Fulton Length Wires

No time for these.

Worried more about power system harmonics, PARTIAL DISCHARGES, protection faults, electrocution deaths etc.etc.


Understand.

I missed an important stock trade today, while posting on HFV, to set something straight. But that HFV post got my full attention.

Jeff
 
06-03-2022 ..... A small follow up on Robert W. Fulton, inventor of Fulton Lengths for audio wire............

I get a kick out of this thread, on two levels. People with various scientific backgrounds are honestly posting as to what they understand about 57 and 1/8th inches, in relationship to their education and experience. Then we have DIYers admirably trying to listen to various lengths, and they can not hear any difference on their systems. Bogus or real??

I would like to encourage all who are in this thread, actively or passively, to take the time to fully read Robert's Biography, written by his son Richard.

Here is the URL :


and a non-Bioography URL :




If you don't do that, here is small section I will post, that would lead one to deduce that Robert was well qualified to think out of the box with those sick baboons, and make his discovery :

1654258721667.png
Best is to read and study both of the above URLs from the referenced web site, even if it was never fully populated.
" Better than best ", is to DIY make the cables as outlined, and give them a listen in your audio system. You will likely thank me, everyone else has !! In a country with 1.3 Billion people, will not one person on HFV do so, and report back to F.Ms ??

Jeff
 
Best is to read and study both of the above URLs from the referenced web site, even if it was never fully populated.
" Better than best ", is to DIY make the cables as outlined, and give them a listen in your audio system. You will likely thank me, everyone else has !! In a country with 1.3 Billion people, will not one person on HFV do so, and report back to F.Ms ??
Some FMS have already reported that they have tried and did not hear any difference. @Hari Iyer has already said he is trying and will report back.
Now assuming some other FM freshly tries and reports negatively, I am sure you will state that his system is not done the way your's is (I guess optimized is the right word).
I know it is fruitless with you, but I suggest that you hold your horses.

Accept that there is no absolute ideal way to reach audio perfection as 'perfection' in audio is an absolute misnomer.

If you feel your way is perfect, so be it, don't be pushy, it is not only fruitless, but also very insensitive.
If someone agrees with your findings, enjoy the thrill, if not just accept and move on.

Your responce to @yogibear counter invitation to @Hari Iyer was in extreme bad taste.
 
Kannan,

Thanks for your post. I can not hear length differences, and already have written that. The baboons - surely did !!!! My current audio Mentor can, and he did do the Bob Fulton length determinations on his truly excellent audio system, in 2020. I surely can take his word. He is far more experienced in audio than I am. My audio system is not equal to my Mentors, and my hearing is not up to snuff to make such a determination now, even if I had his system.

I am very sure about what I post, because I have lived it, and continually hear it.

Its been a 77 year long audio journey. ( Mom nursed me to the first ALTEC 604 duplex, then a field coil ). I don't ever have to doubt a thing that Robert Fulton ever told me, so I accept it all, and employ it as I see fit. I happen to fully understand both of my two audio Mentors' religious backgrounds, and neither would never say things to mislead me. Nor would Our Father. You, and all the others, ( except Hari so far ) , have no experience what so ever, in hearing this equipment, correct??

I understand, with Yogibear being your friend, how you would feel about my comments to him regarding Hari's visit. I am sorry if that disturbed you. I too appreciate and think I understand Yogibear as a nice fellow-human-being, believe me. I can judge him accurately, a good guy for sure.

I am not a loose cannon. I thought-out about saying what I did for 24 hours. I decided it was a fantastic and brilliant thing to suggest. Why, because it would END any controversy, if both of those fellows actually heard the differences in amps and speaker cables together , for once and for all, and ...... on Yogibear's system. It would have been much better if Prem had traveled along from Mumbai with Hari, to also hear it, wouldn't it? That thinking is 100% logical, and, one must consider what my visit suggestion would have easily accomplished.

Allow me to share with you an analogy Kannan.

Let's change the topic from " hearing something, to seeing something."

Let us pretend, ( as it was when I was born ) that NOW in 2022 the only visual reproduction we have is in black and white, for television, photographs and movies .

