dee Bee or not dee Bee

[janneman]

Hi all,

My column in the April diyaudio Newsletter on deciBells ended with a quiz: I asked how much gain there would be in a chain starting with a 1:4 attenuator, then a 60x gain amp, driving a 24 ohms headphone through a 24 ohms output resistor.

I got three correct (sort of ) answers. Now remember the whole slant of my column wasd toward quick and dirty baallpark numbers so we were not looking for a detailed 6-decimal-digits correct answer.

Answers in the next post.

jan didden

[janneman]

Starting with 1, then a quarter of it is 0.25, times 60, is 15, half of that gets 7.5
So far, exact correct.

So, we double the power almost 3 times
x2 +3db
x4 +3db
x7.5 +2.8db
Well, that might be an 8.8 decibel boost

Well, in the whole column we strictly talked about voltage gain. In fact, I cowardly sidestepped power gain because I need something for a future column. A factor of 2 is about 6db as was noted, so in your calculation it would be 6dB + 6dB plus something a bit less than 6dB, say 5,5dB? Total 17.7dB. So it's about double....

Yeah, I don't really know. Generally, audio stuff has either too much gain and clips or insufficient gain and doesn't


jan didden

[janneman]

One simple way of converting attenuation ratios to decibels is this;

For common even whole number attenuation ratios, if one takes the reciprocal of the attenuation ratio and multiplies that by -3dB then one can form a table of DB values.
For example;

1:2 = 1/2 and 1/ 1/2 = 2 and 2 * -3dB = -6db, there for
1:4 = -12dB
1:8 = -18dB
1:10 = -20dB

Neat, yes, I like that. Thanks.

We started with gain of 60 with a 1:4 attenuation driving 24 ohm headphones with a 24 ohm resistor in series with the headphone. The attenuation of the series resistance is 1:2.

So from our table and gain of the amplifier which is 20* Log 60 ~= 35.6dB, okay I cheated a bit here.

35.6dB + -6dB + -12dB = 17.6dB.

Close enough for government work, yes.

Which is roughly equivalent to 20(Log 60 + Log 0.5 + Log 0.25)

Which would be 17.50dB. As I said, close enough.

jan didden

[janneman]

First, ignoring the output resistor and headphone impedance let's look at the gain stages: 4:1 attenuator (1/4) and 60x amplifier (60/1). Multiplied together gives us 15x.

OK.

15x in "dB land" is the arthematic sum of 1.5x dB and 10 dB. From your articles examples, this would be about 3dB + 20dB which is about 23dB.

Hmm. A bit hazy but correct, although 3dB is more 1.4 times than 1.5 times, but lets move on.

Now, let's look at the headphone stuff. Since both resistance values are equal 24 ohm series then a 24 ohm load, this is a simple 2/1 voltage divider. So we'll see half at the headphone output as what the amp puts out. Again, using your articles examples, 1/2 means approx -6dB.

OK

So the final answer we're looking for is 23dB + -6dB which equals 17dB.

OK

Am I even close??

Yes, close, just a couple of % off, I'll buy that.

[janneman]

1:4 or 1/4 is half of half = -6dB + -6dB = -12dB
60 times is 2*30 and in the column I mentioned that 30x is about 30dB so that gives 30dB + 6dB = 36dB.
Then another -6dB at the output.
Totals -12dB + +36dB + -6dB = +18dB. Also a few % off, I'm a bit higher than vwmaker.

Now, the aim of the column was to help interested people to a) get a handle on what dB's are, and b) to get a quick grasp of the numbers and how to come to a ball park result quickly without long and complex calculations.

danielwritesback and davada clearly know more about dB's than I do. Their answers illustrate that there are lots of ways to skin the dB cat. Thanks guys.

vwmaker seems new to dB's but intuitively grasped the issues so my promised F4 or F5 board set goes to him.
I'll tell Mark.

