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Why no tiny output transformers?

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I'm wrapping up my 5W EL84 amp for listening and was thinking about building a little <1W triode se project for my desk at work. I want to keep the build small. For the first time in my life I find myself looking for a tiny output transformer and I'm noticing that there just aren't many below 5W. Is there a physical limitation that makes smaller transformers less ideal? Or maybe I'm looking in the wrong places?
 
Just a little math:

(I squared/R)/2 = rms power
20A Squared into 2 Ohms = 200W rms

Gaussian response, K = 0.35 (good phase response, and smooth frequency response).
K/risetime = 3 dB bandwidth
0.35/3 us = 116.667 kHz

20A * 2 Ohms = 40V
100V/us slew rate
40V/100V = 0.4
0.4 us is much faster than 3us rise time.

Is the Golden Rule's math broken?

My Vinyl and CDs do not have that fast of a rise time, and not that kind of bandwidth.
The microphones used on those recordings do not have that rise time or bandwidth either.

My speakers are not rated for 200 Watts, or even 100 Watts, and they would give me ear damage.
I can not hear to 100 kHz, and my speakers will not reproduce that.

What speakers and what recordings do I need?
 
Love it! The first person to actually do some math on my by-line. BRAVO, Summer.

Key words worth remembering dynamic load, slew rate, mean output. , bandwidth and min current sourcing.

At the upper end of output, 100 V/μs will achieve the 100 kHz bandwidth at 100 kHz. However if we remember

d A⋅sin(ωt) / dt = ωA⋅cos( ωt )

(which is to say, the differentiation which computes slew-rate of a sinusoidal signal with ω frequency (in radians/sec, weird, but useful) has a maximum slew of ωA (A is amplitude). So if nominally, ω = 2π⋅20,000 Hz = 126,000 radian/s, and A is 50 VPEAK envelope volts, then that's only 6.3 V/μs slew rate. For that implied RMS power (50 × .707)² ÷ 8 Ω … = 150 RMS watts, well … perhaps 100 V/μs is overkill. I kind of think it is. Yet I read it on John Curl's blog somewhere.

If like purists, we pride ourselves of getting full output at 30 kHz, or 50 kHz … or even 100 kHz (for no particularly audible reason), and having 70 volt output rails then

(A = 70) x ( ω = ( 100,000 × 2 × π ) ) = 44 V/μs

Pretty close to the 100 V/μs proposition. Such a dragon of an amplifier should easily be able to drive (70 × .707)² ÷ 4 Ω = 600 RMS watts into a nominal 4 Ω load. Since I²R = P then … I = √( 2 P / R ) = √( 1200 ÷ 2 Ω ) = 24 amps.

See? that one works. I think Curl's recommendation summary just sizes up current audiophile thinking in a nutshell. Expect to 'turn it up' to nearly max-output from time to time; expect 100 or more "program RMS watts" from that. Expect transients up to 20 amps; expect real-world speakers to have impedance dips down to 2 Ω at crossover. Expect to actually hear something audible by having bandwidth above 20,000 Hz.

Its like when I listen to Bolero, or the 1812 Overture. The dynamic range of a good 24 bit recording at 96 kHz sample rate … relatively "uncompressed" is remarkable. And its a curious thing: played "at 10", even in the loudest crashes and crescendos, somehow the music doesn't seem significantly louder than you'd encounter sitting in a prime seat in the concert hall. I guess that's the holy grail of audiophile quests.

GoatGuy
 
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PS: your vinyl and CDs of course don't themselves have that kind of rise-time. But per the calculations above, amplified, they just might. Saying (in context) that one has a nominally wonderful 24 bit recording of some uncompressed orchestral piece, and that the output of one's DV D/A codec is 1 volt peak, and it has 96 kHz sampling sporting 44+ kHz bandwidth…

(A = 1 volt) • ( 2π 44,000 ) = 0.28 V/μsec

AS you say. Now, let's amplify that to 100 volt audiophile ($5,000 to $50,000 amp) levels:

(A = 100 V) • ( 2π 44,000 ) = 28 V/μsec

Ah, getting closer to the 100 V/μsec. If one loses their physics/mathematics sanguine mind, and assumes that meaningful audio exists up to 100 kHz, then you get right up to 63 V/μsec. amplified of course. From a 1 volt (envelope) source.

GoatGuy
 
stocktrader₂₀₀;5224261 said:
those specs are so that the 20 - 20khz frequencies are low distortion and no phase shift in the amplifier. I want my amps capable of 300 - 400khz as this will yield greater stability in the audio band via a greater gain phase margin.

Seriously? Wow. Well, there you are then.