What if someone came along in 2022 and said, hey, we are all doing it wrong, we have a much better way to do this, it is called COLOR. People, the general viewing public who have never ever seen color photos, TVs and movies will not have a clue. They may think, I am very satisfied with what I have, why even bother??. It's a gimmick. The scientists and E.E.s will say, this is 100% phoney and it is impossible to even do. This would have been in my College courses and textbooks. Jeff, where is your published Doctoral thesis, and peer review? Jeff, I have a pHD degree, ...... and I need to see all the measurements and full scientific proof, or else I can not believe you.

And then there is " little old Jeff Medwin " in ( 2008 to 2022 ) saying to people,

" Forget black and white, this reproduction in COLOR is a really great idea !! I didn't invent it, my two Visual Mentors did. I can't substantiate it. I am only a Business Administration college graduate. But I believe in what I am seeing! ALL I suggest is you LOOK at it, and judge for yourself. The proof of the pudding is in the eating ", is what I'd will tell them, over and over.

Now my dear audio friends, substitute for "COLOR " : a L.S.E.S. power supply in an audio amplifier, and G.T.O bypass caps, and multiple film cap bypassing, and a two-stage directly-coupled tube amp topology, and some pretty good DIY speaker leads ", and you might just understand my analogy.

Have a great day everyone. Thanks for following along. This will work out, in time. Some people will see the color TV , umm, I mean hear this.

Jeff
 
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Note to self
1. Buy 2 sick baboons
2. Make Fulton length x 2 interconnects
3. Play music for baboons using above interconnects (for how long?)
4. Cure baboons and earn instant karma
5. Give baboons the interconnects so that the next time they feel ill, they can borrow a music system to play music using the interconnects and get cured.

Ffs 🙄
 
Note to self
1. Buy 2 sick baboons
2. Make Fulton length x 2 interconnects
3. Play music for baboons using above interconnects (for how long?)
4. Cure baboons and earn instant karma
5. Give baboons the interconnects so that the next time they feel ill, they can borrow a music system to play music using the interconnects and get cured.

Ffs 🙄

Not quite.

You have to start with healthy baboons, not sick ones.

You do not play music, but rather, 20 kHz test tones, and study how they react. Press a button at feeding time and get food.

Next, increase the test frequency to 60 kHz. The baboons, well tested and documented previously, will become confused and sick.

As a consultant, you will visit the University Lab with electronic measuring equipment. You will see a nice 60 kHZ signal at the output terminals of the tube amplifier. You will also see an almost perfect signal level at the speaker's terminals, some 25 feet away. Maybe down 0.2 dB. No big deal. BUT, when you check phase, at both ends of your 30 foot speaker leads, you will see that it has shifted about sixty degrees, through the speaker wire at the speaker's end, when at 60 kHz.

Your job, as the consultant, is to figure out how to engineer a set of speaker leads, that does not shift phase 60 degrees at 60 kHz. Simple requirement.


Mr. Fulton had a radar and amplifier design background, and he applied himself uniquely in his Lab to solve the speaker wire problem. Mid 1970s. No one else had ever done that in a Lab before then, and seemingly since.

I have nicely had two gifted people as audio mentors. My second audio mentor, Dennis, subjectively confirmed Fulton lengths in 2020 on his excellent audio system. I do not ignore either of these two gifted audio people.

Do you grasp this a bit better?? You should do as you wish. I am only the messenger. Don't shoot me.

Jeff
 
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The scientists and E.E.s will say, this is 100% phoney and it is impossible to even do. This would have been in my College courses and textbooks. Jeff, where is your published Doctoral thesis, and peer review?
Hi Jeff,
With all due respect ,You certainly have a problem with Engineers and Scientists it seems.why do you generalize??
 
It is just from my direct experience with them over many years in audio and doing audio implementations.

They may know four times what I know in theory, etc, but often the systems that they run, are distinctly inferior to what I have been able to put together. with a limited budget and resources. In audio, I subconsciously tend to judge whoever is talking to me by the audio system they put together and use in their home. ( Harbeths !! I looked :) )

I must tell you, there are certainly are some very very good E.E.s I have met and respect,.... regardless of their system ! I respect them greatly from the way they think, and if they have an open mind, VS . a narrowly thinking E.E. type who does everything only by the book. There is a difference between knowledge and wisdom.

