Long-winded capacitor question

[newguy]

OK, please be patient with me. I have the feeling that my question is much more longwinded than it needs to be.

I'm looking into building the Aren van Waarde headphone amplifier, and am confused by (amongst other things), the size of the output coupling capacitor and the associated -3dB low frequency cutoff.

The design document suggests that the cutoff is purely a function of the capacitor and the resistance of the headphones, and I'm struggling to understand how that can be.

Also, the size of the output cap (220uF) requires that I use an electrolytic, which I understand from reading this forum is discouraged. If I only use high resistance (~600 ohm) headphones, can a smaller value non-electrolytic cap be substituted? Does it even make a difference?

Anyway, I wrote up my desperately confused ramblings into a word document complete with pretty pictures and attached it to this message.

I would be very grateful to anyone who feels like helping out the clueless newguy.

Thanks,

P.S. searched the forum, but didn't find anything ... read a document on aikenamps (http://www.aikenamps.com/CommonCathode.htm) that seemed to support the idea that the frequency response has only to do with the size of the capacitor and the resistance of the load, but am still a bit confused

[Brett]

Short answer; simply scale it.
If the author's found that 220u gives a 12Hz LF rolloff with 60R cans, and you want to use 600R Senn's, try a 22u cap. Should be close enough.

Longer answer.
On p2 of your .doc,
Rleft = (ra/(mu+1))//3k3
= (280/3)//3k3 = 90.8 ohms

The F3 eqn should be
1/(2*pi*(Rleft +Rright)*C) which calcs out to
1/(2*pi*(90.8 + 60)*220E-6) = 4.45Hz

[wizdeluxe]

Look for Aerovox motor starting oil caps for AC. They are made in several can configs and are long life. I'm building a similar preamp. James

[newguy]

Great! Thanks very much!

I never would have gotten the Ra/(1+mu) thing ... I really do need to buy a book on this. I wish the new version of the Morgan Jones one would come out already.

Was my understanding of Rright correct? (i.e. that one would need to look at the headphones and grounding resistor in parallel?)

James: thanks for the tip on the Aerovox caps!

Another question ... how can I determine what voltage rating I need? B+ is 150volts, and the circuit is the one at: http://headwize2.powerpill.org/proje...aarde1_prj.htm

[PRR]

> the size of the output coupling capacitor and the associated -3dB low frequency cutoff.

Draw the equivalent circuit:


The 300Ω is the "load" (headphones), the 2K is a resistor often included to drain-off DC leakage and reduce start-up thump. Only the power in the 300Ω is "useful", but the capacitor does not care; it has to drive both resistances. So on one side we have 2,000||300= 261Ω.

On the other side we have the source, which always has an impedance. It may be rediculously low from a high-feedback amp, or very high from a tube plate. Just for talk, let us assume it is 100Ω. Add that to the other resistance. 100+261= 361Ω total resistance. Now ask yerself: what capacitor has 361Ω reactance at my desired bass -3dB cut-off? Counting on my thumbs, I estimate 30µFd for 20Hz response. Students should show calculations to 3 places, but in real-life you don't need much better than 1-digit accuracy.

If you do not know the amp's output impedance, assume Zero. Now we have 0+261=261Ω total resistance, we figure we want about a 40µFd cap. If we are wrong and the "zero ohms" is really 100Ω, we paid about 33% too much and got 15Hz response, no disaster just "a little too good".

What is the output impedance of your tube? I happen to know the van Waarde is a 6SA7/6080 low-Mu triode resistance-coupled cathode follower without feedback. If it were a choke-loaded plate follower (no feedback), it looks easy: the output impedance is the plate resistance, and it says right in the book "280Ω". So we would add 280+261= 541Ω total resistance, we might use a 20µFd cap.

But the book cites one typical (or good-looking) operating condition; the graph shows that plate resistance at likely bias points can be 200Ω to 400Ω. And real 6080 tubes from different factories don't all match the graph (though they will be close over "normal" conditions). So output impedance estimation is always an approximation. If you breadboard the actual tube you will use you can get an exact value. If you design for production, and have to work with any tube the purchasing manager drags in, you better be pessimistic.

For a cathode follower we want to know the "dynamic cathode resistance". This is the same as the plate resistance except at the other end. It is never cited on spec sheets because it is easily derived from values given: plate resistance and amplification factor, or transconductance.

Say that a 6080 has Rp=280Ω and Mu=2. The cathode impedance is then 280/2= 140Ω.

Say that a 6080 has Gm= 7,000µmho. Cathode impedance is 1/Gm or 1/7,000µmho, or 1/(7000/1,000,000). This can be written 1,000,000/7,000 if you prefer. The answer is 143Ω, which agrees with the Rp/Mu result (within slide-rule accuracy).

As Bret says, there is often a "Mu+1" in the exact formula, where I just say "Mu". When Mu is 60, this is negligible. Even when Mu=2, I just ignore it. The output Z may compute to Rp/(Mu+1)= 90Ω instead of 143Ω. But the uncertainty in Mu and Rp is larger than this. For getting a "low enough cutoff", ignore it. For setting a precision filter, you better figure closely, and also get a very exact measurement of tube parameters. Or pad-out with fixed resistors large enough to make tube parameter variation "small".

