# How low can T go?

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#### audio1st

I was wondering if the 2.2uf input coupling caps' are the best way to go?
I can't seem to make any sense of the formula,
fc=1/(2x3.142xRxC)....1/(6.284x20000x0.0022)=0.0036166hz.???
Also is it best to use polarised or non- polarised caps?
I found the larger the value, caused more of a pop at turn on!
I am currently useing 0.47uf (non-polarised) at the moment, because of space, but seem to have all the bass I need.
If these caps are rolling off the bass, why try and go lower than the speakers and over work these little amps for no reason?
My amp sounds way better than un-modded at the moment, but may fit 1uf caps if the formula says I need to go bigger?

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#### classd4sure

1 / (2 * pi * 20 000 * 0.00000047) = 16.9313769

1 / (2 * pi * 20 000 * 0.0000022) = 3.6171578 (see your small oversight there? C is in uF)

The min audible range for humans is said to be 20Hz but there will be some attenuation before the cut off point, so you should make sure that lands in the inaudible range as well.... the 2.2uF is by far the better choice.

#### audio1st

Thank you for that classd4sure...

#### sx881663

Capacative reactance and beyond

classd4sure said:
1 / (2 * pi * 20 000 * 0.00000047) = 16.9313769

1 / (2 * pi * 20 000 * 0.0000022) = 3.6171578 (see your small oversight there? C is in uF)

The min audible range for humans is said to be 20Hz but there will be some attenuation before the cut off point, so you should make sure that lands in the inaudible range as well.... the 2.2uF is by far the better choice.

Chris,
The c is in uf and should have been in farads, right? This is the formula for capacitive reactance and the answer given is in kohm? We are going into a 100k res. and when the level drops to -3db the applied voltage is .7079 * the input. At 20hz this is an input capacitive reactance of 41k and equates to .22uf. (Nearest standard value.) The 10 times rule to minimize effects of the cap makes the ideal value 2.2uf which has been called for all along. Although this is a 2 Hz cutoff it still leaves a .7db loss at 20 Hz. Remember there are other factors to be considered like physical size with a larger cap picking up more noise due to its larger surface area so you just can’t throw a really big cap at the problem.
The sonic effects of the smaller cap size go much higher in frequency than what the equation would lead you to believe. Most systems really don’t go that low so this wouldn’t even be noticed but if there is a separate sub woofer in the system then phase may be the more important parameter and can be significant to a lot higher freq. Phase cancellation at the crossover freq can cause a huge suck out and really hurt the sound.
Roger

#### classd4sure

Hi Roger,

I just plugged in the values he gave me... 20K was his input impedance.

The .7079... I've never seen the 9, but 1/sqrt(2)=0.707106781...I think you may be throwing your results off with the 9, not by anything that would really matter though.

Aside from that it's actually the formula for Fc for either an RC high or low pass filter.

All units are alike (unity).
R=Ohms
Fc will be given in Hertz.

For the purpose of clarity:

Fc=1/(2*PI*R*C) (stays the same for high or low pass)
and
Xc=1/(2*PI*F*C)
where :
Xc= Ohms
F= Hertz

At the half power point where the filter gain is equal to .707, Xc = R.

Hmmmm that's all I know so I'll conclude with an informative link that knows more than me. They lay the math out very clearly, more so than I've seen anywhere else in fact .... I like it.

http://www.play-hookey.com/ac_theory/lo_pass_filters.html

Regards,
Chris

#### sx881663

Utter confusion

Ok it makes sense now, I thought the 20 was 20Hz and wondered how you could confuse Xc with Fc and wondered where the kohm came from. I don't think I have seen the Fc formula done that way before and always did it long hand, Thanks
In this instance 2.2uF is marginal for high end (1/5th the recommended value) but actually perfectly acceptable for most applications, meaning with most speakers that don't do much below 40Hz anyway. I certainly would prefer a 2.2 film cap and give up a little bass than to suffer an electrolytic in its place!
In my old hand book -3db is given as .7079 * input, is this wrong? In the first place is -3db really ½ power? I have just spent hours trying to prove it one way or another. Accepted practice is 1/2 power = -3db. Further research reveled;
One place stated "Half: N = 10 log (0.5) = -3.013dB down"
Another site I got -3.01029. I give up, without a solid starting place how in hell can you come up with a correct answer? Think this is something? Just try to find a real explanation as to how to calculate the log of a number! WOW, massive confusion. Best answer was to use your scientific calculator and I wonder if they all agree. Use a log chart to find a log? Right, just try on line! I do have an expert resource that I can ask as this will drive me nuts. In the mean time,
HELP!!
Roger