Shinto, there are things I do in amp builds, that are drastically opposite what a E.E. trained person has studied. But I positively know - from 40 plus years of building, that what I may do is superior to how an E.E. would execute an amplifier design. One good example, is an almost universal use of two Hammond 159ZA power supply chokes in tube amps, 340 mHY at 1 Ampere at six Ohms DCR. It sure does not meet the E.E's textbook definition of " Critical Inductance ". A typical E.E. would NEVER even consider doing this. But it is one mandatory way towards getting a SE tube amp's power supply, to support the circuit - in an audibly superior way !!


I don't mess around with Scientists too often, regarding audio subjects. If I did, I would also subconsciously consider carefully what their audio system is at their home. How would it compare to mine? If they ever provide useful information to me, I will respectfully thank them nicely, and apply it.

I hope this gives you a better idea of how I tick. Does it answer your question ?? Thanks for asking.

Best wishes,

Jeff

Below, my modest system. The wonderful ALTEC VOTT speakers were gifts to me, from two audiophiles I have mentored :

 
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Not quite.

You have to start with healthy baboons, not
As a consultant, you will visit the University Lab with electronic measuring equipment. You will see a nice 60 kHZ signal at the output terminals of the tube amplifier. You will also see an almost perfect signal level at the speaker's terminals, some 25 feet away. Maybe down 0.2 dB. No big deal. BUT, when you check phase, at both ends of your 30 foot speaker leads, you will see that it has shifted about sixty degrees, through the speaker wire at the speaker's end, when at 60 kHz.

Your job, as the consultant, is to figure out how to engineer a set of speaker leads, that does not shift phase 60 degrees at 60 kHz. Simple requirement.
What kind of wire would cause a 60 degree phase shift over a 25 foot length at 60Khz? I em genuinely asking. What would the wires capacitance and inductance need to be for this to happen?
Are you suggesting that a 60 degree phase shift would cause baboons to get more sick, while no phase shift would cause them to get well?
The way this is going, we may have a candidate for the Darwin awards....
 
What kind of wire would cause a 60 degree phase shift over a 25 foot length at 60Khz? I em genuinely asking. What would the wires capacitance and inductance need to be for this to happen?
Are you suggesting that a 60 degree phase shift would cause baboons to get more sick, while no phase shift would cause them to get well?
The way this is going, we may have a candidate for the Darwin awards....
And without a difference in phase angles between sending and receiving end voltages nothing can flow.

IMG_20220605_112949_hdr.jpg

P = (V1 x V2 x sin ∆) /X,

V1 is sending end voltage,
V2 is receiving end voltage ,
∆ is angle between them and
X is impedance in between

If ∆ is zero no power flow as sine of 0 is 0,
If X is zero P is infinity.

And 60 deg phase difference, what sort of impedance did he include in that cable. A huge reactor??

A simple explanation, Can water flow if there is no slope or pressure differential?
 
It is just from my direct experience with them over many years in audio and doing audio implementations.

They may know four times what I know in theory, etc, but often the systems that they run, are distinctly inferior to what I have been able to put together. with a limited budget and resources. In audio, I subconsciously tend to judge whoever is talking to me by the audio system they put together and use in their home. ( Harbeths !! I looked :) )

I must tell you, there are certainly are some very very good E.E.s I have met and respect,.... regardless of their system ! I respect them greatly from the way they think, and if they have an open mind, VS . a narrowly thinking E.E. type who does everything only by the book. There is a difference between knowledge and wisdom.

Shinto, there are things I do in amp builds, that are drastically opposite what a E.E. trained person has studied. But I positively know - from 40 plus years of building, that what I may do is superior to how an E.E. would execute an amplifier design. One good example, is an almost universal use of two Hammond 159ZA power supply chokes in tube amps, 340 mHY at 1 Ampere at six Ohms DCR. It sure does not meet the E.E's textbook definition of " Critical Inductance ". A typical E.E. would NEVER even consider doing this. But it is one mandatory way towards getting a SE tube amp's power supply, to support the circuit - in an audibly superior way !!


I don't mess around with Scientists too often, regarding audio subjects. If I did, I would also subconsciously consider carefully what their audio system is at their home. How would it compare to mine? If they ever provide useful information to me, I will respectfully thank them nicely, and apply it.

I hope this gives you a better idea of how I tick. Does it answer your question ?? Thanks for asking.

