 'em, being so similar to lower-voltage, heater less triode tubes), with voltage-amplification-per-stage of less than 2x ... yet it only takes 10 steps (2, 1.9, 1.8, 1.7... 1.2, 1.1) to give a voltage gain of 67; the final stage uses (like virtually all semiconductor setups) a complimentary emitter-follower configuration for current-gain, with matched FET-NPN Darlingtons, and very modest NFB. It was run class A throughout, though technically it has a push-pull final.

The result? Sweet ... at low volume, high, between. No apparent coloration, no odd speaker break-up or other nonlinear physics back-EMF issues. Trivial design (really), just using the same "million buck optics theory" approach. 75 watts out.

Stee's idea, using just the Golden Ratio is pretty bogus on its own. However, using many, small-gain, noise-controlled, complimentary stages ... is yet another theory that deserves its own merit.

GoatGuy
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Old 23rd April 2013, 10:17 PM   #9
Stee is offline Stee  Italy
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the golden ratio gain wants to mean a set of counterreaction (40dB) much greater than the actual value (26dB)
it allows for a great effectiveness of the correction within the band allowed (2dB)
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Old 23rd April 2013, 10:52 PM   #10
GoatGuy is offline GoatGuy  United States
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Uh... sorry Stee... but you're smoking goat-chips here. There is not even one value on that pathetic circuit diagram. Not one. What on earth are you going on about?

Read what I wrote, and plagiarize that if you must. Just don't talk about Golden Ratios.

Please.

GoatGuy
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