The Waarde is resistor coupled, using a 3.3K DC load resistor. So the source side impedance is really 140||3,300= 134Ω. We could have neglected this, since 3.3K is much-much more than 140; I just want to show what to do when it is not negligible. Cmoy's posting of the van Waarde shows a 10K drain resistor after the capacitor. If you use only 600Ω cans, then this side is 600||10,000= 566Ω (again we could have neglected this). The total resistance is 134+566= 700Ω. Figure out the cap you need to get your desired -3dB point with 700Ω. For 20Hz, 15µ is close. That gives -1dB at 40Hz from this cap alone. If the cap were cheap, we would super-size it to give negligible drop at 20Hz. But in this particular case, this will be the most expensive signal cap in the whole system, so we don't get crazy. In film-type I'd consider 22µFd.

Waarde specs operation into 60Ω. If we figure 134+60= 194Ω, we need 50µFd just to touch -3dB at 20Hz. That's a monster film-cap, a budget-breaker. Electrolytics can work fine, just not as perfect as film caps. And they are so cheap you can and should supersize them. To get extended bass response, but mostly to reduce the distortion in the "insulator". 3X larger than you "need" is a starting place, or 150µFd. Looks like Waarde rounded-up to the next real-common size, 220.

[Brett]

Excellent explanation PRR.

[fdegrove]

Hi,

Excellent explanation PRR.

Amen.

Give the man a

Cheers or skol...whatever,l

[Brett]

Originally posted by newguy
I really do need to buy a book on this. I wish the new version of the Morgan Jones one would come out already.

I think MJ v3 is available on Amazon. Not sure about other sources.

You've already found Randall Aiken's site, and that one is great. Hove you also looked at the articles at Tubecad?

Was my understanding of Rright correct? (i.e. that one would need to look at the headphones and grounding resistor in parallel?)

Yes. And as your understanding is quite good already, plough through the Tubecad articles, and keep an eye out for a copy of the Radiotron Designers Handbook v4 by F. Langford Smith. This is the reference work, but is very dense in information, however you seem to nut things out well, so maybe it wouldn't be too difficult for you to access the info. I don't normally suggest it to beginners.

James: thanks for the tip on the Aerovox caps!

Also GE and ASC.

Another question ... how can I determine what voltage rating I need? B+ is 150volts, and the circuit is the one at: http://headwize2.powerpill.org/proje...aarde1_prj.htm

My personal rule of thumb is 20% minimum about B+, except for any cap immediately after the rectifier which I like to be about 50%, but this depends on design etc. When selecting the actual caps, always go up to the next igher voltage rating to be safe; it's usually only a small percentage extra cost and can save your circuit under some (even unlikely0 fault conditions. The easiest way to determine what you really need is to model it in the free PSUD II program. Whilst you're there check out the tube database.

[PRR]

> keep an eye out for a copy of the Radiotron Designers Handbook v4 by F. Langford Smith.

Watch out for the Third Edition too. It is very much smaller but can keep you thinking for years. My father bought his new, and it has been continuously read by him then me for over 50 years and is falling apart. I got lucky and found a small local shop that had the Fourth and also a Third, and bought both. The Fourth is much richer, but the Third is much more focused. Do not pass-up a Third if it appears.

Third has publication dates around 1940 (many-many printings in several countries) and about 350 pages. Usually black, though one Australian run was blue. Fourth is about 1953 (through 1960), RED, and about 1450+ pages.

It used to be hard to find these things in the backs of local bookstores. Prices ranged from nominal to excessive. But with eBay and ABE.com they are much easier to find anywhere, which has stabilized prices.

The Third is an absolute steal for $10-$20.

Today on ABE.com I see the Third from $7 to $30. For $7 you get someone else's name written inside (sometimes you can find out "who" they were), no dust jacket (we all threw these away ASAP, if it even had one), "Very Good" which has a specific meaning in the used-book trade. Most will have bumped corners and loose bindings, even "damp" (coffee) stains. Read the description carefully, but most book sellers will not offer a book in less than "VG with bumps" (i.e. perfectly readable) condition except to a hands-on in-store buyer.

Via ABE.com's own order system, you order and pay ABE, the bookstore sends you the book, and then ABE sends the store your money. If too many customers whine to ABE that a store's book was not as described, ABE de-lists that seller. I once found a book in ABE and it turned out it was already sold; the seller was VERY apologetic to me (so I would not tell ABE that his listings were stale). They want to stay in ABE's good graces, so they stay honest with customers. I will trust any ABE.com seller more than I trust Amazon or an eBay dealer with 99.99% positive rating. Its as safe as buying at the local mega-store, selection is better, and you don't have to go out in the rain.

Copies of the Fourth run $50 to $150. There does not seem to be any logic to the prices: the $50 book looks like a scuffed but fine reader and the $120 copy has repairs (meticulously noted in the listing).

AudioXpress has put the Fourth on PDF CD-ROM at about $60, which has set a base price for readable hard-copies.

[wizdeluxe]

I don't have stock in the company but large value caps are made also by Chartereaux and are called Solen Fast Caps but are more expensive that your garden variety Aerovox, GE, Sprague or Mallory motor runs. These are sold by Madisound among others.

Have you toyed around with the idea of transformer coupling a la ultrapath or even a x-former coupled cathode follower refrenced to a large negative supply? Cathode followers have a much slower turn off time than their turn on time therefore their square wave form is very assymetrical. James