Best wishes,

Jeff

Below, my modest system. The wonderful ALTEC VOTT speakers were gifts to me, from two audiophiles I have mentored :

Hi Jeff,
An E.E learns much more than just designing an Amplifier.He learns the basics to implement in different areas of the trade. Circuits are just one of such. The course can only do so much in 4 years.I am an Electrical Engineer myself working in the power industry and I know nothing about Audio amplifier design let alone circuits because it is not my area of study or work and I have no interest in circuits to take it as a hobby.Now when you generalize all E.E s, that's where the problem is .Your comparison should only be to an E.E whose focus is in audio amplifier design for work or as a hobby.then you see the difference.I guess there will be many in the industry.
Regards
Shinto
 
Hi Jeff,
An E.E learns much more than just designing an Amplifier.He learns the basics to implement in different areas of the trade. Circuits are just one of such. The course can only do so much in 4 years.I am an Electrical Engineer myself working in the power industry and I know nothing about Audio amplifier design let alone circuits because it is not my area of study or work and I have no interest in circuits to take it as a hobby.Now when you generalize all E.E s, that's where the problem is .Your comparison should only be to an E.E whose focus is in audio amplifier design for work or as a hobby.then you see the difference.I guess there will be many in the industry.
Regards
Shinto
Well said

And everything boils down to

V = IZ (aka IR)

Whether you like it or not, your amp, speaker wire, interconnect, speaker etc.etc. have to obey it. And also the limits set by other theories like transmission line theory, travelling wave theory etc.etc.
 
Jeff,

Low DCR PS is all I could pick from your builds, rest is not convincing to me, so far.

I would like to experiment with low DCR line up in B + and would actually build two exactly same amps but one with lowest possible DCR chokes, keeping the B + same on both of them.

Are there any options to choose from other than Hammond 159ZA power supply chokes ?

I did come across a chap who owns a vintage tube amp (not sure if it was RCA) with total 10 ohms of the DCR from transformer to B+ lineup and he said it has excellent dynamics. (Though amp alone does not bring out excellent dynamics)

EE or EEE or Physicists or Scientists, don't generalize them. Education does not make them narrow minded, rather it does the opposite.

I am a Physicist by education, a Scientist from experience (two US Patents, and still a practitioner, unlimited lab hours confinement in high vacuum and plasma) and am quite known to be non-stop experimenter (call me crazy) in sound reproduction. Passion for music makes us dare attempt things which we could not imagine to do otherwise.

Your above post absolutely totally and fully delights me !!

At last
, after some time posting on HFV, I have a good DIYer willing to TRY out a new idea, and listen to it !!!! Bravo , Yogibear, Bravo !!!

First of all, I will reprint the late Dr. Chales E. Halijak's letter to me from 1989, " Figure of Merit of a Power Supply ". I suggest we all can use this as an overall general guide to Power Supplies for tube amps. You and others may recall, Dr. Halijak was an audiophile, friends to Dennis Fraker ( my audio Mentor ) and myself. He was also the Dean of the College of Electrical Engineering at the University of South Carolina.


Allow me to repost his letter below, and we will discuss specifics afterwards. here we go :


http://db.audioasylum.com/cgi/m.mpl...+figure+of+merit+of+a+power+supply&r=&session=


1989

Dear Jeffrey,

This letter is concerned with the power supply and the use of chokes.

A choke must have some internal resistance and its non-standard figure of merit is the ratio R over L. The best choke is the one with the smallest figure of merit and the best power supply has the least series resistance. It is not too difficult to obtain R over L = 10 but one can easily obtain R over L = 30 or more. The latter should be avoided but the ongoing shows that in a way it is unavoidable.

The choke input filter controls the diode by timing and not by ohmic losses. ( jm: current vs: voltage waveforms) The best place for a choke is at the input and the worst place is at the other end of a power supply filter chain because resistances tend to be higher there.

Suppose we start with your case and R over L = 10. When diode ( 5U4GB ) and transformer resistances are taken into account we have :

15 ( choke ) + 70 ( rectifier ) + 70 ( power transformer resistances )
------------------------------------------------------------------- = 103
1.5 ( HY )


( the 70 ohm power transformer resistance is a guess )


If four 5U4GB are placed in parallel one has :


15 + (0.25 ) ( 70 ) + 70
__________________ = 68
1.5


Both figures of merit are way above the original 10 but your listening experiment told you that 68 was alright; this actual figure of merit is the best you can do because the largest power transformer was used and the smallest resistance available choke was used. You can see that stock power supplies are not anywhere near being the best cases.