#### audio1st

Just to confuse a bit more, would changing the input resistor for a 36ohm value lower the bass roll off? I know it lowers the output volume a little, but is this acceptable as an alternative to changing the feedback resistore to 20ohms? Any other side effects? Barry..

#### audio1st

Those values are ment to be k ohms ,sorry.

#### audio1st

I now see the reason for getting the Fc to below 2Hz, "signals more than 10 times the cutoff frequency show little or no appreciable phase shift, while signals less than 0.1 times the cutoff frequency are shifted close to 90°". SUCK OUT.

#### nilaus

Originally posted by sx881663 :
In my old hand book -3db is given as .7079 * input, is this wrong? In the first place is -3db really ½ power? I have just spent hours trying to prove it one way or another. Accepted practice is 1/2 power = -3db.

With dBs there's a difference between power (Watts) and amplitude (eg. Volts). That's because power is proportional to amplitude squared (eg. P = U*U*R). So your old book is right (½ appox. = .7079 * .7079). You often disregard any decimals when using dBs; that's why the rule of thumb is -3dB = half power, -6dB = half amplitude.

The rules are:
Power: dB = 10*log(P1/P0)
Amplitude dB = 20*log(U1/U0)

#### nilaus

Sorry, power is proportional to amplitude squared, but the correct equation is P = U*U/R; that is: power (in watts) is equal to voltage squared divides by resistance.
(Unable to edit my last post)

#### classd4sure

Hi,

Now that's why I provided the link.

They do show how/why you get .707, Nilaus you're right with the V^2 thing but then you just said "so you're old book is right"...... please show where that 9 came from then.

sqrt(.5) or (1/sqrt2) or 2^(-1/2) (they're all the same) and give 0.707106781 as the answer...

0.707106781^2 = 0.5 You want to disregard the extra.... use .707 and you can then get 0.499849.

While .7079 is 0.7079^2 = 0.50112241, not much of an error like I said but it's still wrong to round like that. You can actually question the information found in a book and actually you should!!

I'd imagine some older or maybe even cheaper calculators may be more prone to round off or truncation error... maybe some old intel CPU's too? BTW for those who haven't found out yet google is a pretty mean calculator, I haven't opened the windows calc since I found that out, hardly ever excell either.

Roger you poor guy you're cursed just like me, memorizing the equations aren't good enough, we have to understand what/why each term is there..... how it came to be.... and what it all does. But that's not how math is taught now is it...we sure torture ourselves!

That's what I really loved about that link I gave actually, having all the equations in question layed out right there in a very clean way that allowed me to see relations I normally wouldn't have easily seen, most don't go into that kind of detail and either stick wih the 1/wC or S conventions...... that's when I get lost because I honestly require further study.

I asked about the 7079 thing because I thought it would be an old book issue.

BTW I have one book from college for this measurement course I had.... they even got the speed of light wrong in it. My teacher proofread the thing ( before printing, and his name is in the credits) so he knew every mistake in it and nailed us with them constantly. \$120 book that's full of mistakes!~ No doubt put some money in his pocket though. I think he made enough though and I'd rather have a good book.

BTW I can attest to that suck out thing you mentioned sounding very disgusting, I was playing with some DSP EQ settings just the other day and started playing with cut offs ...doing that same effect in hardware would be a huuuuuuuuge mistake and "suck out" is a fairly descriptive term for it.

Oh yeah I've never seen anyone use anything other than "3" as the Fc point, no decimals and also what's usually discarded is the "-" as it's "understood/assumed" to mean that anyway.

I'll point out that websites are alot worse than books when it comes to the quality of information given, some are excellent but others are just enthusiasts who don't fully understand what they're writing about. As long as we're aware of that it's OK.