Thanks for responding guys, and if anybody has a subject he/she would like to be treated in a future newsletter let me know!

cheers,

jan didden

[danielwritesbac]

Originally Posted by janneman

danielwritesback and davada clearly know more about dB's than I do. Their answers illustrate that there are lots of ways to skin the dB cat. Thanks guys.

I think that you know more about decibels than I do.

And my math skills aren't up to engineering requirements so I do have to calculate several different ways/tries until finally arriving at valid-looking answers.

Only today did I finally stop to consider that the preamp may have been internal to the source--a very quiet source.

Otherwise +18 onto a line level source either sets the headphones ablaze, or almost makes a fuzzbox like the error in the Sony XDR-F1HD AF section clipping on dynamics.

It seems that application is problematic.
So, what is the scenario for +3 or for +6?

[DF96]

There is a quick way to estimate the answer. Multiplying up the stages gives a voltage gain of 7.5. This is a bit less than 10, so the answer will be a bit less than 20dB. How much less? Well, 7.5 is not that much different from 7.07, which would be 3dB less than 20dB. So the answer is a bit over 17dB. This level of accuracy is good enough for the early stages of a design, when much of it is still in our head. Later on the calculator/spreadsheet can come out if accurate figures are needed.

Alternatively, 7.5 is almost 8. 8 is 18dB (8=2^3, 18dB=3x6dB). So it is a bit less than 18dB. If necessary one could combine these two estimates and say that it is somewhere around 17.5dB. All done without a calculator!

[vwmaker]

Thanks very much for selecting my entry as the winner! I thought Jan's article was outstanding and very well targeted to anyone new to the concept of dBs in general. So, I tried to format an answer true to that same spirit. Glad it hit the mark.

Now I know I'm going to be shortly asked whether I want an F4 or F5 board for a prize. I'm a bit embarrassed to say that I don't know because I'm that new to DIY audio. I've heard of both of these FirstWatt amps: one's a current source buffer of sorts with 0 FB and the other a departure PP design with FB, but other than that have no clue which is "best" for me. At least I'm informed enough to know there's no such thing as "best" in general terms. I wonder if it would be asking too much for recommendations from my fellow competitors? Maybe it is :-). Otherwise, I'll have to read up on them more and let you/Mark know ASAP.

Thanks again!!
-Rod

[janneman]

Originally Posted by DF96

There is a quick way to estimate the answer. Multiplying up the stages gives a voltage gain of 7.5. This is a bit less than 10, so the answer will be a bit less than 20dB. How much less? Well, 7.5 is not that much different from 7.07, which would be 3dB less than 20dB. So the answer is a bit over 17dB. This level of accuracy is good enough for the early stages of a design, when much of it is still in our head. Later on the calculator/spreadsheet can come out if accurate figures are needed.

Alternatively, 7.5 is almost 8. 8 is 18dB (8=2^3, 18dB=3x6dB). So it is a bit less than 18dB. If necessary one could combine these two estimates and say that it is somewhere around 17.5dB. All done without a calculator!

Yes that's the way I would do such things, although you seem particularly comfortable with the numbers!
My main purpose was to show that dBs are not magic and can be of use without lots of effort.

jan

[janneman]

Originally Posted by danielwritesbac

I think that you know more about decibels than I do.

And my math skills aren't up to engineering requirements so I do have to calculate several different ways/tries until finally arriving at valid-looking answers.

Only today did I finally stop to consider that the preamp may have been internal to the source--a very quiet source.

Otherwise +18 onto a line level source either sets the headphones ablaze, or almost makes a fuzzbox like the error in the Sony XDR-F1HD AF section clipping on dynamics.

It seems that application is problematic.
So, what is the scenario for +3 or for +6?

Daniel,

You are right that my numbers could have been chosen a bit more realistic! A preamp with a gain of 60 is a monster! In fact, with most modern systems you probably can get away with a gain of 1 (0dB ), or even a passive preamp (a vol control) only.
I'll try to be more realistic next time.

jan