*. Most tube and transistor electronic engineers are unconscious about power supplies, but good.

* Also the best cases need not have zero internal resistance - a utopian goal. One strives for minimal non-zero resistance !!


-----------------------------------------------------------------------------------------------------------


On the subjective side, below is what Audio Consulting of Switzerland said about their four and a half ohm DCR @ 10 HY choke, from their literature, please do note everyone, their wording "one optimum" and "only way to make real progress":

"Get micro and macro dynamics out of your amplifier's power supply. Get the power into the music!


First we would like to explain our general philosophy :


There always is one optimum for a given problem.
It costs tremendous amounts of time to find it, but this is the only way to make real progress.


Jeff writes 10-2019 :

Dr. Halijak would have Stancor custom make chokes for him, rated 1 Hy at 8 Ohms, in the 1980s.

This that follows is advertising of Low DCR Ls from a High End Supplier in Europe, maybe Scandanavia or that area North ( 2022 : I think it was Audio Consulting of Switzerland ) :

Low DCR plays a key role in getting life-like dynamics out of an amplifier.

We have noticed that the lower the DCR gets, whether in a SE OPT or in a power supply choke, the more micro-information the system is able to provide.

We have gone as low as 4.5 Ohms for a 10 Hy choke that provides incredible sonic results when used in tube amplifiers.

The 16 Hy / 16 Ohms model is also very good, and maybe more reasonable when it comes to weight and size than the previous one.

More classical chokes of 30 to 50 Hy and 105 Ohms DCR may also be offered."


* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * **


By the way, Charlie's letter was in response to me experimentally paralleling up to four 5U4GBs to a common DYNACO ST-35 amp in 1989.

Let us let the above sink in. Suggest everyone read it more than one time, and revisit it. Rather than dilute Dean Halijak's above letter, allow me to do a follow-up separate HFV Post on specifics. Thanks !!



Jeff
 
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06-05-2022 ............. SPECIFICS on LOW DCR to Yogibear..............

The first thing to point out to all is that the Figure of Merit in Dr. Halijak's letter, does not solely pertain to the DCR of the chokes used !! Rather, it encompasses ( 1 ) the DCR of the Power transformer, (2) the equivalent DCR of the 5U4GB tube rectification, (3) the two main Power Supply chokes, and (4) the DCR of the SE output transformer. It is much like love and marriage " you can't have one without the other " as the song lyrics go.

Allow me to address first power transformers.

My 2022 new " TRIPLE monoblock 6005 " amps will use a 54 Ohm DCR Power Transformer on each amp. That is the high voltage secondary's DCR,, end-to-end measuring 27 Ohms, 0 , 27 Ohms.

Hari Iyer's SE DC KT88 amps use a lovely 320 VA Shilchar R-Core Power Transformer, for his ( my ) DC amplifier circuit. His secondary measures 70 Ohms total end-to-end, across the high voltage secondary , 35 Ohms, 0 , 35 Ohms . It only cost about $65 USD on a custom wind...320 VA !! .

I believe SHILCHAR could easily custom-wind a 30 Ohm total HV DCR Power Trannie if so specified ( 15 Ohms, 0 , 15 Ohms. ) on their 320 VA sized R-Core. Hammond ( Canada ) winds a off-the-shelf 23 Ohm end-to-end E-I Power Transformer, suitable for DC tube amps ( only measuring 11.5 Ohms, 0 , 11.5 Ohms ). It is thier model 278CX at 120 VAC Primary and a 378 CX at a 230 VAC primary, 545 mA. capable !!!! :)

The above will give you a good idea what we are specifically doing, in recent years, to "start off" the amplifier . ( 114 1/4 inch triple 12 AWG power cords, and 20 A. iECs,...... not 15 A. !! )

Second, rectification.

Directly heated rectifiers...use none with a separate cathode. We prefer a E.H. 5U4GB overall. Warning, 75 to 100 hour break in is absolutely required. These are INSTANTANEOUS sounding. Up until 2019, we used one 5U4GB per amp. From 2019, on, we use two per amp. There is a trade off here. A slight skewing one gets with paralleled tubes, and a lack of common mode enhancement found in just one tube. If wired well, we prefer two E.H. 5U4GBs, mainly because the rectification's DCR is cut in half, and when well executed, double 5U4Gs are clearly audible as being slightly less pure, but very nicely - more dynamically nuanced in all forms of music playback. An artistic trade-off. Wiring MUST be impeccable. 5VCT at 6 A. is needed, with good leads.