I however am VERY happy if the first poles are at 15 Hz and 15 kHz. You know, the natural ones that (at the low end) protect the amplifier and speakers from mechanically coupled rumble or substantial subsonic wow, and at the top end start to neck off HF response gracefully to again protect tweeters and tho' not heard, according to US diplomats in Cuba … the ears. Supersonics at high power can still be a hearing killer.

Why say First poles? because in the argot of digital and analog signal processing, one's signal path inevitably has 'poles' in the S-plane around which in the frequency plane response goes from flat (or "nominal") to non-flat. A high pole is both a phase-shifter and a 'peaky' response. (Goes up toward pole, down like a Butterworth on the attenuation side.) Lower poles can be designed to not do that., just gradually rolling off (either low-pass, low-cut, high-pass or high-cut). Stack several conceptual filter/pole sections in series, and you do not necessarily turn a trio of soft-drop low-pass filters into a peaky filter. It just drops off faster. But you do add the phase delay such a HighCut filter section incurs.

Perhaps I'm explaining overly much. I apologize. Its just that I spent several years in university and trade-practice engineering of digital/analog active second and third order response network design to not know such stuff. Without my 40 year old books! LOL. Peace! (I lived when Berkeley's residents were still swatting pterodactyls like flies and tie-dyeing t-shirts in galvanized washtubs with contraband chemistry-lab dyes made by grad students with the hobby. That IS a ways back. You need REALLY big flyswatters for pterodactyls.)

GoatGuy
 
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I'm wrapping up my 5W EL84 amp for listening and was thinking about building a little <1W triode se project for my desk at work. I want to keep the build small. For the first time in my life I find myself looking for a tiny output transformer and I'm noticing that there just aren't many below 5W. Is there a physical limitation that makes smaller transformers less ideal? Or maybe I'm looking in the wrong places?
I may have drawer full of tiny output transformers...anywhere between half a watt to one watt. Are you interested?
 
I hope BJosephs finds some small but good SE transformers for that amplifier. I believe the Hammond 125 series is for 100Hz and up.

I have been doing some low power push pull amplifiers, and the output transformer can be lighter and smaller than a SE transformer for the same wattage. But that is usually a more complex circuit.

One such amp I did starts with one of the the principles of the Odd Watt amplifiers (which was in the literature decades before Odd Watt). But it is less complex than the Odd Watt. I might decide to publish that amp, for non-commercial use, and no, I am not using it for commercial use. It uses a 10W 10K push pull Edcore. I plan on doing another amp like it, but with the 10W 10K push pull Hammond.

Sorry for the critical math words, but I primarily like to worry about how my system sounds with some relatively easily obtainable and reasonably priced equipment and recordings.

More math: Take a typical signal source that is full scale at +/- 3V peak.

Let it rise from 10% to 90% of -3V to +3V in 3 us. That is +/- 2.7V in 3 us. Now, amplify it to +/- 270V. That is +/- 270V, but the rise time is still 3us.

So, the bandwidth is still 116.7 kHz. The amplification did not change the rise time, and the bandwidth did not change. Only the volts per microsecond (slew rate) increased. But the rise time did not change (unless the amplifier has overshoot, not desirable).

You could use a K that is not 0.35. But that would not be Gaussian, and it would either be overshooting, or dribbling up (not screen shots that marketing wants you to see on a review of their amplifier).

As to the 1812 overture, the original Telarc recording had 6Hz signals from the real canon. 6 Hz loudspeakers for all? About a decade earlier, RCA tried the real cannon, but the monitor speaker’s woofer cone jumped out of the speaker basket. Talk about real Hi Fi ! (I wonder what that sounded like, but I bet it did not sound like a canon, and not like the Howitzer I heard in a concert, and not like the shipboard 5” guns we shot in the Gulf of Tonkin).

As to phase, there are other questions. Just one example: Take a stereo system that has a 20,000Hz signal from both loudspeakers, and that are exactly in phase. At a sound velocity of 1080 feet/second, and one cycle of 20,000Hz, that is 0.054 feet. A quarter wave of 20,000Hz (90 degrees) is 0.135 feet. That is 0.162 inches, or just over 1/6 inch. Be sure not to turn your head, left side back 1/12 inch, and right side forward 1/12 inch; If you do, you have disturbed the L and R relative phase by 90 Degrees. Talk about the sweet spot. I will measure the distance to the loudspeakers, and then put my head into a vice, … No I will not do that.

And were the L and R microphones spaced equal distances in front of the oboe?

I do lots of near field listening, with lower power amplifiers and 2 way speakers. I only have a stereo in the living room. Direct sound (near field) has less effect from cancellations caused by room reflections. And just Left or Right channel gets rid of the pan pot effects, and center fill cancellations. Sometimes I combine L and right into mono. It usually just takes the life out, due to recording cancellations.

For the living room, speaker placement, room characteristics, etc. become very important.

I think we have several outer layers of the onion to worry about, before we need to get to the inner layers.
 
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