To be honest with you I personally would like to have a good book or three on filters alone, usually I wind up finding a web applet/calculator because I can be that lazy.

Regards,
Chris

#### sx881663

Thanks guys!

Audio first,
Yes, you could change both resistors to 50k and improve matters significantly as regards bass and still have the same gain. This would make the unit more susceptible to noise pickup which may not be an issue. However you had stated you were getting good results with a .47uf installed so 2.2uf would be a lot better and you really wouldn't need to go any further.
Chris,
Yes, it drives me nuts till I understand the how of it, why alone just isn’t enough. Once I do achieve this level of understanding the formulas are second nature. Looks like I have opened a real can of worms here. One tends to think of mathematics as being precise but when you get into exponential functions 4 significant digits seem to be the rule and to make it worse the way they round off leaves something to be desired. This does bother me, I do like to get the numbers right even if the parts tolerance makes it a moot point, at least I know the starting point is correct. This is why I have always used 3.14159 instead of 3.14. Guess I should invest in a decent calculator and not rely on the computer so much. At least I will get the same answer twice!
I will check out the Google calc.
Thanks all,
Roger

#### nilaus

The 7079 thing

OK, the old book is right because its exact to four decimals!

-3dB (amplitude here) is equal to 10^(-3/20) = 0.70794578438413791080221494218931 ....

The diffence between -3 and -3.01 dB is so small that you ignore it. Anyway you'll have to obtain components with around 0.1% tolerance to get below this difference, so for all practical purposes ignore it - you won't hear the difference anyway.

#### sx881663

Amazing!

Yes, the kind of answer I was looking for! Now the real question, how did you get it? I mean to actually get the log value, I do understand the equation. Like 10^(-3/10)=.5012 would be power, right? Makes me wonder about the other equation they are using that does not give the same answer, 2^(-1/2). Is this just a short cut approximation?
I also agree with your statement that the difference between 3.0 and 3.01 is of no consequence but that doesn't matter as I would like to know what the numbers should be for my own personal edification/enlightenment. In other words how they were derived.
I have a very cynical attitude towards these kinds of things and don’t trust them till I can prove it for myself. Sometimes I will even put something on the bench and test it to prove the numbers. I learned to do this trying to come up with a better RIAA stage. Still don’t know what the numbers there should be as no one seems to agree, another subject for sure.
Anyway, thank you,
Roger

#### BWRX

just use the formula for calculating dB and manipulate it to get rms voltage in terms of dB.

dB=10 log ((V^2)/(Vref^2))=20 log (V/Vref)
(dB/20)=log (V/Vref)
10^(dB/20)=(V/Vref)
with Vref=1Vrms most people just don't bother writing it at all
thus V=10^(dB/20)

#### Yves Smolders

Maths...

And the magic caps value for zero phase shift and loss of db's at 20 hz, yet doing Dc protection isssss.........???

#### sx881663

The perfect cap

Yves,
The perfect cap does not exist or perfect anything for that matter. An approximation would be a circuit that only blocks DC and does nothing else. Nothing easy comes to mind. So the best we can do is to have the undesirable capacitor effects be at a low enough frequency as to not interfere with the signal and at the same time be a high enough freq. to block real low freq. trash. The best compromise seems to be in the range of 2-5Hz cut off or -3db point. 2.2uf into 100kohm as in the UcD input is a well tested example and seems to work fine. An easy extrapolation of this can be applied to other circuits by using a percentage shift. Like for a 1megohm input this same cutoff would require 1/10th the value of cap or .22uf and 50kohm would require twice the value or 4.4uf. In this particular case you would use 4.7uf as the nearest standard value and also the physical size starts to become more important so you would probably still want to use the 2.2uf or go to a 3.3uf space permitting. The exact value is not very important but having all channels the same is.
Ah, the art of compromise. That is what it is all about. The only way we can know for sure if we have made a good decision is testing and ultimately how it sounds.
Roger
.

#### Yves Smolders

Thanks Roger,

Of course my remark was slighty tongue-in-cheek

So when searching high quality input caps on the UcD, I'd better keep the same values than those on the board, just to play it safe.

But this is a t-amp thread, I'm not going to hijack it!

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