Third, chokes.

Do not deviate from ordering two 159ZA Hammonds, for a variety of reasons. The L.S.E.S. supplies use a choke input filter ( always ) but with a Non Critical Inductance choke. This causes large current spikes in L1, and the 159ZA's 1 Ampere rated current easily absorbs all of these, with no stress or choke buzzing at all. Also, we have always found in SE amps, L1 must be the same as L2, in seemingly every instance. If not, you get a nasty-sounding sonic skewing sound, that MUST be avoided. No need to experiment with an unequal L2, Dennis and I already have, on multiple occasions !!! L1 = L2. They sound best with proper lead orientation, ( input lead closest to the core, at the start of the winding ) and with 12 AWG Mil Spec leads for superior transfer efficiency.

Clearly, the best sounding 10 Ohm Ls I know of ( Stancor C-2708s ) did not " cut the mustard " on page one of my 2021 SE 6005 HFV amp write up.



Only two 159ZAs, were acceptable to me !!! My audio mentor ( Dennis Fraker ) had Mike LeFevre wind custom- co-designed 4 Ohm DCR chokes, in brass frames, etc., They were clearly superior to 159ZAs, but at three times the cost, and Mikey has retired, and has closed Magnequest.

Yogibear, in 1982, when Mr. Fulton first ever advised me on how to scratch design and build a tube amp, he gave me the following general advice in this order :

1) Avoid Negative Feedback Loops
2) The chokes all need to be " 20 Ohms or less, IF you can find them ".
3) Choke input filters
4) Triode tubes
5) Mono blocks.

In 1989, the year after Mr. Fulton's September 1988 death, Dennis Fraker's' first 2A3 DC mono amps each used two 10 DCR Ohm Stancor C-2708s in series. I heard them around 2006 or 2007 for the first time, and was hooked. ( R.M.A.F. Denver audio show ).

Fourth, SE Output XFR DCR

Hari Iyer's 5K R-Core Softone RW-20 has a 125 Ohm primary winding DCR. He uses it tapped at about 2.5 K or so.

I also run RW-20 R-Core Outputs, using the full 5K winding in the 2021 single stereo 6005 amps. The new " TRIPLE 6005 " amps will use 77.5 Ohm DCR Hammond 1623 SEAs, with a 2.5 K primary. The DCR of the Output XFR primary is a factor, but all which preceds it, must first be optimal IMHO.

One final word.

Do not use high uF ( microfarad ) power supply caps for C1 and C2 ( in the L.S.E.S. L1/C1/L2/C2 B+ filter ) , or you will KILL dynamics. We need to have the power supply be as fast as the audio circuit, that it feeds.

Smaller uF value caps are fast to discharge, and to recharge. Do not concern yourself with hum. No audible hum is NOT ever the goal and the sign of a really good tube amp. Be concerned with how the amp plays back music, finally in the time of the music, and finally dynamically correct. LOL, just ask Hari !!!

30 to 35 uF for C1 maximum , and usually about 50 uF for C2. WIMA makes a 50 uF MKP4 DC LINK at 800 VDC , 4 PINS, decent sounding, moderate in cost, use that . Do not worry about GTO use. That is an advanced application, when all else is resolved.

We two can coordinate privately, using PSUD, to help you effectively experiment, and for us to get the best overall topology and parts values for you to hear in a L.S.E.S. supply.

Jeff
 
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CORRECTION :

In the post ( right above the photo of the personalized licence plate ), at the very start of the next to last paragraph :

Please change the word " 30 to 35 Ohms ", ........... to .... .. " 30 to 35 uF .".................................. Then, it is correct.. :oops:

( I am not sure if the Moderators will have time to do that ).

Something apropos to my Yogibear comments above :

I just first-noticed ten minutes ago, a comment by my Audio Mentor Dennis in February, describing conceptually what I have been calling a L.S.E.S. power supply :


A Watt.JPG

I do not understand Dennis' use of the word " density ", what he had in mind, .......but all else is understandable.

Jeff
 
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